Evaluation of Relative Density and Its Role in Geotechnical Projects Involving Cohesionless Soils PDF

 

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EVALUATION OF RELATIVE DENSITY DENSI TY A N D ITS ROLE IN GEOTECHNICAL PROJECTS INVOLVING COHESIONLESS SOILS

A symposium presented at the Seventy-fifth Annual Meeting AMERICAN SOCIETY FOR TESTING AND MATERIALS Los Angeles, Calif., 25-30 June 1972

ASTM SPECIAL TECHNI TECHNICAL CAL PUBLICATION PUBLICATION 5 23 E. T. Selig and R. S. Ladd, editors

List pric List pricee $30.75 $3 0.75 04-523000-38

AMERICAN SO CIETY FO FOR R TESTI TESTING NG AN D MATE MATERI RIALS ALS 19 16 Race Street Street,, Philadelphia, Pa. Pa. 19 10 3. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agre

 

(~) BY AMERICAN SOCIETY FOR TESTING AND M ATERIALS 1973 L i b r a r y o f C o n g r es e s s C a t a l o g C a r d N u m b e r : 7 22 - 90 9 0 7 04 04

NOTE Th e Soc iety is not respons responsib ible le,, as a bod y, f oadvanced r th t h e s t a t ei nm et hi n tss publ a n d iocat p i inon. io n s io

Print ed in Baltimore Md. Jul y 19 1973 73

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  oreword A t w o - s es e s s io i o n s y m p o s i u m o n e v a l u a t io i o n o f r e l a ti t i v e d e n s i t y a n d i ts ts r o l e in geotechnical projects involving cohesionless soils was held 25-30 June 1 97 9 7 2 a t t h e S e v e n t y - f i ft ft h A n n u a l M e e t i n g o f t h e A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a ls l s i n ' L o s A n g e le l e s C a li l i f. f. T h e s p o n s o r o f t h e s y m p o s i u m w a s C o m m i t t e e D - 1 8 o n S oi o i l a n d R o c k f o r E n g i n e e ri ri n g P u r p o s e s u n d e r t h e c h a i r m a n s h i p o f E . B . H a l l. l . T h e f o r m a t f o r e a c h se s e s s io io n c o n s i s t e d o f a k e y n o t e a d d r e ss s s , f o l lo l o w e d b y p r e s e n t a t io i o n o f s e le l e c te te d p a p e r s a n d t h e n a panel discussion on the session topic. Session I concerned the factors a f f e c ti t i n g r e l a t i v e d e n s i t y in in c l u d i n g t h e m e a s u r e m e n t o f m a x i m u m , m i n i m u m , a n d in situ d e n s i t y . S e s s i o n I I c o n c e r n e d t h e c o r r e l a t i o n b e t w e e n relative density and properties or performance of soils and gives examples o f t h e u s e o f r e la la t i v e d e n s i t y . T h e k e y n o t e a d d r e s s f o r th t h e f ir i r s t s e ss s s io io n w a s g i v e n b y W . G . H o l t z , Consulting Civil Engineer, Wheat Ridge, Colorado; while for the second s es e s si s i on o n , Y v e s L a cr c r o ix i x , D i r e c to t o r , W o o d w a r d - C l y d e C o n s u l t a n ts ts , N e w Y o r k , N . Y . , p r e s e n t e d t h e k e y n o t e a d d re re s s . T h e s y m p o s i u m c h a i r m a n a n d a l s o m o d e r a t o r o f S e s s io i o n I w a s E . T . S e l ig ig , D e p a r t m e n t o f C i v i l E n g i n e e r i n g , S t a t e U n i v e r s it i t y of o f N e w Y o r k a t B u f fa f a lo lo ; R . S . L a d d W o o d w a r d - M o o r house A s s o c i a te t e s , I n c .,. , C l i ft ft o n , N e w J e r s e y , s e r v e d a s c o c h a i r m a n a n d m o d e r a t o r o f S e s si s i on on I I . T h e s e p u b l i s h e d p r o c e e d i n g s c o n t a i n a ll ll o f t h e a c c e p t e d p a p e r s d e a l i n g w i t h t h e s y m p o s i u m t o p i c, c , m o s t o f w h i c h w e r e n o t p r e s e n t e d o r a ll ll y , a n d t h e two keynote addresses. A concluding paper summarizes the program discussion and provides recommendations. T h e c h a i r m a n a n d c o - c h a i r m a n w o u l d l ik i k e t o e x p r es es s t h e i r a p p r e c i a t i o n to the staff members of ASTM who assisted in the presentation of this s y m p o s i u m a n d S p e c i a l T e c h n i c a l P u b l i c a t io io n , a n d e s p e c i a l l y t o M i s s Jane Wheeler.

C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i c e n s e A g

 

Related S T M P u b l ic ic a ti tio n s U nd er w at e r Soi l Sam pl plii ng, Test ing, ing, an d Const ruct ructiion C o n tr t r ol o l , S TP TP 5 0 1 ( 1 9 7 2 ) , 1 5 . 5 0 Special Speci al Pr ocedures ocedures f or Tes t ing ing Soi l and R ock f or Eng i n e e r in i n g P u r p o se s e s , S TP TP 4 7 9 ( 1 9 7 0 ) , 1 5 . 7 5 L a b o r a t o r y S h e a r T e s t in i n g o f S o i ls l s , S TP TP 3 6 1 , ( 1 9 6 5 ) , 24.50

C o p y r i g h t b y A S T M I n t l ( a l l ri ri g h t s r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreemen

 

  o n t en t s

Introduction

1

D e t e r m i n a t i o n o f R e l a t iv i v e D e n s i t y C o n s i d e r in in g t h e M e a s u r e m e n t o f M a x i m u m , M i n i m u m , a n d I n Si t u D e n s i t y The Relative Den sity Ap proach --Uses a n d S h o r t c o m i n g s - - w . o . H O LTZ

Testing Requirements

R e l i a b il i l it it y

5

Accuracy of Relative Density M easurements: Results of a C om parative Test P r o g r a m - - F . h . TAVENAS, R. S. LADD, AND P. LA ROCHELLE

18

V a r i a b i l i t y o f L a b o r a t o r y T e s t R e s u l t s - - D . A . T IE IE D EM EM AN AN N

61

S t a t i s t i c a l S i g n i fi f i c a n c e o f t h e R e l a t i v e D e n s i t y - -Y - Y O S n l X K I Y O S HI H I M I A ~D ~D IKUO TOHNO

E f f e c t o f V a r i a t i o n s in i n M i n i m u m D e n s i t y o n R e l a t i v e D e n s i t y - - R . c . G UV U V rA rA AND J. D. MCKEOWN

F a c t o r s C o n t r o l l in in g M a x i m u m a n d M i n i m u m D e n s i t i e s o f S a n d s - - T . L . YOUD I n f lu l u e n c e o f G r a i n S h a p e a n d S i z e u p o n t h e L i m i t i n g P o r o s it i t i es es o f S a n d s - E, A.

DI

KIN

74

85

98 113

S o m e O b s e r v a t i o n s o n t h e C o n t r o l o f D e n s i t y b y V i b r a t i o n - - E . w . B RA R A N D 1 21 21 L a b o r a t o r y S t u d i e s o f M a x i m u m a n d M i n i m u m D r y D e n s i ti t i e s o f C o h es e s io i o n le le s s S oi ls- -M . M. JOHNS OHNSTON TON M a x i m u m D e n s i t y D e t e rm r m i n a t io i o n o f S u b b a se se M a t e r i a l s - - o .

CUM

ERLEDGE

141

AND R. J . COMINSKY

C o m p a c t i o n o f S a n d o n a V e r t i c a l l y V i b r a t i n g T ab a b le le --- - R IC I C A R DO DO 2. V. WHIT WHITMAN MAN

133

DOBRY

AND

V i b r a t o r y C o m p a c t i o n in i n t h e L a b o r a t o r y o f G r a n u l a r M a t e r i a l s in in L o n g C o l u m n s - - A . I . JOHNSON AND D. A. MORRIS U n i f o r m i t y o f S a t u r a t e d S a n d S p e c i m e n s - - J . J . EM EM E RY R Y W . D . L IA IA M F IN IN N A N n K. W. LEE

E r r o r s o f I n - P l a c e D e n s i t y M e a s u r e m e n t s i n C o h e s io i o n l es es s S o i l s - D. F. GRIFFIN

156 171 182 195

S o m e T e s t i n g E x p e r i e n c e s a n d C h a r a c t e r i s t ic ic s o f B o u l d e r - G r a v e l F i l l i n E a r t h D a m s - - R . J . F RO RO ST ST

207

R e l a t i v e D e n s i t y T e s t s o n R o c k F i l l a t C a r t e r s D a m - - R . z. z . S T E P H EN EN SO SO N

234

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vi

ONTENTS

C o r r e la l a t io io n e t w e e n R e la t iv e D e n s i t y a n d M e a s u r e d P e r f o r m a n c e o r P r o p e r ti ti e s o f G r a n u l a r S o il s Direct D etermination and Indirect Evalua tion of Relative De nsity and Its U s e o n E a r t h w o r k C o n s t r u c t io i o n P r o je j e c ts t s Y V E S L A C RO R O IX IX A N D H. M. HORN

251

P r e d i c t io i o n o f D r a i n e d S t r e n g t h o f S a n d s fr f r o m R e l a t iv iv e D e n s i t y M e a s u r e m en t s D . H . CO CORN RNFFO RTH RTH

281

Effect of Particle Shape on the Engineering Properties of Granular Soils I . t t O L U B E C A N D E . D ~ A P PO PO L O N IA IA

30 4

E f f e c t o f R e l a t i v e D e n s i t y o n t h e L i q u e f a c t i o n S u s c e p t i b i l it it y o f a F i n e S a n d un de r C ontro lled S tress Lo ad ing G . N. DU UR R HA HA M A ND ND F . C. C . T O W NS N S EN EN D 3 1 9 I n f lu l u e n c e o f R e l a t i v e D e n s i t y o n tthh e S t r e n g t h a n d D e f o r m a t i o n o f S a n d u n d e r P l a n e S t r a i n C o n d i t i o n s ~ . M. M. A L H U S S A I N I

332

C o m p a r is i s o n s of o f V i b r a t e d D e n s i t y a n d S t a n d a r d C o m p a c t io io n T e s t s o n S a n d s w i t h V a r y i n g A m o u n t s o f F i n e s F . c . T O WN WN SEN D

348

Determ ination of Relative De nsity of Sand Below Groundw ater Ta bl e J.

O . O S T E R B E R G A N D S E RG RG E V A R A K S I N

Discussion

U s e o f R e l a ti v e D e n s i t y i n G e o t e c h n i c a l P r o j e c t s

364 376

E x p e r i e n c e w i t h R e l a t i v e D e n s i t y a s a C o n s t r u c t io io n C o n t r o l C r i t e r i o n 381

D . J . LE A R Y A N D R . J . WO O DWA DWA R D~ D~ I I I

D en sity M easu rem ents in a H yd rau lic F ill

s . J . P O UL U L OS OS A ND ND A . H ED ED

402

F i e l d a n d L a b o r a t o r y D e t e r m i n a t i o n o f M a x i m u m D e n s i t y i n C o a rs rs e S a n d s a n d G r a v e l s f o r M i c a D a m w . i . L O W A ND ND C . S EN EN E R

425

C o r r e l a ti t i o n B e t w e e n G r a d a t i o n a l P a r a m e t e r s a n d L i m i t in i n g D e n s i t ie i e s fo fo r C o h e s io i o n l es e s s M a t e r i a l s P l a c e d H y d r a u l i c a l l y m M . R EI EIT Z

444

Comparison of Relative Densities Estimated Using Different Approaches R . A . B E L L A ND ND J .

Relative D ens ity

P. S INGH

T h r e e E x a m p l e s o f I t s U s e i n R e s e a rc rc h a n d P r a c t i c e

K. J. MELZER

D i f f i c u lt l t i es e s i n th th e U s e o f R e l a t i v e D e n s i t y a s a S o i l P a r a m e t e r

455 463

F . A . T A V ~N ~N A S 4 7 8

Summary E v a l u a t i o n o f R e l a t i v e D e n s i t y M e a s u r e m e n t s a n d A p p l i c a t i0 i0 n s AND 1~. S. LADD

E . T . S E Lm Lm

487

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S T P 5 2 3 E B / J u l.

1973

 n t r o d u c t io io n

R e c o g n iz i z i n g t h e i m p o r t a n c e o f r e la l a t i v e d e n s i t y i n e n g i n ee e e r in i n g p r o b le le m s d e a l i n g w i t h c o h es e s io i o n l es e s s s oi o i l s a n d t h e n u m b e r o f A m e r i c a n S o c i e t y fo fo r Testing and Materials standards related to this topic, ASTM Committee D - 1 8 o n S o ilil a n d R o c k f o r E n g i n e e r i n g P u r p o s e s c o n s i d e r e d i t d e s i r a b l e t o o r g a n i ze z e a n d s P o n s o r t h i s s y m p o s i u m . E m p h a s i s w a s p l a c e d o n t h e f o l lo lo w i n g f o u r i t e m s c o n c e r n in i n g t h e e v a l u a t io i o n o f re r e l a t iv i v e d e n s i t y a n d i ts t s r o le le i n g e o t e c h n i c a l p r o j e c t s i n v o l v i n g c o h e s i o n l es e s s s oi o i ls ls : ( 1) 1) d e t e r m i n a t i o n o f r e l a ti t i v e d e n s i t y c on o n s id i d e r in in g t h e m e a s u r e m e n t o f m a x i m u m , m i n i m u m , a n d n s tu o r s a m p l e d e n s i t y a s w e l l a s t h e r e l i a b il i l i ty ty o f r e l a t i v e d e n s i t y a n d t h e f a c t o r s in i n f l u e n c in i n g i t , ( 2) 2) c o r r e l a t i o n b e t w e e n r e l a t i v e d e n s i t y a n d m e a s u r e d p e r f o r m a n c e o r p r o p e r t i e s o f g r a n u l a r s o ilil s, s, ( 3) 3) a p p l i c a t i o n s o f r e l a t i v e d e n s i t y t o g e o t e c h n i c a l p ro ro ~ec ~e c ts ts i n v o l v i n g c o h e s i o n le le s s s oi o i ls ls a n d t h e usefulness of this concept, and (4) evaluation of the existing ASTM s t a n d a r d s c o n c e r n in i n g r e l a ti t i v e d e n s i t y w i t h r e c o m m e n d a t i o n s fo f o r im im p r o v e m e n t s in in t h e f u t u r e . T h e s y m p o s i u m w a s d i v i d e d in i n t o t w o s es e s si si o ns n s . T h e m o r n i n g s es e s s io io n p r i m a r i l y c o v e r e d t h e m e a s u r e m e n t o f r e l a ti t i v e d e n s i ty t y . T h e s es e s si s i on on b e g a n w i t h a n a d d r e ss s s b y W . G . H o l t z w h i c h d e f in i n e d r e l a ti ti v e d e n s i t y a n d a p p l i c a b le l e s oi o i l s , e x p l a in i n e d t h e h i s t o r y o f t h e t e s t s t a n d a r d s , a n d d i s c u ss ss e d t h e r e l i a b i li l i t y o f t h e c o n c e p t . O n e o f t h e h i g h l ig i g h t s o f t h i s s e ss s s io io n w a s t h e presentation of F. A. Tavenas of the results of the cooperative testing p r o g r a m c a r r i e d o u t b y f o r t y - o n e (4 ( 4 1) 1 ) so s o il il la la b o r a t o r i e s i n t h e U n i t e d S t a t e s and Canada to evaluate the accuracy and precision of relative density m e a s u r e m e n t . F i f t e e n p a p e r s o n t h e t o p i c o f S es e s si s i on on I w e r e a c c e p t e d b y t h e s y m p o s i u m c o m m i t t e e . S e v e r al a l o f t h e s e w e r e s e l ec ec t e d f o r p r e s e n t a t i o n t o p r o v i d e f u r t h e r b a c k g r o u n d p r i o r t o t h e p a n e l d i sc s c u ss s s io io n . P a n e l m e m b e r s in in S e ss s s io io n I w e r e : E . T . S e li li g ( m o d e r a t o r ) , S t a t e U n i v e r s i t y o f N e w Y o r k a t B u f f a l o ; D . F . G r if i f fi f i n, n , N a v a l C i v il il E n g i n e e r i n g L a b o r a t o r y ; W . G . H o l t z , C o n s u l t in in g E n g i n e e r ; R . S . L a d d , W o o d w a r d - M o o r h o u s e A s s o c ia i a t es es ; R . J . S t e p h e n s o n , S o u t h A t l a n t ic i c D i v i s io io n L a b o r a t o r y , U .S . A r m y C o r p s o f Engineers; F. A. Taven as, Laval U niversity; and D. A. Tiedem ann, U.S. Bu reau of Reclam ation. The afternoon session dealt with applications of relative density, i n c lu l u d i n g c o r re r e l a ti t i o n w i t h p r o p e r t ie ie s a n d p e r f o r m a n c e a n d a n a s s e s s m e n t o f u s e fu f u l n es e s s . T h e s es e s s io io n b e g a n w i t h i l l u s t r a t io i o n s o f a p p l ic ic a t i o n s o f r e l a t i v e

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REL TIVE DENSITY INVO LVING

COHESIONLESS SOILS

density by Yves Lacroix. Twelve papers were accepted on the topic of S e s s io io n I I . F o l l o w i n g t h e p r e s e n t a t i o n o f s e v e r a l o f t h e s e p a p e r s , a n a c t i v e d i s c u ss s s i o n w a s h e l d b y t h e p a n e l a s w e l l a s p e r so so n s a t t e n d i n g t h e s y m p o s i u m c o n c e r n in i n g t h e r e l i a b i l it i t y o f re r e l a t i v e d e n s i t y a n d i t s u s ef e f u ln ln e s s . T h e p a n e l m e m b e r s f o r t h is i s s es e s s io io n w e r e : R . S . L a d d ( m o d e r a t o r) r) , W o o d w a r d M oorho use A s s o c i a t e s ; W . G . H o l t z , C o n s u l t in in g E n g i n e e r ; I . H o l u b e c , E . D ' A p p o l o n i a C o n s u l t in i n g E n g i n e e r s; s ; Y v e s L a cr c r o ix i x , D i r e c to to r , W o o d w a r d C l y d e C o n s u l t a n t s ; S . J . P o u l o s , G e o t e c h n i c a l E n g i n e e r s ; E . T . S el el i g , S t a t e U n i v e r s i t y o f N e w Y o r k a t B u f f a lo l o ; R . J . S t e ph p h e n s o n , S o u t h A t la la n t i c D i v i si s i o n L a b o r a t o r y U . S . A r m y C o r p s o f E n g i ne n e e rs rs . The papers have been grouped in these proceedings by session topic f o ll l l o w in i n g t h e s e s si s i o n k e y n o t e a d d r e s s . T h e f in i n a l p a p e r e v a l u a t e s t h e e n t i re re w r i t t e n a n d o r a l c o n t e n t o f t h e s y m p o s i u m a n d , o n t h e b a s i s o f t h is is information, summarizes the results and recommends future action by A S T M . I t i s t h e h o p e o f t h e a u t h o r s a n d s p o n so s o r s o f t h is is s y m p o s i u m t h a t this ASTM Special Technical Publication will provide a comprehensive e n o u g h e v a l u a t i o n o f r e l a t iv i v e d e n s i t y a n d i t s r o le le i n g e o t e c h n i c a l p r o j e c t s t o e n a b l e p r a c t i c i n g e n g i n ee ee r s t o f u n c t i o n m o r e e f f e c t i v e l y o n p r o j e c t s i n v o l v i n g c o h e s io i o n le l e s s s oi oi l s . I t i s a l so so h o p e d t h a t t h e a c c u m u l a t e d k n o w l e d g e o f t e s t t e c h n i q u e s , a p p a r a t u s , a n d a p p l i c a ti ti o n s w i l l b e u s e d a s a b a s i s f o r i m p r o v i n g t h e m a n y t e s t s t a n d a r d s a s s o c ia i a t e d w i t h r e l a ti t i v e d e n s i ty ty .

E T Selig ssociate Professor Department of Civil Engine Engineering ering State University of New New York at Buf Buffalo falo

Buffalo, N. Y. R

S

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Laboratory Director W oodward-Moorhouse

Associates,, Inc. Associates

Clifton, Clift on, N. J.

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  eterm et erm i nati nation on of Re l ati ative ve

ens i ty

Consider Consi deriing the the M easuremen t of M axi axim m um Minimum and In Situ Density

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G

H o l tz tz ~

T h e R e l a t iv i v e D e n s it i t y A p p r o a c h - --- U s e s T estin esti n g R eq u i rem r em en ts R el iab i ab i l i t y an d S h o rtco m i n g s

R E F E R E N C E : H o l tz t z , W . G ., ., T h e R e l a t i v e D e n s i t y A p p r o a c h - - U s e s , Eval uat i on of T e s t i n g R e q u i r e m e n t s , R e l ia ia b i l i t y , a n d S h o r t c o m i n g s , Relative Density and Its Role in Geotechnical Projects Involving Cohesionless S o il il s A S T M S T P 5 23 23 A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 19 1 9 73 73 , pp. 5-17.

io n l es e s s s o i ls ls i n A B S T R A C T : T o e v a l u a t e t h e d e n s i t y o f f r e e d r a i n i n g c o h e s io terms of percent relative density, there are three parameters that must be d e t e r m i n e d . T h e s e a r e ( 1 ) t h e m i n i m u m d e n s i t y t h a t t h e s o il il c a n b e s t r u c t u r e d , ( 2) 2 ) t h e m a x i m u m d e n s i t y t h a t t h e s o il il c a n b e s tr t r u c t u r e d , a n d ( 3) 3) t h e d e n s i t y o f t h e s o il il b e i n g e v a l u a t e d . E r r o r s o r v a r i a t i o n s c a n b e o b t a i n e d i n d e t e r m i n i n g e a c h o f t h e s e th t h r e e v a l u e s . T h e r e a s o n s f o r s u ch c h v a r i a t i o n s in in c l u d e ( 1 ) l a c k o f s p e c i m e n s i m i l a r i ty t y , ( 2) 2 ) d i s s im i m i l a r t e s t p r o c e d u r e s u s e d , ( 3) 3) t e s t i n g e q u i p m e n t n o t s i m i la la r o r n o t p r o p e r l y m a i n ta t a i n e d , a n d v a r i a ti t i o n s i n t h e t r a in in i n g a n d expertise of operator. The results of a large num ber of tests by num erous l a b o r a to t o r i e s i n d i c a t e t h a t t h e v a r i a t io i o n s a s s o c ia ia t e d w i t h t h e m i n i m u m a n d m a x i m u m d e n s i t y te t e s t s a r e a b o u t t h e s a m e a s t h o se s e a s s o c i at at e d w i t h t h e i m p a c t compaction tests. The requirement for determination of three parameters to d e t e r m i n e t h e r e l a t i v e d e n s i t y v a lu l u e c a n l e a d t o t h e c o m p o u n d i n g o f e rr r r o rs rs a n d v a r i a t i o n s in i n t h e w o r s t c a s e s. s . T h e u s e o f p r o p e r t e s t m e t h o d s , c l o s e ly ly f o ll ll o w e d ; s p e c if if ie i e d e q u i p m e n t , w e l l m a i n t a i n e d ; w e l l t r a i n e d t e s t p e r s o n n e l, l , a n d c a r e in in s a m p l i n g sh sh o u l d p r o v i d e r e p r o d u c i b l e r e l a t i v e d e n s i t y v a l u e s w i t h i n 1 0 p e r c e n t relative density. K E Y W O R D S : cohesionless soils, density (mass/volume), tests, soils, reproduc ibility, soil com pacting, reliab ility, soil me chanics

Th e

subject

o f t h e r e l a t iv e d e n s i t y a p p r o a c h

t o c e r t a in g e o t e c h n i c a l

p r o b l e m s i s e x t r e m e l y t i m e l y a n d o f g r e a t i m p o r t a n c e t o s o il i l s e n g i n e e rs rs . I w a n t t o b e g in th i s p a p e r b y d e s c r i b in g w h a t w e a r e ta l k i n g a b o u t w h e n w e s p e a k o f r e l a t i v e d e n s i ty , w h y r e l a t iv e d e n s i t y c r i te r i a a re s e n s i bl e a p p r o a c h e s t o c e r t a i n s o il i l p r o b l e m s , t h e o r i g i n of of t h e p r e s e n t A S T M

Test for

i C o n s u l t in i n g c i v i l en e n g i n e e r, r , a n d f o r m e r a s s i s t a n t c h ie ie f , D i v i s i o n o f R e s e a r c h , U . S . B u r e a u o f R e c l a m a t i o n , r e t i r e d ; W h e a t R i d g e , C o l o . 80 80 03 0 3 3. 3.

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REL TIVE DENSITY INVOLVING

C O H E S I O N L E S S S O I LS LS

R e l a t i v e D e n s i t y o f C o h e s i o n le l e s s S o il il s, s , D 2 0 4 99 - 69 6 9 ), ), a n d w h a t w e w o u l d like to accomplish. I a m s u r e t h a t m o s t e v e r y o n e is i s fa f a m i l i a r w i t h t h e r e l a ti t i v e d e n s i t y c o n c e p t, t, b u t b e f o r e I b e g i n , I w i s h t o d e f i n e i t. t. A c c o r d i n g t o A S T M D e f i n i t i o n s o f T e r m s a n d S y m b o l s R e l a t i n g t o S oi o i l a n d R o c k M e c h a n i c s D 6 5 33 - 67 6 7 ), ), r e l a t i v e d e n s i t y i s d e f i n e d a s t h e r a t i o o f 1 ) t h e d i f fe f e r e n ce ce b e t w e e n t h e v o i d r a t i o o f a c o h e si s i o n le l e s s s oi o i l i n t h e l o o se se s t s t a t e e ~ x ) a n d a n y g i v e n v o i d r a t i o e ), ), t o 2 ) t h e d i f f e r e n c e b e t w e e n i t s v o i d r a t i o s i n t h e l o o s e s t e ma m a x) x) a n d i n t h e d e n s e s t e ml m ln ) s t a t e s . I n e q u a t i o n f o r m t h i s b e c o m e s Dd

em

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m

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1 00 00 , i n t e r m s o f v o i d r a t i o

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y ~, m a x -

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X 1 00 00 , i n t e r m s o f d e n s i t y ,

which is the form most of us are concerned with in engineering project applications. T h u s , t h e r e a r e th t h r e e p a r a m e t e r s w h i c h m u s t b e d e t e r m i n e d : 1 ) em e m ax ax o r Y ml m ln , w h i c h d e s c ri r i b e s t h e m o s t l o o se s e s t a t e t h a t a p a r t i c u l a r s o il il c a n b e s t r u c t u r e d ; 2 ) e ml m l n o r y . . . . w h i c h d e s c ri ri b e s t h e m o s t d e n s e s t a t e t h a t t h e s o il i l c a n b e s t r u c t u r e d ; a n d 3 ) e o r -y -y w h i c h is is t h e i n - p l a c e d e n s i t y o f a n a t u r a l d e p o s i t o r f il il l , o r p e r h a p s t h e d e n s i t y o f a l a b o r a t o r y s a m p l e o r r e s e a r c h t e s t s p e c im i m e n , w h i c h w e d e s ir i r e t o d e s c r ib i b e i n t e r m s o f t h a t s oi o i ls ls densest and loosest states. Therefore, the most loose state is zero percent relative density, and the most dense state is 100 percent relative density, and, theoretically, no lower or higher density states, respectively, should e x i st st w i t h o u t c h a n g e s i n g r a d a t i o n . W e a l s o n e e d t o c o n s i d e r w h a t s o il i l s a r e a p p l i c a b l e to to t h e r e l a t i v e d e n s i t y a p p r o a c h . W h i l e t h e t i t l e o f t h i s s y m p o s i u m r e fe f e r s o n l y t o c o h e s i on o n l e ss ss s o il il s, s , i t i s c e r t a i n t h a t c o h e s i o n le l e s s s i lt l t s o r s a n d y o r g r a v e l l y s o il il s c o n t a i n i n g excessive amounts of cohesionless silt are not applicable to the relative d e n s i t y c r it i t e r ia i a . A m o r e d e s c r i p t i v e t e r m m i g h t i n c l u d e t h e w o r d s p e rv rv i o u s , f r e e - d r a in i n i n g , o r p e r h a p s n e a r f r e e - d r a i n in in g . S o m e y e a r s a g o w h e n w e w e r e w o r k i n g o n v i b r a t e d s a n d b a c k f il il l f o r t h e S a n D i e g o A q u e d u c t a n d o t h e r l a r g e c o n d u i t s, s , I p ro ro p o s e d s o m e l i m i t s o f s o il il t y p e s f o r c o m p a c t i o n - b y - v i b r a t i o n p u r p o s e s [1 ] 2 T h e s e l i m i t s w h i c h w e r e b a s e d o n t e s t s o f s e v e r a l d i f f e r e n t s a n d a n d s a n d - g r a v e l so s o i ls ls w i t h d i f f e r e n t a m o u n t s o f - 2 0 0 f in i n e s [2 [2 , 3 ] w e r e a s f o ll ll o w s : 1 . G W , G P , S W , a n d S P s o i ls ls a r e s u i t a b l e . limited to 5 percent by definition.)

T h e f i n e s i n t h e s e s o i ls ls a r e

The ita italic lic numbers in b rackets refer to the list of references references appende d to this paper.

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H OL T Z ON T H E R EL T IVE IVE D EN SI T Y

PPR O C H

2. Borderline GW-GM, GW-GC, GP-GM, and GP-GC soils containing lesss th an 8 percent fines are usual ly suitable. les suitable. 3. Borderline SW-SM, SP-SM, and SP-SC soils are suitable. (Fines in these soils are limited to 12 percent by definition.) 4. SM and an d SC soi soils ls require special special considerat consideration ion and suit s uit abi abili lity ty depends upon gradation of the sand and the plasticity of the fines. Some SM soils wit h fines fines as as high as 16 percent hav e been foun d to be suitable. In this case suitability was defined as limiting amount of fines where the specified minimum percent relative density became less than the specified minimum percent compaction based on ASTM Tests for Moisture-Density Rel at ation ionss of So Soils ils,, Using 5.5-1b 5.5-1b Ra mm er an and d 12-in. Drop, (D 698-70 698-70). ). Based upon lite ratu re recentl y studied, I can find find no reason reason to modi fy the preceeding preceed ing criteria. criteria. We should remember t ha t when we conside considerr compaction by vibratio n, we are are really talking about so soil ilss tha t are adequ atel y perviou perviouss to drain ex exce cess ss water du ring the vibra tion period. We learned long ago ago,, for instance, t ha t loose loose,, silty, loes loessi sial al,, fou foundat ndat ion so soil ilss could could not be compa compacted cted by vibroflotation methods which incorporated a large vibroflot (sand (sand = 44 percent, Silt = 47 percent, - 0. 00 5 m m = 9 percent) [4]. [4]. The research reported by F. C. Townsend in this symposium provides some excellent additional information on this subject. W h y R e l a ti v e

ensity

There are several ways by which the denseness of sand and gravel soils can be expre express ssed ed.. These ma y be simple density, void-ratio, or degree of compaction based upon some impact energy or vibration condition. Many years ago it was suggested that relative density would be an appropriate means to define the looseness and denseness of sand or sand-gravel soils in a meaningful way, because important properties such as shear and consolidation could be correlated quite well by this means [5]. Relative density has been found useful in liquifaction studies and other seismic studies for sand and gravel soil foundations and embankments subject to earthquakes or other vibrational conditions. Relative density is useful to control lab ora tor y test spe specim cimens ens,, to use as a spec specifica ification tion densi ty requirement for fill and foundation construction, and as a means to assess the competence of natural sand-gravel soil deposits for foundation uses. efinitions and Standards

As soon as engineers engineers st start art ed to t o use relative densi de nsi ty as as a soil soil par parame ameter ter we began to confuse ou ours rsel elve ves, s, because we did not have a common definition or set of standards to work from. William T. Cavanaugh, Managing Director of ASTM, wrote in t he April 19 1972 72 issue of Materials Research and Standards The evolution of language in the slow victory over Babel was man's greate st foreward move in his his eternal struggle to bring order out of chao chaos. s.

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R E L A T IV I V E D E N S IT IT Y I N V O L V I N G

C O H E S IO I O N L E S S S O IL IL S

T A B L E 1 V ar io us term s used to descr describe ibe the the st state ate of densen denseness. ess. Relative Relati ve Densit Density, y, perc ent USBR [6] Lambe and Whitman [7]

0

10

20

very loosee loos

loose

Bu rm ister [5] [5]

Meyerhoff [8]

Hough [9] Tschebotarioff [10] Pl u mm e r an d D o re [11]

30

40

50

medium

loose very loose

loose

loose

60

compact

firm medium

80

dense

medium

loose

70

90

100

very dense

very ~ ompact c o m p a c

ense

very dense

com pact

very compact

ense

S t a n d a r d i z a t i o n , o f c o u rs rs e , is n o t h i n g m o r e t h a n t h e f o r c e d - d r a f t c r e a t i o n o f l a n g u a g e . L a n g u a g e i t s e lf lf i s a s e t o f s t a n d a r d s y m b o l s f o r t h i n g s a n d c o n ce c e p ts t s . T h e s t a n d a r d s t h a t A S T M p r o d u c e s c om o m p r i se s e a la la n g u a g e f o r c o m m e r c e , a la la n g u a g e f o r r e s e a r c h , a l a n g u a g e f o r r e g u l a t i o n , a n d a l a n g u a g e , i f y o u w i ll l l , f o r a c c o m m o d a t i n g t h e f r u it i t s o f s c ie ie n c e a n d t e c h n o l o g y to our culture. W e a r e s ti t i ll l l g o in i n g th t h r o u g h a c e r t a i n a m o u n t o f B a b e l w i t h r e s p e c t to to d e s c r i b i n g t h e l o o s e n e ss s s a n d d e n s e n e s s o f s a n d - g r a v e l s oi o i l s. s. T h r o u g h o u t t h e s oi o i ls ls e n g i n e e r i n g l i t e r a t u r e o n e c a n f i n d v a r i o u s w o r d s u s e d t o d e s c r i b e t h e s t a t e o f d e n s e n e s s, s , s o m e o f w h i c h a r e l is is t e d i n T a b l e 1. T h e d i f f e r e n c e s which can be construed from qualitative word groupings can readily be s ee e e n . F o r i n s ta ta n c e , co m pa ct h a s a n e n t ir i r e l y d i f fe fe r e n t m e a n i n g t o B u r m i s t e r t h a n t o M e y e r h o f f . I f t h e s e w o r d d e s c r i p t io i o n s w e r e u se s e d o n d r il il l h o l e l og o g s, s , t h e u s e r o f t h e l og o g s c o u ld ld n o t b e s u r e o f t h e t r u e m e a n i n g t h a t w a s t o b e c o n v e y e d . S o m e e f f o rt r t s h o u ld l d b e m a d e b y S u b c o m m i t te t e e D 1 8. 8 . 9 2 on on N o m e n c l a t u r e f o r S oi o i l a n d R o c k M e c h a n i c s t o p r o v i d e u n i f o r m d e f in i n i ti t i o ns ns . T h e r e a ls l s o w a s n o a g r e e m e n t a s t o h o w t h e r e l a t i v e d e n s i t y o f a s o il il w a s t o b e d e t e r m i n e d q u a n t i t a t i v e l y . I f o n e is t o a n a l y s e a f o u n d a t i o n o r s t r u c t u r e s i tu t u a t i o n , p a r t i c u l a r l y w h e n s e is i s m i c e ff f f e ct ct s a r e i n v o l v e d , o n t h e b a s i s o f s o il i l p r o p e r t i e s , r a t h e r t h a n t e s t i n d ic ic e s s u c h a s p e n e t r a t i o n N v a l u e s, s , i t is i s n e c e s s a r y to t o a s si s i gn g n q u a n t i t a t i v e r e l a t iv iv e d e n s i t y v a l u e s t o t h e s oi o i l . T h u s , t h e n e e d f o r a d e q u a t e t e s t p r o c e d u r e s is is r e a d i l y a p p a r e n t . T h e d e t e r m i n a t i o n o f t h e r e l a t i v e d e n s i t y o f a n y s oi o i l s p e c i m e n o r s o il il m a s s r e q u i r e s t h r e e d e n s i t y d e t e r m i n a t i o n s ; t h i s is is o n e o f t h e s h o r t c o m i n g s o f t h e r e l a t i v e d e n s i t y a p p r o a c h . E r r o r s , o r d i f fe f e r e n t r e s u lt lt s o b t a i n e d

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t  

HOLTZ ON THE RELATIVE RELATIVEDENSITY APPROACH

t h r o u g h d i ff f f e r en e n c e s i n t e s t p r o c e d u r e s , i n v o l v e d in in t h e t h r e e d e t e r m i n a t i o n s can significantly magnify the errors or differences determined for the p e r c e n t r e l a ti ti v e d e n s i t y . R e c o g n i zi z i n g t h a t s o m e k i n d o f s t a n d a r d s w o u l d b e n e c e s s a ry r y , if if w e w e r e a ll l l to t o w o r k o n t h e s a m e b a s i s a n d b e a b l e . t o i n t e r p r e t t h e d a t a o f o t h er er s , Section D, Subcommittee 3, of Committee D-18 was established in June 1 95 95 4 u n d e r t h e C h a i r m a n s h i p o f E a r l F e l t t o w o r k o n s t a n d a r d s f o r d e t e r m i n i n g t h e m i n i m u m a n d m a x i m u m d e n s i ti t i e s o f s a n d s o il il s a n d g r a v e l s o il il s . T h e w o r k o f t h e S u b c o m m i t te t e e r e s u lt l t e d i n t o d a y s A S T M D 2 0 49 4 9 -6 -6 9 which was approved by Committee D-18 in 1964. Probably more cooperat i v e r e se s e a r c h w a s c o n d u c t e d o n t h is i s s t a n d a r d t e s t m e t h o d , p r i o r to to a d o p t i o n , than most any other adopted by Committee D-18 at that time. E a r l F e l t f i rs r s t o rg r g a n iz iz e d a g r o u p o f s u b c o m m i t t e e m e m b e r s f r o m e i g h t organizations who were willing to participate in a cooperative testing and re s e a r c h s t u d y . S a m p l e s o f s ix i x d if i f fe re n t so s o il il s , v a ry i n g fr o m fin fi n e s a n d t o o p e n g r a d e d c r u s h e d r o c k w e r e s e n t t o e a c h o f t h e m e m b e r s . S o m e t w e l v e d i f fe fe r ent methods, including vibration, impact hammer, dropping, tapping (dry a n d s a t u r a t e d ) , e tc t c ., . , w e r e e x p e r i m e n t e d w i t h to to d e t e r m i n e t h e m a x i m u m density. Some six different methods for minimum density determinations w e r e a l so s o c o n d u c t e d . T h e r e s u l t s o f t h i s w o r k w e r e r e p o r t e d a t t h e 1 95 95 8 A n n u a l M e e t i n g o f t h e S o c i e t y [1 [ 1 2] 2 ] . T h e r e s u l ts t s o f si s i m i la la r t e s t s b y i n d i v i d uals and different laboratories were compared. Tentative selections for the m o s t p r o m i s in i n g a n d c o n s i st s t e n t m e t h o d s w e r e m a d e , a n d a s e c on on d p r o g r a m o f t e s ti t i n g , i n v o l v i n g a l i m i t e d n u m b e r o f l a b o r a t o r ie ie s , w a s u n d e r t a k e n . O n t h e b a s i s o f t h e c o o p e r a t iv i v e p ro ro g r a m s , t h e S u b c o m m i t t e e w r o t e t h e t e s t procedures essentially as they are now written in ASTM D 2049-69. It took several years until 1964 to get this standard through S u b c o m m i t te t e e 3 a n d C o m m i t t e e D - 18 1 8 . I t w a s r e c og o g n iz iz e d t h a t t h e r e w e r e s o m e s h o r t c o m i n g s . F o r i n s ta t a n c e , t h e r e m a y b e a f e w s i tu t u a t i o n s w h e r e fi f i el el d compaction of certain soils, that are applicable to the relative density a p p r o a c h , m a y p r o d u c e d e n s it i t ie i e s i n e xc x c e ss ss o f t h e l a b o r a t o r y m a x i m u m v a l u e s o b t a i n e d b y b o t h d r y a n d s a t u r a t e d p r o c ed e d u r e s. s. H o w e v e r , t h e s e appeared to be few, and reproducibility appeared to be as good as those b e i n g o b t a in i n e d b y o t h e r c o m p a c t i o n m e t h o d s s u c h a s A S T M D 6 9 8 - 70 70 a n d A S T M T e s t s f o r M o i s t u r e - D e n s i t y R e l a t io i o n s o f So S o ilil s , U s in i n g 1 00- 1 b R a m m e r a n d 1 8 -i -i n . D r o p , ( D 1 55 5 5 7 -7 -7 0 ). ). I t w a s t h e o p i n i o n o f t h e m a j o ri t y o f Subcommittee members that the benefits of a reasonably good standard method, by which we all spoke the same language, far outweighed any d i s a d v a n t a g e s o f t h e p a r t i c u la l a r t e s t m e t h o d s t h e n p r o p o se s e d . I n a d d i ti ti o n , it was felt that by getting a tentative standard method published, many p e r s o n s a n d o r g a n i z a ti t i o n s w o u l d w o r k w i t h i t , e v a l u a t e i t s s u i t a b i l it it y , a n d s u g g e s t b e n e fi f i c ia ia l m o d i f i c a ti ti o n s a n d i m p r o v e m e n t s . I n o t h e r w o r d s , i t g a v e u s s o m e t h i n g t o s h o o t a t . I t i s w o r t h n o t i n g t h a t i n th t h e e i g h t y e a r s s in in c e t h e a d o p t i o n o f A S T M D 2 04 0 4 9 -6 - 6 9 n o s i gn g n i fi f i c an an t , p r a c t i c a l c h a n g e s h a v e b e e n C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFPE ) Universidade Federal de Pernambuco) pursuant to Lice  

]

REL TIVEDENSITY TIVEDENSITY IN INVOL VOLVIN VING G COH COHESI ESIONL ONLESS ESSSOIL SOILS S

suggested to the Subcommittee. This has been disappointing. As usual, there have been some criticisms, but no one has really brought forward bett er methods tha t can be used for day-t o-day engin engineer eering ing project work. work. It is hoped hoped tha t this symposiu symposium m wi will ll stimulate further stud y and improvements in the present standards, if it is determined that this is advisable.

R e l i a b i l it it y o f R e l a t i v e

ensity Values

eneral If we are to use the relative density approach, we must be able to measure the three required parameters--sample or in-place density, absolute abso lute mi nimum density, density, and absol absolute ute maximum den sit y--w ith suffici sufficien entt accuracy to develop a meaningful relative density reliability. This constit utes the theme for this first ses sessi sion on of the symposium, I will tr y to bring some of the symposium papers papers into foc focus. us. Before we try to analyse the reliability and meaningfullness of the relative density parameters and the relative density value, I would like to review the reliability of some other laboratory soil tests and reasons why duplicatio dupli cation n of tes t values become difficult or imposs impossib ible le.. First, we have three conditions that we must evaluate for comparisons: (1)) how close (1 close can one individual indivi dual duplicate duplic ate his test tes t values; v alues; (2 (2)) how close close can severall individuals in one labo rato ry or organization duplicate each other's severa test values, and (3) how close can several organizations, utilizing oae or more individuals, duplicate each other's test values. In an evaluation of this kind, we must presume (a) that each test is conducted on similar specimens and materials, (b) that the identical test procedures are used, (c) that the same equipment is used and that the equipment is properly maintained and installed in the same manner, and (d) that each operator has adequate and similar expertise in conducting the tests. All of these criteria often are not met, and th ey are diffic difficult ult to as asse sess ss and determi ne.

Specimen Similarit Similarityy

During the conduct of the American Council of Independent Laboratories (ACIL) comparative tests for consistency limits, specific gravity, gradation, and compac compaction, tion, one of the most difficult difficult problem problemss was to assur assuree the likeness of specimens tested by each laboratory. In the papers by Tiedeman, and Tavenas, Ladd and LaRochelle for this symposium, variati ons in the grada tion dat a for supposedly similar spec specimen imenss of fine sand and med ium sand are sho shown. wn. For exam example, ple, with his wide widerr graded medium sand, Tied eman reports varat ions as high as 23 23 percent on the basis of cumulative percent passing the No. 16 screen or 13 percent on this individual screen size. It can be seen, however, that the variations in duplicate tests were les lesss th an for duplicate spec specim imen ens, s, indicating tha t there was considerable variation in the specimens. The true effect of such Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to L  

H OL T Z ON T H E R EL T IVE IVE D EN SI T Y

PPR O C H

v a r i a t io io n s o n t h e m a x i m u m a n d m i n i m u m v a l u e s i s n o t r e a d i l y d e t e r m i n a b le l e . I n h i s p a p e r i n th th i s s y m p o s i u m , Y o u d c o n c l u d e d t h a t t h e e f f e c t o f p a rt i c l e s iz iz e w h i c h w o u l d i n c l u d e m i n o r p a rt i c l e s iz iz e v a ri a t i o n s ) w a s negligable with the minimum and maximum densities being controlled p r i m a r i l y b y p a r t i c l e s h a p e p a r t i c l e s iz iz e r a n g e a n d v a r i a n c e s i n g r a d a t i o n a l c u r v e s h a p e . D i c k e n a ls l s o r e p o r t e d t h a t t h e e f f e c t o f p a r t i c l e s iz i z e o n l im im i t i n g porosities was small compared with variations caused by particle shape paper is included in this symposium). Generally speaking, it is usually more difficult to produce uniform s a m p l e s a n d u n i f o r m s p e c i m e n s o f t h e c o a r s e s a n d a n d g r a v e l s o il il s t h a n f in in e s i l t y a n d c l a y e y so so il il s . A l so s o , th t h e d i f f ic i c u l ty ty u s u a l l y b e c o m e s g r e a t e r w h e n t h e s o il i l s a re c o h e s i o n l e s s a n d a s t h e ra n g e o f p a rt i c l e s iz iz es e s b e c o m e g re a t e r. T h i s i s p r i m a r i l y c a u s e d b y s e g r e g a ti t i o n . S e g r e g a t io io n e v e n c a n e f f e c t t h e u n i f o r m i t y o f s a m p l i n g w h e n c l o s e ly l y c o n t r o l le l e d q u a r t e r i n g a n d s p l i t ti ti n g m e t h o d s a r e u s e d . T h e s c o o p in i n g a n d p l a c in i n g o f c o h e si s i o nl n l es e s s , c o a rs r s e - g r a in in e d s oi o i l s i n m o l d s f o r t h e s t a n d a r d m i n i m u m a n d m a x i m u m d e n s i t y t e s ts ts c a n c a u s e s e g re r e g a ti t i o n w h i c h c a n p r o d u c e n o n h o m o g e n i e t y o f g r a d a t io io n w i t h i n a test specimen and gradation variations between so-called duplicate s p ec e c im i m e n s . T h i s i s a p r o b l e m w e a r e f a c e d w i t h i n c o n d u c t in in g t h e m a x i m u m a n d m i n i m u m d e n s i t y te t e s t s. s . E m e r y , F i n n a n d L e e h a v e d i s c u ss ss e d t h e i r studies and p roblem s in developing uniform sand specimens for shake -table a n d l a b o r a t o r y s h e a r t e s t s i n cl c l u d ed ed i n t h i s s y m p o s i u m ) . dentical Test Procedures

Of course, a principal reason for the Committee D-18 interest in this s y m p o s i u m is i s t o r e - e v a lu l u a t e A S T M D 2 04 04 99 - 6 9. 9. T h e s t a n d a r d w a s d e v e l o p e d s o t h a t m o r e u n i f o r m a n d m o r e m e a n in i n g f u l re r e s u lt lt s c o u l d b e o b t a i n e d b y i n d i v i d u a l s m a k i n g d u p l i c a t e t e s t s , b y i n d i v i d u a l s i n o n e o r g a n iz i z a t io io n b e i n g a b l e t o s e c u re s i m i l a r re s u l t s , a n d fo r d i f fe re n t o rg a n i z a t i o n s t o s e c u re reasonably similar results. This is our objective. To achieve this it is very i m p o r t a n t t h a t t h e A S T M p r o c e d u r e b e f o l lo l o w e d v e r y c l o s el el y u n t i l s o m e t h i n g b e t t e r i s d e v e lo l o p e d . I t w i ll ll b e n o t e d t h a t o t h e r p r o c e d u r e s w e r e u s e d i n s o m e o f t h e s t u d ie i e s r e p o r t e d i n t h i s s y m p o s i u m . S u c h p r a c t i c es es m a k e evaluation and comparison of their work difficult.

quipment If we are to secure reasonable uniformity of results between different l a b o ra r a t o ri r i e s, s , i t is is v e r y i m p o r t a n t t h a t t h e e q u i p m e n t b e t h e s a m e a n d t h a t i t b e i n s t a l le l e d a n d b e m a i n t a i n e d a d e q u a t e l y . I t i s o f t e n s u r p ri r i s in i n g t o f in in d that the vibrating table may not be adequately anchored to the floor, that t h e c y l i n d e rs rs , w e i g h t s , a n d m e a s u r i n g d e v i c e s a r e n o t s t a n d a r d , t h a t t h e p o w e r s u p p l y i s n o t a d e q u a t e , o r t h a t v i b r a t i n g a m p l i tu t u d e s a r e n o t c o r re r e c t. t. R u s t e d o r r o u g h e n e d c y l i n d e rs r s m a y e f fe f e c t t h e r e s u l ts ts . T h e p o u r i n g d e v i c e s may not be as specified. C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L ic ic e n s e A g r e  

 2

REL TIVEDENSITY INVOLVING

C O H E S I O N LE LE S S S O I L S

Expertise of Operators One could hardly expect a novice with no training to produce the same reliabilit y of results as a t rai ned la bora tory engineer engineer or technician who has had ha d considerable ex expe peri rien ence ce.. Yet t her heree are instances where prac practic ticall ally y unt rai ned person personnel nel are performing these tests. On Onee of our mis mission sionss should be to upgrade the quality of soils laboratory work in general. Most of our laboratory tests can be performed by nonprofessional technicians i f they are properly trained by professional or highly experienced technical personnel. However professional guidance alway alwayss should be available and the test results should be reviewed by professional engineers at all times along with their analysis of the data for the problem at hand. Some of the test results obtained during the AC IL ori origin ginal al program program [13] which involved some 99 laboratories were so extreme as to be almost ludicrous if th thee problem proble m was not so se seri riou ous. s. Here ther e was not entir en tirely ely a question questi on of specimen speci men dissimilarity dissimilarity bu t almost cert ainly involved wer weree some some great variances of procedures or poorly trained operators who did not have the slightest comprehension of what th ey wer weree doing. doing.

Reliabilityy of Co m paction Tests Reliabilit Before we look at our abil ity to duplicate relative density tests let us Before review the results of the ACIL supplementary program on the standard compaction compac tion tes tests ts ASTM AST M D 698-7 698-70 0 and D 15 1557 57-7 -70. 0. I summarize summ arized d th thee values which wer weree obtained on the basi basiss of Table 2 of the report on supplemental testing for the AC IL prog program. ram. T A BL E 2

Su m m ar y of res result ultss of the A C IL supplement supplementary ary prog program. ram. Maximum Dry Density, Density, lb /ft 3 D-698 D-1557 All Labs~ Labs ~

Umpire Labs b

All Labs

Umpire Labs

Low plast icity L soi soil, l, avg range range, -4- avg

105.9 15.6 5.1

106.0 2.2 1.0

112.5 13.8 6.1

111.8 1.4 0. 6

Medium plasticity M soil, avg range range, • avg

109.7 18.8 8.6

109.5 1.8 0.8

115.8 26.6 11.5

117.7 1.6 0.7

99.6 14.8 7.5

98.6 2.7 1.4

113.3 8.15 8.2

114.0 3.4 1.5

High plasticity H soil, avg range range, • v7 avg a All laboratories. b Three well known umpi re laboratories.

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to  

HOLTZ ON THE REL TIVEDENSITY PPRO CH

TABLE

3

3--Var 3-Variat iation ionss from mean mean perc percent. ent.

Soill Soi

Standard Deviation Deviati on

Avg of Extremes

Avg, 10 to 90% a

M ax 3 M in 3

M ax 3 M in 3'

M ax -y M in ~/

Johnson

SW A

.. ... .

(9 U SE D l ab s) s) T ied i ed ema ema n (144 US BR Labs) (1

SP (B) Fi n e San d Medium Sand Medium

...... 1 .3 1.8

Tave nas et al al.. (411 gene (4 general ral la labs) bs)

Fine Sand Gra velly Sand

2.7 4.5

4 1.7

4 2.5

4 1.5

4 2.4

1 .4 1.8

4 -1 .4 4 -2 .1 .1 4-3.1

4 -2 .6 -4 -2 .9 4-3.2

4 -1 .4 4 -1 .2 4-2.3

4 -2 .1 4 -2 .0 -4-1.9 -41.9

1.7 2.5

4-6.3 4-8.3

4-3.7 4-5.2

4-2.1 4-3.7

4-2.4 4-2.8

a Average dry de nsity (3' (3')) vari variati ations ons from m ean for 10 and 90 percen t cumulated cumulated frequencies. B r i e f ly ly , f r o m t h i s d a t a , o n e c a n c o n c l u d e t h a t w h e n t h e t e s t s a r e c a r e f u l l y p e r f o r m e d , a s b y t h e u m p i r e l a b o r a to t o r i e s , a m a x i m u m d e n s i t y 5 = 1 .5 .5 p e r c e n t ( o r l e ss s s t h a n 5 = 1. 1. 5 p e r c e n t ) c a n b e a c h i e v e d . O n t h e o t h e r h a n d , w h e n considering all participating laboratories the variations were extremely l a r g e , u p t o a s h i g h a s 5= 1 1. 1.5 p e r c e n t . T h i s w o u l d l e a d o n e t o b e l i e v e t h a t , b e t w e e n l a b o r a to t o r i e s , t h e r e m u s t b e g r e a t d i ff f f e re re n c e s i n e q u i p m e n t , m a i n t e n a n c e o f e q u ip i p m e n t , a n d t h e t y p e a n d t r a in i n i n g o f p e r s on on n e l p e r f o r m i n g t h e t e s ts t s . N o c o n s i s t e n t d i f f e re re n c e s i n t h e s e r e s p e c t s w e r e a p p a r e n t a s regards using ASTM D 698-70 or D 1557-70 methods. S o m e la l a t e r s u p p l e m e n t a l s t u d i e s b y t w o d i f f e re r e n t l a b o r a to t o r i e s, s , e a c h u s in in g three operators and duplicating tests, also showed some wide variations; h o w e v e r , th t h e i r A S T M D 6 9 8 - 70 7 0 a v e r a g e v a l u e s w e r e s o d i f fe fe r e n t f r o m t h e other average ACIL values that there is considerable question as to their t e c h n i q u e s o r o t h e r f a c t o rs r s . T h e i r A S T M D 1 5 5 77 - 70 70 a v e r a g e d e n s i t y a n d range values were close to those of the umpire laboratories. I n. n . t h e p a p e r b y T a v e n a s , L a d d , a n d L a R o c h e l le le , s t a n d a r d c o m p a c t i o n t e s t s ( A S T M D 6 8 99 - 70 7 0 a n d D 1 55 5 5 77 - 70 7 0 ) w e r e m a d e o n d r y f in in e s a n d a n d d r y gravelly sand by the 41 participating laboratories. These results were r e p o r t e d i n t h e i r T a b l e X I I . F o r a b o u t 9 5 p e r c e n t o f t h e t es e s ts ts , a m a x i m u m d e n s i t y 5 = 2 p e r c e n t w o u l d c o v e r al a l l t y p e s o f te t e s t s a n d m a t e r i a ls ls . T h i s i s s l ig i g h t l y h i g h e r v a r i a t i o n t h a n t h a t s h o w n f o r t h e u m p i r e t e s ts ts , b u t i s e x c e e d i n g l y b e t t e r t h a n s h o w n f o r a ll l l la l a b o r a t o r i e s p a r t i c i p a t in in g i n t h e A C I L t e st s t s . I t a p p e a r s t h a t t h e 5 = 2 p e r c e n t v a r i a t i o n is is a r e a s o n a b l e v a r i a t i o n t o e x p e c t w i t h r e a s o n a b l y g o o d te t e s t in i n g p r a c t ic ic e s . O t h e r s h a v e e x p r e s s ed e d t h e s a m e o r d e r o f v a r i a t io io n .

R e l ia i a b i li l i ty ty o f M i n i m u m a n d M a x i m u m

e n s i ty t y T e st st s

T h e p a p e rs r s b y T i e d e m a n , T a v e n a s , L a d d , a n d L a R o c h e l le le , a n d M . M . J o h n s t o n ( i nc n c l u d e d i n t h is i s s y m p o s i u m ) r e p o r t o n a llaa r g e n u m b e r o f t e s t s

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o  

 4

REL TIVE DENSITY INVO LVING

COHESIONLESS SOILS

conducted by seve several ral laboratories laboratories for maximum and minimum densities densities of sand a nd gravel grave l soil soils. s. In some ca case sess several operators performed perfor med the tests t ests in in one labor atory or duplicate tests or bot h were made. made. These data provide an excellent exce llent background on the range of dat a t ha t can be be expected for bot h t he maximum and minimum tests. tests. From the data give given n in these these papers papers the varia variations tions obtained obtained in maximum and min minimu imu m densities by AST ASTM M D 20 2049 49-6 -69 9 for dry soils soils were summarized. Fro m this da ta i t appears tha t, within organizations organizations such as the U.S. U.S. Corps of Engineers USC USCE) E) and the U. U.S. S. Bureau of Reclamati on USBR), their field laboratori laboratories es can produce more uniform unif orm results th an when a large group of laboratories are taken at random such as those reported by Tavenas et al. The results should be in this order, because of more uniform training of the organizational operators; however, we also must keep in mind the number of laboratories involved in each of the comparisons, the random group having a much greater number. Tiedeman and Tavenas et al also report on the results of duplicate tests. As would be expected, the variations were much less, which points up the importance of consistent techniques. techniques. Based on the rando m results of single single tests b y a large number of laboralaboratories, the results of the cooperative relative density tests indicate less variability and better uniformity than those obtained during the original AC IL s tud y of sta ndar d compaction tests. However, However, the st andar d compaccompaction tests performe performed d by the umpire laboratories laboratories showed showed les lesss variab ility and greater uniformi ty tha n the relati relative ve density tests performed performed by the sev severa erall field laboratories of the USCE and USBR. Tiedeman concluded in his paper that the variations associated with minim um and maximu m density tests are about the same or le less ss than those associated with the impact type compaction test. Tavenas et al concluded t ha t t he qual q ualit ity y of the results resul ts would seem sati satisfac sfactory tory co coef effi fici cien ents ts of of variat var iat ion in th e order or der of 2.5 2.5 percent a nd co coef effi fici cien ents ts of reprod reproducibil ucibility ity in th e order of 0.8 percent), but that the standard and modified impact compaction tests exhibit exhibit a bett er quality than the maximum density of of the relative relative density test. O t h er e r C o n s i d e r a t io io n s

The two papers by Tiedeman and by Tavenas, Ladd, and LaRochelle point out how errors or variations in the maximum and minimum density tests are gre atly magnified magnified in the calculation of relative density. Both papers have illustrations showing how widespread the variations in calculated relative densities densities could be. To ill ustrate this point, the d at a of Taven as et al for the maximum and mini mum densities densities of the fin finee sand, which fell fell within thee limits of th of 10 10 and 90 perce percent nt cumula cum ula ted frequencies frequencies assumed to be representative of reasonably good testing), was used to develop Fig. 1. In 1958 19 58,, Merrima Merr ima n [ 4] determined t ha t under good conditions conditions and using good Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/prin ted by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Licen  

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sand-pou ring or sand-cone procedures sand-pouring procedures in-place soi soils ls densities could be dupli cate cated d within abou t =t=2 percent. Of co cour urse se dupli cated da ta i n this order can not be approached appr oached when wh en poor field field test testing ing practices are allowed to be used; for for example stompi ng arou nd a test hole in wet sand. Referri ng to Fig. 1acyif =t= we assume the in-place densioftyrelat is 108 10 l b/ ftsit3yand the e accuracy accur =t =2 percent and average the worst conditions relative ive8 densit den test th ing Copyright by ASTM Int l (all rights reserved); Fr i Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/prin ted by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to  

 6

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T I VE D EN S I T Y I N VOL VI N G

C OH ESI ON L ESS SOI L S

and fie field ld testing all exist exist at the same time---low time---lowest est maximum and m inim um values and highest in-place values by one operator, as compared with the highest maximum and minimum values and lowest in-place values by another operator--the range of relative densities obtained by the two operators could be as great as from 46 to 91 percent. This represents a range from a medium dense to very dense condition, or, perhaps, from an unsuitable density condition to a very satisfactory condition. The magnitude of variations that can be obtained in relative density values due to variations in the related parameters is not new. As an example, this was discussed by Elio D Appolpnia [ 5 ] in 1953 on the basis of research he had conducted at that time. He decided that the relative density values could be kept to about 10 percent, if good practices and suggested criteria criteri a were to be followe followed d in sett ing specification limit limitations ations.. We do not ant icipat e obtaining all of the most unfavorable test situati ons at the same time, and the chances are good that this would not hal~pen. However, in an effort to improve the soil mechanics profession, we should look towards the best possible means to assure competent and reliable end results. This is a reason for taking a hard look at our present relative densit den sit y practices, as wel welll as our relat relative ive den sit y sta standar ndard, d, AS TM D 20 2049 49-6 -69. 9. I am sure th at you will will be confronted with ideas for other approaches to the problem. These could include the use of a certain percent of the maximum density value as obtained by ASTM D 2049-69 in lieu of the relative density approach. Other test procedures will undoubtedly be proposed. We may find that the relative density approach is not the best from the reliability standpoint. However, we must not reach this decision hastily. We have muc h correlative informa tion as to relative de nsit y versus versus other soil properties, relative density versus competence of sand deposits and fills, relative density versus blow counts from sounding devices, etc. Perhaps the changeover would be be easy, perhaps not. One final point to remember is that the studies reported deal with the variations of individual tests. Decisions of design or construction control are not made--or should not be made--on the basis of one or two tests. The y are normally made on the basis basis of an adequate numbe r of tests. tests. For instance, instanc e, we do not require r equire a cont ract or to t o remove 10 00 000 0 yd y d ~ of compact ed sand fill on the basis of one test. It is usually done on the basis of a dozen tests or more. If the standard test methods were followed to reasonable degrees by an operator with a reasonable amount of correct training, the test results should be reasonably close, and the odd-ball determinations would be be readi ly apparent. A wide scattering would indicate poor variable techniques or poor equipment. I think we could do a great deal to answer some of our reliability and reproducibility problems by making greater efforts to improve soil testing practices, and to more closely follow the present ASTM methods.

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Per nambuco) pursuant to Li  

H OL T Z O N T H E R ELA ELA TI TIVE D EN SI T Y A PPR OA C H

7

References [ I] I ] H o l t z , W . G . , i n P a p er e r s o n S o il il s A S T M S T P 2 0 6 A m e r i c a n S o c i e t y f o r T e s t i n g a n d Materials, 1957, pp. 50-66. [ 2 ] M e r r i m a n , J . , R e s e a r c h T e s t s t o I n v e s t i g a t e C r i t e r i a f o r S e l e c ti t i o n B e t w e e n V i b ra ra ~ tory or Imp act Compaction M ethods, Lab oratory Rep ort No. EM-441, U. S. B u r e a u o f R e c l a m a t i o n , 1 9 5 5. 5. [3] 1 97 9 7 2 A n n u a l B o o k o f A S T M S ta ta nd n d ar a r ds ds P a r t 1 1 p p . 7 7 9 - 7 8 4 . [~ ] M e i s s n e r , V . S . , V i b r o f l o t a t i o n E x p e r i m e n t s a t E n d e r s D a m , L a b o r a t o r y R e p o r t N o . 1 7 8 , U . S . B u r e a u o f R e l c a m a t i o n , 1 9 48 48 . [5 ] B u r m i s t e r , D . M . , Proceedings A m e r i c a n S o c i e t y fo f o r T e s t i n g a n d M a t e r i a l s , V o l . 4 8, 8, 1948, p. 1249. [6 ] G i b b s , H . J . a n d M e r r i m a n , J . , S e c o n d P r o g r e s s R e p o r t o f R e s e a r c h o n D e t e r m i n i n g t h e R e l a t i v e D e n s i t y o f S a n d s b y S p o o n P e n e t r a t i o n T e s t in in g , L a b o r a t o r y R e p o r t N o . E M - 3 5 6 , U . S . B u r e a u o f R e c l a m a t i o n , 1 95 9 5 3. 3. [7 ] L a m l e , T . W . a n d W h i t m a n , R . V . , Soil Mechanics W i l e y , N e w Y o r k , 1 9 6 9 , p . 3 1 . [8 ] M e y e r h o f f , G . G . , Jo urn al of the So il Mechanics an d Foundations Foundations Division A m e r i c a n So ciety of Civil Engineers, Jan . 1956, p. 17. [ 9 ] H o u g h , B . K . , Basic Soils Engineering R o n a l d P r e s s C o . , N e w Y o r k , 1 9 5 7 , p . 3 5 7. 7. [10] T s c h e b o t a r i o f f , G . P . , Soil Mechanics Foundations and Earth Structures M c G r a w Hill Book Pu blishing Co., New York, 1951, p. 57. [11] P l u m m e r , F . L . a n d D o r e , S . M . , Soil Mechanics and Foundations P i t m a n P u b l i s h ing Corp., Ne w Y ork, 1940, p. 33. [ 12 12 ] F e l t , E . J . i n S y m p o s i u m o n A p p l i c a t i o n o f S o i l T e s t i n g i n H i g h w a y D e s i g n a n d C o n s tr tr ue ue titi o n A S T M S T P 2 39 3 9 A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 5 8, 8, p p . 89- 110. [13] J o h n so s o n , A . W . a n d G u i nn nn e e , J . W . , R e p o r t o n a S u p p l e m e n t a l T e s t i n g P r o g r a m f o r A C I L S t a n d a r d R e f e re r e n c e S o i l S a m p l e s , f o r t h e R e s e a rc r c h S t e e r in in g C o m m i t te te e o f A S T M C o m m i t t e e D -1 -1 8 . [ 1 4] 4 ] M e r r i m a n , J .,. , L a b o r a t o r y E v a l u a t i o n o f V o l u m e t e r N o . 7 70 70 f o r F i e l d D e n s i t y T e s t Determinations, Labo ratory Rep ort REM -2, U. S. Bureau of Reclamation, June 1958. [ 1 5] 5 ] D ' A p p o l o n i a , E l i o i n S y m p o s i u m o n D y n a m i c T e~ e ~ ti ti n g o f S o il i l s A S T M S T P 1 56 56 A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 5 3 , p p . 1 3 88- 15 15 4 .

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

F. A . Tave Tavenas nas 1 R. S. L a d d / and P. L a l~ocheUe~

A c c u r a c y o f R e la l a ti t i v e D e n s i ty t y M e a s u re r e m e n ts ts R e su s u ltlt s o f a C o m p a r a t i v e T e s t P r o g ra ra m

R E F E R E N C E : Tavenas, F. A., Ladd, R. S., and La Rochelle, P., A c c u r a c y o f R e l a t iv e D e n s i t y M e a s u r e m e n t s : Results of a Com parative T est Program, Evaluation of Relative Density and Its Role in Geotechnical Projects

Involving Coh Involving Cohesi esionl onless essSoils A S T M S T P 5~3 A m e r i c a n S o c i e ty t y fo fo r T e s t i n g a n d Materials, 1973, pp. 18-60.

A B S T R A C T : A c o o p e ra r a ti t i v e te t e s t in i n g p r o g ra r a m w a s c o n d uc u c t ed e d , u n d e r t h e s p o n s o rrs h i p o f t h e A m e r i c a n S o c i e ty t y f o r T e s t i n g a n d M a t e r i a ls l s ( A S T M ) , b y 4 1 so s o il il l a b o r a t o r ie i e s i n t h e U n i t e d S t a t e s a n d C a n a d a t o d e t e r m i n e v a r i a t i o n s a ss s s o c i at at e d snt s, sd, Pmr ioncitm t ~s supseecdi mt oe nds eofi ffi ne nae fth tihnee rwe il taht i gv er a ddeant is oi tny ,t east o ru m c o amnpda cmt iaoxni m t eus m t s od en nid isdiet nyt ti ce as l~ lts s a n d a n d a g r a v e l l y s a n d . D a t a w e r e a n a l y z e d s t a t is i s t i c a l ly l y o n t h e b a s is is o f variations among laboratories and between duplicate tests. Results indicated t h a t : ( 1 ) a l l t e s t s w e r e a ff f f e c te te d b y a l a r g e v a r i a b i l i t y a n d a l o w r e p r o d u c i b i l i t y , ( 2) 2 ) v a r i a t i o n s a m o n g l a b o r a t o ri r i e s w e re r e t w o t o t h r e e t i m e s g r e a te te r t h a n v a r i a t i o n s b e t w e e n d u p l i c a t e t e s ts t s , ( 3) 3 ) r e s u l t in i n g v a r i a t io i o n s o n t h e r e l a t iv iv e d e n s i t y w e r e s u c h t h a t t h i s p a r a m e t e r c a n n o t b e u s e d e f fi f i c ie ie n t ly ly i n p r a c ti ti c e , a n d ( 4) 4 ) r e l a ti t i v e c o m p a c t i o n , e v e n t h o u g h n o t v e r y r e l ia ia b l e, e , is is a b e t t e r p a r a m e t e r f o r e x p r e s s i n g t h e d e n s i t y o f a s o i l. l. s o il il t e s t s, s, d e n s i t y ( m a s s / v o l u m e ) , a n a l y s i s o f v a r i a n c e , c o h e s io i o n l e ssss s oi o i llss , s oi oi l c o m p a c t i n g , t e s t s , s t a t i s t i c a l a n a l y s i s , v a r i a b i l i t y KEY

W ORDS:

I n t h e l a s t t w e n t y y e a r s t h e c o n c e p t o f r e la l a t iv iv e d e n s i t y h a s b e e n u s e d m o r e a n d m o r e o f t e n in i n t h e i n v e s t i g a t i o n o f t h e p r o p e r t i e s o f c oh o h e s io i o n le le s s s oi oi l s . A s a m a t t e r o f f a c t t h e r e l a t i v e d e n s i t y h a s b e c o m e o n e o f t h e b a s i c p a r a m e t e r s o f t h e s e m a t e r i al a l s . I t i s a l m o s t s y s t e m a t i c a l l y u s e d a s a r e f e re re n c e p a r a m e t e r i n la l a b o r a t o r y i n v e s t ig i g a t io i o n s o n t h e m e c h a n ic i c a l b e h a v i o r o f s a n ds ds a n d c o m p a c t i o n s p e c i fi f i c a ti ti o n s a re r e i n c re r e a s i n g ly ly g i v e n i n t e r m s o f a m i n i m u m r e l a t i v e d e n s i t y re r e q u i r e d . A l s o t h e e v a l u a t i o n o f t h e l i q u e f a c ti ti o n p o t e n t i a l o f s a n d d e p o s i ts t s s u b m i t t e d t o e a r t h q u a k e s i s b a s e d o n t h e r e la l a t iv i v e d e n s i ty ty . 1 A s s o c i a t e p r o f e s so s o r a n d p r o f e s s o r, r, r e s p e c t i v e l y , C i v i l E n g i n e e r i n g D e p a r t m e n t , L a v a l Unive rsity, Quebec, Canada. W o o d w a r d M o o r h o u s e & A s s o c i a t e s I n c . , C l i f t o n , N . J . 0 7 0 12 12 . 18

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F i n a ll l l y , t h e r e l a ti t i v e d e n s i t y is i s th t h e s oi oils p a r a m e t e r m o s t c o m m o n l y m e a s u r e d i n s i t u a n d , t h e r e f o r e g o v e r n s t h e g r e a t m a j o r i t y o f d e s i g ns ns i n v o l v i n g cohesionless soils. Along with this increasing use of the relative density, the requirements f o r it i t s a c c u r a t e d e t e r m i n a t i o n h a v e n e c e s sa s a r il i l y b e c o m e m o r e s t ri r i n g e nt nt . F o r example, in the analysis of the liquefaction poten tial of a natural, or r e c o m p a c t e d d e p o s i t, t , t h e m e a s u r e d v a l u e o f t h e r e l a ti ti v e d e n s i t y h a s t o b e c o m p a r e d to t o a c r it i t ic i c a l v a l u e t o g iv i v e a y e s o r n o t y p e o f a n s w e r. r. S u c h p r o c e d u r e b e a r s, s , n a t u r a l ly l y , o n th t h e p r e m i se se t h a t t h e i n s i t u r e l a t i v e d e n s i t y i s d e t e r m i n e d w i t h a n a c c u r a c y s u f f ic i c i en e n t t o e n s u r e a s a t i s f a c t o r y r e l i a b i l i ty ty o f th th e a n s w e r . T h e a c c u r a c y o f r e l a ti t i v e d e n s i t y m e a s u r e m e n t s h a s , f or o r th th e m o s t p a r t , b e e n t a k e n f o r g r a n t e d w i t h o u t t h o r o u g h a n a l ys y s is is . I n d e e d t h e m e t h o d s o f m e a s u r i n g t h e m a x i m u m a n d m i n i m u m d e n s it i t ie i e s h a v e b e e n i n v e s t ig ig a t e d b y d i f f e re r e n t a u t h o r s ( K o l b u s z e w s k i [1 [ 1 ], ], 3 F e l t [ 2 ], ] , P e t t i b o n e a n d H a r d i n [ 3 ]) ]) , b u t t h e p u r p o s e o f t h e s e in i n v e s t ig i g a t io io n s w a s t o c o m p a r e t h e r e l a t i v e m e r i t s o f d i f fe f e r e n t m e t h o d s a n d t o m a k e a s e l e ct c t io i o n w h i c h w o u l d fi f i n a ll ll y l e a d t o t h e proposal of a standa rd such as A ST M Te st for Relative D ensity of C o h e s i o n l e s s S o il i l s ( D 2 0 4 99 - 6 9) 9 ) . E v e n t h o u g h t h e s e i n v e s t i g a t io io n s s h o w e d t h e g r e a t s e n s i t iv i v i t y of o f t h e m a x i m u m a n d m i n i m u m d e n si s i ti t i es es n o t o n l y t o t h e t e s ti t i n g m e t h o d b u t a ls l s o t o t h e o p e r a t o r, r, i t w a s n o t u n t i l v e r y r e c e n t y e a r s t h a t t h e q u e s t io i o n o f t h e a c c u r a c y o f r e l a ti ti v e d e n s i t y m e a s u r e m e n t s w a s s e ri o u s l y ra i s e d . T h e r e l a t i v e d e n s i t y , D r , i s u s u a l l y d e f in in e d a s : D r = Yd Ydma ma_____~X * ~d ~d

~ d - -' Y ~ m i . '~d

m ax

--

~d rain

D u e t o t h e r e l a t i v e m a g n i t u d e o f t h e m a x i m u m (T d m ax ax ) , t h e m i n i m u m (~ ,d m i ,), ,), a n d t h e a c t u a l d r y u n i t w e i g h t (~ (~,, d ), ), t h e re l a t i v e d e n s i t y i s c o m p u t e d f r o m t h e r a t io i o o f s m a l l d if i f fe f e r en e n c e s b e t w e e n l a rg rg e n u m b e r s . T h i s i m p l ie i e s t h a t s m a l l v a r i a t io i o n s o f t h e l a r g e n u m b e r s w i ll l l b e m a g n i f ie ie d t o produce a great variability in the computed result. The simple application o f t h e t h e o r y o f e r r o r s l e d T a v e n a s a n d L a R o c h e l l e [4 [4i] t o c o n c l u d e t h a t a n y l a b o r a t o r y d e t e r m i n a t i o n o f D r w o u l d b e a f f e ct c t e d b y a l a rg r g e v a r i a b i l i ty ty ( h D r m i. i . = 6 p e r c e n t ) , e v e n if if t h e A S T M D 2 0 4 99- 6 9 s t a n d a r d m e t h o d w e r e u s ed e d . T h e s e v a l u e s o f h D r w o u l d b e in i n c r e a se se d b y a b o u t 1 0 p e r c e n t i n t h e c a s e o f t h e i n s i t u m e a s u r e m e n t o f t h e r e l a ti t i v e d e n s i ty ty . W i t h s u c h c h a r a c t e r i s t ic i c s t h e d e t e r m i n a t i o n o f a n y s a t i s f a c t o r y v a l u e o f D r a l J p e ar ar e d p r o b l e m a t ic i c . T h e r e s u l ts ts o f a c o m p a r a t i v e t e s t p r o g r a m r e p o r t e d b y Tiedemann [5] confirmed these conclusions. In this program, 15 U.S. B u r e a u o f R e c l a m a t i o n ( U S B R ) l a b o ra r a t or o r ie i e s p e rf r f o r m e d th th e A S T M D 2 0 4 9 -6 -6 9 s t a n d a r d t e s t s o n id i d e n t i c a l s p e c im i m e n s o f t w o s a n d y m a t e r ia ia l s . A l l a T h e i ta t a l ic i c n u m b e r s i n b r a c k e t s r e f e r t o t h e l i s t of o f r e f e re re n c e s a p p e n d e d t o t h i s p a p e r

C o p y r i g h t b y A S T M I n t l ( a l l r ig i g h t s r e s e r v e d) d ) ; F r i M a r 1 1 1 6 : 1 3 :0 :0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c  

2

REL TIVE DENSITY INVO LVIN G

COHESIONLESS SOILS

l a b o r a to t o r i e s w o r k e d w i t h t h e s a m e t y p e o f e q u i p m e n t a n d u n i f o rm r m l y t r a in in e d o p e r a to t o r s . T h e v a r i a b i li l i t y o f t h e r e s ul u l ts ts w a s a p p r o x i m a t e l y t h e s a m e a s f o u n d f o r i m p a c t - t y p e c o m p a c t io i o n t e s t s : t h e s t a n d a r d d e v i a ti t i o n s w e r e of of t h e order of ~ 1. 6 lb/ ft 3 for the minimum density and • lb /ft 3 for the m a x i m u m d e n s it i t y . H o w e v e r , t h e r e su s u l ti ti n g w i d t h o f t h e 9 5 p e r c e n t i n t e r v a l f o r t h e r e l a t iv iv e d e n s i t y w a s 3 7 p e r c e n t i f n o v a r i a t i o n o f t h e a c t u a l d r y u n i t w e i g h t w a s c o n s id i d e r e d . I n t e r m s o f r e p r o d u c i b i l it it y , t h e s t a n d a r d d e v i a t i o n s w e r e r e s p e c t i v e l y l o w e r a t =t=1 l b / f t 3 l e a d in in g t o a w i d t h o f t h e 9 5 p e r c e n t interval for Dr of 21 percent. While these two investigations indicated clearly that the accuracy of relative density measurement is limited and may have a determining influence on the applicability of this soil parameter, it appeared necessary t o c h e c k t h e v a l i d i t y o f t h e s e c o n c l us u s i o n s o n a m u c h b r o a d e r b a s is is . F o r t h i s p u r p o s e i t w a s s u g g e st s t e d b y t h e s e ni n i or or a u t h o r a n d a c c e p t e d b y t h e A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s A S T M ) C o m m i t te t e e D - 1 8 o n S o il il a n d Rock for Engineering Purposes, Subcommittee D18.09 on Dynamic P r o p e r t i e s o f S oi o i l s , a n d t h e O r g a n iz i z i ng n g C o m m i t t e e o f t h e 1 97 97 2 A S T M Symposium, to perform a large comparative test program. The present p a p e r d e s c r i b e s t h e s c o p e a n d o r g a n i z a t io io n o f t h i s t e s t p r o g r a m a n d p r e s e n t s the results obtained and their analysis.

Scope of the

n v e s t i g a t io io n

In o rder to ensure the broad est possible basis for the com parative test p r o g r a m , 8 7 U n i t e d S t a t e s a n d C a n a d i a n l a b o r a to to r i e s , e q u a l l y d i s t r i b u t e d i n g o v e r n m e n t a g e n ci c i es e s , i n d u s t r y , a n d u n i v e r s it i t i es e s w e r e i n v i t e d t o p a r t ic ic i p a t e . T h e p r o p o s e d p l a n w a s t o s e n d to t o a l l p a r t i c i p a n t s i d e n t ic ic a l s p e c i m e n s o f t w o c o h e s i o n l e s s s oi o i l s , a u n i f o r m f in in e s a n d , a n d a w e l l g r a d e d g r a v e l l y s a n d , a n d t o h a v e t h e f o ll l l o w i ng ng t e s t s p e r f o r m e d : g r a d a t i o n t e s t , m i n i m u m and maximum density tests according to ASTM D 2049-69 or the participants own metho d or both, an d two one-point compaction tests with standard and modified Proctor compaction procedures. Thus, with the results obtained on perfectly identical specimens by a representative selection of all laboratories, a valuable analysis of the variability and reproducibility of these testing methods would be possible. Fourty three laboratories accepted the invitation and were sent the s p e c i m e n s in i n O c t o b e r 1 9 71 71 . F o u r t y - o n e l a b o r a to t o r i e s , a s l is is t e d i n A p p e n d i x I , completed the program. Materials Tested

The materials were selected so as to complete and enlarge the results of the investigation reported by Tiedemann [5]. F in in e S a n d T h e f in in e s a n d u s e d w a s t h e m a t e r i a l d e s i g n a t e d a s 24 24 E - 1 1 i n t h e i n v e s t ig i g a t io i o n b y T i e d e m a n n [ 5 ]. ] . T h e m a t e r i a l w a s p r e p a re re d a t t h e USBR Laboratory in Denver. All specimens were individually composited C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

T VEN

p e + i C ~ c liam { ~

S IET

L ON

R E SU SU L TS TS O F

I

COM P R

s i e ve ve n o

200

I00

60

40

2

T IV E T E S T P R O G R M

s e v e c l im im e n s o n i n i n c h

20

10

~4

I

I

3

92

8C

70 6O

~o il

~

i

/

4O

2

33

IC

0 006

[

o+

02

s

06

[ FIG

~

2

6

~o~

I

2

I TI II l I0

. .. .. .. .. .. .. , , , , I, I, 20

g

,Ith l,,h 60 I00

I

1 G ra ins size disi disiributi ributions ons of the samples.

from screened fractions of a local str eam deposit. The screening was done in an aggregate aggregat e proces processing sing pla nt which separates sands int into o Nos. Nos. 4 8 16 30 50 an and d 10 100 0 siz sizes. es. Th Thee mat m ateri eri al passing the 10 100 0 sieve was washed on a 200 200 sieve. The individual sizes were then combined to match the mean grain size si ze dist rib ributi ution on of th thee soil soil 24E 24E-1 -11 1 as reported b y Ti ede edeman mann n [5]. [5]. Figu Figure re 1 shows sho ws the actua l grain size size di stributi on of the fine sand spe specim cimen. en. The tot al weight of the spec specimen imen was 50 50 lb; t he weig weighing hing of the individual size si zess was was made with a f an-ty pe balance with a 30 lb capacity reading directly to 0.01 lb. For shipment the 30 and 50 sizes were individually bagged as sacks 1 and 2 respectively wi with th tot al weights of 8. 8.60 60 an and d 12.6 12 .62 2 lb. lb. These T hese bags a nd th thee remaini rem aini ng of th thee specimens were double-sacked and shipped. Grave Gra vellly Sa nd T he materi al was was prepared at Lava] University Que Quebec bec Canad a. All samples samples were were indi vidual ly composited from screened screened fractions of a local glacial deposit. After Aft er a first mechanical screening screening th thee final processing processin g was done by han d to separate sep arate in to 1 3/~ and 3/~ in. and Nos. 4 10 20 40 60 100 an and d 20 200 0 siz sizes. es. Th e materi mate rial al passin passing g t he 10 100 0 sieve was washed on a 200 sieve to remove all fines. The individual sizes were then combined to ma tch the selec selected ted grain grain size size distri bution shown on Fig. 1. The weighing was done on a 20-k 20-kg g solution solu tion balance reading read ing directl dire ctly y to i g. Th e 50ol 50 olb b specimens were single-sacked single-sacked an and d p ut in a wooden box for shipment. shipmen t. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to  

 

REL TIVE DENSITY INVO LVIN G

C O H E S I O N L E S S S O I LS LS

Tes t Procedure T h e t e s t s e q u e n c e a n d p r o c e d u r e s w e r e s p e ci c i fi f i ed ed s o a s t o h a v e u n t e s t e d m a t e r i a l u s ed e d w h e n e v e r p o ss s s ib ib l e a n d t o e n s u r e u n i f o r m i t y b e t w e e n t h e participants. The instructions given to the participants are presented in Appendix II.

Data A nalysis After all the data had been received on 29 February 1972, the results were rechecked and each participant was arbitrarily assigned an identification number. The results were analyzed statistically with respect to the variations between laboratories and, whenever possible, to the variations between d u p l i c a t e t e s t s w i t h i n l a b o r a t o r ie ie s . Variations between laboratories--The f o l l o w i n g s t a t i s t i c a l c h a r a c t e r i s t i c s were computed: 1 . T h e m e a n , 4 , w a s c a l c u l a t e d a s ~ = ~ x / n w h e r e ~ - ~ x s th th e s u m m a t i o n o f n i n d i v i d u a l v a l u e s o f x. x. 2 . T h e r a n g e , R , is i s t h e d i ff f f e re re n c e b e t w e e n t h e h i g h e s t a n d l o w e s t v a l u e s of X

3. The cumulative distribution function gives the distribution of the observations in selected intervals within th e range. 4 . T h e s t a n d a r d d e v i a t i o n , S, S , w a s c a l c u l a t e d a s: s:

ix

2 2

n--1 5 . T h e c o e ff f f ic i c i en e n t o f v a r i a t i o n i s d e f in in e d a s t h e r a t i o o f t h e s t a n d a r d d e v i a t i o n t o t h e m e a n . I t i s a ls ls o r e f e r re r e d t o a s th t h e c o e ff f f ic i c i en en t o f v a r i a b i l i t y , a s o p p o s e d t o t h e c o e f f ic ic i e n t o f r e p r o d u c i b i l i t y .

Variations Between Duplicate Tests--The m i n i m u m , m a x i m u m , a n d P r o c t o r d e n s it i t ie i e s w e re r e m e a s u r e d i n t w o d u p l i c a t e t e s ts t s b y e a c h p a r t ic ic i p a n t . T h e d if i f fe f e re r e n c es e s b e t w e e n d u p l i c a t e t e st st s w e r e c o m p a r e d b y c o m p u t i n g t h e f o ll l l o w in in g p a r a m e t e r s : 1. The average R was calculated as:

R Eldl k

w h e r e ~ [ d I i s t h e s u m m a t i o n o f t h e a b s o l u t e d i ff f f e re re n c e s b e t w e e n d u p l i c a t e t e s t s a n d k i s t h e n u m b e r o f p a i rs r s o f d u p l i c a t e t e st st s . 2 . T h e c o m b i n e d s t a n d a r d d e v i a t io io n , S , w a s c a l c u l a t e d a s :

S

= ,/-2d2 K

C o p y r i g h t b y A S T M I n t l ( a l l r ig h t s r e s e rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri n t e d b y ( U F P E ) U n i v e r si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u  

T VEN S ET

L ON

R ES ES U LT LT S O F

COMP

R TIVE TEST PROGR

M

3

3. The coefficient of reproducibility is defined as the ratio of the combined standard deviation to the mean as determined above. C o m po po si si t e R e s u l t s F r o m the test results on minimum, maximum, and Proctor den densitie sities, s, the relati ve density, the rel ative compaction based on the maxi mum density, and t he relat ive compaction based on the st stan anda daYd Yd and modified Proctor densities were computed assuming an actual dry unit weight of 108 lb / ft 3 for th e fin finee sand and 122 lb /f t 3 for the gravelly sand. The composite results were analysed only with respect to the variations between laborato laboratories. ries.

Scale

ccuracy

The two small sacks sacks of the fin finee sand were were included included to obta in an indication of the accuracy of the sc scal ales es used by the participants. The foll followin owing g results were obtained: Sack Sa ck Numbe r

Numbe r of Observations Observ ations

Mean Weight, lb g)

Stand ard Deviation, lb g)

1

37

8.59

0.05

37

3896) 12.61 5720)

24) 0.05 0. 05 24)

2

These variations are considered to be small and any effects they might have on the density determinations would be minimal.

Gradation T ests Fine Sand

Participants were asked to perform gradation tests on 100-g specimens tak en by quartering or or splitting from: a) the unused material Spe Specime cimen n 4-S) b) the materi al after relative densi ty tests Spe Specim cimen en 1-S), and c) the materia l after Proctor tests Spe Specime cimen n 33-SB SB). ). The T he mater ial had to be sieved for 15 min on U.S. Standard sieves 10, 20, 40, 100, and 200. If possible a powered sieve shaker was to be used. The results of the gradation tests are presented in Table 1. Figure 2 shows the mean gradation curves and the limits of plus and minus two standar d deviatio deviations ns from the mean which which contain about 95 percent of the observed values. allow for T e s t s o n S p e c i m e n AS--The tests results on the unu sed materi al allow an evaluation of the accuracy of the gradation test. The mean gradation curve on Fig. 2 is in good concordance concordance with the actua l grai n size size distribution. However, it appears th at this is not due to th e good quali ty of of the test results resu lts but esse essentia ntially lly to their quanti ty. As a mat ter of fact, the variability Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant t  

24

R E L A T I V E D E N S IT IT Y I N V O L V I N G

C O H E S IO IO N L E S S S O IL IL S

T A B L E 1--Stati 1--Statistical stical analysis of the gradation test on the fin e sa nd specimen. Statistics

P e r c e n t a g e P a s s i n g S i e v e S i ze ze 20 40 60 1 00 00

10

200

S p e c im im e n 4 S Mean S t a n d a r d d e v i a ti ti o n C o e ff f f ic i c ie ie n t o f v a r i a t i o n

94 7 0 9 1 0

79 9 5 2 6 5

56 4 5 0 8 9

34 8 4 1 11 7

12 4 3 2 25 5

2 5 1 4 54 5

M aximum Minimum Range

96 7 93 0 3 7

84 4 63 2 23 2

66 1 41 7 24 4

43 8 22 6 21 2

20 4 4 5 15 9

8 7 0 2 8 5

57 4 8 66 44 22

35 4 12 46 25 21

12 2 21 17 5 12

Specimen 1S Mean S t a n d a r d d e v i a ti ti o n C o e ff f f ic i c ie ie n t o f v a r i a t i o n Maxim um Minimum Range

94 1 1 96 92 4

7 0 1 8 0 8

79 4 5 86 60 25

7 4 5 5 7 8

7 9 5 6 3 3

8 6 7 6 0 6

4 6 3 7 4 3

2 5 O 9 35 7 4 7 0 4 4 3

S p e c im im e n 3 S B M ean S t a n d a r d d e v i a ti ti o n C o e ff f f ic i c ie ie n t o f v a r i a t i o n

94 5 1 1 1 2

79 9 3 4 4 3

57 7 5 3 9 2

37 2 4 4 11 8

14 7 3 2 21 7

3 8 1 5 40 0

M m uu m m M ianxii m Range

99 60 15 6 6

86 48 86 16 2

64 51 40 24 4

42 41 75 23 2

2 50 94 14 5

80 73 8 4

p. ,,c ,

diom (ram)

{

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~ le le ~ . c i l m . ~ ,

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i~,,l,,,,J ,

6

2

Ol

FIG

1 ~_

I,i,IJ,h l 6

......... I

I ....

I

I l l hh hl

6

.............

I

2

I

I l~l ~l hl t

6

............

I0

20

I

Jl l hl lhh

60

I00

2--Results of gradation tests fine sand sample 4S.

Copyright by AS TM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 20 16 D o w n l o a d e d / p r i n te te d b y (UFPE ) Universidade Federal de Pernambuco ((U FPE) Universidade Federal de Pernambuco) pursuant to License Agre  

T A VEN A S ET A L O N R ESU ESU LT LT SOF A C OM P A R A T I VE T EST PR OG R A M

5

of the reported results is large: the standard deviations are greater than 4 percent, and the ranges greater than 20 percent on the percentage passing the sieves 20, 40, and 60 which retain about 60 percent of the material. As noted by Tiedemann [5] the magnitude of the variations is related to the percentage of material retained on the sieve rather than to its size. E f f ec e c t o f t h e C o m p a c t i o n T e s t s A s shown on Table 1 none of the statistical parameters computed on Specimen 1S after relative density tests or on Specimen 3SB after Proctor compaction tests, are significantly different from those observed on the unused Specimen 4S. Under such circumstances and taking into account the great variability observed on the results on Specimen 1S, 1S, it appears logical logical to neglect the small small variations on the mean gradation curve and to conc conclud ludee that the compaction tests tests had no infl influen uence ce on the grain size distribution of the material.

G r a vel l y S a n d Grad ati on tests were perform ed on: a) the unused material Specimen 4G), b) the material after compa ctio n tests Specimen 1G 1G)) Due to the testing sequence adopted by most of the participants, it was impossible to consider the infl influenc uencee of the relative d ensity tests on the grain size size distribuTABLE 2 Statistical analys is of the gradation test on the gravelly gravelly sand specimen. Statistics

Mean Mean Standa Sta ndard rd dev deviat iation ion Coeffi Coe fficien cientt of varia variation tion Maximum Maxi mum Minimum Mini mum Rangee Rang Mean Standa Sta ndard rd dev deviat iation ion Coeffi Coe fficien cientt of varia variation tion Maximum Maxi mum Minimum Mini mum Rangee Rang

in. ~ in.

Percentage Passing Sieve Size 4 10 20 40 60

Specimen 4G 90.0 70.8 55 . 7 40.7 28.1 28.1 17. 17.0 0 4.2 5.8 5.7 6.0 5.5 4.1 4.6 8.2 10.2 14.7 19.7 24.3 98.3 83.5 70.0 52.9 40.5 27.5 78.9 53.7 37.5 24.6 15.2 8.7 19.4 29.8 32.5 28.3 25.3 18.8 90.5 3.2 3.6 94.4 73.5 20.9

Specimen 72.0 57.8 3.6 3.6 5.0 6.2 78.6 65.6 57.9 47.5 20.7 18.1

1G 42.9 29.7 19.0 4.1 4.4 3.6 9.5 14.7 19.0 19.0 50.2 38.9 27.9 33.6 19.1 11.4 16.6 19.8 16.5

100

200

11.3 11.3 3.7 32.4 24.1 5.0 19.1

6.2 2.0 32. 8 32.8 11.3 2.6 8.7

0.9 0.5 53.0 2.1 0.1 2.0 2. 0

12.4 2.4 19.1 19.1 17.4 7.3 10.1

6. 7 6.7 1.4 20.0 9.6 3.8 5.8 5. 8

1.3 0.8 58.0 3.0 0.0 3.0

13.9 13.9 3.0 21.7 19.9 7.9 12.0

7.8 2.2 27.9 12.2 3.5 8.7 8. 7

2.0 1.1 55.9 4.3 0.0 4.3 4. 3

Specimen 3G Mean Mean Standa Sta ndard rd dev deviat iation ion Coeffi Coe fficie cient nt of vari variation ation Maximum Maxi mum Mini mum Rangee Rang

91.8 1.9 2.1 95.6 88.1 88. 1 7.5

73.4 60.4 46.2 32 .5 20.7 4. 6 4.4 4.8 5.1 4.1 6.2 7.3 10.4 15.7 15.7 19.8 82.5 69.3 55.9 42.7 28.9 64.3 51. 51.5 5 36.6 22.3 12. 12.5 5 18.2 17.8 19.3 20.4 16.4

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Li  

  6

R E L A T IV IV EDEN SITY INVO LVING

COHESIONLESS SOILS

tion of the specimen specimenss separately), and c) the mat erial after stand ard and modified Proctor Proc tor compaction compactio n tes tests ts only Speci Specimen men 3G) in 30 ca case sess it was possib pos sible le to isolate the eff effect ect of the Proctor compaction tests). The entire specimen specimen,, weighing 150 1500 0 g for Specimen 4G 4G and a nd abo ut 7000 g for Specimens 1G and 3G, was first fi rst sieved on the t he sieves i in., 3/~ in., a/~ in., No. 4, and pan. One hundr ed grams of the mate rial passing passing No. No. 4 was was then sieved for 15 rain on U.S. Standard sieves 4, 10, 20, 40, 60, 100, and 200. The results of the gradat ion tests are presented in Table 2. Figures 3 and 4 show the mean gradation curves and the limits of plus and minus two standard deviations. T e s t s o n S p e c i m e n 4G--The agreement between the observed mean gradation curve and the actual grain size distribution is not as good as for the fine sand, and the deviations between the two curves are observed on sieves 10, 20, 40, and 60, amount to 5 percent. This is possibly due to the testing technique and particularly to the selection of 100 g in the fraction passing the No. 4 sieve after the first sieving. The variability of the results is large with standard deviations greater th an 5.5 per percent cent on the th e sieves sieves a/ a/~ in., 4, 10 10,, and 20 on whic which h 60 60 percent perce nt of th e material is retained and ranges up to 32.5 percent on sieve No. 4. thee fine sand it is difficult to E f fe f e c t o f C o m p a c t io i o n T e s t s A s in th e case of th draw a ny con conclus clusion ion as to the influ influence ence of the relative de nsity tests on the gradation of the material since the variations of the mean curves are very l

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small as compared to the standard deviations. Any comparison is made e v e n m o r e d if i f fi f i c u lt lt b y t h e f a c t t h a t t h e s iz i z e o f S p e c i m e n 1 G w a s f o u r ti ti m e s l a rg r g e r t h a n S p e c im im e n 4 G . T h e q u a n t i t y o f m a t e r i a l t e s t e d h a d a n i m p o r t a n t influence on the variability of the results. For the larger Specimen 1G the s t a n d a r d d e v i a t i o n a v e r a g e d 4 p e r c e n t a n d t h e ra r a n g e 1 8. 8.5 p e r c e n t a s compared to 5.7 percent and 30 percent for the smaller Specimen 4G. More definite conclusions can be drawn as to the effect of the Proctor c o m p a c t i o n t e s ts t s . T h e a n a l y si si s o f t h e r e s u l t s o n t h o s e S p e c i m e n s 3 G w h i c h w e r e s u b m i t t e d t o P r o c t o r c o m p a c t io i o n te t e s t s o n ly ly s h o w s t h a t a c e r t a i n a m o u n t o f p a r t i c l e b r e a k a g e h a s o c c u r r e d l e a d in in g t o a n i n c r e a s e o f 2 t o 5 p e r c e n t o f t h e m e a n p e r c e n t a g e p a s s i n g s i ev e v e s 4 t o 6 0 . S in in c e n o s u c h i n cr c r e a se s e w a s n o t e d o n S p e c i m e n 1 G a f t e r re r e l a ti t i v e d e n s i t y a n d o n e s ta ta n d a r d P r o c t o r c o m p a c t io i o n te t e s t i t c a n b e c o n c l u d e d t h a t t h is i s p a r ti t i c le le b r e a k a g e occurred essentially in the modified Proctor test performed on these s p e c im i m e n s . T h e d e g r a d a t i o n d u r i n g o n e t e s t i s h o w e v e r l im im i t e d . isc~on

A g a i n s t t h e w e l l a c c e p t e d i d e a t h a t t h e g r a d a t i o n t e s t o n c o h e s io i o n l es es s s o il i l s w i t h z e r o p e r c e n t p a s s in i n g s ie i e v e 2 0 0 i s a s im i m p l e a n d t h e r e fo fo r e a c c u r a t e t e s t t h e r e su s u l ts t s r e p o r t e d a b o v e s h o w t h a t t h e v a r i a b i l i ty ty o f s u c h t e s t r e s u l t s i s v e r y i m p o r t a n t . T h i s v a r i a b i l i t y c a n b e r e l a t e d t o v a r i o u s f a c t o rs rs . C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s rree s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e  

 8

RE L TI V EDEN E DEN SITY INVO LVING

COHESIONLESS SOILS

1 . T h e s iz iz e o f t h e s a m p l e . T h e r e s u l t s o n S p e c im im e n s 4 G a n d 1 G s h o w t h e d e f in i n i t e r e d u c t i o n o f t h e v a r i a b i l i t y o f t h e r e s u l ts t s w i t h a n i n c re r e a s in in g w e i g h t o f t h e s p e c im i m e n . T h i s f a c t w o u l d a d v o c a t e f o r th t h e l a r g e s t p o s s ib i b l e s p e c iim e n s , a n d i t h a s b e e n t a k e n s o m e w h a t in i n t o a c c o u n t i n A S T M P a r ti t i c le l e - S iz iz e A n a l y s i s o f S o il i l s D 4 2 22 - 63 6 3 ). ) . H o w e v e r , t h e r e s u l ts ts o n S p e c i m e n 1 G h a v e a l a rg r g e v a r i a b i l it i t y e v e n t h o u g h t h e w e i g h t o f t e s t e d s p e c im im e n w a s m u c h larger than required in ASTM D 422-63. 2 . T h e w e i g h t o f m a t e r i a l r e t a in i n e d o n e a c h s ie i e v e. e. A s p r e v i o u s l y m e n tioned the standard deviations and ranges increased with an increasing weight of soil retained on the sieve. To eliminate this source of error the size of the specimen, particularly in the case of poorly graded materials, should be kept to a minimum. Since this requirement is in complete o p p o s i t i o n to to t h e p r e c e d i n g o n e , i t a p p e a r s t h a t t h e v a r i a b i l i t y o f a n y g r a d a t i o n t e s t s w i ll l l b e v e r y l ar a r g e, e , a n d o f t h e s a m e o r d e r a s r e p o r t e d h e r e in in . 3 . T h e m e t h o d o f s e l ec e c t io i o n o f t h e s p e c im i m e n . Q u a r t e r i n g o r s p l i tt tt i n g p r o c e d u r e s a r e d i f fi f i c u lt lt a n d h a v e a n i n c r e a s e d i n f lu lu e n c e o n t h e r e s u l ts ts a s t h e w e i g h t o f th t h e s p e c i m e n d e c r e a s e s a n d t h e m a x i m u m g r a i n s iz i z e i n cr c r e as as e s . M inim um and M aximu m

e n s i t y T e st st s

T h e m a i n p u r p o s e o f t h is i s p a r t o f t h e c o m p a r a t iv iv e t e s t p r o g r a m w a s t o i n v e s t i g a t e t h e v a r i a b i l i t y a n d r e p r o d u c i b i l i t y o f t h e A S T M D 2 0 4 9 -6 -6 9 s t a n d a r d m e t h o d fo f o r d e t e rm rm i n i n g t h e m i n i m u m a n d m a x i m u m d e n s i t y o f c o h e s i o n le l e s s s oi o i l s . I n a d d i t i o n , t h e p a r t i c i p a n t s w e r e a ls l s o a ll ll o w e d t o u s e t h e i r o w n te t e s t i n g p r o c e d u r e s , t h u s , t h e v a r i a b i l i t y o f t h e l im i m i t in i n g d e n s i t ie ie s with the testing technique could also be analyzed. In each case the maximum and minimum densities were to be measured on two specimens o f e a c h m a t e r ia i a l s o t h a t t h e r e p r o d u c i b i l i t y o f t h e r e s u lt lt s c o u l d b e e v a l u a t e d . All results are summarized in Figs. 5 and 6.

Variabi Vari abili lity ty of A S T M D 2049 69 Test Resu Result ltss T h e A S T M s t a n d a r d p r o c e d u r e w a s u s e d b y 7 5 p e r c e n t o f t h e p a r t ic ic i p a n t s . T h e n u m b e r o f r e p o r t e d t e s t r e s u l t s is i s a b o u t 6 0 , t l ~ at a t i s, s, la la r g e e n o u g h to be statistically analysed. M i n i m u m D e n s it it y T h e m i n i m u m d e n s i t y w a s d e t e r m i n e d b y 6 2 t e s t s f o r t h e f in in e s a n d a n d 6 3 t e s t s f o r t h e g r a v e l l y s a nd nd . T h e s t a t i s t i c s a r e s h o w n o n T a b l e 3 . T h e c o m p u t e d s t a n d a r d d e v i a t i o n s a r e 1 .7 .7 ] b / f t 3 0 .0 .0 3 to to n n e p e r c u b i c m e t e r t / m 3) 3) ) fo f o r t h e f i ne n e s a n d a n d 2 .5 . 5 l b / f t ~ 0 .0 .0 4 t / m a) a) f o r t h e g r a v e l l y s a n d . T h e s e v a l u e s a r e l a rg r g e r t h a n t h o s e r e p o r t e d b y T i e d e m a n n [ 5 ], ], b u t w o u l d n o r m a l l y b e c o n s i d e r ed e d a s a c c e p t a b l e s in i n c e t h e c o e ff f f ic i c i en en t s o f v a r i a t i o n a r e o f t h e o r d e r o f 2 p e r c e n t , n a m e l y , m u c h s m a l le l e r a s th th o s e u s u a l l y o b s e r v e d o n o t h e r s o il il m e c h a n i c s t e s t s [ 6 ]. ]. T h e r a n g e s a r e 7 .1 .1 l b / f t 3 0 .1 .1 1 t / m 8) a n d 1 1. 1 . 8 l b / f t 3 0 .1 .1 9 t / m 3 ) , f o r t h e fine sand and gravelly sand, respectively. These values are slightly larger than

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M ean S t a n d a r d d e v i a t io io n M axim um M inim um Range

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3

R E L AT A T IV IV E D E N S I T Y I N V O L V I N G

COHESIONLESS

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curv rves es,, mini minimum mum density of gravell gravellyy sand A ST STM MD FIG. 8--Frequency distributio distribution n cu ~0~9-e9). d i s t r i b u t i o n c u r v e s , F ig ig s . 7 a n d 8 , s h o w t h a t t h e o b s e r v a t i o n s a r e n o r m a l l y distributed within the range and are nearly symmetrical about the mean. Maximum Density--The d r y m e t h o d m a x i m u m d e n s i t y w a s d e te te r m i n e d b y 5 8 t e s t s f o r t h e f in in e s a n d a n d 5 9 t e s t s f o r th th e g r a v e l l y s a n d . A s s h o w n i n T a b l e 3 t h e s t a n d a r d d e v i a t i o n s a r e 2 . 7 l b / f t 8 0 .0 . 0 4 t / m 3) a n d 4 . 5 l b / f t s 0 . 07 0 7 t / m 3 ) , r e s p e c t i v e l y , c o r r e s p o n d i n g t o c o e f f i c ie ie n t s o f v a r i a t i o n o f 2 . 3 percent and 3.4 percent, that is, 60 percent larger than those observed on t h e m i n i m u m d e n s i t y . W i t h i n r a n g e s o f 1 4 .4 .4 l b / f t 3 0 .2 .2 3 t / m 3 ) a n d 2 2 .3 .3 l b / f t s 0 .3 .3 6 t/ t / m S ) , t h e o b s e r v a t i o n s , a s s h o w n b y t h e f r e q u e n c y d i s t ri ri b u t i o n c u r v e s i n F ig i g s . 9 a n d 1 0, 0 , a r e n o t a s n o r m a l l y d i s t r i b u t e d a s i n th th e c a s e o f t h e minimum densities.

Reproduc Repr oducibilit ibilityy of A S T M D ~0~9 ~0~9-69 -69 Test Testss Result Resultss As mentioned before, each participant performed duplicate tests on each m a t e r i a l . T h e a n a l y s i s o f t h e d i f f e re re n c e s b e t w e e n d u p l i c a t e t e s t s g i v e s a n i n d i c a t io i o n o f t h e r e p r o d u c i b i l i ty t y o f t h e c o n s i d e r ed e d t e s t s . T h e r e s u l ts ts o f t h i s analysis are given in Table 4. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

T

V EN EN

TABLE

S ET

L ON

R E S U LT LT S O F

COMP

R

TI V E TI

TEST PRO GR

M

~ R e p r o d u c i b i l i t y o f A S T M D 2 0 ~ 9 6 9 t e st st r e su su ltl t s. s.

S t a ti t i s ti ti c

M i n i m u m D e n s i ty ty lb/f t 8 t/m a

M a x i m u m D e n s i ty ty lb/f t 3 t/m 3

Fine Sand Nu m ber of tests

31

29

A R av ne rgaeg e

0.56

0. 009

0.59

0.009

Combined standard deviation

0.54

0. 009

0.67

0.011

Gravell Grave llyy S and 32

N u m b e r o f t e s ts ts

31

Average Range

1.10

0.018

1.45

0. 023

Com bined s t a n d a r d d e v i a ti ti o n

1.05

0. 017

1.37

0. 022

I00

90

80

70

~6

so

3

2

I0 0

104

~08

112 116 dry density, L tL

120

124

128

F I G . 9--Frequ ency dist distri ribut bution ion cur curves ves,, m ax im um dens densit ityy of fine sand A S T M D ~0~9~0~9---69)

Copyright by A STM Int l (all rights reserved); Fri Mar 11 1 6:13:06 EST 20 16 Downloaded/printed by (UFPE) Universidade Universidade Federal de Pernambuco ((UFPE) U niversidade niversidade Federal de Pernambuco) pursuant to License Agreem ent. No further  

  4

RELATIVEDENSITY RELATIVE DENSITY IN INVO VOLV LVIN ING G COHE COHESIONLE SIONLESS SS SOILS

I

~ 90

80

~

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II

meOn=133 8

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lO--Frequency dist distri ribut bution ion curves, curves, ma xim um dens densit ityy o f grav gravel elly ly 8and A S T M D

eo49-69 .

io n s a r e 0 . 5 4 l b / f t 3 Minimum Density--The c o m b i n e d s t a n d a r d d e v i a t io

0 .0 . 0 0 9 t / m s ) a n d 1 .0 .0 5 l b / f t 8 0 .0 . 0 1 7 t / m s ) f o r t h e f in in e s a n d a n d g r a v e l l y sand, respectively. They are significantly larger than those reported by

T i e d e m a n n [ 5 ]. ]. T h i s c a n b e e x p la l a in in e d b y t h e f a c t t h a t t h e g r o u p o f o p e r a t o r s participating in the USBR investigation was more homogeneous than in the present case. Th us, the prese nt da ta are not indicative of the repro~ ducibility of the tests itself, but are also influenced in some way by a variability between laboratories; the reproducibility observed here is an a v e r a g e r e p r o d u c ib i b i li l i ty t y . T h e v a r i a ti t i o n s i n t h e m i n i m u m d e n s it i t ie ie s b e t w e e n d u p l i c a te t e t e s t s a r e a b o u t o n e t h ir i r d o f t h e v a r i a ti t i o n s b e t w e e n la l a b o r a to t o r ie ie s . Maximum Density--As f o r t h e v a r i a t i o n s b e t w e e n l a b o r a t o r i e s , t h e c o m b i n e d s t a n d a r d d e v i a t i o n fo f o r t h e m a x i m u m d e n s it i t ie i e s a r e l a rg rg e r t h a n f o r t h e m i n i m u m d e n s i t y , w i t h v a l u e s o f 0 .6 . 6 7 l b / f t a 0 .0 .0 11 1 1 t / m s ) f o r t h e f i ne ne s a n d a n d 1 .3 .3 7 l b / f t 3 0 .0 .0 22 2 2 t / m s) s) f o r t h e g r a v e l l y s a n d . T h e y r e p r e s e n t o n l y 3 0 p e r c e n t o f t h e s t a n d a r d d e v i a t i o n s o f t h e r e s u l t s o b t a i n e d b y d i f fe fe r e n t laboratories. C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e  

TAVENAS El AL O N

R E S U LT LT S O F A C O M P A R A T I V E T E S T P R O G R A M

35

V a r i a b i l i t y B e t w e e n D i f fe fe r e n t T e s t M e t h o d s S e v e n t e e n p a r ti t i c i p a n t s u s e d t e s t m e t h o d s d i ff f f e re re n t f r o m t h e A S T M D 2 0 49 4 9 -6 - 6 9 s ta t a n d a r d . A c o m p l e t e d e s c r i p t io io n o f t h e s e 1 7 m e t h o d s c a n n o t b e g i v e n h e r e. e . T h e m a i n d if i f fe f e r en e n c es es b e t w e e n t h e s e m e t h o d s a n d t h e s t a n d a r d a r e t h e f o ll l l o w i ng ng : f o r t h e m i n i m u m d e n s i t y t e s t , t h e u s e o f a d i f f e r e n t f u n n e l 4 ) 4, a s c o o p 5 ) , a d i f f e r e n t m o l d 6 ) , a n d t h e a p p l i c a t i o n o f K o l b u z e s w s k i [I [ I ] m e t h o d 1 ) ; f o r t h e m a x i m u m d e n s i ty t y , t h e u se se o f a d i f f e r e n t m o l d 4 ) a n d a d i f f e re r e n t v i b r a t i n g t a b l e 2 ), ), a n a d d i t i o n a l v i b r a t o r a t t a c h e d t o th t h e m o l d 1 ), ) , v i b r a t i o n b y l a y e rs r s p r o c e d u r e 1 ), ), P r o c t o r t y p e c o m p a c t i o n 5 ), ) , o r c o m p a c t i o n i n l a y e rs r s w i th t h a v i b r a t in in g h a m m e r 4 ). ) . T h e r e s u l ts t s o f t h e s t a t is i s t i c a l a n a l y s is is o f t h e o b s e r v a t i o n s r e p o r t e d b y t h e d i f f e re re n t p a r t i c i p a n t s a r e p r e s e n t e d i n T a b l e 5 . M i n i m u m D e n s i ty t y T h e s t a ti t i s ti t i c s a r e v e r y c l o se se t o t h o s e c o m p u t e d f o r t h e A S T M s t a n d a r d t es e s ts t s . T h e m e a n i s sl s l ig i g h t ly l y s m a l le l e r f o r t h e f i ne ne s a n d , a t 9 4 .3 . 3 l b / f t a 1 .5 . 5 1 t / m a ) i n s t e a d o f 9 5 .3 . 3 l b / f t 3 1 .5 .5 3 t / m a) b u t i s e x a c t l y t h e s a m e a t 1 14 1 4 .2 . 2 l b / f t a 1 .8 . 8 3 t / m 3 ) f o r th th e g r a v e l l y s a n d . T h e s t a n d a r d d e v i a t i o n s a n d r a n g e s a r e a ls l s o v e r y s i m i la la r . T h i s s i m i l a ri r i t y is i s r e l a t e d t o t h e m i n o r d i ff f f e re r e n c e s i n t h e t e s t in in g t e c h n i q u e s . T h e use of a different funne l or of a scoop for placing the m aterial, o r of a l a r g e r o r s m a l l e r m o l d d i d n o t s e e m t o h a v e a r e a l in i n f l u en en c e o n t h e r e s u l t . TABLE 5

Variab ility of min imu m and maxim um densities measured by different different metho methods. ds. Statistic

Nu mb er of tests

M ini inimum mum Density, Density, lb/ft~ t/m 3

M aximum Density, Density, lb/ft3 t/m 3

Fine Sand 32

38

M ean Standard devi deviat atio ionn

94.3 2.1

1.510 1.510 0.034

114.3 114.3 7.9

1.83 0.13

Maximum Minimum Ran ge ge

97.2 88.2 9 .0

1. 1.560 560 1.410 1.4 10 0 .1 5 4

138.828 138. 102. 102.2 3 6 .6

2.22 1.64 0 .5 8

Num ber of tests Mean

Standard devi deviat atio ionn M aximum M ini inimum mum Range

Gravelly San d Gravelly 25 114 2

2.6 118.1 109.1 9 0

1 830

0.042 1.890 1.740 0 .1 5 0

27 130 3

6.9 140.5 114.2 2 6 .3

2 09

0.11 2.25 1.83 0 .4 2

Num bers in parenthesis parenthesis refe r to th e num ber of participants using using a given method. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

 6

REL TIVEDENSITY TIVEDENSITY INVOLVI INVO LVING NG COH COHESI ESIONL ONLESS ESS SOI SOILS LS

i s s er e r io i o u s ly ly M a x i m u m D e n s it i t y O n t h e c o n t r a r y , t h e m a x i m u m d e n s i t y is influenced by the testing technique. However, this influence is not as evident in the mean values, which happen to be less than in the ASTM tests, as in the standard deviations and ranges which are about twice as l a r g e a s i n t h e A S T M t e s ts t s . S u c h i m p o r t a n t d i ff f f e re r e n c e s a r e d u e t o t h e l a rg rg e d i ff f f e r e n ce c e s b e t w e e n t h e d i f f e re re n t t e s t p r o c e d u r e s r e p o r t e d . I n c i d e n t l y , i t appears that the maximum density for the fine sand as obtained by c oSmTpMa c tsi toann dwairtdh am ev ti hb or adt, o r1y16 i s 1h.8 g6h etr/ mt h3a)n a tsh ac to mo pb at ar ei nde dt ob y1 14 A 1 6h.4 .4a ml m b /ef rt 3is .i8gh 1t4h.9 .9e l b / f t 3 1 .8 .8 4 t/ t / m 3 ) . H o w e v e r , f o r t h e g r a v e l l y s a n d , n o d i f fe fe r e n c e b e t w e e n the two methods is observed.

Discussion B e f o r e c o n si s i d er e r in i n g t h e u s e o f t h e m i n i m u m a n d m a x i m u m d e n s it i t ie ie s t o c o m p u t e t h e r e l a t iv i v e d e n s i t y , s o m e r e m a r k s c o n c er e r n in in g t h e m e a s u r e m e n t s of these parameters ought to be m ade. Testi Tes ting ng M etho d Th e m o s t c o m m o n r e a s o n w h y s o m e l a b o r a t o r i e s u s e t h e ir ir o w n m e t h o d i n s t e a d o f t h e s t a n d a r d A S T M p r o c e d u r e is t h a t t h e y t h i n k t h e y c a n g e t a l o w e r m i n i m u m a n d a h i gh g h e r m a x i m u m d e n s it it y . T h e r e s u l t s r e p o r t e d a b o v e s h o w t h a t t h i s i s n o t t h e c a se se , a t l e a s t o n t h e a v e r a g e . F u r t h e r m o r e , d u e t o t h e m u c h l a rg r g e r v a r i a b i li l i t y o f t h e r e s u l ts ts o b t a i n e d f r o m n o n s t a n d a r d m e t h o d s , a c o m p a r i s o n b e t w e e n te t e s t s re r e s u l ts ts f r o m d i ffe re n t l a b o r a t o r i e s w i ll l l b e v e r y d i ff ic ic u l t,t, i f a t a l l p o s s i b le l e . T h e r e f o re , t h e g e n e ra r a l iz iz e d u s e o f t h e A S T M D 20 2 0 4 99 - 69 69 s t a n d a r d p r o c e d u r e c a n o n l y b e e n c o u ra g e d , a t l e a s t i n t h i s re s p e c t . Influenc Inf luencee o f the Test Tested ed M ate ria l It i s e v i d e n t f r o m t h e t e s t r e s u l t s t h a t t h e m a t e r i a l h a s a m a j o r i n fl fl u e n c e o n t h e q u a l i t y o f t h e r e s u l t i n t e r m s o f r e p r o d u c i b i l i ty t y a s w e l l a s o f v a r i a b i l it it y . T h e t r e n d a l r e a d y m e n t i o n e d b y T i e d e m a n n [5 ] i s c o n f ir i r m e d h e r e : t h e c o a r s e r th th e m a t e r i a l t e s t e d , t h e l a r g e r t h e v a r i a b i l it i t y . T h e s t a n d a r d d e v i a t i o n s T a b l e 3) 3) f o r t h e g r a v e l l y s a n d a r e 6 0 p e r c e n t l a r g e r t h a n f o r t h e f i ne ne s a n d , a n d t h e c o m b i n e d s t a n d a r d d e v i a t i o n T a b l e 4) 4 ) a r e 10 1 0 0 p e r c e n t la l a r g er er . T h i s f a c t s h o u l d b e t a k e n i n t o a c c o u n t , e i t h e r b y i n c re r e a s in in g t h e n u m b e r o f i n d i v i d u a l t e s t s a s t h e m a x i m u m p a r t i c le l e s i ze z e o f t h e m a t e r i a l i n c r e a s es es o r b y s i m p l y b e i n g m o r e c a r e f u l w h e n d e a l i n g w i t h t h e r e l a t i v e d e n s i t y o f g r a v e l ly l y m a t e r i a ls ls . t e r m i ni ni n g Qualityy of the Test R esu lts Th e s t a n d a r d A S T M m e t h o d f o r d e te Qualit t h e m a x i m u m a n d m i n i m u m d e n s i t y o f c o h e si s i o n le le s s m a t e r i a l s y i e l d s r e s u l t s c h a r a c t e r i z e d b y a n a p p a r e n t l y a c c e p t a b l e v a r i a b i l i t y c o e ff f f ic i c ie ie n t o f v a r i a t i o n o f t h e o r d e r o f 2 . 5 p e r c e n t ) , r e p r o d u c i b i l it i t y c o e ff f f ic i c ie ie n t o f v a r i a t i o n o f t h e o r d e r o f 0 .8 . 8 p e r c e n t ), ), a n d b y a n o r m a l d i s t r i b u t i o n o f t h e o b s e r v a t i o n s w i t h i n t h e c o r r e s p o n d i n g ra r a n g e . A s c o m p a r e d t o o t h e r s o il il m e c h a n i c s t e s t s , t h e A S T M D 2 04 0 4 99 - 69 6 9 s t a n d a r d c o u ld l d b e c o n s id i d e r ed ed a s a r a t h e r g o o d a n d reliable test.

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

TAVENAS El AL O N

R E S U L TS TS O F A C O M P A R A T I V E T E S T P R O G R A M

37

Relative Density T h e m i n i m u m a n d m a x i m u m d e n s it i t ie i e s o f c o h es e s io i o n le l e s s so s o il i l s a re re n o t u s e d directly as usual soils parameters. They were defined and are measured o n l y t o f o r m t h e b a s i s o f t h e r e la l a t iv iv e d e n s i t y d e t e r m i n a t i o n b y m e a n s o f t h e well-known formula: Dr

--

max

~ d

~d

X

Td

Td

~

'Yd

max

~

rain

Td

r a in in

B a s e d o n t h e r es e s u l ts t s o f t h e p r e s e n t c o m p a r a t i v e t e s t p r og og r a m t h e q u a l i t y o f t h e m i n i m u m a n d m a x i m u m d e n s it i t y m e a s u r em e m e n t s w a s a n a ly l y z ed ed i n t h e

relative

0 150

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ll V ar i ati on i n rela relattive de density nsity be betwe weeen la labo borat ratories ories A H T M test sts. s.

Copyright by ASTM Int l (all rights rights reserved); reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) U niversidade niversidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. No f  

  8

REL

T I V ED ED E N S I T Y I N V O L V I N G C O H E S I O N L E S S S O I LS LS

previous section of this paper. The next step is to investigate how this q u a l i t y r e fl f l ec e c ts t s o n t h e c o m p u t e d v a l u e o f t h e r e l a ti ti v e d e n s i t y . T h i s c a n b e d o n e , e i t h e r b y c o n s i d e r in i n g t h e r e p r o d u c i b i l it i t y a n d v a r i a b i l it it y o f t h e l i m i t i n g d e n s i t i e s, s , o r b y a n a l y z i n g t h e r e l a ti ti v e d e n s i t i e s a s c o m p u t e d f r o m each participant s results. I nf lue nce of of the the V ar i ab il i t y of . yd m n and yd max on the the R e lat latii ve D e n si t y - - T o analyze the influence of the variability of the limiting densities on the rme il st tei rv e [ d7] i vree sduelt rsatti 7]e nissi t by ,e stth es uui ste t eed .o f Ot hn el y r etlhaet iv l tnss i toyb tgari anpe hd pf rr oo pmo s tehde b yA SBTuM D 2049-69 standard will be considered. The mean and the mean plus and minus two standard deviations of the maximum and minimum densities

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TAVENAS ET AL ON

R E SU S U L TS TS O F A C O M P A R A T IV IV E T E S T P R O G R A M

9

T A B L E 6 Va riab ility o f the relat relative ive density. Statistics

Indirectly Indirect ly D ete rm ine d Directl Direc tlyy Dete Determine rminedd Pro m Figs. 14, 15, 16, Prom Ea ch Particip ant's and 17 Resu lts Variabi Vari abili lity ty R epr od uci- V aria bility Reproduc Reproduciibility bility

M ean Standard deviat deviation ion Coefficie Coeffi cient nt of variation

F i ne Sand 69.0 69.0 11.0 3.5 15.9 5.1

70.0 11.8 16.9

70.0 2.5 3. 6

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Mean Standard de; de;cia ciati tion on Coefficie Coeffi cient nt of variation

43.5 18.0 41 .4

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w e r e r e p o r t e d o n F i g s . 1 1 a n d 1 2, 2 , r e s p e c t i v e ly ly , f o r t h e v a r i a t i o n s o f t h e r e s u l t s b e t w e e n la l a b o r a t o r i e s ( v a r i a b i li li t y ) a n d f o r t h e v a r i a t i o n s w i t h i n t h e d i f f e re r e n t l a b o r a t o r i e s ( r e p r o d u c i b i li l i t y ) . T h e s o li l i d l in i n e j o i n in in g t h e m e a n s represents the average relative den sity as a function of the d ry density. S i n c e t h e d i s t r i b u t i o n o f t h e o b s e r v a t i o n s w a s n o r m a l , t h e d a s h e d l i ne ne s drawn at plus and minus two standard deviations from the means are the l im i m i t s w i t h in i n w h i c h a p p r o x i m a t e l y 9 5 p e r c e n t o f t h e o b s e r v a t i o n s w i ll ll b e c o n fi f i n ed ed . T h e p r o b a b l e s t a n d a r d d e v i a t i o n o f t h e r e l a t i v e d e n s i t y c a n b e computed by dividing the width of this interval by four. Table 6 gives the p r o b a b l e s t a n d a r d d e v i a ti t i o n s o f D r a s c o m p u t e d i n th th i s w a y f o r t h e t w o t e s t e d m a t e ri a l s a l o n g w i t h t h e c o r re s p o n d i n g c o e f fi c ie ie n t s o f v a ri a t i o n s . T h e s e p a r a m e t e r s w e r e d e t e rm r m i n e d f o r an a n a s s u m e d d r y d e n s i t y o f 10 10 8 l b / f t 3 ( 1. 1 . 7 3 t / m 3 ) f o r t h e fi ne n e s a n d a n d 1 2 2 l b / f t 3 (1 (1.. 9 5 t / m 3 ) f o r t h e g ra v e l l y s a n d . T h e m a g n i fi f i ca c a t io i o n o f t h e i n a c c ur u r a c ie ie s o f t h e m a x i m u m a n d m i n i m u m d e n s i t ie i e s i n t h e r e s u l ti t i n g i n a c c u r a c y o f t h e c o m p u t e d r e l a t i v e d e n s i ty ty , a s s u g g e s te t e d b y T a v e n a s a n d L a R o c h e l le l e [ 4 ], ], i s p e r f e c t ly l y e v i d e n t h e r e. e. W i t h s t a n d a r d d e v i a t i o n s a n d c o e f fic fic i e n ts ts o f v a ri a t i o n s o f t h e l i m i t i n g d e n s i t i e s which could be considered as very satisfactory, the resulting minimum c o e f fic fi c i e n ts t s o f v a r i a t i o n (c o rre s p o n d i n g t o D r -- 1 00 0 0 p e rc e n t ) a re e q u a l t o 1 1 a n d 1 8 p e r c e n t f o r t h e f i n e s a n d a n d t h e g r a v e l l y s a n d , r e s p e c t i v e ly ly , a n d a m o u n t t o o n e t h i r d o f t h e s e v a l u e s i f t h e r e p r o d u c i b i l i ty t y o f t h e r e s u l t s is is c o n c e r n e d . S i nc nc e t h e w i d t h o f t h e 9 5 p e r c e n t i n t e r v a l i s a p p r o x i m a t e l y c o n s t a n t fo r t h e fu l l ra n g e o f re l a t i v e d e n s i t i e s , t h e u s u a l c o e ffi c i e n t o f v a r i a t i o n s w i ll ll b e m u c h l a r g e r, r, a t o r d e r s o f m a g n i t u d e o f 2 0 p e r c e n t f o r t h e fine sand and 40 percent for the gravelly sand. V a r i a b i li l i ty t y o f t h e R e la l a ti tiv e D e n s i t y a s M e a s u r e d b y E a c h P a r t i c i p a n t B y a s s u m i n g d r y d e n s i ti t i e s o f 1 08 0 8 l b / f t 3 ( 1. 1. 7 3 t / m 3) 3 ) a n d 1 22 2 2 l b / f t 3 ( 1. 1 . 95 9 5 t / m 3) f o r t h e f in in e s a n d a n d t h e g r a v e l l y s a n d , r e s p e c t i v e l y , r e l a t i v e d e n s i t y v a l u e s C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s id i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i c e  

4

R E LA L A T IV IV E D E N S I T Y I N V O L V I N G

C O H E S I O N L E S S S O fL fL S

w e r e c o m p u t e d f r o m e a c h p a ir i r o f m i n i m u m a n d m a x i m u m d e n s i ti t i es e s r e p o rt rt e d by the participants. The results of the statistical analysis are given in T a b l e 6 , w h i l e t h e c u m u l a t e d f r e q u e n c y d i s t r ib i b u t i o n c u r v e s f or o r t h e f in in e s a n d and the gravelly sand are shown on Figs. 13 and 14, respectively. T h e s t a t is i s t ic i c s a r e i n g o o d a g r e e m e n t w i t h t h o s e e s t a b l is i s h e d i n d i r e c tl tl y i n the previous section. This is logical considering the normal distributions o b s er e r v e d o n t h e m i n i m u m a n d m a x i m u m d e n s it i t y v a lu l u e s. s. T h e m e a n s a n d ss tl iagnhdtal ry d l ad re gv ei ar t itohnasn a re ex poencltye d1 ft ro o 3m p tehr ec e np tr ehciegdhienrg, isnedc it ci oa nt i.n gT hae v ac or ima bb ii nl iet dy standard deviations are I percent smaller, showing a better reproducibility. T h i s c a n p o s s i b l y b e e x p l a i n e d b y t h e f a c t t h a t t h e s o -c - c a l le l e d r e p r o d u c i b il i l it it y o f ~d ~ d m ln ln a n d ~ d . . . . d e t e r m i n e d p r e v i o u s l y , a c t u a l l y i n c l u d e s t h e t r u e reproducibility plus variations of these between laboratories, both parts of t h e t o t a l r e p r o d u c i b i l i ty t y b e i n g m a g n i f ie ie d i n F i g . 1 2 w h i le l e o n l y t h e f ir ir s t p a r t is magnified here. A ccur acy of R ela lattive D ensi ty M eaz azur ur eme ments---S nts---S om omee v e r y i m p o r t a n t i f n o t d r a m a t i c c o n c l u s io i o n s c a n b e d r a w n f r o m t h e p r e c e d in i n g f i n d in in g s . 1 . E v e n t h o u g h t h e A S T M D 2 0 4 99 - 6 9 st s t a n d a rd r d t e st s t s fo f o r d e t e r m i n in in g t h e m i n i m u m a n d m a x i m u m d e n s i t y o f c o h e s io i o n l e ss s s m a t e r ia i a l s c a n b e c o n s id id e r e d as

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v a r i a b i l i t y o f t h e o r d e r o f 2 .5 . 5 p e r c e n t a n d c o e ff f f ic i c ie i e n t o f r e p r o d u c i b i l it it y o f t h e o r d e r o f 0 .8 .8 p e r c e n t t h e u s e o f t h e s e p a r a m e t e r s i n t h e r e l a t i v e d e n s i t y f o r m u l a l e a d s t o a r e s u l t o f p o o r q u a l i t y s in i n c e i t is is c h a r a c te te r i z e d b y c o e f f ic ic i e n ts t s o f v a r i a b i l i t y o f t h e o r d e r o f 1 5 t o 4 0 p e r c e n t a n d b y c o e f fi f i c ie ie n t s o f r e p r o d u c i b i l it i t y o f t h e o r d e r o f 3 t o 1 5 p e r c e n t i n m o s t o f t h e u s u a l c a s es es . T h u s a n d s i m p l y d u e t o t h e f o r m u l a ti t i o n o f t h e re r e l a t iv i v e d e n s it it y t h e v a r i a b i l i t y i s m u l t i p l ie i e d b y a f a c t o r o f 1 0. 0. 2 . A s f o r t h e l i m i t i n g d e n s it i t ie ie s t h e v a r i a b i l i t y o f t h e r e l a t i v e d e n s i t y i n c r e as a s e s a s th t h e m a x i m u m g r a i n s iz i z e s o f t h e t e s t e d m a t e r i a l i n c re re a s e s. s. I n t h e p r e s e n t c a s e t h e s t a n d a r d d e v i a t i o n s w e r e fo f o u n d 6 0 t o 1 0 0 p e r c e n t la la r g e r f o r t h e g r a v e l l y s a n d t h a n f o r t h e f in in e s a n d . S i n c e t h e f in in e s a n d t e s t e d i s cl c l o se se t o t h e i d e a l m a t e r i a l w i t h a s m a l l m a x i m u m g r a i n s iz i z e a n d a c o e f fi f i ci c i e nt nt o f u n i f o r m i t y o f t h e o r d e r o f 3 a n d n o p a r ti t i c l e s p a s s i n g s ie ie v e 2 0 0 t h e v a r i ability and reproducibility observed on this material are the best possible w i t h t h e e x i s ti t i n g t e s t i n g te te c h n i q u e . T h u s i t c a n n o t b e e x p e c t e d t o d e t e r m i n e a n y r e l a t iv i v e d e n s i t y w i t h a w i d t h o f t h e 9 5 p e r c e n t i n t e r n a l l e ss ss t h a n 1 0 p e r c e n t i f t h e r e s u l t s o b t a i n e d b y o n e te t e c h n i c i a n o n l y a re r e c o n s i d er er e d a n d less than 40 percent if the results obtained by different laboratories are analyzed. As shown by Tiedemann [5] the results obtained by different operators in the same laboratory fall in between. 3 . A t h i r d b a s i c p a r a m e t e r i n f lu l u e n c in in g t h e d e t e r m i n a t i o n o f t h e r e l a t i v e

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

4

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C O H E S IO IO N L E S S S O IL IL S

d e n s i t y i s t h e a c t u a l d r y d e n s i t y . T h i s p a r a m e t e r a ls ls o is i s a f fe fe c t e d b y a c e r t a in i n e rr r r or o r . I n t h e m o s t i m p o r t a n t c a s e o f t h e m e a s u r e m e n t o f t h e n s tu d e n s i t y , t h e e x i s t in in g m e t h o d s u n d i s t u r b e d p i s t o n s a m p l i n g , g a m m a - r a y method, sand cone method, Washington method) are such that any value o f ~ c a n n o t b e d e f i n e d w i t h a n e rr rr or or l e s s t h a n 4 - 2 l b / f t ~ 4 - 0 . 0 0 3 t / m * ) . This accuracy was evidenced, for example, by Waterways Experiment Station [8] and Meigh and Skipp [9]. T h e e rr r r or o r o n t h e n s tu d r y d e n s i t y h a s t o b e c o m b i n e d t o t h e p r e v i o u s ly ly discussed variability to give the final variability of the relative density. T h i s w a s d o n e i n F i g . 1 5. 5 . O n t h i s f ig ig u r e t h e d a s h e d z o n e r ep ep r e s e n t s t h e 9 5 p e r c e n t i n t e r v a l f o r t h e c o r r e la l a t io i o n b e t w e e n t h e n s tu d r y d e n s i t y a n d t h e r e l a t iv e 0

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r e l a ti t i v e d e n s it i t y . T h e w i d t h o f t h e 9 5 p e r c e n t i n t e r v a l o f t h e r e l a ti ti v e d e n s i t y i s s h o w n t o b e 6 5 p e r c e n t fo f o r t h e f i ne ne s a n d a n d 9 4 p e r c e n t f o r t h e g r a v e l l y s a n d . I n t h i s s e c o n d c a s e i t i s e v i d e n t t h a t t h e 9 5 p e r c e n t i n t e r v a l is i s c lo lo s e t o the full range of possible values for the relative density. Under such c i r c u m s t a n c e s t h e p r o b a b i l i ty t y o f e v a l u a ti t i n g t h e c o r r e c t r e l a ti ti v e d e n s i t y b y a wild guess is at least equal to that of measuring it by the standard method 4. Due to the very large variability of the relative density between l~boratories, the comparison of relative densities measured by different laboratories will be totally nonsignificant. There are important practical implications of this fact: all established correlations between the relative density and various properties of cohesionless soils such as the standard penetration index, the point resistance in a static penetration test, the f r i c t io i o n a n g l e , t h e m o d u l u s o f c o m p r e s s i b il i l it i t y , t h e s h e a r w a v e v e l o c i t y , e t c .,., a r e u s e le le ss s s t o a n y o n e b u t t h e o p e r a t o r w h o h a s e s ta t a b l is i s h e d t h e m , s in in c e h e i s t h e o n l y o n e w h o c a n r e p r o d u c e t h e r e l a ti t i v e d e n s i t y o f t h e c o n s id i d e r e d s oi oil with sufficient accuracy. Similarly, the existing liquefaction criteria can only be properly used by those who have proposed them. Finally, the control tests for a compaction job will be only valuable when the same o p e r a t o r w h o h a s p e r f o r m e d t h e r e f e re r e n c e t e s t s a l so s o c a r r ie ie s o u t t h e c o n t r o l t e s t. t . I n t h i s r e s p e c t t h e m e a n i n g o f a c h e c k t e s t b y a n i n d e p e n d e n t la la b o r a t o r y t o s o lv lv e a c o n t r o v e r s y b e t w e e n a c o m p a c t i o n c o n t r a c t o r a n d t h e c o n t ro r o l li l i n g l a b o r a t o r y m a y b e p u t i n s e r io io u s d o u b t . 5 . I t a p p e a r s, s , t h e r e f o re r e , t h a t d u e n o t s o m u c h t o t h e v a r i a b i li li t y o f t h e m i n i m u m a n d m a x i m u m d e n s it i t ie i e s b u t e s s e nt n t ia i a l ly ly t o t h e f o r m u l a t i o n o f t h e r e l a t iv i v e d e n s i t y , t h e r e s u lt l t in i n g a c c u r a c y o f t h i s p a r a m e t e r i s s o p o or o r t h a t i ts ts use will be related to m ajor uncertainties (the be st case is of ideal m aterial s u c h a s t h e p r e s e n t f in i n e s a n d , a n d w i ll ll b e p r a c t i c a l l y m e a n i n g l e s s i n m o s t o f t h e o t h e r c a s e s) s) . Standard and

o d i fi e d P r o c t o r T e s t s

T h e p a r t i c i p a n t s w e r e as a s k e d t o p e r f o r m t w o t e s t s e a c h o n t h e f in in e s a n d a n d t h e g r a v e l l y s a n d f o ll l l ow o w i n g t h e s t a n d a r d a n d m o d i f ie ie d P r o c t o r c o m p a c t i o n p ro r o c e d u r e s . I t w a s s p e c if i f ie ie d t o p e r f o r m t h e s e t e s t s o n o v e n - d r i e d m a t e r i a l, l , a t z e ro r o p e r c e n t w a t e r c o n t e n t . I n t h i s w a y t h e i n fl f l u e n ce ce o f t h e o p t i m u m w a t e r c o n t e n t o n t h e v a r i a b il i l it it y o f t h e o p t i m u m d r y d e n s i t y w a s e l i m i n a t e d . A t t h e s a m e t i m e i t w a s e x p e c t e d t o g e t d e n s i ti t i e s c lo lo s e t o t h e u s u a l o p t i m u m s i n ce c e d r y c o h e s io i o n le l e s s m a t e r i a l s c a n b e e a s i ly ly c o m p a c t e d .

Va riability of the roct roctor or Test Result Resultss Seventy-seven tests w ere perform ed on each m aterial with each of the s t a n d a r d a n d m o d i fi f i ed e d P r o c t o r p r o c e d u r e . T h e s t a ti t i s ti ti c s c o n c e r n i n g t h e variations of the Proctor densities between laboratories are given in Ta ble 7.

Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

 

RELATIVE DENSITY iNVO LViN G

COHESIONLESS SOILS

A s e x p e c t e d t h e d e n s it i t ie i e s o b t a i n e d b y t h e m o d i f ie ie d P r o c t o r p r o c e d u r e a r e h i g h e r th t h a n t h o se s e p r o d u c e d b y t h e s t a n d a r d p r o c e d u re r e , b u t t h e d i ff f f e re r e n c es es a r e n o t a s la la r g e a s n o r m a l l y o b s e r v e d , p a r t i c u l a r l y f o r t h e g r a v e l l y s a n d w h e r e ~ i n c r e a s e s o n l y f r o m 1 2 8. 8 . 3 l b / f t 3 2 .0 . 0 6 t / m 3 ) t o 1 2 9 .8 .8 l b / f t 3 2 .0 . 0 8 t/ t / m 3 ) . T h e c o m p u t e d s t a n d a r d d e v i a ti t i o n s v a r y f r o m 2 .0 .0 l b / f t ~ 0 .0 . 0 3 2 t / m 3 ) t o 2 . 7 l b / f t 3 0 .0 . 0 4 3 t / m 3) a n d r e p r e s e n t a b o u t 1 9 p e r c e n t o f t h e o b s e r v e d r a n g e s . H e r e a g a in i n , t h e v a r i a b i l i t y in i n c r e as a s e s w i t h a n i n c r e as as i n g maximum grain size, but this increase is significant only for the results of m o d i f i ed e d P r o c t o r t e s ts t s . T h e v a r i a b i l i ty t y o b s e r v e d h e r e is is v e r y s i m i la la r t o t h a t r e p o r t e d b y L i u a n d T h o m p s o n [ 6 ] f o r t e st s t s p e r f o r m e d i n c o m p l e te te a c c o r d a n c e w i t h t h e A S T M T e s t s f o r M o i s t u r e - D e n s i t y R e l a t io i o n s o f S o il il s , U s i n g 5 . 5 - L b R a m m e r a n d 1 2 -I - I n . D r o p , M e t h o d D D 6 9 88 - 70 70 ) w i t h a v a r i a b l e w a t e r c o n t e n t t h u s i n d i c a t in i n g t h a t t h i s a d d i t io i o n n a l v a r i a b l e h a s n o s ig ig n if i f iic a n t i n f lu lu e n c e o n t h e v a r i a b i l i t y o f t h e o p t i m u m d e n s i t y . R e p r o d u c i b i l i t y o f t he h e P r o c to to r T e s t R e s u l t s

T h i r t y - e i g h t p a ir i r s o f d u p l i c a te te t e s t s c a n b e a n a l y z e d t o d e f i n e t h e r e p r o d u c i b i l i ty t y o f t h e P r o c t o r t e st s t s . T h e c o r r e s p o n d i n g st s t a ti t i s ti ti c s a r e g i v e n in Table 8. T h e b e s t r e p r o d u c i b i l it i t y i s o b t a i n e d f o r t h e m o d i fi fi e d P r o c t o r c o m p a c t i o n o n t h e f in i n e s a n d w i t h a c o m b i n e d s t a n d a r d d e v i a t i o n o f 0. 0 . 76 7 6 l b / f t ~ 0 .0 .0 1 2 t / m S ) ; t h e w o r s t i s o b s e r v e d f o r t h e s t a n d a r d c o m p a c t i o n o n e, e, t h e s a m e m a t e r i a l w i t h a s t a n d a r d d e v i a t i o n t w i c e a s l ar a r g e. e. R e s u l t s f o r t h e g r a v e l l y results. s. T A B L E 7 Va riab ility of Proctor test result

Statist Stat istic ic

Stan dard Proc tor, lb/fts t/m 3 Fine Sand 77

Num ber of tests M ean Standard devi deviat ation ion M aximum M ini inimum mum Range

Num ber of tests Mean Standard devi deviat ation ion M axi aximum mum M ini inimum mum Range

M odif odified ied Proc tor, lb/ft3 t/m 3

110.5 2.3 117.6 105.5 12.1

1.77 0. 03 0377 1.88 1.69 0.19

77 114.3 2.0 120.6 110.2 10.4

Gravelly Sa nd Gravelly 77

128.3 128.3 2.4 134.33 134. 120.1 14.2

2.06 0.038 2.15 1.92 0.23

1.83 0.032 1.93 1.77 0.16

78 129.8 129.8 2.7 135.55 135. 121.3 14.22 14.

2.08 0.043 0.043 1.94 0.23

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i c e n s e A g r  

T A VEN A S ET A L O N R ESU ESU LT LT S OF A C OM P A R A T I VE T EST PR O GR A M

5

TABLE 8 Reproducibility of Proctortest resul results. ts. Statistic

Number of pairs of tests

Standard Proctor lb/ft8 lb/ft 8 t/m3 t/m3

ModifiedProctor Modified lb/ft3 lb/ft3 t/ms t/ms

Fine Sand 38

38

Average range

1.85

0.030

0.83

0.013

Combined Combine d stan standard dard deviat deviation ion

0.76

0.012

Number of pair pairss of test testss

1.53 0.025 Gravell Gra vellyySand Sand 38

Average range Combined Combine d stan standard dard deviat deviation ion

1.35 1.25

1.48 1.37

0.022 0.020

38 0.024 0.022

sand fall between these limits with a reverse reversed d tende ncy. Such values of the combined comb ined standa rd deviation are larger larger tha n those reported reported by Johnson and Guinnee [10] for series of tests performed by a single operator. As for the maximum and minimum density tests it is proba probable ble tha t t he reproduci reproduci-bil ity observed here is the real repr oducibility plus a varia bili ty of this reproducibility between laborat laboratories. ories. Discussion It should be first emphasized that the Proctor compaction tests were performed on on oven-dried oven-dried material and no mentio n was made by t he participants of any problem having occurred during the tests. Comparison Between the Standard and Modified Proce Pro cedur dures es Fr From om the reported results no clear-cut difference between the two methods can be made. However However even if the m ateri al teste d has an influe influence nce it seems seems th at the modified procedure is a better test in terms of a better reproducibility. Thee coeff Th coeffic icie ient ntss of reproducibili reproduci bili ty are 1.38 and 0. 0.97 97 perc percent ent for the fine sand and the gravell y sand respectively ively in case e of dard Proc Proctor test te st as compared to 0.66 0.6 6 andrespect 1.06 percent in the th e cas case ca se ofthe thee stan th modified tor test.. Such a difference test difference is cer certai tainly nly not negli negligi gibl ble. e. On the othe r han d the coef co effi fici cien ents ts of variab ilit y are near ly equal for bot h tests at least on the average and of the order of 2 percent. percent. Compariso Comp arison n Betwee Between n the Proc Proctor tor and Ma xi mu m Density Densit y Tests The main reasons for introducing the use of a vibratory table in performing the maximum density test proc procedu edure re were were th at it would giv givee maximum dry densities higher th an t he modified modified Proctor test th at it would reduce or eliminate the problem of particle breakage often associated associated with t he i mpac t compaction method and t ha t it would be of higher reproducibility. The present investigation sh show owss th at these assumptions assumptions are part ly corr correct ect but to an extent smaller than anticipated. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to  

  6

REL TIVEDENSITY TIVEDENSITY IN INVOL VOLVIN VING G COHE COHESIO SIONLE NLESS SS SOIL SOILS S

TA B LE 9-9---Compar/ -Compar/son son o f A S T M D ~ 0 ~ 9 6 9 a n d A S T M D 1 5 5 7 7 0 te te st st r es es ul ul t s .

Statistics

Modified Proc tor Modified AS TM D 15571557-70, 70, lb/fts t/m 3

Maximum De nsity ASTM D 20492049-69, 69, l b / ft3 t/m a

Fine Sand

M ean Stan dard deviat deviation ion (vari (vari-ability) Sta nd ard deviation (reproducibility

114.3 2. 0 O. 76

1.830 O.032 O. 012

114.9 2.7 O. 67

1.840 O.043 O. 011

G ravel l y Sand

Mean Stan dard deviat deviation ion (vari (vari-ability Sta nd ard deviation (reproducibility)

129.8 129.8 2.7 1.3 7

2.08 O.043 O. 022

133.8 133.8 4.5 1.37

2.14 O. 07 O. 022

A s d i sc s c u s se s e d i n t h e s e c t i o n o n g r a d a t i o n t e st s t s , o n l y th t h e m o d i f ie ie d P r o c t o r c o m p a c t i o n t e s ts t s p r o d u c e d s o m e p a r t ic i c l e b r e a k a g e o n t h e g r a v e l ly ly s a n d s p e c im i m e n . T h i s e f f e c t c a n n o t b e n e g l e c t e d e v e n t h o u g h i t is is v e r y l i m i t e d , s i nc nc e t h e m o d i f i c a t i o n i s t h e p e r c e n t a g e s p a s s i n g s i e v e 4 t o 6 0 w a s o f t h e s a m e o r d e r o f m a g n i t u d e a s t h e s t a n d a r d d e v i a t i o n o n th t h e s e p e r c e n ta ta g e s . T h e a n a l ys y s is i s o f t h e m e a n o f t h e m a x i m u m d e n s i ty ty o b t a i n e d b y t h e A S T M D 2 0 49 4 9 -6 - 6 9 a n d b y t h e A S T M T e s t s f o r M o i s t u r e - D e n s i t y R e l a t io io n s o f S o il i l s , U s i n g 1 0 - L b R a m m e r a n d 1 8 -I - I n . D r o p ( D 1 55 5 5 7 -7 - 7 0) 0) p r o c e d u r e s also shows that the modified Proctor compaction gives lower maximum d e n s i ti t i e s . H o w e v e r , a s s h o w n i n T a b l e 9 , t h e d i ff f f e re re n c e s a r e n o t v e r y important particularly for the fine sand. T h e t h i r d a s s u m p t i o n o f a b e t t e r q u a l i t y o f t h e A S T M D 2 04 0 4 99 - 69 6 9 t e st st s results is proven wrong, since the corresponding standard deviations applicable to the v ariability are 30 to 60 percent higher than for the m o d i f i e d P r o c t o r t e s t s r e su s u l ts t s , w h i le l e t h e r e p r o d u c i b i l i t y is is t h e s a m e f o r both tests.

R e l a t i v e C o m p a c t i o n a n d R e l a t iv e D e n s i t y I n a p r e c e d i n g s e c t io io n t h e r e l a t i v e d e n s i t y w a s s h o w n t o b e a f f e c t e d b y a h i g h v a r i a b i l i t y a n d l o w r e p r o d u c i b i l i t y s u c h t h a t i ts ts u s e w o u l d b e m o s t difficult, if not practically impossible. This does not necessarily mean that t h e c o n c e p t o f e x p re r e s s in i n g t h e d e n s i t y o f a s o il i l r e l a t i v e l y to to p a r t i c u l a r d e n s i t i e s o f t h a t s o il il i s n o t a p p l i c a b l e , b u t t h a t t h e a p p l i c a t i o n o f t h i s c o n c e p t i n t h e f o r m o f t h e r e l a t i v e d e n s i ty t y i s a f f ec ec t e d b y i m p o r t a n t weaknesses.

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

T VEN S ET

L ON RE RESU SULTSOF

COMP R TIVE TEST PROGR M

7

O t h e r e x p r e ss s s i on o n s o f t h e r e l a t i v e s t a t e o f c o m p a c t n e s s o f a s o il il a r e e i t h e r p o s s i b le le o r i n u s e ( s u c h a s t h e r e l a t i v e c o m p a c t i o n ) . T h e q u a l i t y o f t h i s s o i l s p a r a m e t e r w i ll ll b e e v a l u a t e d h e r e . Relative Compaction

T h e c o n c e p t o f r e l a t i v e c o m p a c t i o n i s n o r m a l l y u s e d in in c o n j u n c t i o n w i t h t h e P r o c t o r t e s t f o r t h e c o n t r o l o f t h e c o m p a c t i o n o f fi fi l l s . T h e r e l a t i v e c o m p a c t i o n RC is defined as: RC

~/d Yd

m

x

w h e re Y d i s t h e in situ d e n s i t y a n d - ~ m ax ax i s t h e m a x i m u m d e n s i t y o b t a i n e d b y t h e s t a n d a r d o r m o d if i f ie i e d P r o c t o r t e s t ; h o w e v e r , o n e c o u l d a ls l s o th th i n k o f using the maximum density as a reference. T h e r e l at a t iv i v e c o m p a c t io io n s w e r e c o m p u t e d f r o m e a c h p a r t i c i p a n t s d a t a o n t h e b a s is i s o f t h e s t a n d a r d P r o c t o r , t h e m o d if i f ie i e d P r o c to to r , a n d t h e m a x i m u m density (ASTM D 2049-69 test only) with an assumed unit weight of 108 l b / f t 3 ( 1. 1. 7 3 t / m 3) a n d 1 22 2 2 l b / f t 3 ( 1. 1. 9 5 t / m 3 ) f o r t h e f in in e s a n d a n d t h e gravelly sand, respectively. The corresponding statistics are shown in Table 10, and the cumulated frequency distribution curves are given on Fig. 16 an d 17. A s n o t e d b e fo f o r e , t h e r e l a t iv i v e c o m p a c t io i o n b a s e d o n t h e A S T M D 2 0 49 4 9 -6 -6 9 m a x i m u m d e n s i t y is is t h e l o w e s t, t , b u t a t t h e s a m e t i m e t h e m o s t v a r ia ia b l e . O n t h e o t h e r h a n d , R C b a s e d o n t h e m o d i fi f i ed ed P r o c t o r h a s i n t e r m e d i a t e v a l u e s , w h i c h a re c l o s e t o t h e p re c e d i n g f o r t h e fi n e s a n d b u t a r e s i g n i fic fi c a n t l y le le s s v a r i a b le l e . T h u s , i t a p p e a r s t h a t t h e m o d i f ie ie d P r o c t o r ( o n e p o i n t c o m p a c t i o n T A B L E 10 Com parative anatysis o f the relati relative ve compa ctions. Statistics

Relative Compaction in Percent Based on: Standard Proctor M o d i fi f i ed ed P r o c t o r A S T M D 2 0 4 9 -6 -6 9 Maximum Density

Fine Sand M ean S t a n d a r d d e v i a ti ti o n C o e f fi f i c ie ie n t o f v a r i a t i o n M axim um M inimum Ran ge

97.82 1.99 2.03 1 0 2 .3 .3 7 91.84 10.53

94.54 1.66 1.75 98.00 8 9 .5 5 8.45

94.08 2.29 2.4 4 1 0 1 . 50 50 8 9 . 40 40 12.10

94.05 2.02 2.1 4 1 0 0 .5 .5 8 90.04 10.54

91.26 3.22 3.53 1 0 2 .9 .9 5 8 6 . 65 65 16.30

Gravell Grave llyy S an d M ean S t a n d a r d d e v i a ti ti o n C o e ff f f ic i c ie ie n t o f v a r i a t i o n M aximu m Minim um Ran ge

95.10 1.77 1.86 1 0 1 .5 .5 8 90.84 10.74

Copyright by A STM Int l (all rights reserved); Fri M ar 11 16:13:06 EST 2 016 Downloaded/printed by ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c  

48

RE L A TIV E DE NS ITY INV OL V IN G C OHE S IONL E S S ,S OIL OIL S

I00

1-

I, p,

~ ,/ ,~o ~ /

90

i

/

r

II

80

70

,,

:

1

'

I

6O

50

;

;

r

i

I/

8 40

,

3

2

/ 90

.

.

,Y~ [

(~) (~ )

92

94

:

k

.

/, ~

s ; 88

.

i

i

I

E

/.._/ /

. /

~ ' ~ ; _ ~ ,r ; ' ~

m o d i fi e d p r o to r density

s fo n d a e d

96 913 913 relotive relot ive co mp octlon,~

rOCtOr

I00

~ ,~S itityy 102

104

FIG. 16--Compar/.son of the relati relative ve compacti compactione one based based on Proctor and m ax im um density

te ~ , fine sand. sand.

test on oven-dried soil) leads to relative compactions of a better overall quality. Relative Compac ion versus Rela %e Density

At a first glance, when comparing the statistics concerning the relative c o m p a c t i o n T a b l e 1 0) 0 ) a n d t h e re r e l a ti t i v e d e n s i t y T a b l e 6) 6) , i t w o u l d s e e m t h a t t h e v a r i a b i li l i t y o f t h e r e l a t iv i v e c o m p a c t i o n i s m u c h b e t t e r , s in in c e t h e c o e ff f f ic i c ie i e n ts ts o f v a r i a t i o n s a r e o n e o r d e r o f m a g n i t u d e l o w e r . H o w e v e r , a s s t re r e s s e d b y L e e a n d S i ng n g h [11], t h e p o s s i b le l e r a n g e s o f t h e r e l a t iv iv e c o m p a c t i o n a r e m u c h q o w e r t h a n t h a t o f t h e r e l a t iv i v e d e n s i t y , b e c a u s e no n o s o il il c a n b e f o u n d i n a s t a t e o f z e r o u n i t w e i g h t w h i c h w o u l d c o r re r e s p o n d t o z e ro ro p e r c e n t relative compaction, and the minimum value of R C corresponds to the m i n i m u m p o s s i b l e u n i t w e i g h t o f t h e s o i l c o n s id i d e r e d , t h a t i s, s, o f t h e o r d e r o f 80 percent. T herefore, a prop er evalua tion of the variab ility of bo th p a r a m e t e r s s h o u l d b e b a s e d o n t h e r a t i o o f t h e s t a n d a r d d e v i a t io io n t o t h e C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Dow nloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFPE ) Universidade Federal de Pernambuco) pursuant to  

TAVENAS ET AL ON

RESULT RES ULTS S OF A COMPA RATI VE TEST TEST PROG RAM

9

p o s s i b l e r a n g e r a t h e r t h a n o n t h e c o e f f ic ic i en e n t o f v a r i a t io io n . T h i s r a t i o i s o f t h e order of 11 to 21 percen t for the relative density as com pared to 8 to 10 p e r c e n t f o r t h e r e l a t iv i v e c o m p a c t i o n b a s e d o n t h e m o d i fi f i ed ed P r o c t o r d e n s i t y . T h u s i t c a n b e c o n c l u d e d t h a t t h e c o n c e p t o f r e l a ti t i v e c o m p a c t i o n is is s ig i g n if i f ic i c a n tl t l y b e t t e r t h a n t h e r e l a t iv i v e d e n s i t y in in t e r m s o f a c c u r a c y a n d practicability of the result. I t i s o ft f t e n co c o n s id i d e r e d t h a t a m a j o r a d v a n t a g e o f t h e r e l a ti ti v e d e n s i t y o v e r the relative compaction is that the relative density magnifies small variat i o n s o f t h e i n s i t u d e n s i t y t h u s a l lo l o w i n g a b e t t e r c o n t r o l o f s u c h v a r ia ia t i o n s p a r t i c u l a r l y o n c o m p a c t i o n w o r k s . F r o m t h e p r e s e n t fi f i nd n d in in g s t h i s s u p p o s e d m a j o r a d v a n t a g e a p p e a r s t o b e a m a j o r d i s a d v a n t a g e s in i n c e t h e r e l a ti ti v e density also magnifies the errors on the unit weights to such an extent that t h e c o m p u t e d r e s u l t i s b a r e l y b e t t e r t h a n t h a t o b t a i n e d b y a p u r e g u e ss ss . T h e r e f o re r e t h e u s e o f t h e r e l a ti t i v e c o m p a c t i o n c a n o n l y b e e nc n c o u r a g ed ed n o t o n l y i n c o m p a c t i o n s p e c i f ic i c a ti t i o n s b u t a l so s o in in t h e a n a l y s i s o f n a t u r a l deposits. I00

9C

80

70

60 a,

50

o 40

3

2

0

86

88

90

92 94 96 relative compoctlon~ compoctlon~

98

IO0 IO 0

t02

FIG. 17--C om pariso n of the rel relati ative ve compacti compactions ons based on P roct roctor or and m ax im um densi density ty te~tss grave lly sand . te~t Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

5

R E L A T IV IV EDENS E DENS ITY INVO LVING

COHESIONLESS SOILS

onclusions

F o r t y - o n e U n i t e d S t a t e s a n d C a n a d i a n L a b o r a t o r i e s r e p r e se se n t i n g g o v e r n m e n t s , u n i ve v e r si s i ti t i e s, s, a n d i n d u s t r y h a v e p a r t i c i p a t e d i n a c o m p a r a t i v e t e s t p r o g r a m , t h e p u r p o s e o f w h i c h w a s t o e v a l u a t e t h e v a r i a b i l it it y a n d r e p r o d u c i b i l it i t y o f t h e m o s t u s u a l t e s t s p e r f o r m e d o n e o h e s io i o n i es e s s s o il il s a m p l es e s , n a m e l y , t h e s i ev e v e a n a ly l y s is is , t h e m e a s u r e m e n t o f t h e m i n i m u m a n d m a x i m u m d e n s i ti t i e s a n d o f t h e r e s u l ti t i n g r e l a t iv iv e d e n s i t y , a n d t h e m e a s u r e m i f ie ie d P r o c t o r c oemn pt a cotfi otnh et e smt sa.x i m u m d e n s i t y b y t h e s t a n d a r d a n d m o d if T h e f ir i r s t a n d m o s t g e n e r a l c o n c l u si s i o n o f t h i s i n v e s t i g a t i o n is is t h a t n o n e o f t h e c o n s i d e re r e d t e s t s a r e r e a l ly l y re r e l ia ia b l e a h i g h v a r i a b i l i t y a n d a l o w reproducibility are typical of all these soil mechanics tests). This finding confirms those yielded by similar investigations applied to other geot e c h n i c a l t e s t s s u c h a s t h e i d e n t i f ic i c a t i o n t e s t s f o r c o h e s i v e s oi oils . T h i s g e n e r a l characteristic of soil mechanics tests has been largely ignored up to now, but should be considered most seriously in the future, since it throws some d o u b t s o n t h e v a l i d i t y o f o u r g e n e r a l a p p r o a c h t o t h e e v a l u a t i o n o f s o il il s p r o p e r t ie i e s . M o r e s p e c if if ic i c a ll ll y , t h e r e s u l t s o f t h e p r e s e n t i n v e s t i g a t i o n certainly em phasize the necessity of ma king use of some of the basic p r iAn sci c i pt le loe s t ho ef tthhq eu apl ir toyb aobfi l it thye a vn ad r idoeucsi si s itoe ns t tin rmi eest.h o d s c o n s i d e re i nh ge o ri r e d in in t h i s program, the conclusions may be summarized as follows: 1. The sieve analysis is affected by a large variability with average c o e ff f f ic i c ie i e n ts t s o f v a r i a t i o n s o f t h e o r d e r o f 2 0 p e r c e n t. t. F o r t h e m a t e r i a l t e s t e d t h e r a n g e o b s e r v e d w a s n e a r l y a s w i d e a s t h e r a n g e s s p e c if i f ie i e d f o r m a t e r i a ls ls to be used as selected fills in runways, roads, or filters. The variability of s u c h i m p o r t a n t p a r a m e t e r s a s t h e d l0 l0 , d e 0 , o r d ~ i s s u c h t h a t s e r io io u s q u e s t i o n s m a y b e r a is i s e d a s t o t h e v a l i d i t y o f t h e u s u a l c r it i t e ri ri a b a s e d o n t h e m . 2 . T h e m i n i m u m a n d m a x i m u m d e n s i ti t i es es c a n b e b e s t e v a l u a t e d w i t h t h e A S T M D 2 0 4 9 -6 -6 9 s t a n d a r d m e t h o d . T h i s m e t h o d y i e ld l d s r e s u l t s W h ic i c h a r e, e, on the average, as good as those obtained from other methods, but which can be more easily compared when measured by different laboratories s i nc n c e t h e i r v a r i a b i l i t y is i s m u c h l e ss ss . T h e q u a l i t y o f t h e s e r e s u l ts ts w o u l d s e e m s a t i s f a c t o r y w i t h c o e f fi f i ci c i e nt n t s o f v a r i a t i o n o f t h e o r d e r o f 2 .5 .5 p e r c e n t a n d c o e ff f f ic i c ie ie n t o f r e p r o d u c i b i l i t y o f t h e o r d e r o f 0 . 8 p e r c e n t . T h e q u a l i t y o f t h e result is better for the minimum density test and tests performed on fine materials. 3 . D u e t o i t s f o r m u l a t i o n t h e r e l a t i v e d e n s i t y i s a f f e c te te d b y a v a r i a b i l i t y a n d a r e p r o d u c i b i l it i t y 1 0 t i m e s w o r s e t h a n t h o s e o f t h e l i m i t i n g d e n s i ti ti e s . D u e t o t h is i s h i g h v a r i a b il i l it i t y , w h i c h c a n b e b e s t e m p h a s iz iz e d b y t h e w i d t h o f t h e 9 5 p e r c e n t i n t e r v a l o f f r o m 4 0 t o 1 00 00 p e r c e n t , i t a p p e a r s p r a c t i c a l l y m e a n i n g l e ss ss t o t r y t o m e a s u r e a r e l a t i v e d e n s i t y , s i n c e a p u r e g u e s s i s m o r e likely to give a correct answer.

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFPE ) Universidade Federal de Pernambuco) pursuant to License A  

T VEN S ET

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T IV IV E T E S T P R O G R

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4 . S t a n d a r d a n d m o d i fi f i ed e d P r o c t o r t e s t s e x h ib ib i t a b e t t e r q u a l i t y t h a n t h e m a x i m u m d e n s i t y te t e s t . T h u s , b e c a u s e o f i t s m o r e s a t is is f a c t o r y f o r m u l a t i o n , t h e r e l a ti t i v e c o m p a c t i o n b a s e d o n t h e m o d i f ie ie d P r o c t o r d e n s i t y a p p e a r s t o b e a s l i g h t ly ly b e t t e r t o o l f o r e v a l u a t i n g t h e s t a t e o f c o m p a c t n e s s o f a cohesionless soil so il dep osit.

cknowledgments The authors are indebted to C. B. Crawford for his assistance, to E . B . H a ll l l , C h a i r m a n o f t h e A S T M C o m m i t te t e e D -1 - 1 8 w h o ac a c c e p te te d t o p r o v i d e t h e m o r a l su s u p p o r t o f A S T M t o t h is is c o m p a r a t i v e t e s t p r o g r a m , a n d t o E . T . S e lili g , C h a i r m a n o f t h i s S y m p o s i u m w h o h e l p e d i n p r o v i d i n g a f r a m e f o r t h i s i n v e s t i g a t io io n . T h e p a r t i c ip i p a t i o n o f t h e 4 1 U n i t e d S t a t e s a n d C a n a d i a n l a b o r a to t o r ie ie s , w i t h o u t w h i c h t h i s i n v e s t i g a t i o n w o u l d h a v e b e e n i m p o s s ib ib l e , i s g r a t e f u l l y acknowledged. The very important contribution of D. A. Tiedemann, U.S. Bureau of R e c l a m a t i o n is is a c k n o w l e d g e d. d . H i s p a r t i c i p a t io io n i n t h e p r e p a r a t i o n o f t h e t e s t p r o g r a m , t h e p r o c e s si s i n g o f t h e f in i n e s a n d s p e c i m e n s , a n d t h e d i s c u s s io io n of the present paper was of major imp ortance. The preparation and shipping of the specimens was supported by the U.S. Bureau of Reclamation, the National Research Council of Canada G r a n t A -7 - 7 72 7 2 4, 4, a n d L a v a l U n i v e r s i t y , Q u e b e c . T h e p r e p a r a t i o n o f t h i s p a p e r w a s s u p p o r t e d b y t h e N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a G r a n t A -7 - 7 72 7 2 4. 4. P P E N D IX

I

ist of Participan ts

United Un ited States States Universities State Univers Universit ityy of New Yo rk at Buffal Buffalo, o, Buffal Buffalo, o, N.Y. University of New M exico, Albuquerque, N .M .

Federal Soil Conservation Service, Lincoln, Neb. U.S. Bureau of Reclamation, Denver, C olo. M issouri R iver Division Division Laboratory, Laboratory, Om aha, Neb. U.S. Arm y Engineers, W aterways Experiment Stati Station, on, Vicksburg, M iss. Tennessee Tenness ee Valley Au thority, Knoxvil Knoxville, le, Ten n.

Consulting Engineers Joseph S. W ard Associates, Caldw ell, N .J. W oodw ard-Moorhouse Associates Inc., Clifton, N .J. Dam es M oore, San Francisco, Calif. E . D 'Appolonia Consulting Consulting Engineers Inc., Pitts Pittsburg, burg, Pa. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreem  

5

R E L A T IV I V E D E N S IT IT Y I N V O L V I N G

C O H E S IO I O N L E S S S O IL IL S

La w Engineering Engineering Testing Co ., Jacksonvil Jacksonville, le, Fla.

McClelland Engineers, Houston, Tex. Shannon and Wilson, Seattle, Wash. H aley Aldrich, Inc., Cam bridge, M ass.

Commercial Testing Laboratories The H. C. Nutting Company, Cincinnati, Ohio Geo-Testing Inc., San Rafael, Calif. Smith-Emery Com pany, Los Angeles, Calif Calif..

Canada Universities Universit~ L aval, Q uebec, P.Q. Universit~ P.Q. Ecole Polytechnique, Montreal, P.Q. Universit~~ d e Sherbrooke, Sherbrooke, P.Q. Universit Queen's University, Kingston, Ont. University Universi ty of M anit anitoba, oba, W inni innipeg, peg, M an. Un iversity of Alberta, Edm onton, Alta. University of British Columbia, Vancouver, B.C.

Governm ent s Organizations National Research Council of Canada, Ottawa, Ont. M inis inist~re t~re de la V oir oirie, ie, Quebec, P.Q. Hydro-Quebec, Montreal, P.Q. Department of Highways, Ontario, Downsview, Ont. Ontario-Hydro, Toronto, Ont. Canada Department of Regional Economic Expansion, Saskatoon, Sask. De partm ent of Highways, Edmonton, Alta Alta.. Canadian National Railways, Montreal, P.Q. Manitoba-Hydro, Winnipeg, Man.

Consulting Engineers Geocon Limited, Dorval, P.Q. Terratech Lim it~e, M ontreal, P.Q. M ontrea ontreall E ngineer ngineering ing C o., M ontrea ontreal, l, P.Q. H . Q . Golder and A ssociat ssociates, es, Mississauga, Mississauga, Ont. R. M. Hardy and Associates, Alta. W arnock Hersey, Internati Inte rnational onalEdmonton, Limited, Darmouth, N.S. Dam es M oore, D on M il ills, ls, Ont.

P P E N D IX

II

Sequence and

rocedures for Testing Specimen s

General Gener al Rema rks It is ou r inte intenti ntion on to have each parti participant cipant use un teste d material material whenever possible possi ble in performin performingg the maximum-mini maximum-minimum mum density tests and the compact compaction ion tests. H owever, we realize th at we hav e no t shipped shipped enough soil to accom pli plish sh

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R E L A TI T I VE V ED E N S I T Y I N V O L V I N G C O H E S I O N L E S S S O I LS LS

this. To establi establish sh a standar stan dard d sequence sequence for using test tested ed materia mat eriall we would like each

participant to follow a specified testing sequence.

Fine San d Specimen Specimen Testing Testi ng Sequence Three separate testing testi ng seq sequen uences ces have been prepa prepared; red;

see Tables 11 through 13. One of these testing sequences should be followed in performing the required testing. The sequence which the participant selects should be based on how the participant plans to perfo perform rm the maximum-m maximum-minimum inimum density test. In Table 11 the testing sequence outlined is for a participant to follow if the participant plans to perform the maximum-nimimum density testing using either the ASTM AST M procedure or their standard sta ndard procedur procedure, e, but n ot both. In Table 12 the testing sequence outlined is for a participant to follow if the participant plans to perform the maximum-minimum density testing using both the ASTM procedure and a procedure which is frequently used by the participant and in which a large mold is used. In Table 13 the testing sequence outlined is for a participant to follow, if the participant plans to perform the maximum-minimum density tests using both the ASTM procedure and a procedure which is frequently used by the participant and in which a small mold is used. Sampling Preparation In opening the sack of fine sand you will find two small sacks. The sand in these sacks is part of the sample. Without opening them, weigh them together and individually using the scale that will be used in conducting the relative density densi ty tests. Repo rt the wei weigh ghts ts obtained ob tained on Form Fo rm ]3-1 in Appendix II. After weighing add the contents of these smaller sacks to the contents of the large sack from which they were taken and thoroughly mix the sample. Next, from this thoroughly mixed sample, obtain three specimens weighing between 6.5 and 7.0 kg by using a sample sample splitter, splitter, riff riffle le samp sample, le, or o r ha hand nd quart qu arteri ering ng procedur proc edure. e. In additi a ddition, on, one of these specimens specimens should shoul d be split in half using a sample splitter if possible and label one of these specimens 3S-A and the other 3S-B. The othe ot herr two specimens should be labeled 1S and 2S, respectively. Then place these four spe specim cimens ens in separate containers and oven dry 110 C or 230 F) to a cons constant tant weight. weight. If a large large for force ce draft oven is is ava availa ilable ble,, dryi drying ng over night should be adequate. The excess material should also be placed in a container and oven dried to a constant weight. This material should be labeled Specimen 4S.

Test P racedure raceduress M a x i m u m a n d M i n i m u m D e n s it i t y T e st st s

Maximum-minim um density tests are to be performed in accordance with 1) Maximum-minimum AST M D 2049-69 2049-69 using the dry metho method d only and a 0.1 ft a mold; 2) the test proceduree usually cedur usually us used ed by the participant; parti cipant; or 3) both methods 1 and 2. In addition, the sequence in which the tests are to be performed on the test specimens should be done in accordance with one of the three testin testing g sequenc sequences es outlined in Tables Table s 11 through 13. It should be noted that in all cases the tests should be performed on oven dried dried material. material. Record the da ta and make the necessary ca calc lcul ulat atio ions ns tha t are required required to complete Form B-2 in Appendix Appendix II, and attac at tach h the data sheets used used in performing these tests to this form. One Point Compaction Tests

One-Point Compaction tests are to be performed using oven dried material and compact comp acting ing the mat materia eriall in a 4-in. 4-in. 1/30 ft ~) mold mold.. The sequence sequence to t o be follo followed wed is

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T A V E N A S E l A L O N R ES ES UL UL TS TS O F A C O M P A R A T IV IV E T E S T P R O G R A M

59

t h a t g i v e n i n t h e s a m e f ig ig u r e u s e d f o r p e r f o r m i n g t h e m a x i m u m - m i n i m u m d e n s i t y t e s t s p r e v i o u s ly l y de d e s c ri r i b ed e d . R e c o r d t h e d a t a a n d m a k e t h e n e c e s s a ry r y c a l c ul u l a ti ti o n s

that are required to complete Form B-3 in Appendix II, and attach to this form t h e d at a s h ee t s u s ed i n p e rfo rmi n g t h es e t es t s . Bo th the stand ard and mo dified compaction tests should be performe d u s i n g t h e e f f o r ts ts d e s c ri r i b e d i n A S T M D 6 9 8 - 70 7 0 ( M e t h o d A ) a n d D 1 55 5 5 77-7 0 ( M e t h o d A ), re s p e c t i v el y . P a r t ic ic L e S i z e A n a l y s e s

Pa rt i cl e -s i z e an a l y s es a re t o b e p erfo rmed o n Sp e ci me n s 1 S, 3 S-B, a n d 4 S i n acc o rd an c e w i t h t h e t es t i n g s e q u en c e w h ich i ch t h e p art i c i p a n t fo l lo lo w e d i n p e rfo rmi n g the maximum-minimum density tests, that is, one of the sequences outlined in Tables 11, 12, or 13. A p p ro x i ma t el y 1 0 0 g s h o u l d b e t ak e n fro m t h e s e s p ec i me n s u s i n g a s p l i t t er o r s i mi l a r p ro ce d u re, w ei g h e d aft e r o v e n d ry i n g , an d t h o ro u g h l y w a s h e d o n a 2 0 0 s i ev e . T ra n s fe r th th i s w as h ed ma t e ri al t o a s u i t a b l e c o n t a i n er, o v e n -d ry o v e r n i g h t , and perform a sieve analysis using U.S. Standard sieves 10, 20, 40, 60, 100, 2 0 0, 0 , an d p an . If a p o w ere d s ie i e v e s h a k er is is u s e d , s ie i e v e fo r 1 5 mi n . R ec o rd t h e d a t a and make the necessary calculations that are required to complete Form B-3 p r e s e n t e d in i n A p p e n d i x I I , a n d a t t a c h t h e d a t a s h e e ts ts u s e d i n p e r f o rm rm i n g t h e p a r ticle size analyses to this form.

Gravell Grave llyy San d Specim en Testing Testi ng sequence Two t e s t i n g s e q u e n c e s h a v e b e e n p r e p a r e d . T h e y a r e p r e -

s e n t ed i n T a b l e s 1 4 an d 1 5. 5 . O n e o f t h e s e t e s t i n g s eq u e n ce s s h o u l d b e fo ll ll ow ow ed i n p erfo rm i n g t h e re q u i red t e s ti t i n g . T h e s e q u en c e w h i ch t h e p a rt i c i p an t s elec elec t s s h o u l d be based on how the pa rticipant plans to perform the m aximum -minimum den sity testing. In T ab l e 1 4 , t h e t e s t i n g s eq u e n ce o u t li l i n e d is i s t o b e fol fo l lo lo w e d b y t h e p a rt i ci p a n t i f the participant plans to perform the maximum-minimum density testing using either the A ST M procedure or their standard procedure, bu t no t both procedures. In T ab l e 1 5 , t h e t es t i n g s eq u en c e o u t l i n ed i s t o b e fo l l o w ed b y t h e p art i c i p an t i f t h e p a r t i c i p a n t p l a n s t o p e r f o r m t h e m a x i m u m - m i n i m u m d e n s i t y te t e s t s u s in in g b o t h the AS TM procedure and a procedure which is frequen tly used by the participant. Sam ple Preparation Before p ro c ee d i n g w i t h an y t es titi n g , (1 (1)) t h o ro u g h l y mi x t h e s amp l e ; (2 ) p rep a re t h ree s p e ci me n s w ei g h i n g b e t w e en 6 .5 a n d 7 .0 k g u s i n g a s amp l e s p l i tt t t er, riff riffll e s a mp l er, o r h an d q u art e ri n g p ro ced u re ; (3 ) p la l a ce t h es e t h re e s p e ci men s i n s e p ara t e c o n t a i n ers ; an d (4 (4)) o v en d ry (1 (111 0 C o r 2 3 0 F) t o a co n s t a n t weight. All of the excess material (weighing approximately 1.5 kg) should also be p l ac ed i n a c o n t ai n e r a n d o v e n d ri e d t o a co n s t an t w ei g h t . T h i s ex c es s mat eri a l s h o u l d b e l a b el e d Sp e ci men 4 G , w h i l e t h e o t h er t h re e s p ec e c imen imen s s h o u l d b e lab l ab e l ed 1 G , 2 G , a n d 3 G , res p ect i v el y .

Te st Procedures Procedures M a x i m u m M i n i m u m D e n s it i t y T e st st s

T h e i n s t ru ct i o n s g i v en i n t h e s ec t io i o n u n d er fi n e san s an d ca n b e fo ll ll ow ow e d h e re ex c ep t for the following: (1) testing sequence outlined in Tables 14 and 15 should be foll o w e d a n d ( 2) 2) F o r m B - 5 u s ed e d i n s te t e a d o f F o r m B - 2. 2. N o t e , t h e t e s t s p e c i m e n sh sh o u l d n o t b e s ca l p ed o n t h e ~ - i n . s ie ie v e, e, t h a t i s , t h e -t -t-3 -3~~ -in -in . m a t eri al s h o u l d b e i n c l u d ed in the test specimen.

Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

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R E L A T I V E D E N S IT IT Y I N V O L V I N G

C O H E S IO I O N L E S S S O I LS LS

One Point Compaction Test

The instructions given in the section under fine sand specimen can be followed

h e r e e x c e p t f o r t h e f o l lo l o w i n g : (1 ( 1 ) a 6 - i n c h m o l d s h o u l d b e u s e d ; ( 2) 2) t h e c o m p a c t i o n e f fo f o r ts t s d e s c r ib i b e d i n M e t h o d s D , o f A S T M D 6 9 8 - 7 0 a n d D 1 5 5 77 - 7 0 s h o u ld ld b e u s e d i n s t e a d o f M e t h o d s A ; ( 3 ) t e s t i n g s e q u en e n c e o u t l i n e d in in T a b l e s 1 4 a n d 1 5 s h o u l d b e f o ll l l o w e d ; a n d ( 4 ) F o r m 6 - B u s e d i n s t e a d o f F o r m B - 3. 3. N o t e , t h e t e s t s p e c i m e n s h o u l d n o t b e s c a l p e d o n th t h e ~ - i n . s ie ie v e ; t h a t is , t h e T ~ - i n . m a t e r i a l s h o u l d b e included in the test specimen. Particle Size An alyses

P a r t i c l e si s i ze z e a n a l y s e s a r e to t o b e p e r f o r m e d o n S p e c im im e n s 1 G , 3 G , a n d 4 G i n a c c o r d a n c e w i t h t h e t e s t in i n g s e q u e n c e w h i ch c h t h e p a r t i c i p a n t f o l lo lo w e d i n T a b l e s 1 4 a n d 1 5. 5. I n p e r f o r m i n g t h e p a r t ic i c l e - s iz i z e a n a l y s e s o n t h e s e s p e c i m e n s, s, a f t e r o v e r d r y i n g a n d r e c o r d in i n g th t h e w e i g h t o f t h e s p e c im i m e n , a l l o f th th e m a t e r i a l i n e a c h s p e c i m e n s h o u l d b e s i e v e d o n t h e f o l lo lo w i n g U . S . S t a n d a r d s i e v e s : 1 i n . ~ i n . , N o . 4 , a n d p a n . N e x t , f r o m t h e m a t e r i a l r e t a i n e d i n th t h e p a n , s e l e ct c t a s p e c im i m e n w e i g h in in g a p p r o x i m a t e l y 1 00 0 0 g a n d r e c o r d t h e w e i g h t . T h e n t h o r o u g h l y w a s h t h i s s p e c im im e n o n t h e 2 0 0 s i ev ev e a n d t r a n s f e r t h e w a s h m a t e r i a l t o a s u i t a b l e c o n t a i n e r , o v e n d r y t o a c o n s t a n t w e i g h t , a n d p e r f o r m a s i e v e a n a l y s i s u s i n g U . S . S t a n d a r d s i e v e s 4 , 1 0, 0, 2 0 , 40 4 0 , 6 0 , 10 1 0 0, 0, 2 0 0 , a n d p a n . I f a p o w e r e d s i e v e s h a k e r i s u s e d , s i e v e f o r 1 5 m i n . R e c o r d t h e d a t a a n d m a k e t h e n e c e s sa s a r y c al a l c u la l a t io i o n s t h a t a r e r eq e q u i re re d t o c o m p l e t e F o r m B - 6 i n A p p e n d i x I I , a n d a t t a c h t o t h i s f o rm rm , t h e d a t a s h e e t s u s e d i n p e r f o r m i n g t h e p a r t ic i c l e - s iz i z e a n a ly ly s e s . References

[1] K o l busz ew ski , J. J., Proceedings 2 n d I n t e r n a t i o n a l C o n f e r e n c e o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , V o l.l. 1 , R o t t e r d a m , 1 9 4 8 , p p . 1 58 5 8 -1 -1 65 65 . [ P] Fel t , E. J. i n S y m p o s i u m o n A p p l i c a t io i o n o f S o i l T e s ti ti n g i n H i g h w a y D e s i g n a n d C o n s t r uc uc titi o n A S T M S T P 23 2 3 9 A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 95 95 8 p p . 89- 110. [3 ] P e t t ib i b o n e , H . C . a n d H a r d i m , J ., ., R e s e a r c h o n V i b r a t o r y M a x i m u m D e n s i t y T e s t s f o r C o h e s i o n le le s s S o i l s, s, p a p e r p r e s e n t e d a t t h e 6 7 t h A n n u a l M e e t i n g , A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 64 64 . [~ i] T a v e n a s , F . a n d L a R o c h e l le le , P . , P r o b l e m s R e l a t e d t o t h e U s e o f t h e R e l a t i v e D e n s i t y , R e p o r t S -2 - 2 1, 1 , L a v a l U n i v e r s i t y , Q u e b e c , C a n a d a , 1 97 9 7 0. 0. [5 ] T i e d e r ~ n n , D . A . , V a r i a b i l i t y o f L a b o r a t o r y R e l a t iv iv e D e n s i t y a n d G r a d a t i o n T e s t s , R e p o r t R E C - E R C - 7 1 - 1 7 , B u r e a u o f R e c l a m a t i o n , D e n v e r , 19 19 71 71 . [ 6 ] L i u , T . K . a n d T h o m p s o n , M . R . i n Proceedings N a t i o n a l C o n f e re r e n c e o n ' S t a t i s ti ti c a l Q u a l i t y C o n t r o l M e t h o d o l o g y i n H i g h w a y a n d A i rf r f ie i e ld l d C o n s tr t r u c ti t i o n , U n i v e r s it it y o f V i r g i n i a , C h a r l o t t e s v i l l e , V a . , M a y 1 9 66 66 , p p . 3 7 5 - 3 9 5 . [ 7 ] B u r m i s t e r , D . M . , Proceedings A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , V o l . 48 48 , 1948, pp. 1249-1268. [8 ] D e n s i t y C h a n g e s o f S a n d C a u s e d b y S a m p l i n g a n d T e s t i n g , P o t a m o l o g y I n v e s t i g a t i o n s R e p o r t N o . 1 22 - 1 , W a t e r w a y s E x p e r i m e n t S t a t i o n , V i c k s b u rg r g , M i s s . , 19 1 9 52 52 . [ 9 ] M e i g h , A . C . a n d S k i p p , B . O . , Geotechnique Vol. 10, No . 3, 19 60, pp . 110-126. [10] J o h n s o n , A . W . a n d G u i n n ee e e , J . W . , A R e p o r t o n th t h e C o n s i d e ra r a t io io n o f t h e T e s t R e s u l t s fr fr o m t h e A C I L S t a n d a r d S o i l S a m p l e P r o g r a m A l o n g w i t h t h e S u p p l e m e n t a l T e s ti t i n g C o n d u c t e d i n C o o p e r a ti ti o n w i t h A S T M D - 1 8 , I n t e r n a l R e p o r t , C o m m i t t e e D - 1 8 , A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 19 19 66 66 . [11] L e e , K . L . a n d S i n g h , A . , Jou rna l of t he he Soi l Mech ani cs and Foundati Foundati on on D i vi si on A m e r i c a n S o c i e t y o f C i v i l E n g i n e e r s , V o l. l . 9 7 , S M 7 , J u l y 1 9 71 71 .

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D

A

T i e d e m an an n 1

V a r i a b i lil i ty t y o f L a b o r a t o r y R e l a tit i v e T es t Result Resul t s

e n s it ity

REFERENCE: Tiedemann, D. A., "Variability of L a b o r a t o r y R e l a t i v e Evaluation ation of o f Relati Re lative ve Dens Density ity and Its It s Role in D e n s i t y T e s t R esults," Evalu Geotec Geo techni hnical cal Projec Projects ts Invol Involving ving Cohesi Cohesionle onless ss Soil Soilss A S T M S T P 5~3 American Societ Soc iety y for Test ing and Materials, 197 1973, 3, pp. 6161-73. 73. ABSTRACT: Fourteen Bureau of Reclamation soils laboratories conducted duplicate minimum, and wet and dry metho d maximum density tests on a fine and a medium sand. Data were analyzed on the basis of variations between laboratories and between duplicate tests. tests. Results indicate d tha t: (1 (1)) variation s between laboratories were two to three times greater than variations between duplicate tests;we (2) (2 variations laboratories for minim um and maximum densities were re) the same sa me,, orbetween less than, less variations reported for impact-ty pe compaction compactio n tests tests;; an d (3) exp expres ressin sing g the deg degree ree of compac compaction tion in terms of relative density, as compared to percent of maximum density, requires using different standards for both the level of compaction required and the limits within which compaction would would be conside considered red acceptab acceptable. le. Gr adatio n tests on the two sands were also conducted by 16 laboratories and analyzed in the same manner. K E Y W O R D S : soil tests, density (mass/volume), sieve analysis, eohesionless

soils, soil s, sands, statistical qua lit y control, soil soil compacting, compacting, densi ty measurement, soil mechanics, reproducibility.

The concept of relative density [1]2 [1] 2 is wi dely used for expressing the st at e of compactness of coh cohes esio ionl nles esss gran ula ularr soil soils. s. I t involves comparing the natural, or compacted, compacted, density of a soil soil to t he mi nimum and maxi mum densities of which it can be placed in the laboratory. Various tests have been devised to determine the two limiting densities. While most of the test methods have been in use for more than ten years, very few studies have been conducted to determine the variations associated with their use. Knowledge of these variati ons is needed: 1) for developing developing statis tical 1 Researc Research h civil engineer, engineer, Engineeri ng and Researc Research h Center, Bureau of Reclamation, Denver Den ver,, Colo. Colo. 802 80225. 25. The ita lic numbers in brackets refer to the list of ref refer eren ence cess appended to this paper. 6

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RELATIVEDENSITY RELATIVE DENSITY INV INVOLV OLV NG COH COHESI ESIONLE ONLESS SS SOILS

q u a l i t y c o n t r o l m e t h o d s , a n d ( 2 ) f o r d e t e r m i n i n g t h e r e l i a b il i l i ty t y o f r e l a t io io n s h i p s b e t w e e n a s o i l s r e la la t i v e d e n s i t y a n d i t s p h y s i c a l b e h a v i o r , s u c h a s

load-settlement characteristics, permeability, penetration resistance, and s t a t i c a n d d y n a m i c s tr t r e n g t h s . T h i s i n f o r m a t i o n b e c o m e s o f i n c r e a se se d i m p o r t a n c e w h e n d a t a d e v e lo l o p e d b y o n e la l a b o r a t o r y i s u s e d b y a n o t he he r .

Purpose and Scope of Investigation I n 1 96 96 0, 0, t h e B u r e a u o f R e c l a m a t i o n ( B u r e a u ) a d o p t e d t h e v i b r a t o r y table method as a standard test procedure for determining the maximum density of cohesionless soils. This method is essentially the same as the A S T M T e s t f o r R e l a t i v e D e n s i t y o f C o h es e s io i o n le l e s s S o il il s ( D 2 0 4 9 -6 -6 9 ) . T h e m i n i m u m d e n s i t y t e s t p r o c e d u r e o f p o u r i n g d r y s o il il h a s b e e n i n u s e f o r a l o n g e r p e r i o d o f t im i m e . A n d , o f th t h e t w o l im i m i t i n g t e s t s , i t h a s t h e l e s se se r v a r i a t i o n b e t w e e n l ab a b o r a to t o r ie i e s . R e l a t i v e d e n s i t y i n v e st s t ig i g a t io io n s c o n d u c t e d by the Bureau [~-5] and others [6-16] have been concerned mainly with c o m p a r i n g t h e r e s u lt l t s o b t a i n e d u s i n g d if i f f e re re n t m a x i m u m d e n s i t y t e s t p r o c e d u r e s o r w i t h s t u d y i n g t h e e f f e c ts ts o f v a r i a b l e s s u c h a s t h e m a g n i t u d e , t im i m e , a n d d i re r e c t io i o n o f v i b r a t i o n h a v e o n t h e m a x i m u m d e n s i t y o b t a in in e d . I n o n l y t w o s t u d i e s [ 17 18] h a s t h e v a r i a b i l i t y i n r e s u l t s o b t a i n e d b y a n y o n e g i v e n m e t h o d b e e n i n v e s t ig ig a t e d . T o o b t a i n t h is i s i n fo f o r m a t io i o n , a B u r e a u c o o p e r a t iv i v e te t e s t in in g p r o g r a m w a s c o n d u c t e d [19]. F o u r t e e n B u r e a u s oi o i l s l a b o r at a t o r ie ie s c o n d u c t e d m i n i m u m , and wet and dry method maximum density tests, in duplicate, on a fine a n d a m e d i u m s a n d . I n c o n j u n c t i o n w i t h th t h e s e t e s t s, s, 1 6 l a b o r a t o r i e s c o n ducted gradation tests on the sands. The results obtained from this prog r a m a r e p r e s e n te t e d i n th th i s p a p e r .

M a t e r ia ia l s T e s t e d T w o g r a d a t io i o n s o f c le l e an a n , p o o r l y g ra ra d e d s a n d ( S P ) w e r e p r e p a r e d f r o m s c r e e n e d fr f r a c t io i o n s o f a l o ca c a l s t r e a m ( C l e a r C r e e k ) d e p o s i t m a t e r ia ia l . O n e s a m p l e , d e s i g n a t e d a s 2 4 E - 11 1 1 , w a s p r e d o m i n a n t l y a fi f i ne ne s a n d a n d t h e o t h e r , 2 4 E - 1 2 , w a s p r e d o m i n a n t l y a m e d i u m s a n d . T h e s e s oi o i ls ls c o n t a i n e d l e ss s s t h a n 5 p e r c e n t o f p a r t i c le le s f i n e r t h a n t h e N o . 2 0 0 s i e v e o r c o a r s e r t h a n the No. 4 sieve. F i f t y - p o u n d s a m p l e s o f e a c h s a n d w e r e s e n t t o t h e p a r t ic i c i p a ti ti n g l a b o r a tories. The samples were prepared by shoveling the soil at random from t h o r o u g h l y m i x e d s t o c k p il i l e s . T o p r e v e n t t h e l os o s s o f f in i n e p a r ti t i c le le s , p l a s t i c lined sacks were used for shipmen t.

Data Presentation and

n a ly ly s e s

After all the data had been received each laboratory was assigned an a l p h a b e t i c a l d e s ig i g n a t io io n . W h e n m o r e t h a n o n e s e t o f d u p l i c a t e t e s t s w a s conducted by the same laboratory, the operator or operators were given a numerical designation. C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n te te d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A  

TIEDEMANN ON VARIABILITYOF VARIABILITY OF LABORATORYTES LABORATORYTES T RES RESUL ULTS TS

6

T h e r e s u lt l t s w e r e a n a ly l y z e d i n t w o w a y s : ( 1) 1 ) t h e r e p r o d u c i b i li l i ty ty b e t w e e n l a b o r a t o ri r i e s , a n d ( 2 ) th t h e r e p e a t a b i l i t y b e t w e e n d u p l i c a t e t e s ts ts . I n a n a l y z i n g

t h e r e s u l t s , t h e f o l lo l o w i n g s t a t i s t i c s w e r e c a l c u l a t e d [ 2 0 ]. ]. R e p r o d u c i b i li l i ty t y B e t w e e n L a b o r a t o r ie ie s R a n g e - - T h e r a n g e ( R ) is i s th t h e d i ff f f e re re n c e b e t w e e n t h e h i g h e s t a n d l o w e s t values. A v e r a g e - - T h e average (:~) or arithmetic mean was calculated as =

r x /n

w h e r e Z x is is t h e s u m m a t i o n o f t h e i n d i v id i d u a l v a lu lu e s , a n d n i s t h e n u m b e r of these values. S t a n d a r d D e v i a t i o n - - T h e s t a n d a r d d e v i a t i o n ( s ) w h i c h e x p r e s se se s t h e d e g r e e o f v a r i a t i o n w i t h r e s p e c t t o t h e m e a n w a s c a l c u l a te te d a s s =

/Y.( x -

X ) 2/ n

-

1

F o r n o r m a l l y d i s t r ib i b u t e d d a t a , t h e i n t e rv r v a l b e t w e e n tw tw o s t a n d a r d d e v i ations on both sides of the mean will contain approximately 95 percent of the values, and if the results used in determining the standard deviation are representative, 95 percent of any future tests would be expected to fall within these limits. For purposes of discussion, the results from these t e s t s w e r e a s s u m e d t o m e e t t h e s e r e q u ir i r e m e n t s. s. R e p e a t a b i l it it y B e t w e e n D u p l i c a t e T e s t s A v e ra r a ge g e R a n g e - - T h e a v e r a g e r a n g e ( /~ /~ ) w a s c a l c u l a t e d a s [~ = Z I d l / k

w h e r e Z I d I i s t h e s u m m a t i o n o f t h e a b s o l u t e d if i f fe f e r e nc nc e s b e t w e e n d u p l i c a t e tests, and k is the n um ber of duplicate tests. C o m b i ne n e d S t a n d a rd r d D e v i a t i o n - - T h e c o m b i n e d s t a n d a r d d e v i a ti ti o n , s , w a s calculated as s = v -5 -5/e /ek k W h i l e i t w a s re r e c o g n i z e d t h a t t h e v a r i a b i l i t y b e t w e e n l a b o r a t o r i e s is is influenced by the repeatability within each laboratory [~I], no attempt w a s m a d e t o s e p a r a t e t h e t w o w h e n a n a ly l y z i ng n g t h e r e p r o d u c i b i l it it y b e t w e e n laboratories. Gradation Tests

Procedure

The gradation tests were conducted primarily as a check on the uniformity of the samples. Results were obtained from 16 laboratories, about o n e h a lf l f o f w h i c h p e r f o r m e d d u p l i c a t e t e s ts ts . T h e t e s t s w e r e c o n d u c t e d b y dry sieving the samples as received for 10 to 15 rain.

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6

R E L A T IV I V E D E N S IT IT Y I N V O L V I N G

C O H E S I O N L ES E S S S O IL IL S

T A B L E 1 ~ um m a ry of gradat gradation ion test uari uariati ations ons between/abor between/aborator ator/es /es.. =

P e r c e n t a g e p a s s in in g , b a s e d o n d r y w e i g h t o f t o t a l s a m p l e . ( P e r c e n t a g e r e t a i n e d o n i n d i v i d u a l s i ev ev e s , b a s e d o n d r y w e i g h t o f t o t a l s a m p l e . ) Statistical feature

Sieve Size No . 4

No. 8

No. 16

No. 30

No. 50

No . 100 No . 200

Fine Sand Ran ge Av erag e S t a n d a r d d e v i aation

1 0 0 -9 -9 8 (0-2) 100 (0.2)

97-92 (3-6) 96 (4.2)

90-84 (7-10) 87 (8.5 )

7 5 -- 6 6 (15-20) 70 (17.1)

50-42 (21-30) 45 (25.0)

1 44- - 9 (29-38) 11 (33.8)

5-2 (7-10) 3 (7.8)

0.6 (0.6)

1.0 (0.8)

1.4 (1.0)

2.4 (1.3)

2.4 (1.8)

1.6 (1.9)

0.9 (0.9)

Medium Sand Ra nge

100-98 (0-2)

85-75 (15-25)

56-33 (32-47)

33-14 (17-30)

13-4 (9-16)

7-2 (2-6)

4-0 (1-4)

A ve r ag e

100 (0.3)

81 (1 9 . 0 ) (1

43 (37.9)

22 (29.3)

9 (12.7)

4 (4.8)

2 (2.4)

S t a n d a r d d e v ia ia tion

0.6 (0.6)

3.1 (3.2)

5.6 (3.7)

4.6 (2.6)

2.2 (2.0)

1.2 (1.1)

0.7 (0.9)

D a t a b a s e d o n r e s u l t s o f 2 5 g r a d a t i o n t e s ts ts . U .S .S . S T A N D A R D =200

=1 00

50

SIEVE

~r

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~-~-MEDIUM ~-~MEDIUM SAND (24E-12)

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. 14 14 9

DIAM ETER I

297

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1 .1 .1 9

i I 2 .3 8 4. 76

9.52

O F P A R T I C L E IN IN M I L L I M E T E R S FINE

ISAND M E D I U M ICOARSE]

F I G . 1 Av era ge gradation gradation curve curvess fo r test samples samples..

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T I E D E M A N N O N V A R I A B IL IL IT IT Y O F L A B O R A T O R Y T E S T R ES ES UL UL TS TS

TABLE 2

S u m m a r y o f g r a d a t i o n t e st s t v a r i a t i o n s b e tw tw e e n d u p l i c a t e t e~ e~ ts ts .

6

P e r c e n t a g e p a s si s i n g b a s e d o n d r y w e i g h t o f t o t a l s am am p l e Sieve Size No. 4

No. 8

No. 16

No. 30

No. 50

No . 100

N o. 200

5 0 1.7 1.7

1 0 0.6 0.5

1 0 0.4 0.5

2 0 1.2 1.0

2 0 0.6 0.7

2 0 0.4 0.6

Fine Sand a M ax im um M in im um Average range S t a n d a r d d e v iiation

0 0 0 0

3 0 1.1 1.2

5 0 2.1 1.9

6 0 2.6 2.3

Medium Sand b M ax im um M ini m um Average range S t a n d a r d d e v iiation

1 0 0.2 0.4

5 0 2.2 2.1

8 0 4.0 3.5

5 0 2.4 2.0

a B a s e d o n t h e r e s u l t s f r o m s e v e n p a i r s o f d u p l i c a t e t e s t s. s. b B a s e d o n t h e r e s u l t s f r o m e i g h t p a i r s o f d u p l i c a t e t e s t s. s.

Test Results The variations between laboratories were analyzed in two ways: on the basis of the p ercentage passing each sieve and the p ercentage retained on t h e i n d i v i d u a l s i e v es e s . T h e s u m m a r y o f t h e s e r e s u l ts t s is is p r e s e n t e d i n T a b l e 1 and the average gradation curves are drawn in Fig. 1. The variations b e t w e e n d u p l i c a t e t e s t s w e r e a n a ly l y z e d o n l y o n t h e b a s is i s o f t h e p e r c e n ta ta g e passing each sieve. These results are presented in Table 2.

D is c u s s io n W h e n t h e r e s u l ts ts a r e a n a l y z e d o n t h e b a s i s o f t h e p e r c e n t a g e p a s s i n g e a c h si s i ev e v e t h e s t a n d a r d d e v i a t i o n s a re r e a s h i g h a s 5 .6 .6 p e r c e n t a n d a s f o u n d in similar investigations [8 22 28] do not appear to have any definite relationship to the average values. However when analyzed on the basis o f t h e p e r c e n t a g e r e t a i n e d o n t h e in i n d i v i d u a l s ie ie v e t h e s t a n d a r d d e v i a t i o n s a r e d e c r e a s e d a n d a s s h o w n in i n F ig ig . 2 a r e r e l a t e d t o t h e a v e r a g e p e r c e n t a g e s retained. The duplicate test and between-laboratory standard deviations are s i m i l a r fo f o r t h e f i n e s a n d b u t d i f fe fe r f o r t h e m e d i u m s a n d . T h e s e d i f f e re re n c e s are attributed to the variability in medium sand samples furnished the p a r t i c i p a t i n g l a b o r a to t o r i e s . T h e m e d i u m s a n d u n l i k e t h e f in in e s a n d t e n d e d t o s e g r e g a t e w h e n m i xe x e d . D i f fi f i c u l ty ty i n o b t a i n i n g i d e n t i c a l s a m p l e s h a s b e e n e n c o u n t e r e d i n o t h e r c o o p e r a t i v e t e s t i n g p r o g r a m s [ 8 22].

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R E L A T IV IV E D E N S I T Y I N V O L V I N G

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M i n im u m

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Procedure

All of the laboratories tha t received samples were requested to con duct d u p l ic i c a t e m i n im i m u m , a n d d u p l i c a te t e w e t a n d d r y m e t h o d m a x i m u m d e n s i ty ty t e s t s f o ll ll o w i n g t h e p r o c e d u r e s o u t l i n e d i n D e s i g n a t i o n E - 1 2 , P a r t B , o f t h e Earth Manual [ 2 4] 4 ] . T h i s t e s t d e s i g n a t i o n i s e s s e n t ia ia l l y t h e s a m e a s A S T M D 2 0 4 9 -6 - 6 9 ) a n d u ti t i li l i ze z e s a v i b r a t o r y ta t a b l e fo f o r d e t e rm rm i n i n g t h e m a x i m u m d e n s i t y . T h e 0 .1 .1 f t 3 m o l d w a s u s e d i n a l l t e s t s . Results

T h e r e s u l t s f r o m 1 4 l a b o r a t o r i e s a r e p r e s e n t e d i n F i g . 3. 3. E a c h s e t o f d u p l i c a t e t e s t s i s r e p r e s e n te te d b y a h a t c h e d b a r ; t h e e n d s o f t h e b a r s a r e drawn at the individual test values. These results were analyzed on the b a s i s o f t h e r e p r o d u c i b i li l i t y b e t w e e n l a b o ra r a t o r ie ie s a n d t h e r e p e a t a b i l i t y b e t w e e n d u p l i c a te te t e s t s . r m i n i n g t h e v a r i a b i li li t y b e Reproducibilit y Betw een Laboratories In d e t e rm t w e e n l a b o r a t o r i e s , t h e f o ll ll o w i n g v a l u e s w e r e s e l e c t e d f r o m t h e d a t a reported by each laboratory: the lowest minimum density, the highest dry method and the highest wet method maximum densities, and the h i g h e s t m a x i m u m d e n s i t y o f t h e t w o m e t h o ds ds . W h e n a l a b o r a t o r y r e p o r t e d more than one set of duplicate tests by the same test method for either s a m p l e , t h e f ir i r s t s e t o f t e s t s w a s u s e d . T h e r e s u l ts t s o f t h e s t a t i s t ic ic a l a n a l y s e s a r e s u m m a r i z e d i n T a b l e 3 . S t a n d a r d d e v i a ti t i o n s fo fo r t h e m i n i m u m a n d m a x i m u m o f e i t h e r m e t h o d ) d e n s i ti t i e s a r e 1 .3 .3 a n d 1 .1 .1 l b / f t 3, r e s p e c t i v e l y ,

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3 Su m m a ry o f rel relati ative ve densi density ty test tests. s.

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  8

REL

TIVEDENSITY INVO LVIN G

C O H E S I O N L E S S S O IL IL S

TABLE 3 Betw Between een labo laborator ratoryy varia variations tions in mini mi nimu mum m and ma maxi ximu mum m density density tests. tests.

Minimum

Maximum

MaximumDry Density

Dry Den si sity ty lb/ft~

Dry Densi Den sity ty lb/fta lb/fta

Dry Met Metho hod d Wet Wet Me Meth thod od lb/ft~ lb/ft~ lb/ftaa lb/ft

Fine Sand Num be r of tests Range Average Standard deviation

14 92.9- 98.5 96.2 1.4

14 113.9-118.8 115.8 1.3

14 113.6-118.8 115.4 1.3

14 110.0-117.8 114.2 2.1

14 117.4-122.7 119.7 1.8

14 113.5-124.9 118.6 3.2

Medium Sand Num be r of tes ts Range Average Standard deviation

14 95.2-101.5 97.8 1.8

14 117 4-124.9 120.4 2.2

for the fine sand and 1.6 and 1.8 lb /f t 3 respectively respectively for the mediu m sand. I n comp compariso arison n sta ndar d deviations ranging from 1.9 to 2. 2.9 9 lb /f t ~ have been reported [22] for impact-type compaction tests on fine-grained soils. Of the two maxi mum densi ty proc procedur edures es the d ry met hod had t he lower lower standard deviations. This would be expected since the wet method is subject to the same sources of errors as the dry method plus those associated with the additi on of water. Also Also in only 3 of the 14 laboratories was was the maximum density obtained by the wet method. Thus it would appear th at the dry method was not only more more consis consistent tent but tha t it also gene generally rally produced the ma ximum density. However However this may not be entirely true. In the wet method the densi ty obtained is is related to the degree degree of satu rati on [10 24] as shown shown in Fig. 4 where the wet met hod dry dens densities ities are plot ted as a function of the water content. Also plotted in this figure are the degrees of sat ura ti tion on for a spec specif ific ic gravi gra vity ty of 2.6 2.65. 5. The Th e maj ori ty of specimen specimenss had degrees of saturation varying from 80 to 90 percent which would explain in part the lower densities and higher st and ar ard d deviat deviations ions as asso soci ci-ated with the wet method tests. It is interesting to note that the lower densities dens ities were obtained for the higher water contents indicati ng th at sufficient water was present to saturate the samples but that the entrapped air and excess water could not be vibrated free. This behavior would not normally be expected for the types of material tested because of the small amount of fines contained. Repeatabilit Repeatabil ityy Between Duplicat Duplicatee Tests---B y analyzing the results on the basiss of the dif basi differe ference ncess between duplicate tests the va riations in samples samples errors erro rs in equipme nt calibrations and differenc differences es in equipm ent performance are minimized and an indication of operator repeatability is obtained. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Li  

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V a r i a t i o n i n m a x i m u m d e n s i t y a s d et e t er er m in in e d b y w e t m e th th o d. d.

T h e r e s u l t s o f t h e s t a t i st s t i ca c a l a n a l y s e s o f t h e d u p l i c a te te m i n i m u m , a n d w e t and dry method maximum tests are presented in Table 4. The variations between duplicate tests are one half, or less, of the variations between laboratories and are in agreement with results reported b y o t h e r s fo fo r t h e s a m e t e s t p r o c e d u r e s [ 8 ] a n d f o r i m p a c t - t y p e c o m p a c t i o n

TABLE 4

V a r i a t i o n s be be tw tw e en e n d u p l i ca c a t e m i n i m u m a n d m a x i m u m d e n s i t y t e st st s. s.

Minimum Dry Density lb/f t ~

Maximum Dry Density Dry Method Method lb/ft 3

Wet Method lb/ft 8

18 O.5 O. 5

18 1.3 1. 1

18 1.0 0.9

17 1.2 I. 1

Fine Sand

Num ber of tes tests ts Aver age range Combined standar d deviation

18 O. 3 O. 2 Medium Sand

Num ber of tes tests ts Average range Combined Combin ed standard deviation

18 0.6 0.6

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70

R E L A T IV IV E

DENSITY

INVOLVING

COH ESIONLES S

S O I LS

t e s t s [1 7 2 6 ] . T h e m i n i m u m d e n s i t y v a r i a t i o n s a r e a l s o a b o u t t h e s a m e a s t h o s e o b t a i n e d b y a s i n g le le o p e r a t o r f o r s i m i la l a r m a t e r ia i a l s [ 3] 3] . T h e m i n i m u m

and dry method maximum test variations were smaller for the fine sand than for the medium sand; however the wet method m aximum test varia t io i o n s w e r e a b o u t t h e s a m e f o r b o t h s a nd nd s . T h i s i s a t t r i b u t e d t o t h e g r e a t e r s e n s i t i v i t y o f t h e d e n s i t y o f t h e f in in e s a n d t o c h a n g e s i n t h e d e g r e e o f s a t u r a t i o n [ 2 5 ] w h i c h o f fs f s e t t h e d if i f f er e r e nc nc e s b e t w e e n t h e m e d i u m s a n d samples.

Relative

ensity

I n t h e p r e c e d in i n g s e c ti t i o n t h e v a r i a t io i o n s a s s o c i a te te d w i t h t h e m i n i m u m and maximum density test procedures were discussed. Since these tests are t h e b a s i s f o r d e t e r m i n i n g t h e r e l a t i v e d e n s i ty t y t h e c o n c e r n in in t h e t e s t v a r i a t i o n s i s i n t h e i r i n fl u e n c e o n t h e c a l c u l a t e d r e l a t i v e d e n s i t y . I n F i g .... 5 the average minimum and maximum densities determined for the medium s a n d a r e p l o t t e d a s 0 a n d 1 00 0 0 p e r c e n t r e l a ti t i v e d e n s i t y r e s p e c t i v e ly ly . F r o m t h e s o li l i d l in in e jo j o i n i n g t h e s e t w o l i m i ti t i n g d e n s i ti ti e s t h e r e l a t i v e d e n s i t y o f a n y i n t e r m e d i a t e d e n s i t y c a n b e r ea e a d i ly l y d e t e r m i n e d . T h e d a s h e d l in in e s connect the plus and minus two standard deviation intervals about the minimum and maximum densities as determined for the medium sand. T h e o u t e r s e t o f l in in e s r e p r e s e n ts t s t h e b e t w e e n - l a b o r a t o r y v a r i a t io io n s a n d the inner set the duplicate test variations. Approximately 95 percent of the test results would be expected to fall within these intervals. For the extreme variations in both the minimum and maximum density a dry den sity of 110 lb /f t 3 could be reported as a relative d ensity varyin g from 4 0 t o 7 6 p e r c e n t o n a b e t w e e n - l a b o r a t o r y b a s is i s o r f r o m 5 2 to to 6 6 p e r c e n t i f t h e l im i m i t in i n g d e n s i ti t i e s w e r e d e t e r m i n e d b y a s i n g le le o p e r a t o r . Compaction control testing is usually conducted by one or more oper130,

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MA X IMU M D E N S IT Y S C A LE

V a r i a t io io n i n m i n i m u m a n d m a x i m u m d e ns ns itit i es es f o r m e d i u m s a n d s am am p le le s. s.

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

TIEDEM NN O N V RI BILI BILITY TY OF L BOR

TORY TEST RE RESUL SULTS TS

7

ators in the same laboratory. The variations that might occur can not be determined directly from this study since no one laboratory conducted a s u f fi f i c ie i e n t n u m b e r o f t e s t s. s . H o w e v e r t h e s e v a l u e s w o u l d b e e x p e c t e d to t o f a ll ll

between the two cases studied and at best would be like those for the d u p l i c a t e t e s ts t s . F o r a p a r t i c u l a r e n g i n e e ri r i n g fe f e a t u r e t h e m i n i m u m a l lo lo w able relative density would be that which experience or laboratory testing has shown to provide a satisfactory condition for the application involved. B e c a u s e o f t h e t e s t v a r i at a t io i o n s t h e a v e r a g e r e l a ti ti v e d e n s i t y w o u l d h a v e t o b e g r e a t e r t h a n t h e m i n i m u m a l lo l o w a b l e v a l u e. e. O n t h e b a s i s o f t h e d u p l i c a t e t e s t v a ri r i a ti t i o n s a n a v e r a g e r e l a ti ti v e d e n s i t y o f a p p r o x i m a t e l y 9 2 p e r c e n t w o u l d b e n e e d e d t o m e e t a c o m p a c t i o n r e q u i re r e m e n t o f n o t l es es s t h a n 8 5 p e r c e n t r e l a t i v e d e n s i ty ty . I n c l u d e d i n t h e t e s t r e s u l t s w o u l d b e a n u m b e r o f relative densities of 100 percent or greater. Since most compaction control thinking is oriented towards the concept o f p e r c e n t m a x i m u m d e n s i ty t y o r p e r c e n t P r o c to t o r t h is is m a y a p p e a r t o b e a l ar a r g e v a r ia i a t io io n . H o w e v e r i n t e r m s o f p e r c e n t m a x i m u m d e n s i t y t h e m i n i m u m a l lo l o w a b l e v al al u e w o u l d b e 9 7 p e r c e n t a n d t h e a v e r a g e 9 8 p e r c e n t w h i c h i s o n l y a v a r i a t i o n o f 1 p e r c e n t . T h e r e f o r e i n u si si n g t h e r e l a t i v e density concept for compaction control instead of the p ercent m aximu m density it is not on ly necessary to change the degree of com paction required bu t also the limits of acceptance. While these examples might be considered unrealistic since the extreme c o n d i t io io n s w e r e a s s u m e d t h e y d o i n d i c a t e t h e v a r i a t i o n s t h a t c o u l d o c c u r . It should be noted that the tests were performed in laboratories using the s a m e s t a n d a r d m e t h o d s a n d m o s t o f t h e o p e r a to t o r s o r t h e i r s u p e r vi v i s o rs rs h a d r e c e i v e d f o r m a l tr tr a i n i n g i n t h e t e s t p r o c e d u r e s . H a d t h e t e s t s b e e n performed by laboratories using different methods or by inexperienced o p e r a t o r s t h e v a r i a ti t i o n s w o u l d h a v e p r o b a b l y b e e n c o n s i d e ra r a b l y g re r e a t er er . In an ASTM cooperative relative density testing program reported in 1 95 9 5 8 [ 8] 8 ] f iv iv e m e t h o d s w e r e u s e d t o d e t e r m i n e t h e m i n i m u m d e n s i t y a n d six methods were used to determine the maximum density. The data obt a i n e d w e r e a n a ly l y z e d o n t h e b a s i s o f b e t w e e n - l a b o r a t o r y v a r i a ti ti o n s a n d the results are presented in Table 5. The standard deviations for the minimums are about the same as found for the Bureau laboratories; howe v e r t h e s t a n d a r d d e v i a t i o n s fo fo r t h e m a x i m u m s a r e c o n s i d e r a b l y h i g h e r v a r y i n g f r o m a b o u t 3 t o 6 l b / f t 3. T h e s e v a l u e s w o u l d c a u s e v e r y l a rg rg e variations in the relative density. A n o t h e r f a c t o r n o t c o n s i d e r ed ed i n t h i s p r o g r a m w a s t h e s e n s i t i v i t y o f t h e relative density to variations in the in-place dry density. For the sands tested a variation in dry d ensity of 1 lb /ft 3 corresponds to a variation in r e l at a t i v e d e n s i t y o f a b o u t 3 ~ p e r c e n t. t . O t h e r s t u d ie ie s [ 2 7 ] h a v e i n d i c a t e d t h a t t h e v a r i a t i o n i n r e l a t iv iv e d e n s i t y f o r a 1 l b / f t 8 c h a n g e c a n b e a s h i g h a s 5 p e r c e n t . T h u s s m a l l c h a n g e s in i n t h e in i n - p la la c e d r y d e n s i t y c a n g r e a t l y affect the calculated relative density. C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuc o ((UFPE) Universidade Federal de Pernambuco) pursuant to Licens  

7 2

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T I V ED ED E N S I T Y I N V O L V I N G C O H E S I O N L E S S S O I LS LS

T A B L E 5-5---Bet -Between-l ween-laborator aboratoryy vari variati ations ons in m in im um and m ax im um densi density ty tests. tests. M ini inimum mum D ensit ensityy

Maximum Density

8oil

Averag Aver age, e, lb/ft s

Standard Standa rd Deviation, lb/ft a

A ve ra ge , b / fta ft a

Standard Deviation, lb/ft 3 lb/ft3

1 2

90.8 100.4

1.6 2.1

112.0 121.7

4.3 2.9

3

98.2

1.5

124.0 124.0

6.3

Data obtai obtained ned from l~f. 8. Summary

B a s e d o n th t h e r e s u l ts ts o b t a i n e d f r o m t h e B u r e a u c o o p e r a t i v e t e s t p r o g r a m reported in this paper and other studies, it appears that the variations associated with the minimum and maximum density tests investigated are about the same as, or less than, those associated with the impact-type c o m p a c t io i o n t e s t. t . H o w e v e r , w h e n t h e r e s u l ts t s a r e u s e d to t o c o m p u t e t h e r e la la t i v e d e n s i t y , l ar ar g e v a r i a t i o n s c a n o c c u r . T h e m a g n i t u d e o f t h e s e v a r i a t i o n s pmaucst ti o bn e o rc oren sl ai dt ienrge dt hw e hpehny sui cs ai nl gb erheal avti iovre o df ecnoshi et ys i of no lre scso ns ot ri ol sl .l i n g t h e c o m Acknowledgments

T h i s s t u d y w a s c o n d u c t e d u n d e r t h e s u p e r v is is i o n o f C . W . J o n e s , H e a d , S p e c i a l I n v e s t i g a t i o n s a n d R e s e a r c h S e c t i o n , E a r t h S c i en en c e s B r a n c h . H . J . Gibbs is Chief of the Earth Sciences Branch. The cooperation of the personnel of the foUowing B ure au labo ratories wh o participated in this s t u d y i s a p p r e c i a t e d : E a r t h S c i e nc nc e s B r a n c h , D i v i s i o n o f G e n e r a l R e s e a r c h , D e n v e r , C o l o. o . ; G r a n d C o u l e e T h i r d P o w e r p l a n t C o n s t r u c t i o n O f fi fi c e , G r a n d Coulee, Wash.; Columbia Basin Project, Othello, Wash.; Chief Joseph Dam, Oroville, Wash.; Fresno CVP Construction Office, Fresno, Calif.; SCaanli a lai rf .s;o nS aCn i tLyu, i sN U , L l i f. f.L;u iLs a hUonni tt ,a nC VBPa,s i C n o Pa lrionjgeac,t , C C e vn.i;t , SCa cVr Pa m e notso BRa ni voes r, D i v i s io i o n , C V P , W i ll l l o w s , C a li l i f. f. ; M e a d C o n s t r u c t i o n O ff f f ic ic e, e, B o u l d e r C i t y , N e v . ; S o ld ld i er e r C r e e k D a m , C e n t r a l U t a h P r o j e c t , D u c h e s n e , U t a h ; S i lv lv e r J a c k D a m , C u r e c a n t i U n i t , M o n t r o s e , C o lo lo . ; S a n J u a n - C h a m a P r o j e c t , Chama, N. M.; Glen Elder Construction Division, Kansas River Project, Beloit, Kan.; and Fryingpan-Arkansas Project, Salida, Colo. References

[I] B urm ister, D. M., Proceedings, Am erican Society for T esting and M aterials, Vol. 48, 1948, pp. 1249-1268. [$] M cNeel, O. F., M echanical Dynam ic Com pacti paction on Experiments, Earth M ateri aterials als Laboratory Report No. E M -208, Bureau of R eclamation, Denver, Colo., M ay 19 1949 49.. Copyright by AST M Int l (all rights rights res reserved); erved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/printed nloaded/printed by (UFPE) U niversidade niversidade Federal de Pernambuco ((UFPE) Un iversidade iversidade Federal de Pernambuco) pursuant to License Agreem ent. No further repro repro  

TIEDEM NN

ON

V

RI BILITY OF

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BOR

T O R Y T E S T R E SU SU L TS TS

7

[3 ] P e t t i b o n e , H . C . , D e v e l o p m e n t o f a M a x i m u m D e n s i t y T e s t f o r C o h e s i o n le le s s S o i l by a Vibratory M ethod, Earth L abora tory Re port No. EM-557, Bureau of Reclam a t i o n , D e n v e r , C o l o .,., M a y 1 96 9 6 1. 1. [~ ] P e t t i b o n e , H . C . a n d H a r d i n , J . in i n C o m p ac a c titi o n o f S o i ls l s , A S T M , S T P 3 7 7, 7 , J u n e 1 9 64 64 ,

pp. 3-19. [ 5 ] H a r d i n , J .,. , L a b o r a t o r y T e s ts t s to t o R e f in in e t h e M a x i m u m D e n s i t y P r o c e d u r e f o r C o h e s io i o n l e s s S o i ls l s U s i n g a V i b r a t o r y T a b l e , S o i ls ls E n g i n e e r i n g B r a n c h R e p o r t N o . EM-697, Bureau of Reclamation, Denver, Colo., March 1965. [ 6 ] K o l b u s z e w s k i , J . J . , Proceedings, 2 n d I n t e r n a t i o n a l C o n f e r e n ce ce S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , V o l . 1 , J u n e 1 9 4 8 , p p . 1 5 88- 16 16 5 . [ 7 ] M a x w e l l , A . A . a n d B u r n s , C . D . , M i s c e l la la n e o u s L a b o r a t o r y T e s t s , S o i l C o m p a c [8 ] [9]

[10] [11] [ 1 2] 2]

[13] [ 1~ 1~ ] [15] [16] [17] [18] [19] [ 2 0] 0] [21]

t i o n I n v e s t ig i g a t i o n , R e p o r t N o . 5 , U . S . A r m y C o r p s o f E n g i n ee e e r s, s, W a t e r w a y s E x p e r i m e n t S t a t i o n , V i c k s b u r g , M i s s .,., J u n e 1 95 9 5 0. 0. F e l t , E . I . i n S y m p o s i u m o n A p p l i c a t i o n o f S o i l T e s titi n g i n H i g h w a y D e s ig i g n a n d C o nns tr tr uc u c titi o n, n, A S T M S T P 2 3 9 , 1 9 5 8 , p p . 8 9 - 1 1 0 . Sel i g, E. T. i n Proceedings, 2 n d P a n A m e r i c a n C o n f e r e n c e S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , V o l . 1 , J u l y 1 9 63 6 3 , p p . 1 2 99 - 14 14 4 . F o r s s b l a d , L . , I n v e s t ig ig a t i o n s o f S o i l C o m p a c titi on on b y V i b r a t i o n , C i v i l E n g i n e e r i n g a n d B u i l d i n g C o n s t r u c t i o n S e r i es e s N o . 3 4, 4, A c t a P o l y t e c h n i c a S c a n d i n a v i c a , S t o c k hol m , 1965. D ' A p p o l o n i a , D . J . a n d D ' A p p o l o n i a , E . , Proceedings, 3 r d A s i a n R e g i o n a l C o n f e r e n c e S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , V o l . 1 , S e p t . 1 9 6 7 , p p . 2 6 6 -2 -2 6 8 . W o o d w a r d - C l y d e - S h e r a r d a n d A s s o c ia ia t e s , R e s u l t s o f L a b o r a t o r y T e s t s o n S o i l Sam ples, in Detailed Investiga tion of Bolsa Island Site, App endix H, Bechtel, Oct. 1967. F o r s s b l a d , L . , Highway Research Record, N o . 1 7 7 , 1 9 6 7 , p p . 2 1 9 - 2 2 5 . Do bry, R . and W hitm an, R. V ., Densification of Sand by V ertical Vibrations in ' S t a n d a r d ' M o l d s , P r o g r e s s R e p o r t N o . 7 , S o i ls ls P u b l i c a t i o n N o . 2 51 51 , M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , D e e . 1 96 9 6 9. 9. D o v e , R . P . , W i l l i a m s o n , T . G . , a n d W a l s h , H . R . I . , Highway Research Record, N o . 284, 1969 , pp . 37- 50 . T r a v e n a s , F . , C a p e l l e , J . F . , a n d L a R o c h e l l e, e , P . , Canadian Geotechnieal Journal. V o l . 7, 7, N o . 3 7 , F e b . 1 9 7 0 , p p . 3 7 - 5 3 . S u m m a r y R e p o r t o f S o il il S t u d i e s , P o t a m o l o g y I n v e s ti t i g a t io i o n , R e p o r t N o . 1 2 -2 -2 , U . S . A r m y E n g i n e e r s , W a t e r w a y s E x p e r i m e n t S t a t i o n , V i c k s b u r g , M i s s . , 19 1 9 52 52 . T a v e n a s , F . a n d L a R o c h e ll l l e, e , P . , P r o b l e m s R e l a t e d to t o t h e U s e o f t h e R e l a t iv iv e D e n s i t y , R e p o r t S - 21 21 , D e p t . o f C i v i l E n g i n e e r i n g , L a v a l U n i v e r s i t y , Q u e b ec e c , 19 1 9 69 69 . Tiedemann, D. A., Variability of Lab oratory Relative Density and Gradation T e s t s , S o il i l s E n g i n e e r in in g B r a n c h R e p o r t R E C - E R C - 7 1 - 1 7 , B u r e a u o f R e c l a m a t i o n , Denver, Colo., Feb. 1971. Ben nett, C. A. and F rank lin, N. L., Statistical Analysis in Chemistry and the 9 5 4. 4. C h e m i c a l I n d u s t r y , W i l e y , N e w Y o r k , 1 95 M a n d e l , J . , Materials Research and Standards, V o l . 1 1 , N o . 8 , A u g . 1 9 7 1 , p p . 8 - 1 5

and 52. [ 2 2] 2 ] L i u , T . K . a n d T h o m p s o n , M . R . i n Proceedings, N a t i o n a l C o n f e r e n ce ce o n S t a t i s t i c a l Q u a l i t y C o n t r o l i n H i g h w a y a n d A i r f ie ie l d C o n s t r u c ti t i o n , U n i v e r s i t y o f V i r g i n ia ia , Ch arlottesville, Va., M ay 1966, pp. 375-395. [ 2 3] 3] T a v e n a s , F . A . , L a d d , R . S . , a n d L a R o c h e l l e , P . , T h e A c c u r a c y o f R e l a t i v e D e n s i t y M e a s u r e m e n t s : R e s u l ts t s o f a C o m p a r a t i v e T e s t P r o g r a m , i n c lu l u d e d i n th th i s symposium. [2~] E a r t h M a n u a l , B u r e a u o f R e c l a m a t i o n , F i r s t E d i t i o n , R e v i s e d i 9 6 3 , D e n v e r , C o l o . [ 2 5] 5 ] B r o m s , B . B . a n d F o r s s b l a d , L . i n Proceedings, S p e c i a l t y S e s s io io n 2, 2, 7 t h I n t e r n a t i o n a l C o n f e r e n c e S o il i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , A u g . 1 9 6 9 , p p . 1 01 0 1 -1 -1 18 18 . [ 2 6 ] S h e r m a n , G . B . , W a t k i n s , R . O . , a n d P r y s o c k , R . , Highway Research Record, N o . 177, 196 7, pp . 157-185. [ 2 7 ] L e e , K . L . a n d S i n g h , A . , Proceedings, A m e r i c a n S o c i e t y o f C i v i l E n g i n e e rs r s , V o l. l. 97, N o. SMT , Jul y 1971, pp . 10491049-1052. 1052.

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

Yoshiaki

Yoshim i 1 and Ikuo

Tohn o ~

Statistical Significance of the Relative ensity

R E F E R E N C E : Yoshimi, Yosh iaki and Tohno, Ikuo, Statistical Signific a n c e o f t h e R e l a t i v e D e n s i t y , " Evaluation of Relative Density and ts Role

in Geotechni Geotechnical cal Proj Project ectss Invol Involvi ving ng Cohes Cohesion ionle less ss Soi Soils ls A S T M S T P 523 A m e r i c a n Society for Testing an d M aterials, 1973, pp. 74-84. ie s o f l a b o r a t o r y t e s t s a n d a l i t e r a t u r e s u r v e y , A B S T R A C T : O n t h e b a s i s o f a s e r ie

t h e m a x i m u m a n d m i n i m u m d e n s it i t ie i e s f o r t h e d e t e r m i n a t i o n o f t h e r e l a t iv iv e density of sands involve random errors from a fraction of one percent to one p e r c e n t , a n d s y s t e m a t i c e r ro ro r s r e a c h i n g s e v e r a l p e r c e n t . C o n c e r n i n g r a n d o m e r r o rs r s i n d e n s i t y m e a s u r e m e n t s , t h e c o e ff ff ic ic ie ie n t o f v a r i a t i o n o f t h e r e l a t i v e d e n s i t y i s ex ex p r e s s e d a s a f u n c t i o n o f t h o s e o f t h e s p e c i m e n d e n s i t y a n d t h e l i m i t i n g d e n s i t ie ie s . F o r g i v e n d i s p e rs r s i o n i n t h e d e n s i ti ti e s , t h e c o e ff f f ic ic ie ie n t o f v a r i a t i o n o f t h e r e l a t i v e d e n s i t y i n c r e a s e r a p i d l y a s t h e r e l a t i v e d e n s i t y d e c r ea e a s e s. s. A numerical analysis of the influence of systematic errors in the limiting d e n s i ti ti e s o n t h e r e l i a b i l i t y o f t h e r e l a t i v e d e n s i t y s h o w s t h a t t h e r e l a t i v e d e v i a t i o n i n t h e r e l a ti t i v e d e n s i t y m a y r e a c h t e n s o f p e r c e n t if if a r b i t r a r y m e t h o d s are used. I n v i e w o f t h e s e n s i t i v i t y o f th th e r e l a t i v e d e n s i t y t o v a r i a t i o n s i n t h e d e n s i t y measurem ents, the need for rigidly standa rdized test m ethods for the limiting d e n s i t ie i e s i s e m p h a s i z e d , a n d c r i t e r i a f o r th th e s t a n d a r d m e t h o d s a r e s u g g e s t e d . K E Y W O R D S : e o h e s i o n l es e s s s o i ls ls , d e n s i t y ( m a s s / v o l u m e ) , c o e f f ic ic i e n t o f v a r i -

a b i l i ty t y , e r r o r a n a l y s i s , sa sa n d s , t e s t s

I t h a s b e e n r e c o g n i z e d t h a t s m a l l ch a n g e s in th e m i n i m u m d e n s i t y o r i n t h e s p e c i m e n d e n s i t y c a n c a u s e c o n s i d e r a b le v a r i a ti o n s i n t h e r e l a t i v e d e n s i t y . T h i s f a c t p l u s t h e l a c k o f r i g id l y s t a n d a r d i z e d

procedures for

d e t e r m i n i n g t h e m i n i m u m a n d m a x i m u m d e n si ti es t e n d s to d e t r a c t f r o m t h e r e l ia b i l it y o f t h e r e l a t i v e d e n s it y . I n t h i s p a p e r t h e a u t h o r s i n t e n d t o s h o w h o w t h e r e l a t i v e d e n s i t y i s i n fl u en c e d b y r a n d o m

and system atic

e r r o r s i n th e l i m i t i n g d e n s it i e s a n d t h e s p e c i m e n d e n s i t y . 1Professor and assistant, respectively, To kyo Ins titute o f Technology, O-oka yam a, Meguro-ku, Tokyo, Japan. 74

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Y O S H I M I A N D T O H N O O N S T A T IS IS T IC IC A L S I G N I F IC IC A N C E

7

F a c t o r s A f f e c t i n g t h e R e l i a b i l i ty ty o f R e l a t i v e D e n s i t y The relative d ensi ty of a given soil soil,, D ~ is computed from from the maximum dry density, y . . . . the minimum dr y density, Ym Ymin, and the dry density

of the specimen, y(the usual subscript, d, being dropped for the sake of simplicity) as follows: D.

=

1/~m ,. 1/~m l. -

1/~ 1/~x

=

~m~x ~ ~ ~m.~ --

~i~ )

I)

~i~

In this paper Eq 1 is preferred to the alternative form in terms of the void ratio, D~ = (em~ - e) e)/( /(em em~z ~z - em emi~ i~), ), because th e dr y de nsi ty is related mor moree directly to measured quantities quantities tha n the void ratio. ratio. The dry density is is computed from two measured quantities, quantities, th at is is,, the dr y weight and th e volume of the soil, soil, both of which involve ran dom errors inherent in any measurement. In addition to the ra ndom erro errors, rs, there may be systematic errors due to lack of rigidly standardized methods for the determinat ion of the maximum and minimum densitie densities. s. Because the relative density of a given given so soil il is proportional to (~ - ~i n) /~ ', even a small vari ati on in Ymi~ or in 7 ma y cause a considerable var ia iati tion on in the relative relative density when r - ~ , is sma small, ll, th at is, is, when the relative relative dens ity is lo low. w. For example, when ~m ~mi~ = 1.350 g/ cm 3, y ~ = 1.63 1.637 7 g/ cm cm3 3, and ~/= 1.4 1.425 25 g/c m 3, th e relat ive den si sity ty is 30 30.0 .02 2 percent. If ~/ ~/~i ~i~ ~ is increased increase d by 1 percent t o 1.3635 g/ cm cms, s, the relative density becomes 25.83 percent which is 14 percent lower than the initial value. Thus, the relative deviation in the relative density is 14 times tha t in the minimum density, th at is is,, AD~/D~ = - 14.0Ay~in/5'ml~ 14.0Ay~in/5'ml~ (2) The fact tha t the relative densit y is sen sensitiv sitivee to variations in the density measurements measurem ents has prompted the authors to exam examine ine the reliab reliability ility of the relative density.

Random Errors in Dry Densities S p e c i m e n D e n s i t y - - T h e precision of measurements of the volume and dry weight for the determination of the specimen density may be different for the la borat ory and fiel field d cond conditions. itions. For a careful research in the labora TABLE l--P hy sica l propert properties ies of soils. Soil So il

Grain Sh Shape ape SpecificGravity SpecificGravity Effective EffectiveSize, Size, Uniformity of Solid Solids, s, G, D10 ( m m ) Coe ffic Coeff icie ient nt,, ~

Toyoura Toyo ura s a n d

roun ro unde ded d

2.65 2.6 5

0.14 0. 147 7

1.39 1. 39

Tokyo Tok yo s a n d

subang sub angula ula r

2.73 2. 73

0.17 0. 178 8

1.68 1. 68

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7

REL

TABLE 2

Soil

T IV I V E D E N S IT I T Y IN IN V O L V I N G

C O H E S I O N L ES E S S S O IL IL S

Coe~ci Coe~ cient entof variation of m ax im um dry density determined determined by verti vertical cal vibrat vibration ion with no surcharge.

No. of Te sts

Ma x i mu m D ry D en s i t y

Mean, g/c m 3

Standard Dev iati iation, on, g/cm*

Coefficie Coeffic ient nt Ra nge/M ean, of Variation,

To you ra sand

16

1.538 1.5 38

0.0035 0.0 035

0.23

0.8

To kyo sand Quartz sand ~

16 12bb 12

1.423 1.4 23 1.6 1.615 15

0.0075

0.53

1.9 2.4

~ Specifi Specificc gra vity -- 2.64 ; mesh 10-60; subangular. subangular. b c c e l e r a t i o n -- 1.31 g; frequen cy = 32 Hz . t o r y u s in i n g c o m p a c t e d s p e c im im e n s , b o t h t h e v o l u m e o f t h e c o n t a i n e r a n d t h e d r y w e i g h t c a n b e m e a s u r e d w i t h s u ff f f ic i c i en en t a c c u r a c y . O n t h e o t h e r h a n d , f ie i e ld l d m e a s u r e m e n t s o f u n d i s tu t u r b e d s p e c im im e n s o r t h e i n s i t u m e a s u r e m e n t s o f d e n s i t y m a y i n v o lv l v e c o n s i d e ra r a b l y g r e a t e r e r ro r o r s. s. L a b o r a t o r y t e st s t s w e r e c o n d u c t e d t o e v a l u a t e t h e v a r i a t io i o n s i n t h e l i m i ti ti n g d r y d e n s i ti t i e s o f T o y o u r a s a n d a n d T o k y o s a n d w h o s e p h y s ic i c a l p r o p e rt r t ie ie s a r e g i v e n in in T a b l e 1. M a x i m u m D e n s / ty t y - - -F - F o r t h e m a x i m u m d e n s it it y , o v e n - d r y s a n d w a s p l a c e d i n a c o m p a c t i o n m o l d ( 10 1 0 0 m m i n d i a m e t e r a n d 1 27 2 7 m m d e e p ), ), a n d s u b j e c te t e d t o v e r t ic i c a l v i b r a ti t i o n w i t h o u t s u r c h a r g e a t a n a c c e l e r a t io io n o f 2 . 0 g a n d a f r e q u e n c y o f 4 2 . 5 H z f o r 1 0 r a in in . A c c o r d i n g t o p r e v i o u s s t u di d i e s [ 11 - 3] 3] 2 t h e p r o c e d u r e j u s t d e s c r i b e d w a s e x p e c t e d t o g i v e a d e n s e p a c k i n g w i t h o u t c r u s h i n g t h e s oi o i l p a r ti t i c le le s . A s s h o w n i n T a b l e 2 , t h e c o e ff f f ic i c i en en t o f v a r i a t i o n o f t h e m a x i m u m d e n s i t y f o r 1 6 t e s ts t s e a c h o n T o y o u r a a n d T o k y o s a n d s w a s i n th t h e o r d e r o f a f r a c t io io n of one percent. Also given in the table is the result of 12 tests on a quartz s a n d b y D o b r y a n d W h i t m a n [ 1 ] , s h o w i n g a si s i m i la l a r d e g r e e o f d i sp s p e r si si o n . M i n i m u m D e n s i ty F o r t h e m i n i m u m d e n s i t y , t h e t i l t i n g t e s t a n d t h e s p o o n t e s t [ 4, 4, 5 ] w e r e c o n d u c t e d . I n t h e t i l t i n g t e s t , a fi fi x e d q u a n t i t y ( w e i g h t) t ) o f o v e n - d r i e d s a n d w a s p l a c e d i n a 1 0 0 00- m l g r a d u a t e , w h i c h w a s s l o w l y t i l te te d s e v e r a l t i m e s h o l d i n g o n e h a n d o v e r t h e o p e n e n d , a n d t h e v o l u m e w a s r e a d d i r e ct c t ly l y . I n t h e s p o o n t e st st , o v e n - d r i e d s a n d w a s p o u r e d g e n t l y i n a c o n t a i n e r ( 5 9. 9 . 93 9 3 m m i n d i a m e t e r a n d 3 9 .6 .6 5 m m d e e p ) f r o m a n e g l ig i g i b le l e h e ig i g h t . A f t e r t h e c o n t a i n e r h a d b e e n f il i l le le d a b o v e t h e r i m , e x c e s s s a n d w a s r e m o v e d b y q u i c k l y sl s l id i d i n g a s t ra ra i g h t e d g e , t a k i n g e x t r e m e c a r e not to jar the container. Then the sand in the container was weighed. T h e r e s u lt l t s of o f t h e m i n i m u m d e n s i t y t e s ts ts a r e s u m m a r i z e d i n T a b l e 3 . A l l t h e d a t a b y t h e t i lt lt i n g t e s t w e r e o b t a i n e d u s i n g o n e m e a s u r i n g c y l i n d e r . Th e ital italic ic num bers in b racke ts refer to the list of refe references rences appended to this paper.

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Y O S H I M I A N D T O H N O O N S T A TI TIS T IC IC A L S I G N IF IF IC IC A N C E

Therefore, there m ay be additional varia tion due to errors in volum e g r a d u a t i o n s i f d i ff f f e r en e n t c y l i nd n d e r s a r e in in v o l v e d . S u c h v a r i a t i o n m a y b e r o u g h l y e s t i m a t e d o n t h e b a s i s o f t h e t o l e r a n c e o f th t h e g r a d u a t e . B e s iidd e s, s,

the precision in reading the volume of dry sand in the cylinder is rather p o o r , a n d t h e r e i s m a r k e d s e g r e g a t i o n o f s o il i l g r a i n s. s. T h u s , t h e o v e r a U r e l ia i a b i li l i t y o f t h e t i l ti ti n g m e t h o d is p r o b a b l y n o t a s g o o d a s T a b l e 3 m a y indicate. F o r T o y o u r a s a n d , t h e s p o o n t e s t y i e ld l d e d s m a l le le r s c a t t e r t h a n

the

t i lt l t i n g m e t h o d , a l t h o u g h t h e m e t h o d o f t e s t h a d l it i t tl t l e in i n f lu lu e n c e o n t h e m e a n v a l u e. e . F o r T o k y o s a n d , h o w e v e r , t h e s p o o n t e s t y ie i e l d e d 2 to to 3 p e r c e n t s m a l l e r m e a n v a l u e s t h a n t h e t i l ti t i n g te te s t , a l t h o u g h t h e m e t h o d o f t e s t h a d l i t t l e i n f l u e n c e o n t h e c o e f f ic ic i e n t o f v a r i a t i o n . A s a w h o le l e , T a b l e 3 s h o w s t h a t t h e c o ef e f fi f i c ie ie n t o f v a r i a t i o n o f t h e m i n i m u m d e n s i t y m a y b e c o n s i d e re re d t o b e f r o m a f r a c t i o n o f o n e p e r c e n t t o o n e percent.

Systematic Errors in Dry Densities A s y s t e m a t i c e r r o r i n t h e s p e c i m e n d e n s i ty t y m a y a r is is e f r o m l a c k o f p r o p e r c a l i b ra r a t i o n o f m e a s u r i n g i n s t r u m e n t s o r f r o m i m p r o p e r h a n d l in in g T A B L E 3 Coe~w ient of variat variation ion of minimu m dry density. density. S o ilil

Toyoura

s

Method Tech- No. of nician nici an a Te sts

nd

Tokyo sand

M i n im im u m D r y D e n s i t y

D r y W e i gh gh t of Specimen, Mean, Sta nd ard Coeffic Coefficient ient g g / c m 3 De viation, of Variag / c ma tion,

tilting

B B B B

16 16 16 16

1.38 1.37 1.36 1.36

0.0146 0. 0146 0.0061 0. 0061 0.0072 0. 0072 0.0045 0. 0045

1 .06 0.45 0.53 0.37

spoon

A B C

17 15 16

1.349 1. 356 1.353

0.0031 9.0038 0.0C ,52

0.2 3 0.2 8 0.4 6

tilting tilt ing

A A A A B

16 16 16 16 16

1.23 1.24 1.24 1.23 1.23

00.0 .0060 060 0.0067 0. 0067 0.0072 0. 0072 0.0077 0. 0077 0.0068 0. 0068

0.49 0.54 0.58 0.63 0.56

spoon

A B C

19 15 18

1.202 1.212 1.210

0.0099 0.0114 0.0078

0.8 3 0 .94 0 .65

353.1 406.5 484.3 555.5

320.5 386.1 438.4 481.0 437.1

-- skill skilled ed geologi geologist; st; B = gra du ate stud ent in engineer engineering; ing; C -- you ng wo m an w ith no technical background.

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  8

RELATIVE RELA TIVE DENSITY INV INVOLV OLVING ING COHE COHESIO SIONLE NLESS SS SOIL SOILS S

TABLE 4--Systsmatic errors in density measurements. Cause of Errors

A~//~, %

AT

axl

~ .. . %

h-~i=/ ~=~., ~=~ ., %

Ref

Remarks

Shock during handling Lack La ck of experi experience ence Surcharge on soil Insufficient acceleration below optimum Excess acceleration above optimum Insufficient Insufficie nt frequency below optimum Excess frequency above optimum Saturation (acceleration = 1.3 g) Saturati Satu ration on (acc (accele elerati ration on = 3.5 g) Moisture Crushing of soil grains Segregation of soil grains

+

+2 -t-1

-4--5 -5 --5

[2] [2] [1,, 3][1 [1,, 3] [1

--

[3]] [3

--

[3]] [3

-8

[1]

-44-4 4

[1]] [1

--t--t

[1]] [1

vertical vibration with zero surcharge

of soil specimens prior to measurements. Although the former, of course, should be avoided, the latter may be unavoidable when undisturbed specimens of loose cohesionless soils are involved. As long as different methods are used for the determination of the limiting densities, there may be systematic errors of considerable magnitude. Probable causes of the systematic errors are listed in Table 4, with rough estimates of the relative deviations where data are available. The systematic errors may be defined as deviations from the density values determined with an ideal metho d which which is yet to be est establ ablish ished. ed. Influence

of

Rand om

E r r o rs

in

Dry

Densities

on

the

Relative

Density

According to statistics the stan dard deviation of the relati relative ve density, SDr, can be expressed as a function of the standard deviations of the dry densitie s, S ~ , S~mi S~ min n, an d S~, S~, as follows [6] [6]::

3)

\ 0~

From Eqs 1 and 3 the following expression is derived: 2D. = C 2~v

~~=

C ~~ v

2~, ~

4)

C~v~ 2

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YOSH IMI AN D TO HN O

ON

S T A T IS IS T IC IC A L S I G N IF IF I C A N C E

79

in which S r r

v~ .= -- ,

S~ Tmax

x

v ~ ,~ ,~ ,. =

S ~m ~ m in in Train

,

S~

v~ = --

T

( 5 a) a)

C .1,m a x

~

Ym n

~ma x

--

groin

, ,,, , ,,, , ~ , , x 1 - C , y , = , ,,, ,

=

(y ....

--

D ,)

1 --

, /m /m , ~ , ) D ,

=

( C ~ , = , ,,, , , - t -

7 m~ C'z =

( ') ' ) 'm 'm a x - -

C~ ,+

~/m in)D r

--

1

1)

5b)

D - -- -~ 1

D

=

D,

--

1

The terms v's give the coefficient of variation, and C s may be called the e r r or o r p r o p a g a t i o n f a c t o r s. s. Equations 5b show that the error propagation factors for the minimum d e n s i t y a n d s p e c i m e n d e n s i t y , C ~ m i, i, a n d C ~ , i n c r e a s e a s D , d e c r e a s e s u n t i l t h e y b e c o m e in i n f in i n it i t e w h e n D r e q u a l s z er e r o, o, w h e r e a s C ~ is independent o f D ~. ~. T h e e r r o r p r o p a g a t i o n f a c t o r s a r e p l o t t e d i n F i g . 1 a g a i n s t D T f o r C ~ x = 4 . 7 w h i c h i s s e l ec e c t e d a s a r e p r e s e n t a t iv i v e v a l u e f o r c l e an an s a n d s having low uniformity coefficients [4, 7]. 5

tfl

n,, 0

25

0

2 Z 0

V 15 0 n,. n 0

O

W

20

40

RELATIVE

FIG.

60 DENSITY,

80

OO

Dr,%

1 E r r or propagat propagation ion fact factors for rela relattive de density. nsity.

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80

R E L A T IV IV E D E N S IT IT Y I N V O L V I N G C O H E S IO IO N L E S 5 S O IL IL S

I n a s p e c i a l c a s e i n v o l v i n g e q u a l c o e f f i ci ci e n t s o f v a r i a t i o n , t h a t i s , v ~ . = = v ~ . i . = v~ , E q 4 y i e l d s

v~,

=

~Tmsx ~Tms x

v~,

=

VTmin VTmi n

v~__z~=

0

=

~ /C ~ ,.

+

C 2 ~ m l.l . +

C~

(6)

V

T h e v a l u e o f C i s c o m p u t e d f o r t h e c a s e w h e r e C , . = = 4 .7 .7 , a n d t h e r e s u l t is plotted in Fig. 2 against the relative density.

Required Num ber of M easure easurements ments for the D ry Densit Densities ies

I t c a n b e s e e n i n F i g . 2 t h a t t h e c o e ff f f ic i c i en en t s o f v a r i a t i o n o f t h e d r y d e n s i t ie i e s m u s t b e li li m i t e d t o a s m a l l v a l u e i f o n e w i s h e s t o a t t a c h q u a n t i t a t i v e s ig i g n i fi fi c an a n c e t o t h e r e l a t i v e d e n s i t y o f l o o s e s a n d s , a s i n t h e l iq iq u e f a c t i o n p r o b l e m w h e r e t h e c y c li l i c s h e a r s t r e s s r e q u i re r e d t o c a u s e li li q u e f a c t i o n i n s a t u r a t e d s a n d i n a g i v e n n u m b e r o f s t r e s s c y c le l e s f o r a g i v e n i n i ti ti a l c o n fi f i n in in g s t r e s s is is r e p o r t e d t o b e p r o p o r t i o n a l t o t h e r e l a t i v e d e n s i t y [ 8 , 10] I n o r d e r t o r e d u c e t h e c o e ff f f ic i c i en e n t o f v a r i a t i o n o f t h e d r y d e n s i ti ti e s , o n e must first eliminate any systematic errors by establishing rigidly standardized procedures. That having been achieved, one can reduce the standard d e v i a t i o n b y i n cr c r e as a s in in g t h e n u m b e r o f m e a s u r e m e n t s f o r e a c h o f t h e d r y d e n s i t ie i e s a c c o r d i n g t o t h e f o ll l l o w i n g r e l a ti ti o n s h i p : ~

=

~/~ /m

( 7)

in which a is the stand ard dev iation of a population, m is the nu m be r of m e a s u r e m e n t s ( or o r s p e c i m e n si s i z e ) , a n d Sm Sm d e n o t e s t h e s t a n d a r d d e v i a t i o n of the m ean of m measurem ents. I f t h e c o e ff f f ic i c i en e n t o f v a r i a t i o n o f t h e r e l a t i v e d e n s i t y m u s t b e l im im i t e d t o

I

80 60 40

-

~ 'm 'm l n

~

rm ox -r,.,,

i

20

,- 4 7

--

f

i

|0 8 6 4

0

20

40

60

80

RE L A TIV E DE NS ITY , FIG. 2

Rat/o

I00

D ,

o f coeffwient o f variati variation on of relative relative density to that that of dry d ens ity

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YOSH IMI AND T OH NO ON STA STATI TIST STIICAL SI SIGNIRCA GNIRCANCE NCE

40

v 20

\\\\

-

= v =; v . . ~ m ln ~'m .x ~ ' , .i .

4

7 -

81

,o

2 -< \'\~

\\ \

m

20

4

0

40

R EL E L AT A T IV IV E

'- 4

~

60

DE NS ITY.

80

IO O

D r,

FIG. 3- -N um be r of measurements required for a given coe.ff coe.ffwient wient of variation variation of relative relative

density.

v'D,, each of the coefficients of variation of the dry densities must be limited to V j , / C , pr ov ovii de ded d t h a t V~m~x= V~mln= V~. On t h e ba basi siss of Eq Eqs 6 and 7, the number of measurements for each of the dr y densities is given given by m

=

r

~

8)

Th e re rela lati tions onshi hip p of Eq E q 8 is ev eval alua uate ted d for f or ~'ml ~'mln/(Tm n/(Tm~ ~ -- 7mi,) ------4.7 an d plotted in Fig. 3. For example, if D, = 50 percent, v'j), = 5 percent, and v~ = 1 percent, seven tests each must be made for th e maxi mum, minimum, and specimen densities, and the mean value must be used for the determination of the relative density from Eq 1. For the same combination of v'D, and v~, the required number of measurements will be two if D , = 85 percent, an and d 40 40 if Dr = 22 percent. I n f l u e n c e o f S y s t e m a t i c E r ro r o rs rs i n

ry

ensities on Relative

ensity

There has been a considerable accumulation of information on the relationship between mechanical properties properties of granular soils soils and the relativ e density [9]. But difficulty arises when test data by different researchers are compared, because different methods for the maximum and minimum densities are are often involved. If two different methods give different values of the limiting densities for the same soil, the difference constitutes a systematic error error which cannot be treat ed statistically. The relative deviation deviation in the relative density, A D , / D , , due to a deviation in any a ny one of th thee d ry densities, Aym~x, &Y~n, A ma y be derived from

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82

RELATIVE RELATI VE ENSI ENSITY TY NV OL VING COHESIONLESS OILS

E q 1 , a n d e x p r e s s e d a s f o l lo lo w s : 7min

Dr

A7min_AT~ 0

7~ ,x

--

7 r a in in J r A T m a x

A7max 7max

9a)

: _

. : .

~,~ ---,,~o

D, Tm.x

AD__rZ

=

D , J ~ T~ - -~ -~ Tm i .-.- -O -O

--

7rain

--

7rain

A Ttain)

7 )'m i. A7 (7 -- 7m ~.)(7 + A 7) 7

(9 c )

T h e p r e c e d i n g e q u a t i o n s a r e re r e d u c e d t o t h e f o l lo lo w i n g f o r m i f A ) m , = a n d h T m ln ln a r e n e g l ig i g i b le l e c o m p a r e d t o 7 m a ~ - 7 ra ra in in , a n d i f ~ 7 i s n e g l ig i g i b le le compared to 7:

A D ,]

C T . ,., . ATm,______

A T m i n ~ A T==0,A T==0,A Tm a x( (T (T n ~ x .-.- - T r ai ai n

10a)

7max

A'Tmin / rJ

A T m a ~ A 7 ~ 0 , A T ra r a in in (( (( T m a r . . T ra r a in in

1 0 b)

7 m in

~D._~__.rl ~D._~__. rl / ) , J A Tn~x= = ATm ATm i n~0 , A T(< T(< , ,

~ C 7 A.... A....~. ~.~~ 7

10c)

in which C s are the same as the error propagation factors of Eq 5b.

w rT

5o

I

D r " 5 0% r =30 %

X ; o l t /// /

jail 30

--

- - / -J -J l

/

//~r'~

7 1 r f 20

) ///

0 s

--

I00%

t/I/ 9 D

=

/ 0

0

2 I A tilt

FIG.

/

0

2

4

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T h e r e l a t i o n s h i p o f E q 9 is i s s h o w n i n F i g . 4 i n f u ll l l l in in e s , a n d t h a t o f E q 10 in dashed lines. It is evident in the figure that for small deviations in t h e d r y d e n s i ti ti e s , s a y l e s s t h a n 1 p e r c e n t , t h e f u l l l in i n e s a g r e e c l o s e ly ly w i t h the dashed lines. Although the full lines diverge from the dashed lines at g r e a t e r r e l a t i v e d e v i a ti t i o n s , E q 1 0 c a n s t il il l g i v e a c o r r e c t o r d e r o f m a g n i t u d e o f 5Dr/D~. T h e n u m e r i c a l e x a m p l e o f E q 2 is i s c h e ck ck e d b y s u b s t i t u t i n g 7mi, = 1. 1.350 350 g /c m 3, 7m,x = 1. 1.637 637 g /c m ~, D~ = 30.02 pe rce nt, a nd AT~i, = 0 . 01 0 1 3 5 g / c m a i n t o E q 9 b. b. F o r t h e c a s e i n w h i c h b o t h m a x i m u m a n d m i n i m u m d e n s it i t ie ie s a r e s u b j e c t to deviations while the deviation in the specimen density is ignored, the r e l a t i o n s h i p a m o n g hD /D~ h T ~ x / T m , ~ , a n d A T m i n / Y m i n i s e v a l u a t e d f r o m E q 1 f o r D ~ = 5 0 p e r c e n t a n d C , m ~ . = 4 .7 .7 , a n d t h e r e s u l t i s p l o t t e d i n F i g . 5 , a s a f a m i l y o f c o n s t a n t ~ D /Dr. I f ~ 7 m = / Y ~ a ~ = A Y m i - / 7 ~ , AD /D~ i s a p p r o x i m a t e l y 1 0 t i m e s t h e r e l a t i v e d e v i a t i o n s o f t h e l i m i t i n g d e n si s i ti t i es e s . O n t h e o t h e r h a n d , i f A v ~ , ~ / v m ~ = - ~ 7 ~ i , / 7 ~ i = , AD~/Dr i s s m a l l d u e t o f o r t u i t o u s c a n c e l l a ti t i o n o f e r ro ro r s . I n v i e w o f r e l a ti t i v e l y la l a r g e v a l u e s o f ~ 7 ~ o r a ~ /m /m in in a s i n d i c a t e d i n T a b l e 4 , it it i s c o n c e i v a b l e t h a t ~ / D ~ m a y r e a c h t e n s o f p e r c e n t . I f , f o r e x a m p l e , re l a t i v e d e n s i t y o f 5 0 p e r c e n t r e p o r t e d b y t w o AD~/D~ = : i:i : 2 0 p e r c e n t , a re r e s ea e a r c h e rs r s u s in i n g d if i f f e re re n t m e t h o d s f o r 7 m ~ a n d 7 ~ = m a y r e a l l y r e p r e s e n t 4 0 a n d 6 0 p e r c e n t . Q u a n t i t a t i v e c o m p a r i s o n o f s u c h r e l a t iv i v e d e n s i t ie ie s s h o u l d b e d o n e w i t h g r e a t c a u ti ti o n .

r it i t e ri ri a o f L i m i t i n g D e n s i t y T e s t s I n v i e w o f t h e f a c t t h a t t h e r e l a t i v e d e n s i t y i s s e n s i ti ti v e t o s m a l l c h a n g e s in the limiting densities, it is essential that a rigidly standardized test m e t h o d b e es e s t a b li li s h e d f o r e a c h o f m a x i m u m d e n s i t y a n d t h e m i n i m u m C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n te te d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e  

8

RELATIVE RELATI VEDENSITY DENSITY INV OL VIN G COHESIONL COHESIONLES5 ES5 5OILS

d e n s i ty t y . I n s e l e c ti t i n g t h e s t a n d a r d m e t h o d s , e m p h a s i s sh sh o u l d b e p l a c e d m o r e o n m i n i m i z i n g d i sp s p e r s io i o n t h a n o n o b t a i n i n g t h e a b s o lu lu t e m a x i m u m a n d m i n i m u m d e n si s i ti t i es e s . T h e s t a n d a r d t e s t s h o u ld l d s a t i sf s f y t h e f o llll o w in in g conditions:

1 . T h e t e s t s h o u l d b e f r e e f r o m c r u s h i n g o f t h e s oi o i l p a r t i c le le s , s o t h a t t h e test can be repeated on the identical specimen. 2. The density should be as insensitive as possible to variations in the test conditions. 3 . T h e t e s t s h o u l d b e e a s il i l y r e p r o d u c i b le l e b y a t e c h n i ci ci a n o f o r d i n a r y skill. T o e n s u r e t h a t t h e t e c h n i c i a n h a s t h e r e q u i r e d s k i ll ll , i t w o u l d b e d e s i r a b l e t o e s t a b l i s h a c o n t r o l t e s t i n w h i c h a s t a n d a r d v a l u e o f l i m i t i n g d e n s i ti ti e s a r e t o b e o b t a i n e d o n a n i d e n t ic i c a l s p e c i m e n s u p p l ie ie d f r o m t h e s a m e b a t c h . onclusions

T o i m p r o v e r e l i a b i l i ty t y o f t h e r e l a t i v e d e n s i t y o f g r a n u l a r s oi o i l s, s , i t is is e s s en e n t ia i a l t h a t r i gi g i d ly l y s t a n d a r d i z e d t e s t s b e e s t a b li li s h e d f o r t h e m a x i m u m a n d m i n i m u m d e n s it i t ie i e s . F o r l o w r e l a t i v e d e n s i ti t i e s, s , i t is i s a l so so n e c e s s a r y t o m a k e s u ff f f ic i c ie i e n t n u m b e r o f m e a s u r e m e n t s f o r th t h e l i m i t in i n g d e n s it i t ie ie s a n d t h e s p e c i m e n d e n s it i t y , t h e r e q u i r e d n u m b e r b e i n g d e t e r m i n e d o n t h e b a si si s o f statistics. References

[I] Dob ry, R. and W hitm an, R. V., Densifi Densificati cation on of Sand by Vertical Vertical Vibrati Vibrations ons in 'Sta nda rd' Molds, Resea Research rch R epo rt R70-05 R70-05,, Soils Publ Public icati ation on No. 251, M assachu setts Ins titu te of Technology, Cambridge, 196 1969. 9. [2] D'Appoloni D'Appolonia, a, D . J. and D'Appoloni D'Appolonia, a, E ., D eterm ination of the Ma xim um De nsity of Cohesionless Soils, Proceedings, 3rd Asian Regional Conference on Soil M ech anics an d F oun dation Engineer Engineering, ing, VoL 1, 1967, pp. 266-268. [3] Selig, E. T., Eff ect of Vibrat Vibration ion on D ens ity of San d, Proceedings 2 n d P a n a m e ri can Conference on Soil Mechanics and Fo und ation Engineer Engineering, ing, Vol. 1, 1, 1969, pp. 129-144. [4i] Hutchins Hutchinson, on, B. and Tow nsend, D., So m e G rading -D ensity Relati Relationship onship fo r San ds, Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, 1961, pp. 159-163. [5] Ko lb l b u sz sz e wsk wsk i,i, J . J . , An E x p e ri m e n t al S t u d y o f t h e M a x i m u m a n d M i n i m u m Porositi Porosi ties es of Sands, Proceedings 2nd Inte rna tion al Conference on SOil Mechanics and Fou nda tion E ngineer ngineering, ing, Vol. 1, 1948, pp. 158-165. [6] Worthing, A. G. and Geffner, J., Treatmen t of Experimental Da ta Wiley Wiley,, New Y ork, 1943, pp. 205-214. [7 ] W h i t m a n , R . V. , H y d ra u l i c F i l ls l s t o S u p p o rt S t ru ct u ra ra l L o a d s , Journal Soil Mechanics a nd F oun datio n Divisi Division, on, Am eri erican can Society of Civil Engineer Engineers, s, V ol. 96, No. SM 1, 1970, pp. 23-47. [8]] Lee, K . L. an d Seed, H . B., C yc lic Stress Conditions C ausing Liquefaction [8 Liquefaction of S an d , Journal Soil Mechanics and Foundation Division, American Society of Civil Engineers, Vo l. 93, No. 1, 1967, pp. 47 -70. [9] Lambe, T. W. and Whitman, R. V., Soil Mechanics Wiley New York, 1969. [10] L e e, e , K. L . an d S in i n g h, h, Awt a r, R el at i v e Den s i t y a n d R e l a t iv i v e C o m p a ct i o n , Journal Soil Mechanics a nd F oun dation Divisi Division, on, Am eri erican can Society of Civil En gineers, V oL 97, N o. SM 7, 1971, pp . 1 049-1052.

Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreem ent. No  

R . C . G u pt p ta a n d J . D . M c K e o w n ~

E ff f f e c t o f V a r i a t io i o n s in in M i n i m u m Relative ensity

e n s i ty ty o n

R E F E R E N C E : Gupta, R. C. and McKeown, McKeown, J. D., "Eff ect o f V a r i a t i o n s i n ati ve ve D ensi t y and M i n i m u m D e n s i t y o n R e l a t i v e D e n s i t y , Eval ua t i on of Rel ati

Its Role in Geotechni Geotechnical cal Projec Projects ts Involv Involving ing C ohesi ohesionles onlesss Soils A ~ T M S T P 5~3 American Society for Tes ting and Materials, 19 1973 73,, pp. 85-97.

ABS TRA CT: T his paper de desc scri ribe bess the results of of an in vestigati on carried out to study the ef effe fect ct of variations in minimum density on relative density test results. The material selec selecte ted d for the investig ation wa wass ob tained dur ing construction of Kettle Generating Station. The test results were statistically analysed. For the materials tested, the influence of variations in minimum densi ty on relative de nsity results is startling. This creates a dilemma for efeffective quality control in the field in terms of enforcing the requirements of design density.as spelled out in a contract specification based on percentage relative cohesionless soils, density (mass/volume), tests, earth fills, soil so il compacting, statistical analysis, construction control KEY W ORDS:

R e l a t i v e d e n s i t y i s u s ed e d q u i t e e x t e n s i v e ly ly f o r c o n t r o l o f c o m p a c t i o n o f c o h e s io i o n l e ss s s s oi o i ls ls i n e a r t h f i ll ll s t r u c t u r e s . T o u t i li li z e t h e m e t h o d , m a x i m u m a n d m i n i m u m d e n s i t ie i e s ar a r e o b t a i n e d a s s t a n d a r d s , a n d r e l a t i v e d e n s i t y is is calculated as follows: Rd =

~d

m s x ( 'Y 'Y d

--

Y d r a in )

' ~ d ( '~ d m a x

--

Yd rain)

X 100

where R d = relative density, percent, ~/dd -~/ -----in -p la ce d e n si ty , l b / f t s

~ d = ~ --- m a x i m u m d e n s i t y , l b / f t 3, a n d 3 d r a in = m i n i m u m d e n s i t y , l b / f t L Geotechnical engineer, Construction Division, Manitoba Hydro, Winnipeg, Man., Canada. 2 So Soil ilss an d instru mentati on supe supervi rvisor, sor, Kettle Generating Station, Station, Manitoba Hydro Hydro,, Gillam, Man., Canada. 85

opyright by ASTM Int (all rights reserved); Mar 11 16:13:06 EST 2016 Copyri Cop yright ght9 9 byl ASTM Internat Inte rnationa ionalFri l www.astm.org Downloaded/printed Downloaded/p rinted by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreeme  

8

R E L A T IV I V E D E N S IT IT Y I N V O L V I N G

C O H E S I O N L E S S S O IL IL S

A t t h e K e t t le l e G e n e r at a t in i n g S t a ti t i o n b e i ng n g b u i lt lt i n N o r t h e r n M a n i t o b a and nearing completion, the contract specifications required that the semipervious materials should be compacted to obtain acceptable densities as determined according to ASTM Test for Relative Density of Cohesionless

Soils D 2049 -69). D u r i n g t h e f i e ld ld c o n t r o l o f c o m p a c t i o n i t w a s p o s s i b l e t o c o r r e l a te te t h e field density test results when expressed as a percentage of maximum v i b r a t e d d e n s i ty t y t o t h e m o v e m e n t o f t h e c o m p a c t io i o n e q u i p m e n t. t. H o w e v e r , it was virtually impossible to visually detect any direct relationship between changes in relative density to changes in field compactive effort. In s u c h c a s e s, s , c o n s id id e r a b l e t i m e w a s s p e n t o n t h e i n t e r p r e t a t i o n o f r e l a t i v e d e n s i t y d a t a , p a r t ic i c u l a r l y w h e r e t h e s e d a t a w e r e s li l i g h tl tl y b e l o w o r b o r d e r l in i n i n g t h e s p e c if i f ic i c a t io i o n li l i m i ts t s . I n a c c o r d a n c e w i t h t h e d e s ig ig n r e q u i r e m e n t s f o r q u a l i t y c o n tr t r o l, l , v a l u e s o f r e l at at i v e d e n s i t y w e r e c o m p u t e d a n d c o m p i l e d statistically. However, in actual practice the day to day construction c o n t ro r o l r e v e r t e d t o t h e p e r c e n t a g e c o m p a c t i o n m e t h o d , w h e r e b y t h e f ie ie ld ld d e n s i t y t e s t v a l u e w a s c o m p a r e d t o a n d e x p re r e s se se d a s a p e r c e n t o f t h e laboratory maximum vibrated density for the material. B e c a u s e o f t h e i r r e g u l a ri r i ti t i e s i n t h e r e l a t i v e d e n s i t y t e s t r e s u l t s, s, a p r o g r a m w a s c o m m e n c e d t o i n v e s t i g a t e t h e p o s s i b l e s o u r c e s o f e r ro r o r , a n d t h e e f f ec ec t i t h a d o n t h e f ie i e l d a p p l i c a t i o n o f th t h i s t e s t m e t h o d . V a r i a t i o n s a f f e c t in i n g t h is is s t a n d a r d m e t h o d c o u l d b e a t t r i b u t e d t o o n e o r m o r e o f t h e f o l lo l o w i n g: g: 1 . t h e p o s s i b l e e r ro ro r i n t h e m i n i m u m d e n s i t y t e s t p r o c e d u r e , 2. the possible error in the m axim um den sity test procedure, 3 . t h e p o s s i b l e e r r o r i n t h e f ie i e ld ld d e n s i t y p r o c e d u r e , t h e a p p a r a t u s a n d the technique for using them in the field, 4 . t h e e f fe f e c t o f v a r i a t i o n i n t h e g r a i n s i ze z e d i s t r ib ib u t i o n s , m o i s t u r e c o n t e n t a n d c l im i m a t i c c o n d i t i o n s o n t h e d e n s i t y o f t h e i n -p - p l a c e m a t e r i a ls ls , a n d 5. the hum an factor. It was decided to investigate initially the minimum density test proc e d u r e . T h i s p a p e r d e s c r i b e s t h e i n f lu lu e n c e o f v a r i a t i o n s i n m i n i m u m d e n s i t y o n t h e r e l a ti t i v e d e n s i t y v a lu l u e s . T h e r e s ul u l ts ts o f t h e m a x i m u m d e n s i t y p r o g r a m a r e in i n a s t u d y s t a g e a n d m a y b e r e p o r t e d i n t h e f u tu tu r e . Materials

T h e s e m i p e r v i o u s m a t e r i a l s u s e d i n t h e e a r t h f il il l c o n s t r u c t i o n w e r e obtained from two kame-eskers, and as such consisted predominantly of r o u n d e d t o s u b r o u n d e d s o r t e d s a n d s a n d g r a v e l [ 1 ] 3. The classification of the materials according to the Unified Soils Classification System was S P - S W ) . T h e q u a l i t y o f t h e s e m a t e r i a ls l s w e r e c o n s id i d e r e d e x c e ll ll e n t f o r s T h e i t a l i c n u m b e r s i n b r a c k e t s r e f e r t o t h e l i s t o f r e fe fe r e n c e s a p p e n d e d t o t h i s p a p e r

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earthworks construction. The petrographic analysis carried out on mat e ri r i a ls l s o b t a i n e d f r o m t h e e s k e r re re v e a l e d t h e p e r c e n t p r e d o m i n a n t r o c k a n d m i n e r a l t y p e s t o b e a s fo fo l lo lo w s : l i m e s t o n e 4 5 g r a n i t e 2 1 q u a r t ~ 1 5 b a s i c ig n e o u s 1 2 a n d f e ld s p a r s 5 . Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

 

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9

RELATIVE DENSITY

LeD Sample

No.

INVOLVING

COHES IONLESS

SOILS

545

Lob.

Samp le

No.

708

F-H w

o 7

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DENS|TY

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lie (P.C-F)

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No. 9873 I. I. I. I. I.

III

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of tests

corresponding Graph

be low

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in

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D[NSITY

1 12 12 (PC

lie F.)

FIG. 2 T yp i ca l hi st st ogram ogram and cum ulat ulatii ve ve frequenc frequenc y cur curves ves.. M i n i m u m D e n s i ty t y I n v e s t i g a t io io n Material for the minimum density investigation was selected from quality control storage specimens during earthworks construction. Comp a r a t i v e t e s ti t i n g o n t e n s p ec e c im i m e n s t a k e n a t r a n d o m i n d i c a te te d t h e m a t e r i a l C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t ttoo L i c  

GUPTA AND

MCKEOWN

ON

V A R IA IA T IO IO N S I N M I N I M U M

D E NS N S IT IT Y

9

to be fairly representative of the fill placed during construction. Figure 1 presents the grain size distribution and the specification limits for semipervious pervi ous material mate rials. s. Also shown on th e figure are th e co corre rrespo spondi ndirig rig co coeff effiicients for uniformity C u ) and coefficients of curvature Cc). The minimum density tests were performed in accordance with ASTM

D 20 2049 49-6 -69. 9. To provide provi de for poss possible ible hu huma man n error, four technicians carried out ten tests on each specimen. In this way a universe of 40 test results was created for each specimen. The mini mum densit y test results were statistic ally analysed [2 [2, 3] 3] using a computer program for each of the ten tests and the universe of 40 tests to obtai o btai n the comput com puted ed averages ~) ~),, limit limitss for for 2 for 95 perce percent nt confidence confidence level,, st level stand and ar ard d devi deviati ation on z), co coef effi fici cien entt of vari ati ation on v), range, and numb number er of tes tests ts required re quired for =t=0.5perce percent nt variat va riat ion. The results of th thee analysis ana lysis are shown in Table 1. The frequency histograms and accumulated frequency distribution curves for each specimen for a universe of 40 test results were plotted. Figure 2 shows such plots for laboratory specimens 345, 708, and 9873. Subsequent analysis will indicate that these specimens, in the above order, represent the best, average, and worst in-test variations in terms of the spread in the minimum density test results. results. Analysis

of Data

For the purposes of this analysis the data from four technicians was pooled to create a universe of 40 te test st results. In some ca case sess the da ta did not meet the statistical tests for homogeneity at a specified level. An inference about human error could be made in such cases. However, in practice only one minimum density test is performed to establish the relative density. The one result, as such, could fall anywhere in the range. In the analysis of the test results only those within the middle 90 percent spread were used. The relative deg degree ree of accuracy of each each technician is is presented in Table 2. The comparis comparison on was obtained by sele selectin cting g the largest and smallest sta ndar d deviation values recorded within each specimen group. The statistical analysis of the data consisting of 40 tests is based on certain assumptions and qual qualifica ifications tions.. To make practical use of this i nvestigation, it was necessary to know t he TABLE 2-- M ini m um density, technician technician accur accuracy acy compar comparis ison. on. Tech Te chni nici cian an

Most Acc Accura urate te

1 2 3 4

3 3 3 1

Least Acc Accura urate te ... '4 6

Perc Pe rcen entt nflu nfluence ence 15 15 35 35

C o p y r i g h t b y A S T M I n t l ( a ll ll r i g h t s rree s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFPE ) Universidade Federal de Pernambuco) pursuant to License Agreem  

9 ~

R E L A T I V ED ED E N S I T Y I N V O L V I N G

COHESIONLESSSOILS

required number of tests it would take to obtain a desired degree of accuracy. The number of tests was calculated in accordance with the recommended practice detailed in ASTM Practice for Choice of Sample Size to Es ti ma te the th e Average Qua Qualit lit y of a Lot or Proces Processs E 122-5 122-58) 8) [3]. This value can be considered as an amplification of the standard deviation for

any group of data and is an ideal parameter by which other variabilities can be correlated. It is generally believed that some variation in relative density test result data can be attributed to the grain size distribution characteristics that exist between different materials. A comparison of the values of coefficient of uniformity and coefficient of curvature for the materials tested and the number of tests required to obtain a desired degree of accuracy of one one percent, howev however, er, did not sho show w any such definite definite relationship.. Fur ship Furthe thermo rmore, re, i t has al also so been suggested el else sewh wher eree [4] th at in moisturemoistur edensity relationships, maximum vibrated density tests, or unit weight measurements, there is a direct relationship between the resulting density value and the percentage greater than the No. 4 screen size. It is also of interest to note that such a relationship was not clearly evident in the casee of mini mum density. cas Without having made an examination of the possible error in each of the procedures previously mentioned, a reasonable estimate was believed to be • percent 1 percent rang range). e). When equated howe however, ver, the • percent resulted in relative density value outside the desirable limits. For example, assuming that +0.5 percent error was added to a field density th at corr correspo esponds nds to 50 percent relative densit y and compared to a - 0 . 5 percent error in maximum and minimum density, the relative density would be equal to 55 percent. The inverse of this situation would equal 45 percent. Thus, a 50 percent relative density could range from 45 to 55, or • 10 percent error. The spec specif ifie ied d requi remen rementt for compaction at Ke Kett tt le Generating Station was 75 percent relative density. The range for this value resulting from the previous assumptions would be from 70 to 79, or • percent err error. or. Bot h exam examples ples are calculated with typica l maxi mum and minimum density values obtained from this investigation. Three specimens were selected to illustrate the best, average, and worst in-test variations obtained from this program and are shown in Fig. 3. The relative density plots show the influence that the 90 percent limits of minimum density test values have on relative density for a universe of 40 tests. This is for the condition that maximum vibrated density and field densi ty remain constant. The values given given wer weree calculated using the actu al maximum density for the particular material. Figure 3 a) shows the results for the best case for Specimen 345. A 50 percent relative density value could, in fact, vary from 47 to 52, or • percent error. At 75 percent relative density this variation would be from 74 to 76 76,, or • percent. perc ent. Th Thee result resultss for an avera average ge cas case, e, Specimen 70 708, 8, Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/ printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agree  

GUPTA

I~0

Lab

Sample

AND

MCKEO WN

ON

V A R IA T IO N S

NOI 345

1gO

ii

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IN

M I N IM U M

D E N S IT Y

93

z~ 47 ~o 5z *

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Sample

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J

50

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(Actual)

708

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ioo

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5o

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, TECH. i

T[ c ~ 12

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TEC H4

ALL TECH

Z5

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(b) Lab

Sample

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(Actuot)

N O. O. 9 8 7 3

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I

I

I

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/j j~ //

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TECH.2

TECH.3

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LEGEN D Lorgelt

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ALL TECH.

%Rd

(C)

Tett

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90% Lrmil$

(Actual} The

rs g h f rs

hand

error

~n

minimum

where Comp~lld ~ A,,toC e, ~ Smole~

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show

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density

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test

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O,vio~o.s~ ~N o o f T es es ,*,* Rlq'a 1%~ A c c . ra ra c T Colculoled

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FIG. 3--E ffects of va variri at ations ions in min imu m de density nsity on rela relattive de density nsity.. are shown in Fig. 3(b). A 50 percent relative density value could, in fact, v a r y f r o m 4 1 t o 5 7 , or o r i 1 6 p e r c e n t . A t 7 5 p e r c e n t r e l a ti ti v e d e n s i t y t h i s v a ria t io n w o uld b e f ro m 7 1 t o 7 9 , o r =l=5 .7 .7 p ercen t erro erro r. r. T he w o rst ca se, Specimen 9873, is presented in Fig. 3 ( c ) . A 50 percent relative density v a l n e v a r i es es f r o m 3 8 t o 6 4 , o r • p e r c e n t . A t 7 5 p e r c e n t r e l at a t i ve ve d e n s i t y

C o p y r i g h t b y A S T M I n t l ( a l l r ig i g h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n t ed ed b y ( U F P E ) U n i v e r si s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A g  

94

RELATI REL ATIVE VEDENSITY DENSITY INVO INVOLVING LVING COHESIONLESS SOILS

t h i s v a r i a t i o n i s f r o m 6 9 t o 8 0, 0, o r • percent. It mus t be pointe d out t h a t f o r S p e c i m e n 9 87 8 7 3 , t h e r e l a t i v e d e n s i t y b o r d e r l im im i t s a r e n o t e q u i d i s t a n t f r o m t h e c e n t e r . T h i s d i ff f f e r en e n c e i s a t t r i b u t e d t o t h e s k e w n e s s in in t h e n o r m a l d i s t r ib i b u t i o n o f t h e t e s t r e s u l t d a t a w h e r e t h e l o w e r 90 90 p e r c e n t l i m i t i s f u r t h e r a w a y f r o m t h e m e d i a n t h a n t h e u p p e r l im i m i t. t.

T h e p r e c e d i n g c o m m e n t s h a v e b e e n m a d e o n t h e b a si s i s o f t h e a n a ly ly s i s carried out on the test results ~4thin the middle 90 percent spread in a u n i v e r s e o f 4 0 r e s u l ts ts . I f c o n s i d e r a t i o n w a s g i v e n t o t h e r a n g e , t h e l a r g e s t and smallest test data recorde d by an y one technician in a set of ten tests, the error in relative density would be greatly increased. F u r t h e r m o r e , i t w a s in i n t e r e s ti ti n g t o n o t e t h a t t h e l o w e s t v a l u e o f t h e m i n i m u m d e n s i t y w a s o b t a i n e d i n t h e f i r st s t te t e s t t r i a l f o r 2 0 o u t o f 4 0 sp s p e c iimen groups. This will definitely influence the field control based on only o n e te t e s t. t . T h e a u t h o r s , h o w e v e r , h a v e n o r e a s o n a b l e e x p l a n a t i o n f o r th th i s p h e n o m e n o n a t t h e p r e s e n t ti ti m e .

M a x i m u m D e n si sit y Maximum density tests were performed on the materials used in the m i n i m u m d e n s it i t y p r o g r a m a c c o r d i n g t o A S T M D 2 0 4 9 -6 - 6 9 . T h e r e s u l t in in g v a l u e s a s w e l l a s t h e c o r r e s p o n d i n g c o e ff f f ic i c ie i e n ts t s o f u n i f o r m i t y a n d c o ef e f fi fi c i e n t s o f c u r v a t u r e a r e g i v e n in in T a b l e 3 . I t i s i n t e re r e s t in i n g t o n o t e t h a t S p e c i m e n 3 4 5 a ch ch i e v e d t h e g r e a t e s t m a x i mum density value, and in the minimum density investigations, the same m a t e r i a l r e s u l t e d i n th t h e l o w e s t p e r c e n t a g e e r r or o r . I t c a n b e se se e n f r o m t h e T a b l e 3 t h a t b y a n d l a r g e t h e v a l u e s o f c o e ff f f ic i c i en en t o f u n i f o r m i t y s h o w a n i n c r e a s i n g t r e n d w i t h i n c r e a si s i n g m a x i m u m d e n s i ti t i e s. s . S u c h a r e l a t io io n s h i p w a s n o t a p p a r e n t i n th th e c a s e o f m i n i m u m d e n s i t y p r o g r a m . I n t h e c a s e o f c o e ff f f ic i c ie i e n t o f c u r v a t u r e v a l u e s , n o d e f i n it i t e re re l a t i o n s h i p w a s a p p a r e n t f o r increasing maximum density. T A B L E 3--Maximum density and values of C u and Cc. La b o rat o ry Sam p le le No . M ax i m u m Den s i t y , lb/ft a 352 139 708 483 98733 987 502 99255 992 97511 975 1299 12 345

128.0 131.5 136.0 138.2 138.2 140.0 140.0 141.0 141.3 145.0

Cu

Cc

7.1 7.0 24 .4 11.0 20.0 14.4 21.8 19.5 21.8 22.6

1.1 1.0 O. 8 1.3 0.6 1.1 1.3 1.2 1.5 1.3

C o p y r i g h t b y A S T M I n t l ( a l l r ig ig h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A g r e e  

GUPTA GUP TA AND M CK EOW N ON VARI VARIATI ATIONS ONS IN M INIM UM DEN DENSIT SITY Y

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Copyright by AS T M Int l (all ri rights ghts reserved); F ri Mar 11 16:13:06 ES T 2016 Downloaded/printed Downloaded/print ed by (UF P E) U niversidade niversidade F ederal de P ernambuco ((UF P E ) Universidade F ederal ederal de P ernambuco) pursuant to License Agreemen  

96

RELATIVEDENSITY RELATIVE DENSITY INV INVOL OLVI VING NG COHES COHESIONL IONLESS ESS SOILS

It may be of interest to mention here that during the earlier stages of the program, prog ram, pilot te sts were carrie carried d out for determining maximum density. Because of the particle breakdown resulting in each progressive test, progressively higher values of maximum density were obtained upon reusing the material.

Field Density

The fie field ld dens densitie itiess at Kett le Generating Station were were obtained by using the Washington Densometer and the suggested ASTM procedure [5] for this equipment. It has been reported elsewhere [6] that there may be an error of close to • percent Of the volume in the Washingt on Densomet Densometer er proc procedur edure. e. It must be pointed out that this error has been reported for tests carried out under laboratory conditions. Figure 4 shows the influence or effect th at the variations in mi nimum density have on relative relative density combine combined d wit h a poss possib ible le error in the fie field ld dens ity measurement. The present ation is self-explanatory. Figure 4(a) shows the results for the best case for Specimen 345. A 50 percent relative density value, in fact, could vary from 32 to 65 65,, or -44-33 33 perce percent nt error. Th e result r esult for the averag averagee case case,, Specimen 708 708,, and for the worst case, Specimen 9873, are shown in Figs. 4(b) and (c), respectively. It may be pointed out t ha t the resu results lts from Specim Specimen en 987 9873 3 we were re termed as the worst case because of the spread in minimum density test results. If the combined error due to field density and minimum density results taken together is compared with the results from Specimen 708, the total percentage vari atio n is is higher in the ca case se of Spec Specimen imen 708 708.. This is at tr ib ibut ut ed to the fact t ha t the avera average ge mini mum density in the ca case se of Spe Specim cimen en 987 9873 3 is lower than that obtained for Specimen 708. The lower average value of the minimum density, as obtained in the case of Specimen 9873, is considered closer to the actual value. Under these conditions the trend observed in Fig. 4(c) is explainable. Figure 4 furthermore does not take into account any error which, may or may not exist in the maximum density determination. Any such error is likely to amplify the sprea spread d in th e value valuess of relative relative density. Conclusions

In terms of stati stical si sign gnif ific ican ance ce,, the effe effects cts of variati ons in m in inimu imu m density on relative density are startling. Although this variation will decrease at increasing values of relative density, it still creates a dilemma for effective quality control in the field in terms of enforcing the requirements of design as spelled out in a contract specification. A problem definitely exists if the case in question is that of a contract specification asking for lower relative densities, say in the range of 50 to 75 percent. Seemingly, there is an urgent need for establishing an effective criterion

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i n v ie i e w o f t h e e x t r e m e s e n s i t iv i v i t y o f t h e m i n i m u m d e n s i t y t e s t v a l u e s. s. I t i s c o n s id i d e r e d t h a t t h e m i n i m u m d e n s i t y t e s t r e s u l ts t s a r e d i ff f f ic i c u lt lt t o reproduce. T h e t e s t s d e s c r ib i b e d h e r e i n w e r e c o n d u c t e d i n a n o n - s i te te l a b o r a t o r y , a n d , t h e r e f o r e , w e r e n o t p e r f o r m e d u n d e r t h e s t r i c t c o n t r o l n o r m a l l y a s so so c i a t e d

w i t h r e s e a r c h w o r k ; h o w e v e r , c o n d i t i o n s w e r e C e r ta t a i nl n l y ty ty p i c a l o f n o r m a l field construction control--the one which is most likely to be encountered in practice. I t m a y a ls l s o b e p o i n t e d o u t t h a t t h e r e s u lt l t s a r e b a s e d o n te t e s t s c a r r ie ie d o u t o n a s p ec e c if i f ic i c m a t e r i a l . T h e s t a ti t i s ti t i c a l a n a l y s is is w a s p e r f o r m e d u n d e r c e r t a i n a s s u m p t i o n s . I n a d d i t io i o n , s u c h t h i n g s a s c o m p a c t i o n e q u i p m e n t , f ie i e ld ld moisture content, grain size distribution, climatic conditions, and test proce dure are some of the variables which ma y hav e a bearing on the me asured value of relative density. Conseq uently, caution m ust be exercised in using the data. Acknowledgments

T h e r e s e a r c h p r o g r a m r e p o r t e d h e r e i n w a s c a r r i e d o u t in i n a n o n - s i te te l a b o r a t o r y u n d e r t h e s u p e r v i si s i o n of of t h e s e c o n d a u t h o r . T h e a u t h o r s a c k n o w l e d g e t h e e n c o u r a g e m e n t a n d c o o p e r a t io i o n re r e c e iv i v e d d u ri ri n g t h e p r o g r a m f r o m W . H . K a s p e r s ki k i , re r e s i d e n t m a n a g e r , K e t t l e G e n e r a t in in g S t a t i o n a n d A. Koropatnick, geotechnical manager, Construction Division. The authors a r e t h a n k f u l t o K . J . F a l li l i s, s , d i r e c t o r o f t h e C o n s t r u c t i o n D i v i s i o n fo fo r t h e permission to publish the results. References

[1] Flint, R. F., Glacial and Pleistocene Geology, W il iley, ey, New York, 1969. [2]] Nev ill [2 ille, e, A. M . and Ken nedy, J . B., Basic Statistical Methods for Engineers and Scientists, International Tex tbook Company, Company, New Y ork ork,, 19 1964. 64. [3] M a n u a l o n Q u a l i ty ty C o nt nt r ol o l o f M a t e r i a ls ls , A S T M S T P 1 5 -C -C , American Society for Testing and Materials, 1951. [4] Burmister, D. M. in F i el e l d T e st st in in g o f S o il i l s, s , A S T M S T P 3 22 2 2 , Am eri erican can Society Society fo r Testing an d M aterial aterials, s, 1963, pp. 67-97 . [5] Humphres, H. W. in Special P rocedure roceduress for Testing S oil and R ock for E ngineering P u rp rp os o s es e s , A S T M S T P ~ 7 9, 9 , Am eri erican can Society for Te sting and Material Materials, s, 1964, pp. [6] 451-457. " A Stu dy of In-Plac In-Placee De nsity Determinations Determinations for Soils," Soils," T M No. 3-415, U. S. Army Corps of Engineers, Waterw ays Ep xeriment Stati Station, on, V icksburg, M iss. iss.,, 1955. 1955.

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7'. L. Youd~

Fa c to t o r s C o n t ro r o lll l i n g M a x i m u m a n d M in i n im im u m

D e n s i tit i e s o f Sa Sa n d s *

R E F E R E N C E : Y o ud u d , T . L . , " F a c t o r s C o n t r o l l in in g M a x i m u m a n d M i n i m u m D e n s i t ie i e s o f S a n d s , " Evaluation of o f Relative Density and Its I ts Rol Rolee in GeoGeo-

technical techni cal Projects Inv Involv olving ing Cohesi Cohesionl onless ess Soi Soils, ls, A S T M S T P 5~ 5~8, 8, A mer ican Society for Testing a nd M aterial aterials, s, 1973, pp. 98-112. A B S T R A C T : M ax imu m an d min imu m d en s ity tes ts , co n d u cted o n a v ar iety

o f clean s an d s , s h o w th at th e min imu m an d max imu m v o id - r atio limits ar e controlled primarily by particle shape, particle size range, and variances in the grad ation al-cu rve shape, an d th at the eff effect ect of particle size is negl negligi igible. ble. C u r v es w ere ere d ev elo p ed fo fo r es timatin g m in imu m an d max im u m v o id r atio atio s f r o m g r ad atio n al an d p ar ticle- s h ap e p ar ameter s . Es timates f o r s ev er al n atu r al an d co mmer cially g r ad ed s an d s ag r ee w ell w ith min imu m an d max imu m v o id r atio s meas u r ed in in th e lab o r ato r y . M in im u m d en en sit sitie iess ( max imu m v o id r atio atio s ) W ere er e d eter min ed b y th e s ta n d ar d A m er ican ican S o ciety f o r Tes tin g a n d M ater ials ( A S TM ) min im u m d e n s ity tes t m eth o d ( Tes t f o r R elativ e D en s ity o f C o h es io io n less Soils (D 2049-69)), except that smaller molds were used. Maximum densiti si ties es (minim um void ratios) were determ ined by repeated straining in simple s h ear, ear, a m eth o d w h ich h as b een een s h o w n to g iv e g reater r eater d en sit s ities ies th a n s tan d ar d v ib r ato r y meth o d s . K E Y W O R D S : cohesionless soils, compacting, density (mass/volume), grain

structure, grain size, sands, soil mechanics.

T h e d e t e r m i n a t i o n o f r e l at a t i v e d e n s i t y v a l u e s f or o r sa sa n d s w o u l d b e g r e a t l y f a c i l it i t a t e d i f r e li l i a b le l e e s t i m a t e s o f m a x i m u m a n d m i n i m u m d e n s it i t i es es c o u l d b e m a d e f r o m s oi o i l i n d e x p r o p e rt rt i e s r a t h e r t h a n f r o m e l a b o r a t e l a b o r a t o r y t e st s t s. s . C r i t e r i a p r e s e n t ly l y a v a i la l a b l e fo fo r e s t i m a t i n g m a x i m u m a n d m i n i m u m d e n s i ti t i e s a r e i n a d e q u a t e b e c a u s e , ( 1 ) t h e y a r e t o o i m p r e c is is e , ( 2 ) i m p o r t a n t p a r a m e t e r s a r e n o t a d e q u a t e l y c o n s i d er e r e d , a n d ( 3 ) t h e l a b o r a t o r y t e s ts ts t h a t w e r e u se s e d t o d e v e lo l o p t h e c r i te t e r ia ia d o n o t p r o v i d e a n a d e q u a t e m e a s u r e o f m a x i m u m d e n s i ty ty . * Pub lication au thorized b y the Director, U. S. Geologi Geological cal Survey. 1 Re searc h civil civil engineer engineer,, En gine ering Ge ology Branc h, U . S. Geological Geological S urv ey, Menlo Park, Calif. 94025. 98

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YOUD ON FACTORS CONTROLLING DENSITI DENSITIES ES OF SANDS

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This report describes which soil properties control maximum and minim u m d e n s i t y li li m i t s a n d , o n t h e b a s i s o f t h e s e p r o p e r t i e s , d e v e l o p s g e n e r a l iz i z e d c r i te t e r i a f o r e s t i m a t i n g m a x i m u m a n d m i n i m u m d e n s i t ie ie s o f c l e a n sands. P r e v i ou s W o r k

B u r m i s t e r [1-3] 2 r e p o r t e d t h a t t h e m o s t i m p o r t a n t f a c t o r c o n t r o l l i n g m a x i m u m a n d m i n i m u m d e n s it i t ie i e s is i s th t h e r a n g e o f p a r t ic ic l e s i z e s - - t h e g r e a t e r t h e r a n g e o f p a r t i c l e s iz iz e s, s, t h e g r e a t e r t h e d e n s i t y . O t h e r f a c t o r s h e c o n s i d e r e d i m p o r t a n t w e r e t h e t y p e o f g r a d i n g c u r v e , p a r t i c l e si s i z e, e, a n d p a r t i c l e s h a pe p e . I n B u r m i s t e r 's ' s s t u d y , m a x i m u m d e n s i t y v a l u e s w e r e o b t a i n e d e i th th e r b y v i b r a t i n g - t a m p e r o r i m p a c t p r o c ed e d u r e s , a n d m i n im im u m d e n s i t y v a l u e s b y p o u r i n g s a n d t h r o u g h a f u n n e l i n t o a m o l d [ 4] 4] T h e a p p l ic i c a t io i o n o f c u r v e s d e v e l o p e d b y B u r m i s t e r f o r e s ti ti m a t i n g m a x i mum and minimum densities is limited because, (1) the methods used to obtain maximum density values do not provide an adequate measure of maximum density [5] and, (2) the single-value density correction he s p e ci c i fi f i es e s f o r so s o il il s w i t h m o r e t h a n 3 5 p e r c e n t a n g u l a r f r a g m e n t s o r c r u s h e d m a t e r i a ls l s i s to t o o a r b i t r a r y a n d t o o im i m p r e c i se se t o a c c o u n t a d e q u a t e l y f o r t h e i n fl u e n c e o f p a rt i c l e s h a p e . K o l b u s z e w s k i a n d F r e d e r i c k [ 6] 6] d e m o n s t r a t e d t h a t t h e d e n s i t y li l i m i ts ts o f s a n d s i n c re a s e w i t h i n c re a s i n g p a rt i c l e s i z e a n d d e c re a s e w i t h i n c re a s i n g angularity; however, insufficient data were given in their report to formulate criteria for estimating density limits for sands in general. They obt a i n e d m i n i m u m d e n s it i t ie i e s b y t h e t ip i p p i n g m e t h o d d e s c r ib ib e d b y K o l b u s z e w s k i [7] and maximum densities by depositing sand in a vacuum. M a x i m u m a n d m i n im i m u m d e n s i ty t y v a lu l u e s f o r a n u m b e r o f s a n ds ds f r o m Ontario, Canada, were statistically correlated with Bagnold grading par a m e t e r s [ 8] 8] b y H u t c h i s o n a n d T o w n s e n d [ 9] 9 ] . A r e a s o n a b l y g o o d c o r r e la l a t io io n w a s f o u n d f o r m a x i m u m d e n s i ty t y , b u t o n l y a p o o r c o r r el e l a ti ti o n w a s o b t a i n e d b e t w e e n m i n im i m u m d e n s i ty t y a n d t h e B a g n o ld l d p a r am a m e t e r s. s . M a x i m u m d e n s i ty ty v a l u e s w e r e o b t a in in e d b y t h e v i b r a t i n g - t a m p e r m e t h o d [ 7 ] , a n d m i n i m u m densities were obtained by both the tipping method [7] and the spooning m e t h o d d e s cr c r ib i b e d b y W u [10]. T h e a p p l i c a ti t i o n o f H u t c h i s o n a n d T o w n s e n d ' s d a t a i s l im im i t e d b e c a u s e the com paction method used to obtain ma ximum density values does not p r o v i d e a n a d e q u a t e m e a s u r e o f m a x i m u m d e n s i t y [ 5 ] , B a g n o l d g r a d in in g p a r a m e t e r s a r e n o t d e f i n ab a b l e f o r al a l l s a n d s , a n d t h e i n f lu lu e n c e o f g r a i n s h a p e was not considered. K a b a i [11] s h o w e d t h a t t h e r e w a s a g o o d c o rr r r e la l a t io io n b e t w e e n m a x i m u m and minimum densities determined in the laboratory and the coefficient o f u n i f o r m i t y f o r D a n u b e R i v e r s a n d s. s . M i n i m u m d e n s it i t ie ie s w e r e d e t e r m i n e d 2 The itali italicc num bers in brackets refe r to the list of references append ed to this pape r. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

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RELATIVEDENSITY IN RELATIVEDENSITY INVO VOLV LVIN ING G COH COHESIO ESIONLES NLESS S SOIL SOILS S

by pouring sand through a funnel into a mold, and maximum densities were obtained by impact-compaction tests, using procedures similar to those outlined in the ASTM Test for Moisture-Density Relations of Soils Using 10-Lb. Rammer and 18-In. Drop (D 1557-70). The value of Kabai's criteria is limited because the impact-compaction test does not generally give maximum density values for sands that are

as high as those given by vibratory or shear-straining methods [5, 12, 18], and the influenc influencee of particle shape was not cons consider idered. ed.

Laboratory Investigation

In the first part of the labor atory investigation, investigation, maximum and minimum density tests were conducted on sieved fractions and artificially proportioned gradations of commercially available sands in order to confirm and extend previous findings findings concerning the factors tha t control maximum and minimum densities and to construct a generalized set of curves for estimating thes thesee density limits. limits. In the second second part of the laboratory stu dy, the maximu m and mi nimum densitiess of a vari ety of nat ura l and commercially graded sands were densitie were determined in order to test the validity of the generalized prediction curves. Pr ocedur e

Minimum densities were determined by the procedures outlined in the AST M Test T est for Relati ve Densi Den si ty of Co Cohe hesi sionl onles esss So Soil ilss (D 20 2049 49-6 -69) 9),, except th at a 94 9488-cm cm3 (0 (0.0 .033 33-f -fP) P) mold was used rather rath er th than an the stand standardize ardize d 2832-c 283 2-cm m ~ (0. (0.1010-fP) fP) mold. (Because partic par ticle le siz sizes es were very ver y small comp c ompare ared d to the mold size and because the technique used gave values consistent with minimum densities obtained by the standard method on two of the sands tested, the influence of the smaller mold size is believed to be very small.) Minimum density is sensitive to the procedures used to determine i t [12, 14]; however, because the ASTM standardized procedures give consistent and generally lower values than other methods [5], they were used in this study. Maximum densities were determined by the repeated straining in simple shear procedure described previously by Youd [13, 15]; this procedure was shown to give greater densities than the procedures outlined in the ASTM D 20492049-69 69.. The procedures outlined by Youd [13] were followed for sands sands th at wer weree highly resistan resistantt to crushing and included the application of 10 000 cycles of shear strain (2 to 5 percent strain) to specimens contai ned in a simple shear device. device. The norma no rmall stress stress applied was 9. 9.6 6  104 N / m 2 (20 (2000 00 psf). For specimens that were less resistant to crushing, the procedure was modified to reduce crushing by reducing the normal stress to 4.8 X 104 N / m 2 (1000 ps psf) f) and the numb n umber er of cycles cycles of str strain ain to 4000. The modified procedure held crushing to what was considered to be an acceptable miniCopyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Lice  

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m u m . I n a ll l l s p e c i m e n s t h e i n c r e a s e o f p a r t i c l e s p a s s i n g t h e N o . 2 00 0 0 s ie ie v e , w h i c h w a s f o u n d t o b e a g o o d i n d e x o f c r u s h i n g , w a s h e l d t o l e ss s s t h a n 1 .5 .5 p e r c e n t o f t h e t o t a l s p e c i m e n w e i g h t , a n d t h e m a x i m u m i n c r e a s e o f p a r t ic ic l e s p a s s i n g a n y s i e v e w a s g e n e r a l l y le le s s t h a n 2 p e r c e n t . T e s t s o n c r u s h i n g r e s i s t a n t s p e c i m e n s b y t h e m o d i f ie ie d p r o c e d u r e y i e l d e d a r e l a t i v e d e n s i t y o f a t l e a s t 98 98 p e r c e n t ; t h u s , a n y e r r o r d u e t o i n c o m p l e t e c o m p a c t i o n w a s

s m a l l a n d w o u l d h a v e b e e n o f fs f s et e t i n p a r t b y t h e s m a l l in i n c r e a se se i n d e n s i t y due to crushing. Soil Prop erties

T h e p a r a m e t e r s u s e d t o d e s c ri r i b e t h e p h y s i c a l p r o p e r t i e s of of t h e s a n d s i n c l u d e d t h e m e a n p a r t i c l e s iizz e ( ds ds 0 ), ), t h e c o e f f ic i c i e n t o f u n i f o r m i t y ( C a ), ), t h e t y p e o f g r a d i n g c u r v e , th t h e p a r t i c l e r o u n d n e s s ( R ) , a n d t h e s p ec e c i fi fi c gravity (G,), where d s 0 = t h e m e s h s iz i z e t h r o u g h w h i c h 5 0 p e r c e n t o f t h e p a r t i c le le s , b y w e i g h t , passes, l0 a r e t h e m e s h s i z es es t h r o u g h w h i c h 6 0 Cu = d6o/dlo, w h e r e d60 a n d d l0 p e r c e n t a n d 1 0 p e r c e n t o f t h e s a n d p a r t i c l e s p a ss ss , r e s p e c t i v e l y , a n d R = ti hmea gr ea t it oo ot hf et hrea daivuesr aogf e t hoef tmh ea xr iam d iui mo f ctir onf ab es ain ihr cl ce l ec ot hr na et r sc aof i nn ds c gr ib irbaei nd within the grain image [16]. T h e t y p e o f g r a in i n - s iz i z e d i s t ri r i b u t i o n c u r v e w a s d e s c r i b e d q u a l i t a t iv iv e l y i n T A B L E 1--Roundness criteria and values. Roundness Roundness Classaa Class

Roundness Roundness Int erv al

M ean Roundness Roundn ess ~

V e r y a n g u la la r Particles with unworn fractured sur surfac faces es and multiple sharp corners and edges

0.12 -0.1 7

0.14

Angular

Particles with sharp corn corners ers and approxi-

0.17 -0.25

0.21

Subangular

m ately prismoid prismoidal al or tetrahed ral shapes Particles with disti distinct nct bu t blunted or sl slig ightl htlyy rounded corners and edges

0.25 -0.3 5

0.30

Particles with disti distinct nct bu t well well-r -rounde oundedd edges 0.35 -0.4 9 and corners

0.41

Subrounded

De scription b

R o u n d ed

Irregularly shaped rou rounded nded particles with no distinct corners or edges spheri erical cal or el elli lipsoi psoidal dal parW ell rounde roundedd Sm ooth nearly sph ticles

0.49 -0.7 0

0.59

0.7 0-1 .00

0.84

a After Powers [17]. b Descript Descriptions ions repre sen t the classifica classificati tion on criteria used in this stu dy a nd are no t based on a recalculation of Wadell roundness .values.

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RELATIVE RELATI VE DENSIT DENSITY Y INVO LV ING COHESI COHESIONLESS ONLESS SOIL SOILS S

t e r m s o f t h e s t a t i s ti t i c a l c h a r a c t e r i s ti ti c s o f t h e c u r v e , f o r e x a m p l e , n o r m a l l y distributed, skewed, bimodal, or gap graded, etc. These soil properties were chosen as descriptors because of their common usage, and because each is uniquely definable for any given sand specimen. The R values were determined by the procedure suggested by Powers [17] b u t m o d i f i e d t o c o n s i d e r p a r t i c l e s f r o m e a c h s i z e f r a c t i o n r a t h e r t h a n

t h e s p e c i m e n a s a u n i t . B r i e fl f l y , t h e p r o c e d u r e s u s e d f o r th th i s s t u d y c o n s i s t e d o f e x a m i n i n g u n d e r a m i c r o s co co p e a r e p r e s e n t a t i v e n u m b e r o f s a n d p a r t i c l e s (a t l e a s t 5 0 ) fro m e a c h s i e v e fra c t i o n a n d v i s u a l l y a s s i g n i n g e a c h p a rt i c l e to a category listed in Table 1 (also modified from Powers). Figure 1 shows typical particles assigned to each category. The average R value f o r t h e s i e v e f r a c t i o n ( R j ), ) , w a s t h e n c a l c u l a t e d f r o m t h e e q u a t i o n R ~. = ( Z R i ) / n , w h e r e R i i s t h e r o u n d n e s s v a l u e f r o m T a b l e 1 a s s ig ig n e d t o p a r t i c l e i , a n d n i s t h e n u m b e r o f p a r t i c le le s e x a m i n e d . T h e a v e r a g e v a l u e f o r t h e s a n d s p e c i m e n w a s t h e n c a l c u l a t e d f r o m t h e r e l a t i o n R = (F, (F,P PjR~)/IO0, w h e r e P i i s t h e p e r c e n t ( b y w e i g h t) t ) o f p a r t ic ic l e s r e t a i n e d i n t h e a p p l i c a b l e s i e v e fra c t i o n .

FIG. 1--Particle sha pe classe classes. s. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agree  

h a C

o

z

Z

O

~

I

N0

~Z

O

~ f

o o e

s m L y

n m e

4 0

4 0

4 0

4 o

4 4 5 0 0 0

5 0

6 0

7 7 7 6 7 8 0 0 0 0 0 0

h u N

D

7 0

m e

7 0

7 0

7 o

7 8 9 0 0 0

0 1

e m e

1 2 2 3 3 4 1 1 1 1 1 1

2 1

A c L o

4 0

R

3 0

3 0

6 o

4 3 2 0 0 0

2 0

2 2 1 1 1 1 0 0 0 0 0 0

2 0

u

R

p

o ra a s a m c o a a D 2

04 0 2

Rm z S c G y

01 5 0

01 5 0

50 20 50 2 1 2 0 0 0

20

10

1 0

0 0

0 0 2

02 0 1

01 5 0

50 20 10 2 0 10 00

b m n P d a

2

6 6 6 6 6 2 2 2 2 2

6 2

6 2

S a G

6 2

8 8 8 8 8 8 2 2 2 2 2 2

6 2

F

E 0

  M D a m s s a n M

  M D a m s s a n M

e % 1 v c p 1 1 c d z % n p ef e e e e e e a e M c c c c c c 1 g % a q z n z 3 p p p p p p f m % z s z z z 8 q %q s % 1 a % b b b b b b 1 q q q q 4 e a %c n %%%%%% s c e % % % a a s s e M c 6 1 1 1 1 1 1 e e a a c 1 1 1 s p w %w a a a a a a w r e p a s e z as e 5 e e a b b b b b b s a s a s o L a o o o r s g c e q e w w w Mp M 6 M6 h h h h h h a a a % o d u u u u u u %o L 1 c M5 MO O O D e f D 3 D 3 c c c c c c

A T o p D

a

02 0 1

R

Ce S

1 5

1 1

L

M

3 3 6 1 6 1 1 3 6 3  M MO O O D

1 O 6 M D

2 1 M D

2 1 3 6 1 1 5 1 1 3 6 1 CCCCCC

d

1 1

v

1 a M

U

F

U

v

b m n

e s

P

g

d a

a l F n   b Me n d A p v b U g o w

C D U (

 

10.4

RELATIVEDENSITY INVO RELATIVEDENSITY INVOLVIN LVING G COHESIONLESS SOILS

'~176 op

~.

,, \ '\

'\

\

\

,,\

,\ '\', \

"

\

~/--MIXl

~,/~MIX 2 MIX3 " \ , \ \ ' ~

,ix

,

='~ -7

40 ~

,\'\) '\ I

! ol

\ ,

I0

I0

PARTICLE

I

\~'~ "\ "\ Ol

DIAMETER DIAM ETER,, mm

rves fo r a rtificia lly p rop rop o rti rtioo n ed sa n d m ixtu res. FIG. 2 --G ra in -size d istrib u tio n cu rves T A B L E 3 - -D a t a o n a rtificia rtificia lly pro pro po po rtio rtionn ed sa n d m ixes . Code

Mix No.

MOL" MOL MOL MOL MOL CB b CB CB CB

1 2 3 4 5 1 2 3 4

G,

2.64 2.64 2.64 2.64 2.64 2.8 5 2.85 2.85 2.85

C.

R

1.4 2.5 4. 3 8.0 4. 3 1.4 2.5 4.3 8.0

0.34 0.35 0.37 0.37 0.37 0.1 9 0.19 0.19 0.19

Densit y Limits emax

emin

0. 79 799 9 0.688 0. 57 577 7 0.491 0. 64 0. 641 1 1. 25 257 7 1. 09 099 9 0.993 0. 80 800 0

0.458 0. 37 0. 370 0 0.300 0.271 0.335 0. 70 705 5 0.590 0.480 0.439

-MOL mixes were proportioned from sieve fractions of Monterey, Ottawa, Lapis Lustre and Del Monte sands, in that order. b CB mixes were proport ioned fr om sieve fractions of crushed basalt. I

\

f "

OS

\ 1\

I09

\

yDM # \

k

,<

TR

2

%\. ~0

OI

IO

1.0

O .I

1.0

0.1

PARTICLE DIAMETER, mm

F IG . 3 --G ra in -size d istrib u tio n cu rves fo r n a tu ra l a n d co m m ercia lly g ra d ed sa n d s. C o p y r i g h t b y A S T M I n t l ( a l l r ig ig h t s r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s iidd a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A g r e e  

YOUD ON FACT FACTORS ORS CONTROLLI CONTROLLING NG DEN DENSI SITI TIES ES OF S AN DS

105

Sands

T h e c o m m e r c ia i a l ly l y a v a il i l a b le le s a n d s t h a t w e r e f r a ct c t i o n ed ed a n d c o m b i n e d into artifically proportioned mixes included Ottawa sand (Ottawa Silica Co., Ottaw a, Ill.), Ill.), M on terey sand (M ontere y Sand Co., M onterey, Calif.) Calif .),, D el M on te wh ite sand (W edro n Sil Silic icaa Co., Paci Pacifi ficc G rove, Calif. Calif.), ), L apis

TABLE 4 - - D a t a o n n a t u r a l a n d c o m m e r c i a l ly ly g ra ra d ed ed s a n d s . Code

Locatio n an Location and d Approxi Approximate mate Composition

Specific Specif ic Gravity, G~

Mean Coefficie Coeffi cient nt Roun Roundness dness,, Partic le of UniformR Size, Ds0 mi ty , Cu

0190

O tt tt a w a s a n d A S T M C 1 90 90 : 100% quartz

2.65

0.68

1.3

0.60

0109

O tt t t aw aw a s a n d A S T M C 1 0 9 : 100% quartz

2. 65

O . 36

1.8

0.42

RC #2

Rodeo Cove, Calif., beach sand: minerals minera ls same as RC # 1

2.67

0.57

2.9

0.42

RC #1

Rodeo Cove, Calif., beach sand: 60% chert, 20% quartz, 20% "green stones" (genera (generally lly basaltic particles)

2.67

0.79

3.9

0.37

SGB

San Gregorio, Calif., beach s a n d : 80% quartz, 10% feldspar, 10% other

2.65

0.31

1.9

0.30

SGD

Sa n G regori regorio, o, C alif., dune san d: minerals same as SGB

2.65

0.23

1.7

0.28

SFB

Ravenwood Point (San Franciseo ci seo Ba y), C alif., 6 m bel below ow surface: 50% shale particles, 50% quartz an d feldspar

2.65

0.76

4.5

0.28

AC #1

Ala m e da C reek, reek, C alif., sand: 50% shale fragments, 50% quartz, feldspar and chert

2.65

0.62

3.1

0.28

AC #2

Alam eda C reek, C alif., sand: minerals same as AC # 1

2.65

0.55

2.0

0.25

DM

D e l M o n t e w h i t e s a n d : 80% quartz, qua rtz, 15% 15% feldsp feldspar, ar, 5% chert

2.65

0.37

2.4

0.25

TR # 1 T r i n i t y R i v e r , C a l i f . , s a n d : 85% amphibolite particles particles,, 5% quartz, 5% epidote particles, 5% talc

2.98

1.10

2.8

0.23

TR #2

T r i n i t y R i v e r , C a l if i f . , sa sa n d : minerals same as TR # 1

2.98

0.64

3.4

0.21 0.2 1

CB

W a shed crushe crushedd basalt, basalt, N ap a, C alif.: 100% bazsalt particles

2.85

1.02

5.6

0.19

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to L  

106

R E L A T I V E DENSITY INVOLVING COHESIONLESS SOILS

9 CRUSHED BASAL ALT Cu : 14

16

X LAPI LAPIS S LUSTRE SAND

1.4 o

~

E 12

(D

1.0

9 OTTAWA SAND 0 DEL MONTE WH WHITE ITE SAND 9 MONTEREY SAND

0 0

0

::'<

1.8

9

9

9

X

9

X

0G G 1.0 ~ 0.8 Q:: ~ ~ 0.6

~

0 9

E

O4 ~

02

::~

0.0

2OO

0

us,5 SIEVE RANGE 60 35 18

120

I

~

I0

t -- - - q

i

,5

i'.o

o.I

M EAN

PA RTICLE

D IA M E T E R ,

D 50

IN m m

F I G . 4 --D en sit y lim its versus versus m ean grain size size for lab laborat oratory ory fractions w ith C u

k

~ O I-'-.

1.4.

9 Ottawa sand 0 De Dell Monte w hile sand 9 Monterey s a n d x kopis Lustre sand 9 Crushed b o s o l l Cu:l.4

\ 9

1.4

=

10

-

void ratio, emax.

Maximum

o

e'-,0.8 e'-, 0.8

~Jl~

\o

0.E

O'X--'-~O~

e ~ 0.4

Very An gu la r L

o2

o'l

:,~ ,~

olz

Mtnt Mt ntmum mumvo id rati o, em emiin -nm~

x

Subangular

Roun Ro unde dedd

J' Subr Subrou ounde ndedd ~1 ~1..

o13 o ',' , ~ RO UNDNESS, R

o's

o'e

F I G . 5 - - D e n s # y l i m i t s a s a f u n c t i o n o f g r a i n s h a p e f o r la l a b or or at a t or or y f r a c t i o n s w # h C . =

1.4.

Copyright by AS T M Int l (all (all rights rights reserved); F ri Mar 11 16:13:06 ES T 201 6 Dow nloaded/printed nloaded/printed by (UF P E ) Universidade F ederal de P ernambuco ((U F P E) Un iversidade iversidade F ederal de P ernambuco) pursuant to License Agreeme  

YOUD O N FACT FACTORS ORS CONTROLLI CONTROLLING NG DEN DENSI SITI TIES ES OF S AN DS

107

Lustre sand (Pacific Cement and Aggregates, San Francisco, Calif.), and c r u s h e d b a s a l t ( B a s a l t R o c k Q u a rr r r y, y , N a p a , C a l i f. f. ) . Properties of the sand fractions are listed in Table 2. Gradation curves and descriptive data for the artificial mixtures are presented in Fig. 2 and T ab le 3. Properties of the natural and com m ercially graded sands are given in Fig. 3 and Table 4.

Results The influence of specific gravity on the test results was normalized by converting maximum and minimum densities to minimum and maximum v o i d r a t i o s (emia a nd em ax ax ), ), resp ect iv e ly . T he em ax a x a nd em i~ i~ a re t a b ula t e d in Table 2 for the sand fractions and in Table 3 for the artificial mixes. The data plotted in Fig. 4 show that no unique relation exists between m e a n p a r t i c l e d i a m e t e r a n d e m a~ a~ o r e m i , . H o w e v e r , t h e s a m e v o i d - r a t i o data plotted against R on Fig. 5 form a well defined curve. These results s h o w t h a t g r a i n s h a p e i s a n i m p o r t a n t f a c t o r c o n t r o l li l i n g em em ax ax a n d e m i , a n d t h a t p a r t i c l e s i z e p e r s e h a s n o s i g n i fi fi c a n t i n f l u e n c e . I n F i g . 6 , e . . . a n d emin f o r t h e a r t if if ic ic i a l s a n d m i x t u r e s a r e p l o t t e d a g a i n s t

9 MOL mixes J,2,5,4 X MOL mix 5 9 CB mi x e s ; , 2 , 5 , 4

9 !2

F--

R=02

LO

c:::

3o= X

~o~

0,6

~'--~A

J.--

~o~

R:02

>So4 Z 0.2

,

~

~

.

4

.

.

.

6

.

.

.

COEFFI CI ENT OF UNfFORMI TY,

I0

Cu

FIG. 6 - - D e n s i t y l i m i t s a s a f u n c t i o n o f g r a d at a t i o n f o r a r tit i f i c i a l ly l y p r o po po r t i on on e d s a n d m i x e s .

C o p y r i g h t b y A S T M I n t l ( a l l r i g h ttss r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE) U niversidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreeme  

108

RELATIV RELA TIVE E DENS DENSITY ITY INVOLVING COHE COHESiONL SiONLESS ESS SOI SOILS LS

Cu. For constant values of R and for gradational curves of the normally distributed type, these data form well defined curves, indicating that range of particle sizes is another important factor controlling the density limits. Data from MOL Mix 5 (gap graded) are also included on Fig. 6 and plot appreciably above t he da ta from 1VI 1VIOL Mix 3 (normally graded), which is characterized by an equivalent Cu. Thus, the type of gradational curve is also a controlling factor.

A genera generalized lized set of curves curv es (Fig. 7), rel relati ati ng em~ em~x an and d em emin in to Cu with particle roundness as a parameter, were constructed from the data in Figs. 5 and an d 6. The T he va vali li di ty of these th ese curves for est estimat imat ing ema emaxand emin for normally or approximately normally distributed sands was examined by comparing estimated void ratios for the sands listed in Table 4 with maximum and minimum void ratios measured in the laboratory. Two methods meth ods of estimat est imat ion were used. Firs t, emaxand emln were est ima ted fro from m the index properties C~ and R. Second, an R value was estimated from

:,< ,< 14

E O" 12 I.-..-

I.C

=E X i

06, R O U N D E D ~

o"

i

0.4

~:~ 02 02

I

7 BRo 2

3

4

6

IO

15

COEFFICIENT OF UNIFORMI UNIFORMITY, TY, Cu

F I G . 7--Generalized curves for estimating

em~xand emln rom gradational and particle

shape characte characteristics. ristics. Curves are are only valid for clean sands sands with normal to moderately skewed grain-size distributions. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/ printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agree  

YOUD ON FAC FACTOR TORS S CONTRO CONTROLLI LLING NG DE DENS NSIITI TIES ES OF SA ND S

109

T A B L E 5--Measured and esti estimated mated density limits limits for for sands listed in Table 4. Code

Measured

Estimates Fro m Fig. 7

B u r m i s t e r~ r~

Hutchison and Townsend b

Ka bai ~

emax

emin

emaxd

emin d

emia e

emax

emin

emax

emin

0 19 19 0

0.70

0.42

0 . 71 71

0.42

0.42

0.82

0.66

.. .. ..

0R10 1C0 9 # 2 RC #1 SGB SG D SFB AC #1 AC #2 DM TRI TR2 CB

00 .. 75 55 0.57 0.79 0.81 0.74 0.73 0.90 0.91 0.87 0.91 0.96

00 .. 43 11 0.29 0.41 0.48 0.39 0.39 0.54 0.51 0.48 0.51 0.45

00 .. 76 00 0 . 61 61 0.81 0.88 0.70 0.75 0 .9 .9 3 0.88 0 .9 .9 1 0.92 0.93

00 .. 33 93 0 .3 .3 1 0.42 0.48 0.36 0.39 0.50 0.48 0.48 0.50 0.48

00 .. 43 01 0 .3 .3 1 0.42 0.43 0.38 0.37 0.48 0.50 0.46 0.48 0.50

00 .. 77 84 0.70 0.81 0.83 0.70 0.73 0.98] 1 . 00 00 s 0 . 91 91 ] 0.93] 0.98]

. 65 60 00 ..6 0.40 0.60 0.60 0.46 0.49 0.73] 0.70] 0.63/ 0.62] 0.61]

0...8. 1. . . 0.86 0.94 0.97 0.76 0.88 0.91 0 .9 .9 3 . .. .. . 0 .8 .8 7 0.82

0.50 0.47 0.57 0.64 0.38 0.50 0 .4 .4 9 0.57 0.50 0.42

emax

emia

0.76

0.64

00 .. 75 09 0.53 0.70 0.73 0.51 0.58 0.67 0.64 0.58 0.56 . .. .. .

00 .. 54 88 0.42 0.59 0.62 0.41 0.47 0.56 0.52 0.48 0.46

E s t i m a t e d f r o m F i g s . 3 a n d 4 o f B u r m i s t e r [ 3 ], ] , a s s u m i n g G , = 2 .6 .6 7. 7. b E s t i m a t e d f r o m H u t c h i s o n a n d T o w n s e n d ' s E q s 1 a n d 3 [ 9 ]],, a s s u m i n g G , = 2 .6 .6 7. 7. c E s t i m a t e d f r o m F i g . 1 0 o f K a b a i [11]. d E s t i m a t e d f r o m R a n d C ~ v a l u e s i n T a b l e 4 ( M e t h o d 1 ). ). e E s t i m a t e d f r o m C u a n d t h e m e a s u r e d em ~x ~x ( M e t h o d 2 ) . ] I n c l u d e s 4 4 N ( 10 10 -1 -1 b ) c o r r e c t i o n f o r c r u s h e d p a r t i c l e s .

Cu, a n d

the

em ~x m e a s u r e d

in

the

labo rato ry;

this

R

v alue

a nd

C~

w e r e t h e n u s e d t o e s t i m a t e e m l, l,. T h e s e e s t i m a t e s a n d t h e c o m p a r a t i v e l a b o r a t o r y r e s u l t s a r e l i s te te d i n T a b l e 5 . F o r t h e 1 3 s a n d s p e c i m e n s u s e d i n t h e c o m p a r i s o n , t h e d i ff f f e re re n c e b e t w e e n t h e e s t i m a t e d a n d m e a s u r e d e ~ b y t h e f i rs r s t m e t h o d w a s 0 .0 . 0 1 1 • 0 .0 . 0 2 4, 4, a n d t h e d i f f e r e n c e b e t w e e n t h e e s t i m a t e d a n d m e a s u r e d e ~ , i n w a s - 0 . 0 0 4 -4 - 0 .0 . 0 1 4. 4. B y t h e s e c o n d m e t h o d , t h e d i f f e r e n c e b e t w e e n t h e e s t i m a t e d a n d m e a s u r e d e ~ n w a s - 0 . 0 1 1 =i= 0 .0 .0 1 8. T h e s e d a t a s h o w t h a t t h e c u r v e s i n F ig . 7 a r e v a l i d f o r e s t i m a t i n g e ~ a n d e m in in f o r c l e a n s a n d s w i t h n o r m a l to to m o d e r a t e l y s k e w e d g r a i n - s i z e distribu tion curves. Clean sands are defined as hav ing less tha n 5 perc ent p a r t i c l e s b y w e i g h t p a s s i n g t h e N o . 2 0 0 s i ev ev e . N o r m a l t o m o d e r a t e l y s k e w e d g r a in i n - s iz iz e d i s t ri b u t i o n c u r v e s in c l u d e c u r v e t y p e s " S " a n d " L " a n d u p t o t h e m o d e r a t e l y c o n c a v e o r c o n v ex fo r m s o f c u r v e ty p e s " C " a n d " E " , r e s p e c t i v e l y , a s d e f i n e d b y B u r m i s t e r [ 2] 2] . T h e g r a i n s i z e d i s t r i b u t i o n c u r v e s i n F i g . 3 fa f a l l w i t h i n t h e s e c a t e g o r ie ie s .

C o m p a r is i s o n W i th t h P r e v io i o u s W o rk rk E x c e p t f o r t h e l a c k o f i n f lu l u e n c e o f p a r t i c l e s iz i z e , th th i s s t u d y c o n f i r m e d t h e f i n d in i n g s o f p r e v i o u s i n v e s t i g a t o r s [1-3] t h a t p a r t i c l e s h a p e , p a r t i c l e s i ze ze

Copyright by AS TM Int l (all rights reserved); Fri Mar 11 16:13:06 E ST 2016 Dow nloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i  

1 10

RELATIVE DENSITY INVO LVIN G COHES COHESION IONLES LESS S SOILS

range, and type of grading curve are the primary factors controlling em~x and emin. The appa ren rentt discrepancy as t o the influe influence nce of particle size size ma y possibly be explained by the fact that, for most natural sands, there is a correlation between particle size and particle shape. That is, the larger the particle size, the more rounded it tends to become through natural processes [ 1 8 ] . Thus, for any given sand, e ... and emin tend to decrease with particle size because of the shape factor; the data plotted on Fig. 4

follow this trend for each sand. Thee em~xand emin est Th estimat imat ed according to th thee criteria of previous investi investi-gators for the sands listed in Table 4 are shown in Table 5 where they can be compared with estimated and measu measured red values values from this study. Because Burmister [3] used a procedure very similar to the procedure used in this st ud udy y to measure em, em,x x (sand poured throu th rough gh a funnel fun nel into a mold), one would expect that estimates from his curves would agree well with values from this study. This is true for R values between 0.28 and 0.30 (subangular), which include sands SGB, SGD, AC#I, and SFB. With the suggested correction for crushed and broken particles applied, em~xvalues from Burmis ter's curves are consistant with measured d at a for sands with R values between 0.19 and 0.21, for example, sands TR#2 and CB. The T he agree agreement ment between betwe en estimat es timates es of em em~xfrom Burmister's curv curves es and the measured values for the other sands is not very good, chiefly because the single-value correction for crushed and broken particles does not adequately account for all of the density variation due to particle shape. For all of the sands, emi emin values es timate d from Bu rmiste r's curves are greater than those measured in this study. This result is consistant with the fact t ha t the methods used used by Burmister to obtain maximum densiti densities es (vibrating tamper or impact) do not give values as great as the simple shear method used in this study. The criteria for estimating estimating maximum an d minimum density established established by Hutchison and Townsend [9] did not include any variance for grain shape.. Thus, a general direct comparison between esti mated en~ shape n~x x and emin from their criteria and the measured values can not be made. It is noted th at the em~xestimated by their criteria is approximately approx imately equal in val ue to the measured em em~x for sands with an R of 0. 0.25 25 (sands A C # 2 and DM). However, this R is considerably different from the R of 0.50 to 0.55 determined from several specimens of beach and dune sands used by Hutchison and Townsend in their study. Several factors could contribute to this discrepancy, including, (1) possible differences in the methods used to determine R, (2) the beach and dune specimens used for this study may have been more more rounded than the beach and dune sands used used by Hutchison and Townsend, and (3 (3)) the tipping tip ping test procedure they used for determi ning minimum densities may have yielded appreciably lower e ... values than the funnel method used in this study.

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YOUD ON FACTORS CONTROLLING DENSITI DENSITIES ES OF SANDS

11 1

The determinat ion of the Bagnold grading parameters is another pos possi sible ble source of error in estimating maximum and minimum densities by the Hutc hiso hison n and Townsend criteria. criteria. These parameters are unique un ique ly definable for many sands, such as those with S-shaped gradation curves. For others, such as those with linear, concave, or convex gradation curves, their evaluation is subject to som somee subjective subjective interpretat ion or n ot defi definabl nablee at all, hence, hence, th e omiss omission ion of some some dat a from Table 5.

All of of the e~in estimated by the Hutchiso n and Townsend criteria criteria are greater than those measured in this study, indicating that maximum densities obtained by the vibrating tamper-compaction method, which they used in deriving their criteria, gives smaller densities than the simple shear method. The values of em ema~ esti mated from Kaba i's [11] curves agree approximat ely wi th the em~xfrom thi s st ud y for R values between 0. 0.37 37 an d 0. 0.42 42 (sands 0109, 0109, RC # 1 and RC # 2). 2). Kaba i's em em~ ~ values are based on fu nnel meth od mi nimu nimum m den densit sit y tests, as are those tho se in this stud y. The emi~ for these same sands estimated from Kabai's curves are considerably greater than those measured in the laboratory by the simple shear method, indicating th at the sim simple ple shear shear method gives gives considerably considerably greater ma ximum densities than the impact method used by Kabai. Because Kabai did not consider the influence of particle shape on maximum and minimum densities, further comparisons with data estimated from his curves are not warranted. Conclusions

1. The results of this st ud udy y confirm the findings of previous studies th at the primary factors controlling the maximum and minimum void-ratio limits of clean sands are particle shape, particle size range, and the shape of the gradational curve. Contrary to previous studies, it was found that particle size p e r s e has no significant influence on the density limits. 2. The curves in Fig. 7 are val id for fo r est ima ti ting ng e~ax e~ax and emi min n for clean sands with normal to moderately skewed grain-size distributions. Acknowledgments

The assistance of Terry Craven, who performed the compaction tests, and Julius Schlocker, who assisted with the mineral identifications, is gratefully acknowledged. References

[1] Burmister, Burmister,D. D. M., Proceedings, AmericanSocie Society tyfor for Testingand Testingand Materi Materials, als, Vol.38, 1938, pp. 587-596. [2] Burmister,D. Burmister,D. M., Proceedings, American AmericanSociety Societyfor for Testin Testing g and Materials, Vol. Vol. 48, 48, 1948, pp. 1249-1268. [3] Burmi B urmister ster,, D. M. in F i e ld ld T e st s t in in g o f S o i ls ls , A S T M S T P 3 22 22 , Americ American anSociety Societ yfor Testing and Materials Materials,, 196 1962, 2, pp. 67-9 67-97. 7.

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RELATIVE DENSITY INVOLVING COHESI RELATIVEDENSITY COHESIONLESS ONLESS SOILS

[ $ ] B u r m i s t e r , D . M . i n Procedures fo r Testing Soils, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , P h i l a d e l p h i a , P a . , 1 9 6 4 , p p . 1 7 55 - 17 17 7 . [ 5] 5 ] F e l t , E . J . i n Application o f Soil Testing Testing in Highw ay Design Design and Construct Construction ion,, A S T M 10 8 . S T P 2 3 9 , A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 5 8 , p p . 8 9 - 10 [ 6] 6] K o l b u s z e w s k i , J . J . a n d F r e d e r i c k , M . R . , Proceedings, E u r o p e a n C o n f e r e n c e o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , W i e s b a d e n , 1 9 6 3 , V o l. l. I , p p . 2 5 3 - 2 6 3 . [ 7] 7] K o l b u s z e w s k i , J . J . , Proceedings, 2 n d I n t e r n a t i o n a l C o n f e r e n c e o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , R o t t e r d a m , 1 9 4 8 , V o l. l . 1 , p p . 1 58 5 8 -1 -1 65 65 . [ 8] 8] B a g n o l d , R . A . , The P hysics of Blown S an d a nd D ese esert rt Dunes, M e t h u e n a n d C o . L t d . ,

London, 1941, pp. 113-116. [ 99]] H u t c h i s o n , B r u c e a n d T o w n s e n d , D a v i d , Proceedings, 5 t h I n t e r n a t i o n a l C o n fe f e r e n ce ce o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , P a r i s , 1 9 6 1 , V o l . 1, 1, p p . 1 5 99 - 16 16 3 . , T il . HEn . , gine [10] W Jou rna of the the So il Mechanics Mechani Foundation D ivi ivision, sion,23.A m e r i c a n S o c i e t y of uCiv ers,l 1957, V oL 83, No. cs SMand 1, pp. 1161-11 to 11611161-23. 1161i n Proceedings, 3 r d B u d a p e s t C o n f er e r en en c e o n S o i l M e c h a n i c s a n d F o u n d a [11] K a b a i , I . in t i o n E n g i n e e r i n g , B u d a p e s t , 1 9 6 8 , p p . 1 1 55 - 12 12 6 . [ 1 2] 2] J o h n s o n , A . W . a n d S a l l b e r g , J . R . , " F a c t o r s In In f l u e n c i n g C o m p a c t i o n T e s t R e s u l t s , " H i g h w a y R e s e a r c h B u l l e t i n 3 1 9, 9 , 1 96 9 6 2. 2. i n i n g i n S i m p l e S h e ar ar , [13] Y o u d , T . L .,. , " M a x i m u m D e n s i t y o f S a n d b y R e p e a t e d S t r a in Hig hw ay Research Reco rd No. 374, 1971, pp. 1-6. [14i [1 4i]] Kolbu szew ski, J. J., Proceedings, 2 n d I n t e r n a t i o n a l C o n f e re r e n c e o n S o il il M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , R o t t e r d a m , 1 9 4 8 , V o l. l . 7, 7, p p . 4 7 - 4 9 . [15] Y o u d , T . L ., Jo urn al of the Soil Mechanics an d Foundations Foundations Divis Division, ion, A m e r i c a n Soc iety of Civil Engineers, 1972, V ol. 98, No. SM 7, pp . 709-725. [16] W a d e l l , H a k o n , Journ al of Geology, Geology, V ol. 43, 1935, pp . 250-280. P o w e r s , M . C . , [17] Jou rnal of Sedimen tary Petrolo Petrology, gy, V ol. 23, No . 2, Ju ne 1953, pp . 11 7119. [18] T w e n h o f e l , W . H . , Principles of sedimentation, M c G r a w - H i l l B o o k C o . I n c . , N e w Yo rk, 1950, pp. 302-311.

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E. A. Dicki n I

In f lu l u e n c e o f G r a i n S h a p e a n d S i ze ze u p o n t h e L i m i t in i n g P o r o s it i t i e s o f Sa n d s

c k in i n , E . A ., ., " I n f l u e n c e o f G r a i n S h a p e a n d S i z e u p o n R E F E R E N C E : D i ck t h e L i m i t i n g P o r o s it i t i es e s o f S a n d s , " E valuation of R elative Density and Its

R ole ole in Geotechni Geotechnical cal P roject rojectss Involving Cohesio Cohesionl nless ess Soils, A S T M S T P 5~3, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 7 3 , p p . 1 1 33- 12 12 0 .

A B S T R A C T : T h e s t a t e o f p a c k i n g o f a m a s s of o f s a n d g r a in i n s is i s d es e s c ri ri b e d b y i t s r e l a ti ti v e p o r o s i t y n ~ w h i c h d e f i n e s t h e p a c k i n g r e l a t i v e t o m a x i m u m a n d m i n i m u m p o r o s i t ie i e s o f t h e m a t e r i a l . T h e s e l im i m i t i n g p o r o s it it i e s d e p e n d i n t u r n upon the physical characteristics of the grains themselves. In the research d e s c r ib i b e d h e re r e i n , t h e i n fl f l u en e n c e o f g r a in i n s h a p e a n d s iz iz e u p o n t h e l i m i t i n g p o r o s i ti t i e s o f q u a r t z s a n d s a n d g l a ss s s b a l l o t in in i w a s s t u d i e d . T h e m a x i m u m p o r o s i ti ti e s w e r e d e t e r m i n e d b y d e p o s i t i o n o f t h e s a m p l e t h r o u g h w a t e r a s s u g g e s t e d b y K o l b u s z e w s k i ( 19 1 9 48 4 8 ) w h i le l e m i n i m u m p o r o s i ti ti e s were obtained by vibration under w ater. Shape param eters for the sand s were determined from a correlation between the time of flow of a 0.5-kg specimen a n d t h e s p h e r i c i t y m e a s u r e d b y e x a m i n a t i o n o f in i n d i v i d u a l g r a in in s . B o t h m a x i m u m a n d m i n i m u m p o r o s i ti t i e s d e c r e a s e d w i t h i n c r e a si si n g s p h e r i c i t y w h i l e t e s t s o n g l a s s b a l l o t i n i i n d i c a t e d t h a t t h e e f f ec e c t o f g r a i n s i~ i~ e w a s n e g l i g i b l e . T h e p o r o s i t y i n t e r v a l w a s a p p r o x i m a t e l y 12 12 .5 .5 p e r c e n t f o r a l l t h e s a n d s a n d 1 1 p e r c e n t f o r s p h e r i c a l b a ll l l o t in in i . M i x t u r e s o f s a n d a n d b a l l o t i n i g a v e r e a s o n a b l e agreement with the trend shown by the separate materials. K E Y W O R D S - e o h e s io i o n le l e s s s o il i l s, s, d e n s i t y ( m a s s / v o l u m e ) , v i b r a t i o n , m e a s u r e m e n t , c l a s si s i f ic ic a t io io n s , s a n d s

Nomenclature

d

A v e r a g e g r a in d i a m e t e r ( m m )

n

Porosity M a x i m u m p o r o s it y M i n i m u m p o r o s it y

n rilax

nmin

n, q ~0

R e l a t i v e p o r o s i ty F l o w t i m e (s ) A n g l e o f i n t e r g r a n u l a r f r ic t i o n Sphericity

: L e c t u r e r i n C i v i l E n g in in e e r i n g , T h e U n i v e r s i t y o f L i v e r p o o l , E n g l a n d . 113

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1 14

RELATIVEDENSITY RELATIVE DENSITY INV OLV ING COHESIONL COHESIONLESS ESS SOILS

P o r o s i t y h a s b e e n w i d e l y u s e d t o d e s c ri ri b e t h e s t a t e o f p a c k i n g o r i r r e g u l a r sand grains although its inadequacy has been demonstrated by both K o lbu szew sk i [1 ]2 ] 2 a n d A m i r s o l e y m a n i i [ 2 ] . K o l b u s z e w s k i [ 3] 3] c o n s i d e r e d that relative porosity (nr) gave a better assessment of packing. This is defined as nr

~-

nmax nmax

~ --

n nmin

where

n~. x

and n~in are the limiting porosities of a sand and n its actual

porosity. He proposed standard tests to determine the limiting porosities a n d c o n c l u d e d t h a t i n t e n s i t y o f d e p o si s i ti t i o n a n d m a t e r i a l p r o p e rt r t i es es w o u l d i n f lu lu e n c e t h e p a c k i n g . T h e e f f e c t o f g r a i n s h a p e a n d s iz iz e o n t h e l i m i t in i n g p o r o si s i ti ti e s h a s b e e n s t u d i e d b y K o l b u s z ew e w s k i a n d F r e d e r i c k [ 4] 4] w h o f o u n d t h a t : ( a) a ) t h e l i m i t i n g p o ro r o s i ti ti e s i n c r e a s e d a s a n g u l a r i t y i n c r e a s e d ; ( b ) t h e m a x i m u m p o r o s i t y d e c r e a s e d w i t h d e c r e a s i n g u n i f o r m i t y co co ef ef f i cient; and (c)) th e p o ro sity in te rv a l n ~ az (c az - n mln ml n w as o f th e o rd e r o f 10 10 to 1 2 p e rce n t for all the sands considered, the interval decreasing slightly as roundness in creased . They assumed a single shape value for each sand, although different s i ev e v e f ra r a c t i o n s w e r e u s e d . T e s t s o n g l a ss ss b a l lo lo t i n i i n d i c a t e d t h a t t h e m a x i m u m p o r o s i t y d e c re r e a s e d w i t h i n c r e a si s i n g g r a i n si s i z e, e, a l t h o u g h t h e m i n i m u m p o r o s i t y a p p e a r e d t o b e i n d e p e n d e n t o f s iz iz e. e. A l y a n a k [ 5] 5] c o n c l u d e d t h a t t h e p o r o s i t y i n t e r v a l w a s o n l y a r e f le l e c t io io n o f t h e r e l a t i v e m e r i t s o f t h e m e t h o d s b y w h i c h t h e l i m i ti t i n g p o ro ro s it i t ie ie s w e r e o b t a i n e d a n d w a s i n d e p e n d e n t o f p a r t i c l e s h a p e a n d s iz i z e d i s tr tr i b u t i o n . H o w e v e r , S m i t h [ 6] 6] fo f o u n d a 3 p e r c e n t d e c r e a s e i n n m a z - - n m i n as g rain s i n c r e as a s e d i n r o u n d n e s s f r o m v e r y a n g u l a r ( c r us u s h e d b a s a l t) t) t o r o u n d e d (Erith sand), which is consistent with the trend observed by E1-Sohby [7] w h o r e p o r t e d a 5 .7 .7 p e r c e n t d i f fe f e r e n c e b e t w e e n t h e v a l u e s f o r c r u s h e d f e ld ld s p a r a n d g l as a s s b a l lo l o t i n i.i. E 1 - S o h b y i n d i c a t e d t h a t t h e p o r o s i t y i n t e r v a l increased as the angle of intergranular friction increased, but he defined h i s m a x i m u m p o r o s it it ie i e s a s t h o s e o f h is i s l o o s es e s t c y l i n d r ic i c a l c o m p r e s s io io n t e s t s p e c i m e n s , a n d i t i s u n l i k e l y t h a t h is is n ~ , z v a l u e s w o u l d b e a s h i g h a s c o u l d b e o b t a i n e d b y t h e d e p o s it i t io i o n m e t h o d s o f K o lb l b u s ze z e w s k i. i. S m i t h a l o n e t o o k account of the variation of particle shape with size although he finally used weighted values to describe the shapes of his graded sands. In the research described herein, the variation of limiting porosities with shape of sieve fractions of five natural sands--Biddulph, Erith, Ham River, L e i g h t o n B u z z a r d , a n d S t o n e c o u r t - - w a s c o n si s i d er e r e d. d. 2 T h e i t a l i c n u m b e r s i n b r a c k e t s r e f e r t o t h e l i s t o f re r e f e re re n c e s a p p e n d e d t o t h i s

paper.

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DICKIN DI CKIN O N IN INFL FLUEN UENCE CE OF GRAIN S HAPE AND SI ZE

115

Experimental Procedure

D e t er e r m i n a ti ti o n o f M a x i m u m P o r o s it it y

T h e m a x i m u m p o r o s it i t y w a s d e t e r m i n e d fr f r o m t h e v o l u m e o c c up u p i ed ed b y 1 kg of the specimen after deposition through water as suggested by K o l b u s z e w s k i [ 3 ] . V a l u e s o f s pe p e ci ci f i c g r a v i t y u s e d i n p o r o s i t y c a l c u l a ti ti o n s w e r e o b t a i n e d f o r e a c h s a n d b y t h e B r i ti ti s h S t a n d a r d d e n s i t y b o t t l e m e t h o d

(BS 1377). D e t e rm r m i n a t io io n o f M i n i m u m P o r o s it it y

T h e m i n i m u m p o r o s i t y w a s o b ta t a i n e d b y v i b r a t i o n u n d e r w a t e r i n p r e f e rre n c e to t o m o r e s e v e r e m e t h o d s w h i c h c a u s e p a r t ic i c l e d e g r a d a t io io n . T h e m e -

FIG. 1--Photomicrographs of sands. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreem  

116

RELATIVE RELATI VE DENSI DENSITY TY INV OLV ING COHESI COHESIONLESS ONLESS SOI SOILS LS

c h a n ic ic a l v i b r a t o r u s e d w a s d e v e l o p e d b y S m i t h [ 6 ] w h o f o u n d t h a t t h e d e n s e s t p a c k i n g s w e r e o b t a i n e d f o r a f r e q u e n c y o f 3 7 .8 .8 H z a n d a n a m p l i t u d e o f 0 . 6 m m . S p e c i m e n s w e r e p r e p a r e d b y v i b r a t i n g f o r 5 r a in i n i n a 1 02 02 m m d i a m e t e r b y 1 02 0 2 m m h i g h m o u l d a n d w e r e l a t e r s u b j e c t e d t o a x i s y m m e t r ic ic c o m p r e s si s i o n te t e s t s [ 8 ] . T h e p o r o s i t y w a s c a l c u l a te te d f r o m t h e v o l u m e o f water displaced by the specimen in the compression cell as described by Lee [9].

Determination of Grain Shape eisn sw earned d w e teerrem idneefdi n ebdy ienx atm n as t io i oo fn Ro if l epyh'os t oi m i n dGi vr ai di nu asl h ag pr aes e rim n siccrriobgerda pchisr c loef s p h e r i c i t y [10]. T y p i c a l p h o t o m i c r o g r a p h s o f t h e s a n d s a r e il il l u s t r a t e d i n Fig. 1. D i r e c t m e t h o d s o f e s t i m a t i n g p a r t ic ic l e s h a p e b e c o m e l e n g t h y i f a t r u l y representative specimen of a sand is to be examined and are therefore unsuitable for routine use. Thus, indirect methods have been developed in which a bulk property of the material, which is strongly influenced by grain shape, is measured in a standard test. A good correlation was found b e t w e e n t h e t i m e t a k e n f o r 0 . 5 k g o f t h e s p e c i m e n t o f lo l o w t h r o u g h a 6 . 3 55m m d i a m e t e r o r if i f ic i c e a n d s p h e r i c it it y . T h e f l o w t e c h n i q u e h a s b e e n r e p o r t e d b y K i n g a n d D i c k i n [11] a n d w a s b a s e d o n a t e s t d e v i s e d b y R e x a n d Pd ieacm k e[12]. e ri) c bi tyy (~b0) w a s re l a t e d t o fl o w t i m e (q s ) a n d a v e r a g e g ra i n t e r ( dSpmh m te ~b0--

196d+ 144-- q 146d + 112

This emperical equation yielded a more reliable value of sphericity than w o u l d b e o b t a i n e d b y d i r ec e c t m e a s u r e m e n t a l on o n e s in in c e a la l a r g er er n u m b e r o f g r a i n s w e r e c o n s i d e re r e d . I n s e r t i o n o f d a n d c o r r e s p o n d in in g q v a l u e s g i v e n i n T a b l e 1 i n t o t h e e m p i r i c al al e q u a t i o n y i e l d e d t h e v a r i a t i o n o f s p h e r i c i t y with grain size shown in Fig. 2. Stonecourt sand excepted, a marked deTABLE Ave rage Grain Diameter, mm

0.510 0.388 0.325 0.272 0.230 0.181 0.121

1--F low times of sieve sieve fracti fractions ons of sands. sands.

Biddulph

Flow time, s Ham River

Erith

90.8 84.0 81.8 78.0 74.8 69.8 . . . . . .

77.5 74.3 70.9 68.0 66.7 62.8

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L e ig h t o n Buzzard

S t o n e c ou r t

82.4 74.6 72.6 70.3 ... ... ...

88.0 81.2 77.3 72.4 70.2 68.0 66.2

C o p y r i g h t b y A S T M I n t l ( a l l r ig ig h t s r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n te d b y (UFPE ) Universidade Federal de Pernambu co ((UFPE) Un iversidade Federal de Pernambuco ) pursuant  

DICKIN DIC KIN O N IN INFLU FLUENCE ENCE OF GRAIN SHA PE AND SI Z E

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FIG. 2--Variation of spheri sphericit cityy with grain size size for sands. c r e a s e i n s p h e r i c i t y a c c o m p a n i e d d e c r e a s e i n g r a i n s iz iz e. e. U p o n c l o s er er e x a m i nation, Stonecourt sand was found to contain significant quantities of angular nonquartz material, mainly haemetite and calcite, in the larger s i e v e s iz iz es es . T h i s m a t e r i a l n o t o n l y g a v e a n i n a c c u r a t e e s t i m a t i o n o f s p h e r i c i t y f r o m p h o t o m i c r o g r a p h s b u t y i e l d e d s p u r io i o u s f lo l o w t i m e s d u e t o d i f fe fe r ences in surface texture. V alues of sphericity for Ston ecou rt sand w ere t a k e n a s th t h o s e o b t a i n e d b y i n d i v id i d u a l e x a m i n a ti ti o n . R esults

and

D i s c u s s io n

T h e In f lu l u e n c e o f G r a i n S h a p e o n th th e L i m i t i n g P o r o s i ti ti e s o f S a n d s

The limiting porosities for sieve fractions of the five sands are plotted against sphericity in Fig. 3. A general decrease in both maximum and minimum porosities with increasing sphericity is observed, although the p o r o s i t y i n t e r v a l n m ax a x - - n m in in d o e s n o t a p p e a r t o c h a n g e s i g n if i f i c an a n t ly ly w i t h g r a i n s h a p e o v e r t h i s l i m i t e d r a n g e o f s p h e ri r i c it i t ie ie s . T h e i n t e r v a l i s a p p r o x i m a t e l y 1 2. 2 . 5 p e r c e n t w h i c h is is o f t h e s a m e o r d e r a s t h a t r e p o r t e d b y K o l b u s zewski and Frederick [4]. T h e In f l u e n c e o f G r a i n S i z e u p o n t h e L i m i t i n g P o r o s i ti ti e s

Tests were carried out on sieve fractions of glass ballotini in order to investigate the effect of variation in grain size alone upon the limiting p o ro s i t i e s . T h e re s u l t s a re s h o w n i n Fi g . 4 , a n d i t i s s e e n t h a t n o s i g n i fi c a n t v a r i a t i o n i n e i t h e r m a x i m u m o r " m in in im im u m p o r p s i t y o c c u r s o v e r t h is is r a n g e C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

118

RELATIVE DENSITY INVOLVING COHESIONLESS SOILS 55

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FIG. 4--Limiting porosities of glass ballotini. Copyright by AS TM Int l (all ri rights ghts reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. No further  

DICKIN ON INFLUENCE OF GRAIN SHAPE AND SIZE

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FIG. 5---Limiting porosities of quartz sands an d glass ballotini ballotini.. o f s iz iz es es . T h i s r e s u l t d o e s n o t c o n f i r m t h a t o f K o l b u s z e w s k i a n d F r e d e r i c k w h o f o u n d t h a t t h e m a x i m u m p o r o s i t y o f b a l lo l o t in i n i d e c r e a s e d w i t h i n c r ea e a s in in g gra in si size. ze. T h e p o r o s i t y i n t e r v a l f o r b a l lo l o t in in i w a s a p p r o x i m a t e l y 1 1 p e r c e n t w h i c h co n firms p rev io u s rep o rts [4 , 7 ] th at sm aller n ~ ax ax - - n m i n v a l u e s a r e o b t a i n e d f o r b a l l o ti ti n i t h a n f o r s a n d s . I t i s n o t c l e a r w h e t h e r t h e t r e n d i s d u e t o s h a p e d i ff f f e r en e n c e s o r t o t h e c o n s i d e r a b l y l o w e r a n g le le o f i n t e r g r a n u l a r f r i c t i o n f o r g la l a ss s s b a l lo l o t in in i ( ~ ~ 15 d e g ) c o m p a r e d w i t h t h a t o f q u a r t z s a n d s ( ~ u s u a l l y b e t w e e n 2 4 a n d 2 8 d e g ). ). The variation of limiting porosities for 100 percent quartz sands and glass ballotini is illustrated in Fig. 5. Intermediate values of sphericity were achieved by mixing Leighton Buzzard sand with glass batlotini in e q u a l p a r t s b y v o l u m e . V a l ue u e s o f m a x i m u m p o r o s i t y f o r t h e m i x t u r e s w e re re c o n s i s te t e n t w i t h t h e g e n e r a l t r e n d , b u t m i n i m u m p o r o si s i ti t i es e s w e r e n o t a s lo lo w a s m i g h t h a v e b e e n e x p e c te te d . Conclusions

Both the maximum and minimum porosities decrease with increasing s p h e r i c i t y f o r t h e f iv iv e s a n d s c o n s i d e r e d i n t h i s r e s e a r c h . T h e e f f e c t o f v a r i a t i o n i n g r a i n s iz iz e h a s b e e n s h o w n t o b e n e g l i g ib ib l e f o r g l as a s s b a l lo l o t i n i, i , a n d i f t h i s r e s u l t is is a s s u m e d t o a p p l y t o s a n d s , t h e v a r i a t i o n i n m a x i m u m a n d m i n i m u m p o ro r o s it i t ie i e s i n F ig ig s . 3 a n d 5 i s a t t r i b u t a b l e t o C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e  

120

RELATIVE RELATI VE DENSIT DENSITY Y INVO LVIN G COHESIONLESS COHESIONLESS SOIL SOILS S

c h a n g e s i n g r a i n s h a p e . L i m i t i n g p o r o s i ti ti e s d e c r e a s e w i t h i n c r e a s i n g g r a i n s iz i z e f o r a n y o n e s a n d a s a re re s u l t o f t h e i n h e r e n t i n c r e a s e i n s p h e r i c i t y w i t h g r a i n s iz i z e i n n a t u r a l q u a r t z s a n ds ds . T h e p o r o s i t y i n t e r v a l w a s a p p r o x i m a t e l y 1 2. 2.5 p e r c e n t f o r t h e s a n d s considered, while tha t for glass ballotini was only 11 percent. It w as not c l e a r w h e t h e r t h i s w a s d u e t o d i ff f f e r en e n c e s i n s h a p e o r i n i n t e r g r a n u l a r f r ic ic t i o n , a l t h o u g h t h e e f f e c t o f d i f f e r e n t a n g l e s o f i n t e r g r a n u l a r f r i c t io io n w o u l d p r o b a b l y b e s m a l l a t t h e r e l a t i v e l y l o w st s t re r e s s l ev e v e ls l s e n c o u n t e r e d i n t h e se se

tests. V a l u e s o f m a x i m u m p o r o s i t y fo f o r gl g l as a s s b a l l o t i n i / s a n d m i x t u r es e s f o ll ll o w e d t h e t r e n d o f o t h e r r e s u lt l t s m o r e c l o se s e l y t h a n d i d v a lu lu e s o f m i n i m u m p o r o s i t y .

References [1] Kolbuszewski, J. J. in Proceedings, M id lan d s S o il il M ech an ics an d F o u n d atio n s E n g ineering Society, Birm ingham , N o. 4, 1961, pp. 9-18. [2] A mir mirsol soleyman eymanii ii,, "Pa ckin g of Gra nular M aterials with Special Special Reference to Triaxial Tes ting," P h.D . thesi thesis, s, U niversity of Birm ingham , 1964. [3] Kolbuszewski, J. J., Proceedings, 2nd International Conference of Soil Mechanics, V ol. 1, 1948, p. 158. [~]] Kolbusz [~ Kolbuszewsk ewski, i, J. J. a nd Frederick, M . R., " T he Signifi Significan cance ce of Particle Sha pe and S ize ize o n th e M ech an ical B eh av io u r o f G r an u lar M ater ials ials ," Eu r o p ea n C o n f eren er en ce o f Soil Mechanics and Foundations Engineering, Yol. 1, 1963, pp. 253-263. [5] Alyanak, I. in Proceedings, M id lan d s S o ilil M ech an ics an d F o u n d atio n s E n g in eerin eer in g Society, Birmingham , No. 4, 1961, pp. 3737-42. 42. [6] SStre [6] mith , D T h eds," I n f lu lM u en ce thesi o fesis, P ar h apty e oofn Liver th e Limitin g P o r o s itie itiess an d S h ear ngt h .,of "San . E. th s, ticle U nivSersi Liverpool pool,, 1965. [7 ] Ei- S o h b y , M . A ., " Th e B eh av io u r o f P ar ticu lar M ater ials u n d er S tr es s ," P h .D . thesis, thes is, U nive rsity of M anc heste r, 1964. [8]] Dickin, E. A., "Th e Influence of Grain Sh ape and Size on the S hear Streng th Com [8 ponen ts of Qu artz San ds," P h.D . th thesi esis, s, Un iversity of Liverpool, 1971. 1971. [9] Lee, I. K., Proceedings, Am erican Society of Civil Engineers, V ol ol.. 92, SM2, 196 1966, 6, pp. 79-103. [10] Riley, N. A., Jour nal of Sedimentary Pet Petrol rology, ogy, V ol. 11, No . 2, 1 941, p. 94. [11] King, G. J. W . and Dickin, E. A., Ma terials an d Structures, Structures, V ol. 4, No. 2, 1972. [I~] Rex, H. M. and Peck, R. A., Journ al of Public Roads, Roads, Yol. 29, No . 5, 195 6 pp. 118 120.

Copyright by A STM Int l (all rrights ights reserved); Fri Mar 1 1 16:13:06 EST 2016 Dow nloaded/printed by (UFPE ) Universidade Federal de Pernamb uco ((UFPE) U niversidade Federal de Pernambu co) pursuant to to License Agreem ent. No furt  

E. W. Bran d ~

Some Observations on the Control of D e n s i ty t y b y Vi Vi b r a t i o n

R E F E R E N C E : B r an an d , E . W . , " S o m e O b s e r v a t i o n s o n t h e C o n t r o l o f D e n s i t y b y V i b r a t i o n , " Evaluation of Relative Density and Its Role in Geotechnical

Projects Invol Projects Involving ving Cohesi Cohesionle onless ss Soil Soils, s, A S T M S T P 523, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 73 73 , p p . 1 2 1 - 13 13 2 .

A B S T R A C T : B e c a u s e v i b ra r a t i o n t e ch c h n i q u e s ax a x e c o m m o n l y u s ed ed f o r t h e p r e p a r a t i o n o f l a b o r a t o r y t e s t s p e c im i m e n s , t h i s s t u d y w a s c a r r ie ie d o u t t o e x a m i n e s o m e of the factors which affect the densities obtained. A simple, one-degree-off r e e d o m v i b r a t i n g t a b l e d e v i c e , e q u i p p e d f o r control o f b o t h a m p l i t u d e a n d frequency, was used to give a sinusoidal wave form of vibration. Tests were carried out with four size ranges of sand and with single size glass balls, and observations were made on the effects of time of vibration, intensity of vibration, and container size. itthi es eess ew de er en saict ie in w g liet hv at li umee oof ft hvei bmr aatxi oi m a c cMe laexriamti t i ou nm i rne leaatci vh e cdaese sen,s it iheise vi en dc r ae ta sain i nsgin n uump t o a b o u t 3 0 r a in in . O n l y lo l o w s t a t e s o f c o m p a c t i o n w e r e o b t a i n e d f o r so so m e o f t h e v i b r a t e d s p e c i m e n s , a n d i n n o c a se se w a s 1 0 0 p e r c e n t r e l a t i v e d e n s i t y a c h i e v e d . By far the most significant experimental results related to the variation of d e n s i t y t h r o u g h o u t t h e v i b r a t e d s o il il s p e c im i m e n s . T h i s w a s in in v e s t i g a t e d u s i n g a s p l i t c y li l i n d e r , w i t h f o u r e q u a l p a r ts ts , w h i c h c o u l d b e d i s m a n t l e d a f t e r v i b r a t i o n enabling separate density m easurem ents to be made. C onsiderable density varia t i o n s e x i st s t e d t h r o u g h o u t t h e s p e c i m e n s a t v i b r a t i o n i n t e n s i t ie ie s b e l o w t h e o p t i mum value. Only where the average relative density was high was an approxim a t e l y h o m o g e n e o u s s p e c i m e n o b t a in in e d . T h i s f a c t i s i m p o r t a n t t o t h o s e c o n cerned with the preparation of test sections in the laboratory. K E Y W O R D S : vibration, compacting, tests, sands, density (mass/volume),

porosity, cohesionless soils

V i b ra r a t io io n t e c h n i q u e s a r e c o m m o n l y e m p l o y e d i n t h e p r e p a r a t i o n o f l a b o r a t o r y t e s t s p e c i m e n s o f g r a n u l a r m a t e r ia i a l s . I n s u f f i c ie i e n t r e g a r d is is o f t e n paid to the complex nature of the mechanics of the process of dynamic c o m p a c t i o n , h o w e v e r , a n d t h e p r e s u m p t i o n t h a t h o m o g e n e o u s sa s a n d s p ec e c iim e n s o f a d e s i r e d r e l a t iv i v e d e n s i t y c a n b e e a s i ly ly a n d c o n s i s t e n t l y a c h i e v e d 1 A s s o c i a t e p r o f es e s s or or , G e o t e c h n i c a l E n g i n e e r i n g , A s i a n I n s t i t u t e Bangkok, Thailand.

of Techno logy,

12 1

opyright by AST reserved); Fri Mar 16:13:06 Copyright 9 M Intbyl (all ASrights TM Int Internat ernational ional ww11 w.astm.org w.ast m.org EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

122

RELATIVEDENSITY RELATIVE DENSITY INV INVOL OLVI VING NG COHE COHESION SIONLESS LESSSOILS

by means of a vibrating table is erroneous. Published literature pertaining to compaction by vibration is scant, the only contributions which are d i r e c t ly l y r e l e v a n t t o t h e c o n t ro ro l o f d e n s i t y i n t h e l a b o r a t o r y b e i n g t h o s e b y M o g a m i a n d K u b o [ 1] 1] ~, ~, F e l t [ 2 ] , A l y a n a k [ 3 ] , S e li li g [ 4 ] , P e t t i b o n e a n d Ha rdin [5], Kolbuszew ski and A lyanak [6], and D'App olonia and D'A ppo lonia [7]. T h e p e r f e c t te t e c h n i q u e f o r p r e p a r in i n g s a n d s p e c im i m e n s w o u l d b e o n e w h i ch ch p e r m i t t e d a b s o l u t e c o n t r o l o v e r t h e r e l a ti t i v e d e n s i t y a n d w h i c h r e s u lt lt e d i n

the formation of completely homogeneous specimens. It would also enable t h e a c h i e v e m e n t o f r e l a t i v e d e n s it i t ie i e s c l o se s e t o 1 00 00 p e r c e n t , a n d w o u l d r e n d e r a s i n si s i g n if i f ic i c a n t t h e e f f e c ts ts o f t h e m o l d i n w h i c h t h e m a t e r i a l w a s c o n t a i n e d . I n o r d e r t o a s s e ss s s t h e p o s s i b i li l i ti ti e s t h a t a v i b r a t i o n d e v i c e m i g h t b e d e v e l o p e d in i n t o t h i s p e r f e c t in i n s t r u m e n t o f s a m p l e m a n u f a c t u r e , a b r ie ie f e x p e r i m e n t a l s t u d y w a s c a r ri ri e d o u t w h i c h y i e l d e d t h e r e s u l t s r e p o r t e d i n this paper. It is hoped that a few observations made during tests using a s i m p l e o n e - d e g r e e - o f - f re r e e d o m v i b r a t i n g t a b l e d e v i c e w i ll l l b e o f so so m e i n t e r e s t t o t h o s e c o n c e r n e d w i t h m e a s u r e m e n t s o n g r a n u la l a r m a t e ri r i al a l s. s. T h e G r a n u l a r M a t e ri al s

Description t i oonf gtleasss f os uwr e dr er yd eqs ui ganr at zt e ds aansd Fs i naen dS aonnd e, s p eVciibmr ea nti stss b w a lels al l sr .e Tchoen ds ua nc dt e ds p ewciim itmh e nfo M e d i u m S a n d , C o a r s e S a n d a n d G r a d e d S a n d , a n d t h e p a r t ic i c l e s iz iz e r a n g e s w e r e c o n t r o l l e d b y U . S . S i e v es e s 5 0 - 1 0 0 , 3 0 - 5 0 , 1 6 - 3 0 , a n d 1 6 - 1 0 0, 0, r e s p e c ti t i v e ly ly . T h e G r a d e d S a n d w a s c o m p o s e d o f e q u a l p a r t s o f t h e o t h e r three sands. The Fine Sand was from a residual deposit and consisted of s h a rp a n g u l a r p a rt i c l e s , w h i l e t h e o t h e r t w o s i n g l e -s i z e s p e c i me n s w e re f r o m r i v e r b e d s a n d w e r e c o m p o s e d o f l es e s s an a n g u l a r a n d m o r e r o u n d e d g r ai a i ns ns . The glass balls were almost perfectly spherical with sizes governed by Si e v e s 2 0 a n d 3 0. 0.

Maximum and Minimum Densities In order to assess the results of the vibration tests in terms of relative d e n s i t y , m a x i m u m a n d m i n i m u m d e n s it i t ie ie s w e r e m e a s u r e d f o r e a c h m a t e r i a l u s i ng n g t h e m e t h o d s d e v i s e d b y K o l b u s z e w s k i [ 8 ] . T h e m i n im im u m d e n s i t y ( m a x i m u m p o r o s i ty t y ) w a s d e t e r m i n e d b y p l a c in in g 1 k g o f t h e m a t e r i a l i n a measuring cylinder of 2 litres capacity, shaking the cylinder, then quickly i n v e r ti t i n g i t t w i ce c e , a n d r e a d i n g t h e v o l u m e o f t h e s p e c im im e n . T h e m a x i m u m density (minimum porosity) was measured by compacting the material w i t h 1 5 m i n a p p l ic i c a t i o n s o f a n e l e c tr tr i c v i b r a t i n g h a m m e r t o e a c h o f t h r e e l a y e r s of o f t h e m a t e r ia i a l p l a c e d u n d e r w a t e r in in a s t a n d a r d P r o c t o r c o m p a c t i o n 2 The ital italic ic num bers in in brac kets refer to the list of references append ed to this paper. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

BRAND ON TH THE E CONTROL OF DENSITY DENSITY BY VIB RAT ION

123

TABLE 1--Pro perties of th thee granular materi materials. als. Material

Fine sand Mediu Me dium m sand Coarse sand Graded Gra ded s a n d

Particle,, Maximum, Particle Maximum, Minimu Minimum m Minim Minimum um Ma Maxi ximu mum m Specific Specific Size, U.S. Den sity, Den sit y, Por osi ty, Por osi ty, Gr Grav avit ity y Sieve No. gm/cm gm/cm~ ~ gm/cma gm/cma % % 50-100 50-100 30 -5 0 16-30 16-3 0 16-1 16 -1 00

1.67 1.77 1.7 7 1.78 1.83 1. 83

1.35 1.47 1. 47 1.49 1.53 1. 53

37.1 32.0 32. 0 31.15 30.0 30. 0

48.9 43.45 43. 45 42.2 41.5 41. 5

2.64 2.60 2.6 0 2.58 2.61 2.6 1

Glass balls

20-30

1.88

1.72

36.1

41.55

2.95

mold. Degradation of the particles by this process was found to be a problem in the case of the glass balls, and this permitted only a small force to be exerted on the hammer. The results of the measurements of the limiting densities, and of specific gravity determinations made with a pycnometer, are shown in Table 1. It should be remembered that the limiting densities obtained by the preceeding methods outlined might not be the extreme values, but they are used herein as defining 0 and 100 percent relative density for the specimens used in the vibration tests. T h e V i b r a t io io n T e s t s

Equipment Used The main features of the small vibration table constructed for the experiment s are shown in in Fig. 1. The 30-cm square steel table was allowed to execute only vertical displacem displacements. ents. Th e displacem displacement ent was governed by the two ball bearings with their outer shells screwed to the table. These were fitted with an eccentric shaft driven by a variable speed d-c motor. This arrangement resulted in a sinusoidal wave form of vibration of the table. Two sets of bearings were available for use, the eccentricities of these (and, consequently, the available amplitudes of vibration) being 0.794 and 1.588 mm. The maximum frequency that could be maintained by the motor aboutbe1500 cpm,towhich meant that a maximum acceleration of about 4was g could applied the table. The molds used to contain the specimens during vibration were 27-cm long perspex cylinders with base plates which could be bolted to the vibrati ng table. F or most of the tests, a 9.4 9.40-c 0-cm m diameter cylinder was used but, in order to investigate size size eff effec ects, ts, other diameters were later employed. Experimental Procedure A specimen was prepared by pouring the sand through a funnel at a fixed height into the cylinder to give a low relative density. The surface of the sand was levelled, and the filled cylinder was weighed prior to viCopyright by ASTM Int l (all rights reserved); Fr i Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/prin ted by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to  

124

REL ATIV E DEN DENSI SITY TY I NV OL V IN G COH COHESI ESIONL ONLESS ESS SOI SOILS LS

(o)

o)

Side

Elevation

--2

HR

v a ri ri a bl e s p e e d

motor

DC

.o_

- - -

Bearings

screwe d to top

__

o:7

__

_

-st., h .... s

I.

3 o am

'I (b)

Plan

(top

p l at e

remove d)

table. e. FIG. 1--D etails of the vibration tabl

bration. A small rubber pouch containing containing sand was attached to th e top of the cylinder so that sand was continuously supplied to the cylinder as compaction occurred. occurred. Ap art from the th e negl negligib igible le eff effect ect of the smal smalll head of sand in the pouch, no surcharge loading was used during vibration. After a period of vibration at a fixed frequency and amplitude, the cylinder was reweighed reweighe d after the pouch had been removed and the sand surface level levelled. led.

E xperim ental Results Effect of Time of Vibration

The effect of time of vibration on the state of compaction of each of the four sands and the glass balls for a maximum acceleration of 1.75 g is shown in Figs. 2 and 3. The states of compaction in Fig. 2 are given in terms of porosity, while they are shown as relative densities in Fig. 3. The general shape of these curves is the same as observed by previous investigators. The relative density increased continuously with time to a constant value in each case. Densification occurred rapidly at first, but the rate of compaction gradually decreas decreased ed with time of vibration. These relative density changes changes refle reflect ct the stability of the partic particle le arrang ement at any time which, in turn, is related to the shear strength of the granular medium. It might be mentioned that the specimens of glass balls generally Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to L  

BRAND ON

50

[

THE CONTRO L

i

'

:

.... a /

, Graded

Sand

Coarse

Sand m

Medium

Sand

j

52

i

54 I

~56

O F D E N S I TY TY B Y V IB IB R A T I O N

:

i

]25

o 58

1 I

44

OJ

i Fine

-~

0.2

(a

1

E

i

I

05

Time

T

of

r

I

5

I0

Vibration

F I G . 2 - - V a r i a t i o n s i n p o r o s it it y w i t h t i m e

=

0.794

Sand

i

ram.) i

20

Loo

50

, min.

of vib vibration ration

(~ = 1.75 g).

rea ched a sta ble pa ck ing under a g iv en intensity o f v ibra tio n m uch m o re ra pidly tha n the sa nds. This is tho ug ht to be indica tiv e o f the rela tiv ely lo w shea s hea ring ring resis resista ta nce o f the spherica l pa rticles ena bling reo rient r ientaa r to ta ke pla ce ra pidly under the disturbing fo rce. Figure 4 shows the density-time curves for the Graded Sand vibrated i~

C)

_o a) c(

02

0.1

0, 5

I

T im e

FIG. 3--Variations in

2

of

5

Vibration

relative d~asity

I0

20

50

I00

, min

with time

of vib vibrr at ation ion

(~ = 1.75 g).

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i c e n s e A g r e e  

126

RELATIVE RELATI VE DENSIT DENSITY Y INVO LVING COHESIO COHESIONLESS NLESS SOI SOILS LS

50

ioo

52

80

54

6o

Legend f , cp m o , turn

J 4o

0: 82 g

- --

$

0 [3 &

680 1400 1200 860

1.588 1. 588 0.7 94 1588

o

~6

138

~_

X

j:9 o{

0 2

05

2 Time

of

5

Vibration

,

1400 I0

i 20

0794 50

rain.

FIG. 4 --E ffe ct of inten sity o f vibr vibrati ation on on variat variations ions in relative relative dens ity with time for dif-

fere nt intensities intensities of vibration (Graded Sa nd ).

at several different intensities. The maximum accelerations (/~) were calculated from the relationship: 5) = (2~ (2~f)~ f)~.a .a

(1)

where f and a are the fre quency and a mplit ude of vibratio vibration. n. I t can be be seen that a constant relative density was reached in all cases after a period of about 30 rain, and this was adopted as the standard time of vibration in all subsequent tests. Effect of Inten sity of Vibration

The intensity of vibration, which is expressed herein by the maximum applied acceleration, acceleration, greatl y affected the rate of compaction of the samples and the final relative density achieved, as can be seen in Fig. 4 for the Graded Sand. T he infl influen uence ce of intensity of vibration on the state of comcompaction of each of the single-size materials is summarized in Fig. 5, where the porosity achieved achieved is is plotted against the maximum acceler acceleratio ation. n. I n all cases, the minimum porosity was obtained where an acceleration of about 1.4 1. 4 g was used used.. Th e p orosit y increased rapi dly as the in ten sit y of vib vibrati rati on decreased below the optimum value and decreased gradually as the intensit y incre increased. ased. The sharp peaks in the porosity-acceleration curves illust rate how critical the acceleration is to the achievement of the maximum possible state of compaction. The acceleration imparted to a medium enables reorientation of the particles to t he exten t th at the applied force force is suffic sufficient ient to overcome the shear stresses between the particles. These stresses are a function of the interparticle contact area and contact pressure, as well as the shape and surface texture of the particles, and both of these increase as the porosity decreases under the applied force. This decrease in porosity continues with increase in particle acceleration, therefore, until the rate of Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Lice  

BRAND BRAN D ON THE CONTROL OF DENSI DENSITY TY BY VI VIBRAT BRATION ION

/• 

34 !

~

73 v~

)~ = 7 6 % 3. -. .- ., .I Sand

36 Glosss b alls Glos 58

127

:,:_ 4O o

~ = 6 5 %

o D42

,

----. Fine

Sand

46

48

0

I

2

Maximum

5

Acceleration

,

4

g

F I G . 5-- Ef fec t o f intensity of vibrati vibration on on ultimate state of compaction. 50

I00

... .. 8

0

-

Vr = 95 % -

-

52

34 ~

60

g~ >

36

'N

g_

40

r,,"

38

20 I

0

0

7

4O

I

Maxim um

2

Ac c e l e r a t i o n

3

, g

F I G . 6-- Eff ect of intensi intensity ty of vibrati vibration on and initial densi density ty on ultimate ultimate stat statee of compaction compaction

(Graded (Gr aded San d).

C o p y r i g h t b y A S T M I n t l ( a l l r ig ig h t s r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s iidd a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A g r e e  

128

R E L AT AT I V E D E N S I T Y I N V O L V I N G

COHESION LESS

S O IL IL S

interparticle shear becomes such that the particles can no longer occupy their most favorable positions and, consequently, the porosity increases wit h fu rth rther er increase increase in acceleratio acceleration. n. At hig high h accele acceleration rations, s, an equilibrium porosity is reached which is independent of the acceleration, the rate of shear being such that the particles exist in a state akin to liquifaction. Specimens of the Graded Sand were made up at different initial relative densities to ascertain whether this was an important influence on the ultimate state of compaction. It is clear from Fig. 6 that this was very important at accelerations below the optimum value. At the optimum

value and above, however, the initial density appeared to be unimportant to the ult ima te state of compaction compaction obtaine obtained. d. The maximum relative densities achieved by vibration for the five materials are marked on Figs. 5 and 6. In no case was a relative density of 100 percent obtained. Values in excess of 90 percent, however, were obtained at the opt imu imum m acceleration acceleration in the ca case sess of the glas glasss balls and the Graded Sand. For the single-size sands, the peak relative densities were quite low, that of the Fine Sand being only 65 percent. The maximum relative density th at can be achieved achieved by vibration, therefore, therefore, is is obviously a fu nctio n of particle size size and particle shape.

Effect of Con tainer Size To investigate container size effects on the state of compaction after different times of vibration, four cylindrical molds were used, the internal diameters of which were 3.87, 5.34, 9.40, and 14.60 cm. The results shown in Fig. 7 were obtained using the Medium Sand. The only observations that can be made on the basis of these results are that, where a small cylinder was employed, erratic density values were obtained, and no con-

F

8O

70

1

lZ1

~

.~_

,

,....-------I

50

4O .

30

0.11 0.

|

__~

t ! ,

0.2

0.5

Ti m e

of

cylind cyl inder er dia diam. m. = 0 [3

,, ,

9

V ib r a t i o n

5.87 cm. 55 4 9 .4 0

14,60 I~)

2'0

~o

57 n

l i

~

36

58

,,

50

, m in.

7--JF, 7--J F, fect of mold diameter diameter on variations in density w ith time of vibr vibrati ation on (M edi um Sand: ~ = 1.75 g ) . FIG.

C o p y r i g h t b y A S T M I n t l ( a l l r iigg h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n t ed b y ( U F P E ) U n i v e r s id i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e rraa l d e P e r n a m b u c o ) p u r s u a n t t o L i  

B R A N D O N T H E C O N T R O L O F D E NS NS IT IT Y BY B Y V I B R A T IO IO N

22.5

o

c o

1 5 - 0

55 I

'

Poros ity

, %

54

55

52

!

I

!

129

E o o

a3 E 7 . 5 - -

/

c

50

5

I0 m i n

60

70

(o = 0.794 mm ) I 80 90

Relative

Density

, %

8-- Variat 8--Var iation ionss in densi density ty throu throughout ghout speci specimen men with time of vibration vibration (Graded (Graded Sand: = 1.75 g ) .

FIG.

stant density was achieved after a considerable period of vibration. The cause of these difficulties was undoubtedly the significant side friction e f fe f e c ts t s o f t h e s m a l l c y li l i n d e rs r s . T h e t w o l a r g er er c y l i n d e r s b o t h a p p e a r e d t o b e s a t i s f a c t o r y c o n t a i n e r s f o r t h e s a n d e v e n t h o u g h s m a l l d if if f e re re n c e s i n r e l a t i v e d e n s i t y w e r e m e a s u r e d f o r a g i v e n p e r io i o d o f v ib i b r a t io io n .

Density Variations within Specim Specimens ens T h e e x p e r i m e n t a l r e s u lt lt s r e p o r t e d s o f a r w e r e b a s e d o n t h e a v e r a g e v a l u e s o f d e n s i t y m e a s u r e d f o r t h e v i b r a t e d s p e ci c i m e n s. s . T h e m o s t s i g n if i f ic ic a n t results obtained from the study, however, related to the variations in d e n s i t y t h r o u g h o u t t h e s p e ci c i m e n s . T h i s w a s i n v e s t ig i g a t e d b y u s i a g a 2 2 .5 .5 - cm cm long perspex cylinder wh ich was split into four equal parts and held together by jubilee clips. After vibration for a given period of time, the c y l i n d e r c o u l d b e d i s m a n t l e d p ie i e c e b y p i ec e c e so so t h a t s e p a r a t e d e n s i t y m e a s u r e m e n t s c o u l d b e m a d e o n t h e s a n d c o n t a i n e d in in e a c h s e c ti t i on on . The results of the tests to determine the density variations within specimens of the Graded Sand are shown in Figs. 8, 9, and 10. It can be s e en e n t h a t t h e d e n s i t y v a ri r i e d g r e a t l y t h r o u g h o u t t h e s p ec e c im i m e n s w i th th t h e time of vibration (Fig. 8) and with the intensity of vibration (Figs. 9 and 10). In addition, a comparison of the data in Fig. 9 with that in Fig. 10 Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

130

RELATIVE DENSITY INVOLVING COHESIONLESS SOILS

Poros ity 40 No

g

-

i,,

,r

v,broh on

, %

38

36

54

I

I

i

I

t

32 I '

30

._~ a

a = 0

0

20

40 Relative

60 Dens ity

.

mm.)

80 ,

I00

%

F I G . 9- -V ar iat ion s in density througho throughout ut specim en w ith intensity of vibration (G (G raded raded S a n d : a = 0 . 7 9 ~ ra ra m ) .

Porosity 4O

22.5

38 w

i

, %

36 ,

54 i

32 3.4 8 g

50

o

.E

~3

0

i

5

-

-

~a

o rn

E 7 ' . 5 - o

C~ 0

I 0

20

40

(o = 1.588 mm.) 60

Relative Density

80

I00

, %

F I G . l( l ( N - V a r i a E o n s in de nsity throughout throughout spe cime n with inte nsit y of vibr vibrati ation on (Grad (Graded ed

S a n d : a = 1 . 5 8 8 ra ra m ).).

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BRAND ON TH THE E CONTROL OF DENSITY DENSITY BY VIBRATI VIBRATION ON

131

indicates the infl influenc uencee of the amplitude of vibration (at co nstant maximum acceleration) in the process of dynamic compaction. Considerably more longitudinal variation in density existed where the larger amplitude was employed. The main observations to be made from the results shown in Figs. 9 and 10 are that the preparation of specimens by vibrating at intensities appreciably below below the opti mum value resulted in large inhomogeneit inhomogeneities ies in the specimens. Only where the intensity of vibration was at or above the opt imum we were re specim specimens ens obtained t h a t we were re even approximately homo-

geneous. At the optimum intensity (1.75 g) fairly homogeneous specimens were obtained. Conclusions

There are many problems involved in the use of vibration techniques for the preparation of test specimens of granular materials. The relative density is a function of time and intensity of vibration and appears to be affected by secondary factors such as amplitude amplitu de and mold siz size. e. The hi ghest density for a particular material can be achieved achieved only by vibrating at the optimum intensity, but the relative density obtained is unlikely to reach a value of 100 percent. Large density variations throughout vibrated specimens will probably exist where intensities of vibration below the opti mum are empl employed. oyed. The results reported herein generally agree well with those obtained earlier by Alyanak [3], Selig [4], and Kolbuszewski and Alyanak [6]. Acknowledgments

The experimental results presented in this paper were obtained at the University Univers ity of of Nottingham, England by M. P. Rog Roger erss to whom the auth or ~ishes to express his thanks. References

[1] Mogami, T. and Kubo, K., "The Behavio Behaviour ur of Soil during Vibration," Vibration ," Proceedings, 3rd Internatio Int ernational nal Conference Conferenceon on Soil Mechanics, Zuri Zurich, ch, 1953, 1953, Vol. 1, pp. 152 152-15 -155. 5. on [~] Appli Felt, cation E. on J., of "Laboratory "Laborat ory of Compacting Soils," Applicati Soil Testing Test ingMethods in Highway Design and Granular Design Construction Construct ion, , A S TSymposium M S T P 239, America Ame rican n Society for Testing and an d Material Materials, s, 1959, 1959, pp. pp. 8989-110 110.. [3] Alyanak Alyanak,, I., "Vibrati "Vibration on of Sands Sand s with Speci Special al Referenceto the Minimu Minimum mPorosit Porosity y Test for Sands," Proceedings, Midland Soil Mechanicsand Found Foundation ation Engineering Society,Birmingham,Eng Birmingham,England land,, 1961, 1961, pp. 37-72. [4] Selig,E. Selig,E. T., "Effect of Vibrationon Density of Sand," Proceedings, 2nd Panameriean Conference Conferen ceof Soil S oil Mechanics,Rio de Jane Janeiro iro,, 1963,Vol. 1, pp. 129 129-1 -144. 44. [5] Pettibo Pettibone, ne, H. C. and Hardin, J., "Research on Vibratory Density Test for Coh Cohesi esiononless Soils", C om pac titi on American nSocietyfor Society for Testing and on of Soi Soill s, s, A S T M S T P 377, America Materials, Materi als, 1964,pp. 3-19. [6] Kolbuszewski,J. Kolbuszewski,J. and Alyanak,I., "Effects of Vibrations Vibrations on the Shear Strength and Porosity of Sands," Surveyor and M unici Vol.. 123, No. 3756, 1964, pp. unicipal pal Engineer, Vol 23-27, and No. 3757, pp. 31-34.

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132

RELATIVEDENSITY INVOLV RELATIVEDENSITY INVO LVING ING COHES COHESIIONLES ONLESS S SOIL SOILS S

[ 7] 7] D ' A p p o l o n i a , D . J . a n d D ' A p p o l o n i a , E . , " D e t e r m i n a t i o n o f t h e M a x i m u m D e n s i t y o f C o h e s i o n l e s s S o i l s ," ," Proceedings, 3 r d A s i a n R e g i o n a l C o n f er er e n c e o n S o i l M e c h a n ics, H ails, 1967, V ol. 1, pp. 266-268. [ 8] 8] K o l b u s ze z e w s k i , J . , " A n E x p e r i m e n t a l S t u d y o f t h e M a x i m u m a n d M i n i m u m P o r o s it i t ie ie s o f S a n d s , " Proceedings, 2 n d I n t e r n a t i o n a l C o n f e re re n c e o n S o i l M e c h a n i c s , R o t h e r d a m , 1948, Vol. 1, pp. 158-165.

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

M . M . J o hn h n s to to n 1

L a b o ra r a to t o r y St u d i e s o f M a x i m u m a n d M i n i m u m D r y D e n s i tit i e s o f Co h e s io i o n le s s Soils

R E F E R E N C E : Johnston, M. M., " L a b o r a t o r y S t u d i e s o f M a x i m u m a n d M i n i m u m D r y D e n s i t ie i e s o f C o h e si s i o n le l e s s Soils," Evaluation of Relative

Den sity and Its R ole ole in Geot Geotech echni nical cal P roject rojectss Involvi Involving ng Cohesionl Cohesionless ess Soils, A S T M S T P 5 2 3 , American Society Society for for Testing and Materials, 1973 1973,, pp. 133-1 133-140. 40.

A B S T R A C T : Some of the differences in results of tests for the maximum and

minimum dry densities of cohesionless soils are examined. A comparative test program to investigate reproducibility of results of maximum and minimum densities for two typ types es of sands is discussed, and an empirical correlation of the uniformity coefficient versus maximum and an d minimum densities is presented. A comparison made of the Providence Vibrated Density method and the vibratory table is method. I t is shown shown th that at one of of the impor important tant varia variables bles in determ determining ining the maximum maximum density of cohesionless soils using the vibratory table method is the amplitude of the vibrating mold. K E Y W O R D S : density (mass/volume), tests, cohesionless soils, vib vibrat ratory ory

compacting, coefficient of uniformity, value analysis

With the increased need for defensive design of earth dams to resist ear thq uake damage, the density of the the co cohe hesio sionle nless ss zone zoness of emban kment s and their foundations becomes increasingly important. Unfortunately, ther e has been no general general agreement on methods for determining the maximum and minimum dry densities of cohesionless soils. The concept of using relative density as a construction control method bega n as far bac k as 19 1942 42 when K. S. La ne [1 [1]z ]z,, the n of the Provid ence, Rhode Island District, U. S. Army Corps of Engineers, began developing a standard test for determining the maximum density of cohesionless soils. 1 Civil engineer, Soil Mechanics Mechanics Branch, Engineering Div., Officeof the th e Chief of Engineers, U. S. Army Corps of Engineers, Washington, D. C. 20314. 2 The italic numbers in brackets refer to the list of references appended to this paper. 133

opyright byght ASTM l (all rights Inte reserved); Fri Mar 11 16:13:06 EST Copyri Cop yright 9 Intby ASTM Internat rnationa ional l www.astm.org www.astm.or g 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. No fu  

134

RELATIVEDENSITY INV OLV ING COHESIONLESS SOILS RELATIVEDENSITY

F r o m L a n e ' s s tu t u d ie i e s e v o l v e d a t e s t p r o c e d u r e th th a t is t e r m e d t h e P r o v i d e n c e V i b r a te t e d D e n s i t y ( P V D ) t e st st . R e s e a r c h b y t h e U . S. S . B u r e a u o f R e c l a m a t i o n i n 1 9 61 6 1 [ 2] 2] a n d 1 9 65 6 5 [3 [3] r e s u l te t e d in i n t h e d e v e l o p m e n t o f a t e s t m e t h o d f o r d e t e r m i n in in g t h e m a x i m u m d e n s i t y o f a c o h e si s i on o n l es e s s so s o il il u s i n g a n e l e c t r o m a g n e t i c t a b l e - t y p e v i b r a t o r t o w h i c h is i s a f f ix i x e d a s t e e l c y l i n d e r c o n t a i n i n g t h e m a t e r i a l . I n 1 96 96 5 , t h e U . S . A r m y C o r p s o f E n g i n e e r s [5 [5] a d o p t e d t h e t a b l e - t y p e v i b r a t o r m e t h o d ( w i t h S y n t r o n v i b r a t o r ) a s a s t a n d a r d t e s t p r o c e d u r e , b u t s ti t i ll ll p e r m i t t e d t h e P r o v i d e n c e V i b r a t e d M e t h o d , s o m e w h a t m o d i fi f i ed ed , a s a n a l t e r n a t i v e

f o r u se s e i n l o c a t io i o n s w h e n a v i b r a t o r y t a b l e i s n o t r e a d i l y a v a i la la b l e .

C o m p a r i s o n o f t h e M o d if i f ie i e d P ro r o v i d en e n c e V i b r a te te d D e n s i t y ( M P V D ) and the Vibratory Table Density Test Results B e c a u s e o f t h e b a s i c d i f fe f e r e n ce c e s i n t h e m o d i f ie ie d P r o v i d e n c e V i b r a t e d D e n s i t y ( P V D ) a n d t h e v i b r a t o r y ta t a b l e te t e s t m e t h o d s , th th e C o r p s o f E n g i n e e r s in i n 1 97 9 7 0 m a d e a c o m p a r i s o n o f t h e v a l u e s o f m a x i m u m d r y d e n s it i t ie ie s o b t a i n e d u s in i n g e a c h p r o c e d u r e . T a b l e 1 l is i s ts ts t h e r e s u l t s o f a c o m p a r a t i v e test program using oven-dry specimens of cohesionless soils tested in acc o r d a n c e w i t h t h e t w o m e t h o d s o u t li l i n e d i n E n g i n e e r M a n u a l ( E M ) 1 11 1 1 00-2 1906, Laboratory Soils Testing [5, 6, 7]. For the materials tested, the two p r o c e d u r e s g i v e c o m p a r a b l e r e s u lt l t s, s , a l t h o u g h t h e r e i s a s l ig ig h t t r e n d f o r t h e v i b r a t o r y t a b l e m e t h o d t o g i v e l o w e r v a l ue ue s .

C o m p a r i s o n o f O r ig i g i na n a l P V D a n d M o d if i f ie ie d P V D T e s t M e t h o d s T h e o r ig i g i n al a l P V D t e s t m e t h o d i n c l u d e d t h e u s e o f a c o i le l e d s p r in in g t o d e l i v e r a s u r c h a r g e h a v i n g a n a v e r a g e p r e s s u r e o f 2 6 p s i.i . B e c a u s e i t iiss T A B L E 1--C om par ison of result resultss of M P V D and vibr vibrator atoryy table tes testt methods. Soil Classi Classifi ficati cation on

Maximum D ry Densit Density, y, lb /ft 3

W ell ell-grade -gradedd gravel (GW ) Silty sandy gravel (GW -GM ) W ell ell-grade -gradedd sand (SW) W ell ell-grade -gradedd sand (SW) W ell ell-grade -gradedd sand (SW) Poorly-graded sand (SP) Poorly-graded san d (SP) W ell ell-graded -graded sand (SW) W ell ell-grade -gradedd sand (SW) Poorly-graded sand (SP)

Modifiedd Modifie Provid Prov idence ence V ib ibrat rated ed Method

V ibratory Table M ethod

139.2 137.5 133.2 132.7 130.7 125.2 124.6 120.7 118.2 117.8

139.7 135.0 131.9 128.5 131.3 124.7 123.7 118.6 118.7 115.5

Referenceaa Reference

5 7 6 6 7 6 6 5 5 5

a Num bers refe r to the li list st of references references appended to this paper.

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JOHNSTO JOH NSTON N ON MAXIM UM AND M INI INIM M UM DRY DENS DENSITI ITIES ES

135

TABLE 2--C om pa rison of result resultss o f origi original nal P V D and modif modified ied P V D tes testt methods. Maximum Maxi mumDry Density, Ib/ Ib/ft ft~ ~

Soil Cla Classi ssific ficat ation ion San dy gra Sandy gravel vel (GP) Gravelly Grav elly sand (SW (SW)) Silty Sil ty sand sandy y grav gravel el (GW (GW-GM -GM))

Providence Vibrated Density Method

Modified Providence Vibrated Density M e t h o d

Reference

143.2 141.2 141.0

139.3 139.3 137.4 137.5

7 7 7

Sandy gravel Gravelly sand san d(GP) (SW) (S W) Gravelly Grave lly sand (SW (SW)) Gravelly Grave lly sa sand nd (SW (SW)) Gravelly Grave lly sand (SW (SW)) Gravelly Gravell y sa sand nd (SW (SW)) Poorly-graded sa sand nd (SP) Sandy gravel (GW (GW))

139. 139.5 5 139.4 132.2 120.3 118.4 117.2 113.2 133.7 133. 7

136. 136.2 2 135.8 130.7 118.7 116.6 115.5 117.2 137.8 137. 8

7 7 7 7 7 7 6 6

Numbers refer to the list of reference referencess appended to this paper. awkward to mainta in this con stant surcharge surcharge by a spring as the specimen specimen densities during vibration, the test was modified in 1965 to incorporate a dead weight as a surcharge. For convenience in testing, a weight was selected selec ted th at delive delivers rs I psi surcharge. surcharge. A comparison of the two proce procedures, dures, using oven-d ov en-dry ry specimens specimens of cohe cohesi sionl onles esss so soil ils, s, was made by b y t he U. S. Ar my Waterways Experiment Station (WES) and the U. S. Army Engineer Division, New England, and the results are listed in Table 2 [6, 7]. For the materials tested, the maximum densities derived from the original PVD method are generally generally higher th an those obtained using the modi modifie fied d PVD method. This poss possibil ibily y may be attrib uted to the fact th at the heavier surcharge used for the original PVD procedure reduces rebound of the individual granular particles and reduces segregation during vibration as compared to lighter surcharge effects. Further, the higher amplitude induced by the lighter surcharge in the modified method tends to produce greater particle segregation. C o r r e l a ti t i o n o f G r a in in - S i z e D i s t r i b u t i o n a n d M a x i m u m - M i n i m u m D e n s i t y o f C o h e s i o n l e s s S o i ls ls

Since the maximum and minimum dry densities of cohesionless soils are functions of their grain-size distribution and specific gravity, an empirical relationship was sought. The coefficient of uniformity, C~, is one indicator of grain-size distribution. A plot of C, on a logarithmic scale versus the minimum and maximum dry densities on an arithmetic scale is shown in Fig. 1. These data were collected from several Division laboratories within the Corps. The correlation is based on the results of tests on

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136

RELATIVE RELATI VE DENSIT DENSITY Y INV OLV ING COHESI COHESIONLESS ONLESS SOIL SOILS S

COEFF ICIENT 14(

13G

120

2

OF

UNIFOR MITY-

5

10

20

C)

MAXIMUM

|

Je

Cu

~

I

110

k~ ~

1011

Q ~7

\--MINIMUM

9(1

Gffi2.65

FIG. 1 - - E m p i r i c a l r e l a t i o n s h i p b e t w e e n m a x i m u m a n d m i n i m u m d e n s i t i e s v e r s u s c o e f -

f i c ie ie n t o f u n i f o r m i t y .

subangular to rounded granular soils having all material retained on the U . S. St a n d a rd 2 0 0 s i e v e a n d s p e c ifi ificc g ra v i t i e s ra n g i n g fro m 2 .6 5 t o 2 .8 9 . T h e v a l u e s h a v e b e e n n o r m a l i z e d f o r a s p e ci c i fi fi c g r a v i t y o f 2 .6 . 6 5 . T h e r e l a ti ti o n ship can serve to estimate values of maximum densities, if the grain-size d i s t r i b u t i o n a n d t h e s p e ci c i fi fi c g r a v i t y o f t h e m a t e r i a l a r e k n o w n . E n t e r t h e c h a r t w i t h t h e v a l u e o f Cu C u , s e l e c t t h e d r y d e n s i t y , a n d c o r r e c t b y m u l t i p ly ly i n g b y G A d i v i d e d b y 2 .6 . 6 5 , w h e r e G A i s t h e a c t u a l s p ec e c if i f ic ic g r a v i t y o f t h e ma t e ri a l . C o m p a r a ti t i v e T e s t P r o g r a m t o D e t e r m i n e R e p r o d u c i b i li l i ty ty o f R e s u l t s U s i n g U n i fo r m T e s t M e t h o d s

To determine the variations in the minimum and maximum density values among Corps laboratories, samples of two types of sand were prep a r e d a t W E S a n d s e n t to t o e a c h o f t h e n i n e D i v is i s i o n l a b o ra r a t o ri r i e s. s. O n e sample, designated Sand A, was a well-graded, sub-rounded clean sand; the other, Sand B, was a poorly-graded, sub-rounded clean sand. The laboratories performed grain-size distributions, maximum density, and

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JOHNS JO HNSTON TON ON M AXIM UM AND M IN INIMUM IMUM DR DRY Y DEN DENSI SITI TIES ES

137

TABLE 3-3---G~rai -G~rainn s~e s~e d~ tri tribut~ but~ vn.

Laborator Labor atory y No.

Sand A

Sand B

Percent Passing U. S. Sieve S i z e Percent Passing U. S. S. Sie Sieve ve S~e 4 10 20 40 60 100 100 200 4 10 20 40 60 100 200 1 2 3 4 5

100 100 100 100 100

58 58 60 61 61

38 37 39 40 40

17 16 17 17 18

11 8 12 12 10

4 4 5 4 4

1 1 1 0 1

100 100 100 100 100

87 86 85 86 86

65 66 65 66 64

33 35 34 34 33

13 14 15 13 12

4 4 4 3 3

1 1 0 0 1

6 7 8 9

100 100 100 100

58 61 63 61

37 40 40 39

17 17 19 17

10 12 11 12

4 4 4 4

01 0 1

100 100 100 100

86 86 85 86

63 66 66 64

32 34 33 34

13 13 14 13

3 3 3 3

01 0 1

minimum density tests on each sample using the procedures given in the Corps Engineer Manual, "Laboratory Soils Testing," EM 1110-2-1906, 1965 edition [4]. All tests were performed using oven-dry material. The results are shown in Tables 3 and 4. As indicated by Table 3, the grain size distributions of the nine specimens are virtually identical. Table 4 shows that large variations in maximum and minimum density values were obtained. A study [8] made at the Corps Southwestern Division laboratory indicates that the amplitude delivered by a vibratory table to the compaction mold exerts considerable influence on the value of the dry density. A plot of maxim um dr y density versus mold amplitude (F (Fig ig.. 2) suggests suggests tha t there is an opt imu m amplitude for each type of granular material. material. This opt imu m amplitude varies with the rheostat setting. The amplitudes obtained deTABLE 4--Results of maximum and minimum density Ses~. Laboratory Labora tory No.

Sand A

Sand B

Maximum Dr Maximum Dry y Minim Minimum um Dr Dry y Maximum Maximum Dr Dry y Minim Minimum um Dr Dry y Densit Den sity, y, lb/ft lb/ ft 3 Den Densit sity, y, lb/f t 3 Den Densit sity, y, lb/f lb /ftt s Den Densit sity, y, lb/ft lb/ ft s 1 2 3 4 5 6 7 8 9

132.1 131.6 130.1 130.0 129.8 129.0 128.4 128.4 127.8

115.1 114.7 115.3 115.2 113.3 111.9 112.1 108.8 110.8

124.3 124.0 123.4 122.8 122.7 122.7 122.5 122.3 120.9

107.2 108.6 110.3 107.1 108.7 108.0 105.0 107.1 107.0

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138

RELATIVEDENSITY RELATIVE DENSITY INV INVOL OLVI VING NG COHESI COHESIONLE$S ONLE$S SOILS

SAND

:= tJ

o,j X

B-~

~SAND

A

3 :S

o :E

2

0 110

115

M A X tM tM U M

120

DRY

125

D E NS ITY -

130

135

L S S /C /C U F T

FIG. 2 --R e~tio nsh iy of mold a mplitude mplitude versus versus m a xim um dry dens densit ityy using using a Syntron Syntron

VP-80 vibratory table.

pend on the time given for the springs of a vibratory table to return the d e c k o f t h e t a b le l e t o o r a b o v e i ts t s e q u i l ib i b r i u m e l ev e v a ti t i o n. n. T h u s , t h e o p t i m u m amplitude required must be determined by trial for each type of table, s u r c h ar a r g e , a n d t y p e o f m a t e r ia i a l b e i n g t e s t e d i n o r d e r to to o b t a i n t h e m a x i m u m d r y d e n s i ty t y . O n e o f t h e p r i m a r y r e a s o ns n s f o r t h e d i ff ff e re r e n c es es s h o w n i n Table 4 is that all Division laboratories did not determine the optimum aptitude to give the maximum density using their particular vibratory tab le. I t i s p r o b a b le l e t h a t t h e l a rg r g e d i ff f f er e r e nc n c e s i n m i n i m u m d r y d e n s i t y v a lu lu e s w e r e c a u s e d b y v a r i a t i o n s i n m e t h o d s o f " s t r ik i k i n g o f f " o r le le v e l in in g t h e s a n d s u r f a c e s w i t h a s t r a i g h t e d g e a n d b y s l ig ig h t d i f f er e r e n c es e s i n h e i g h t o f fa fa l l o f the sand particles, permitting varying degrees of segregation. Discussion

Because the value of the relative density is quite sensitive to small c h a n g e s i n t h e v a l u e s o f m a x i m u m , m i n i m u m , a n d i n s i t u densities, it is important that testing techniques and equipment be universally stand-

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c  

JOHNSTON ON MAXIMUM AND MINIMUM DRY DENSITIES

139

ardized. For example, an increase in the apparent maximum density of only 2 lb /f t 3 wi will ll lowe lowerr the value of the relative density from 82 to 76 percent under certain circumstances. This could be the difference between acceptance or rejection of a pervious fill or foundation. It should be noted th at while the maxi mum dry d ensi ty of a cohes cohesio ionl nles esss so soil il ma y be obtai ned by use of vibratory methods, there are other methods, such as use of a modified compactive effort using a falling weight, which give equal or higher values. Conclusions

For the specific material discussed in this paper, it is concluded that: 1. The M PVD method and the electromagne electromagnetic tic vibr atory table method for determining maximu m dry density produce essentially essentially the same values values consider cons idering ing the deviations with n ormal testing. 2. The original PVD method gives higher values for maximum dry density tha n those derived derived from the MPVD method. A genera generall correlati correlation on ma y be fou nd between the uni for mity coe coeff ffic icie ient nt,, C~, and the maxi mum and minimum densities of cohesionless sands if less than 5 percent of the material passes the No. 200 sieve. 3. The value of the maximum density using the electromagnetic electromagnetic vibratory table method is dependent on the amplitude of the mold, with the optimu m amplitude being approximately 0.0 0.01 1 in. for the table tested. The large variations in the minimum dry density values reported from nine Corps laboratories using nearly identical techniques and samples a r e probably prob ably due t o segregati segregation on and va ryin g degree degreess of disturb disturbance ance in leveling leveling off the ex exce cess ss sand after initial pouring. The importance of the relative density test indicates a need for standardization of techniques and equipment to produce consistent maximum and mini mi nimum mum densit den sit y values for cohes cohesion ionle less ss so soils ils.. More Mo re research researc h using a wide range of soils is required to examine the variables such as amplitude, frequency, surcharge, effect of saturation, segregation, degradation during vibration, and mold size encountered during the performance of the maximum density test. References

[1] Lan Lane, e, K. S. in Proceedings, SecondIntern International ational Confere Conference nceon on Soil M e c h a n i c s a n d Foundat Fou ndation ion Engineerin Engineering, g, Rot Rotterd terdam, am, 194 1948, 8, pp. 243 243-24 -247. 7. [2] "Develop "Development ment of a Maximum Density Test for Cohe Cohesionl sionless essSoil by a Vibrato Vibratory ry Method," Method ," Earth Laborato Laboratory ry Report No. EMEM-557, 557,U.S. Bureau of Reclamation, 196 1961. 1. [3] "Laborat "Laboratory ory Tests to Refine he MaximumDens MaximumDensity ity Procedure Proced ure for Cohesionless CohesionlessSoils Soils Using a Vibrato Vibratory ry Table," Earth Laborat Laboratory ory Report No. EM-69 EM-697, 7, U.S. Bureau of Reclamatio Recla mation, n, 1965. 1965. [4] "Laboratory Soils Testing," Engineer Manua l, EM 11 1110 10-2 -241 4190 906, 6, Hea Headq dqua uart rters ers,, Dept. of the Army, Off Office iceof of the Chi Chief ef of Engineers, Eng ineers, 1970 1970.. [5] Compton, J. R. and Strohm, W. E., Jr., "Compact "Compaction ion of Cohesionl Cohesionless essMaterial Materials," s,"

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140

RELATIVE RELATI VE DENSIT DENSITY Y INVO LVIN G COHESIONLESS ,S ,SOI OILS LS

Miscellaneous Miscellan eous Pape r S-68-15, S-68-15, U . S. A rm y Engineer Engineer W aterwa ys Exp erimen t Station, Corps of Engineers, 1968. [6]] "C om parison of Modifi [6 Modifieded-Prov Provide idence nce a nd V ibratory Tab le Method s for De term ini n g Max i m u m Den s i t y , " u n p ub ub li li sh sh ed rep o rt b y U. S. Arm y W at erway s Ex p eri m en t Station, 1971. [ 7] 7] "C o m p ari s o n o f a Li m i t ed N u m b er o f M ax i m u m Den s i t y Te s t R es u l ts t s , " u np n p u bl bl is is hed h ed Re por t by U . S. A rm y Divisi Division, on, N ew England. England. [8]] "M inimu m -M axim um De nsity Te sts of Stand ard Samples," [8 Samples," unpubli unpublishe shedd rep ort by U. S. A rm y Corps of Engineers Engineers,, Southwestern Divisi Division on La bor ator y, 1969.

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G. Cum Cumber berled ledge ge 1 and R. J. Com ins ky 1

M a x i m u m D e n s i ty t y De t e r m i n a t i o n o f Subbase Materials

R E F E R E N C E : Cumberledge, G. and Cominsky, R. J., "Maximum D e n s i t y D e t e r m i n a t i o n of Subb ase Mater Materials~ ials~ ~ E valuation of R elative Density and Its Role in Geotechni Geotechnical cal Proj Project ectss Involving Involving C ohesi ohesionles onlesss Soils, A S T M S T P 5~3, American Society for Testing Test ing an d Materials, Ma terials, 197 1973, 3, pp. 141 141-15 -155. 5.

AB ST RA CT : The objective of this st udy is to establish a satisfactory method ABST of determining maximum density of cohesionless material, such as subbase, that will provide compaction criteria for these materials and be compatible with current methods of density determinations in the field. To establish a procedure for determini ng the maximum density of a subbase material, three different methods of tests are employed. These tests include the standard AASHO AASH O impact test methods (Methods C and D) , a vibr atin g table type of compactive effor effortt (ASTM T est for Relat R elative ive Densi De nsi ty of Coh Cohesi esionl onless ess Soils Soils (DThe 2049-69) a rectangular frompress surface. effect eff ectss),ofand mold size,, amplitud size amp mold litude, e,vibrated surcharge prthe essure ure, , an and d du rat ration ion of vibration are investigated and analyzed. In addition, three types of subbase materials--gravel, lim limest estone, one, and sl ag--are use used d in this stud y to examine the effects of subbase type on maximum density. It is concluded that the i nte nterac rac tio tion n eff effect ectss of aggreg aggregate ate type, mold size size,, amplitude, surcharge pres pressu sure re,, and durati on of v ibration are st atistically sig sig-nificant on maximum dry density. T he i mpact tests consistently produc producee higher densities densiti es with the inv estigated subbase materials th an the vibr ator y methods. There is a ve ry high degree degree of correlation between the densities obtained obtaine d from the impa ct methods and the vib rato ry method wher wheree th e subbase materials are vibrat vib rated ed at 0.0 0.03030-in. in. amp litud e an d a surcharg surchargee pressure of 1 psi is applied. Esti matin g equations are developed for for predicting maximu m density of subbase material from the vib ratory test data. KEY WORDS. cohesionless soils, density (mass/volume), vibratory compacting, impact tests, tests, mo mold lds, s, pa veme nt bas bases es,, vibration , subgrades subgrades

The Pennsylv Pennsylvania ania Departme Department nt of Transportation Transportation (PennD (PennDOT) OT) currently utili uti lizes zes sta standa ndard rd AASHO AASHO compaction compa ction tests for the control of fie field ld comcom1Assis Assistant tant engineer of tests and soi soils ls research engineer, respectively, Burea u of MaM aterials, Testing and Resea Researc rch, h, Pen nsyl vani a Depa rtme nt of Trans portat ion, Harrisburg, Pa. 17120. 141

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142

RELATIVEDENSITY RELATIVE DENSITY INV INVOL OLVI VING NG COHE COHESION SIONLESS LESS SOILS

p a c t i o n o f s u b b a s e m a t e ri r i al al s . T h e p r e s e n t t e s t m e t h o d s ( A A S H 0 T - 9 9 , M e t h o d s C a n d D ) , w h i c h i n v o l v e i m p a c t c o m p a c t i o n d o n ot o t , in in m a n y c a se s e s, s , p r o d u c e a " t r u e " m a x i m u m d e n s i t y s in in c e c e r ta ta i n t y p e s o f s u b b a s e s generally become more dense under repeated traffic loading. A research project was initiated to determine the maximum densities of s u b b a s e m a t e r ia i a l u t il i l iz i z in i n g v a r i o u s v i b r a t o r y c o m p a c t i o n m e t h o d s. s. S t a n d a r d AASHO compaction tests were also conducted for direct comparisons of maximum densities among the various test methods with hopes that a new density criterion for subbase materials might be established. The effect of moisture on maximum density of subbase materials is not

o f p a r t i c u l a r c o n c e r n i n t h i s s t u d y , s in in c e m o i s t u r e c o n t e n t i s n o t r e a l l y t h e predominant factor in controlling the field density. It has been established that greater density can be achieved at a lower moisture content by inc re a s i n g t h e c o mp a c t i v e e ffo rt [ I, 2 , 3 , ~ ] ~ . The optimum moisture contents associated with subbase materials are s u c h t h a t p l a c e m e n t o f t h e m a t e r i a ls l s i n th t h e f i e ld ld a t t h e s e m o i s t u r e c o n t e n t s would be physically impossible, since the conditions would be entirely too wet for equipment maneuverability. Therefore, contractors will generally place the subbase materials at a lower moisture content and rely on heavier e q u i p m e n t ( h ig ig h er e r c o m p a c t i v e e n e r gy g y ) t o a c h i e v e m a x i m u m d e n s it it y . S i nc n c e P e n n D O T ' s c u r r e n t m e t h o d o f p a v e m e n t d e s i gn g n c on o n s id i d e rs rs t h e s t r e n g t h o f s u b b a s e m a t e r i a l s, s , e m p h a s i s is is p l a c e d o n d e v e l o p i n g a b e t t e r u n d e r s t a n d i n g o f t h e b e h a v i o r o f v a r i o u s s u b b a s e m a t e r ia ia l s u p o n c o m paction and correlating the laboratory test findings to field compaction results to provide more meaningful pavement design criteria. T e s t M e t h od s

Three methods of tests were utilized to establish a procedure for det e r m i n in i n g t h e m a x i m u m d e n s i t y o f a s u b b a s e m a t e r ia i a l . M e t h o d I w a s th th e impact method as described in the standard AASHO Procedure T-99, M e t h o d s C a n d D , o r in i n a c c or o r d a nc n c e w i th t h A S T M T e s t s fo f o r M o i s tu tu r e - D e n s i t y o f S o i l s , U s i n g 5 .5 .5 -1 -1 b R a m m e r a n d 1 22 - i n . D r o p , ( D 6 9 8 - 7 0 ) . C y l i n d r ic ic a l mo l d s i z e s o f 4 i n . (1 0 .2 c m) i n d i a me t e r a n d 6 i n . (1 5 .2 c m) i n d i a me t e r, 0 .0 3 ft 8 (8 ( 8 5 0 c m 8) a n d 0 .1 0 ft 3 (2 8 3 2 c m 3 ), re s p e c t i v e l y , w e re e m p l o y e d . M e t h o d I I w a s a v i b r a ti t i n g t a b l e t y p e o f c o m p a c t i v e e f fo fo r t a n d w a s conducted essentially according to ASTM Test for Relative Density of C o h e s i o n le l e s s S o i ls ls ( D 2 0 4 9 - 6 9 ) , e x c e p t t h a t t e s t s w e r e c o n d u c t e d a t v a r i o u s a m p l i t u d e s a n d s u rc h a rg e p re s s u re s . C y l i n d ri c a l m o l d si s i z es e s o f 6 i n . (1 5 .2 c m) a n d 1 1 i n . (2 7 .9 .9 c m ) i n d i a m e t e r, 0 .1 0 ft 3 (2 (288 32 3 2 c m 3) an d 0.50 ft 3 (14,1 (14 ,161 61 cm 3), resp ectiv ely, w ere utilized. M e t h o d I I I w a s e s s e n ti t i a ll l l y a v i b r a t o r y t y p e c o m p a c t i v e ef e f f or o r t u ti t i li l i zi z i ng ng a r e c t a n g u la l a r m e t a l m o l d w i t h t h e v i b r a t o r f o rc r c e a p p l ie ie d t o t h e t o p o f t h e 2 T h e i t a l i c n u m b e r s i n b r a c k e t s r e f e r t o t h e l i s t of o f re r e f e r e n ce ce s a p p e n d e d t o t h i s p a p e r .

C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p ri ri n t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

CUMBER CU MBERLE LEDG DGE E AND COM INSKY ON SU SUBBASE BBASEM ATERI ATERIALS ALS

143

specimen. The equipment consisted of a metal rectangular mold 15 in. (38. (3 8.1 1 cm) by 17 in. (4 (43. 3.2 2 cm) by 12 in. (3 (30. 0.5 5 cm). A rot ar y electric vi vibr brat ator or was att ac he d to a 15-in. (38.1 (38.1-cm -cm)) b y 1717-in. in. (43.2-cm (43.2-cm)) b y 0.50-i 0.50-in. n. (1. (1.3-c 3-cm) m) plate, which was placed on top of the spec specime imen. n. The vibra v ibra tor was equipped with a variable speed control and was capable of producing a maximum 3000-1b (1364-kg) force at 6000 rpm. The specimens were vibrated for various durations with predetermined surcharge pressures. With the use of these three methods of tests, the effects of gradation, amplitude, surcharge pressure, time of vibration, and type of subbase material on maximum dry density were investigated and analyzed. The

analysis of variance procedure utilizing the F-test was employed to determine if the effects of the variables considered within a particular test were statistically significant on the maximum dry density obtained. Also, linear correlation and regression analyses were performed on selected test methods. Material Types

The subbase materials selected for this study were chosen because they were readily accessible and widely used in Pennsylvania. Three types of material--gravel, limestone, and slag--were employed in this study. The source of the subbase type was varied and a total of eight sources was utilized. Subbase Gradation

The gradation was chosen to be within the limits of subbase materials according to PennDOT specifications (Form 408). The grading is shown in Table 1. Methods I and II were employed to test the effects of the amou nt of coar coarse se and fi fine ne material on d ensity. The percent percentage age of material retained on the No. 4 sieve (+No. 4) was designated as coarse material, while whi le the perce percentage ntage of material tha t pas passed sed through th e No. 4 sie sieve ve ( - No. TABLE 1--Sel 1--Selected ected gradati gradations ons to to eval evaluate uate gradation eff effect ect on m axim um dry densit density. y. Siev Si evee De Desi sign gnat atio ion n

Percen Per centt Re ta in ed

P er c e n t as assi sing ng

11/~in in.. (3 (38. 8.1 1 ram) 1 in. (25 (25.4 .4 mm) 3/~in in.. (1 (19. 9.1 1 ram) in. (9 (9.5 .5 mm) No. 4 (4 (4.7 .75 5 mm) No. 10 (1 (1.6 .65 5 mm) No. 20 (830 ~m) No. 40 (420 ~m) No. 60 (250 ~m ~m)) No. 100 (149 ~m)

0 12 15 22 14 13 7 5 5 3

100 88 73 51 37 24 17 12 7 4

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144

RELATIVEDENSITY RELATIVE DENSITY INV INVOL OLVI VING NG COHES COHESIONL IONLESS ESS SOILS

4 ) w as ch arac terize d as fin e m aterial. T h e 6 -in -in.. (1 5 .2 .2 -cm) mo ld size size w as c h o se s e n , a n d t h e A m i t y H a l l g r a v e l w a s s e le l e c t e d a s t h e t e s t m a t e ri r i a l. l.

Reproducibility of Tests T h e r e p ro r o d u c i b il i l it i t ie ie s o f M e t h o d s I a n d I I w e r e e v a l u a t e d . W i t h M e t h o d II, th e amp litu d es o f v ib ratio n w ere 0. 01 8 6 in . (0 . 0 4 7 cm), 0 .0 2 3 7 in . (0.. 0 6 0 cm ), an d 0 .03 (0 .0 3 0 in . (0 .0 .0 7 6 cm). T he su rch a rg e p ressu res app lied w ere 0, 1 psi (0.07 kg/cm2), 2 psi (0.14 kg/em~), and 3 psi ( 0 . 2 1 k g / c m 2 ) . T h e Amity Hall gravel was utilized as the test material. The arithmetic mean (,~) of the maximum densities for each test was determined, and the

reproducibility of each test was expressed as the standard deviation (~) about the arithmetic mean.

Effect of Air-Dried and Saturated Material on Maximum Density The literature indicates that the highest densities with granular mat e r ia i a l s a r e o b t a i n e d w h e n t h e s p e c i m e n s a r e v i b r a t e d i n e i t h e r a n a i r -d -d r i e d o r a c o m p l e t e l y s a t u r a t e d c o n d i t i o n [ 3, 3, 5 ] . T o e v a l u a t e t h e p r e v i o u s c o n d i t io io n s , t e s t s w e r e c o n d u c t e d e m p l o y i n g t h e 6 -i -i n . ( 1 5. 5 . 22- c m ) m o l d o f M e t h o d I I a n d v i b r a t i n g t h e s p e c im i m e n s a t 0 .0 .0 30 3 0 -i -i n . ( 0 .0 .0 76 7 6 -c -c m ) a m p l i t u d e w h i l e a p p l y i n g v a r i o u s s u r c h a r g e p r e s s u re r e s . A l l e ig ig h t s u b b a s e s o u r c e s w e r e t e s t e d , f i rs r s t i n a n a i r -d - d r i e d c o n d i ti t i o n a n d t h e n i n a s a t u r a t e d s t a te te .

M old Size, Am plit plitude, ude, Surcharge Pressure, and Duration o f Vibrati Vibration on F o r s b l a d d [ 3 ] s t a t e d t h a t " t h e r e h a s b e e n n o s y s t e m a t i z e d e ff ff o r t t o d e t e r m i n e t h e r e l a t i v e e ff f f e ct c t s o f d i a m e t e r a n d d e p t h o f m o l d i n d i v id id u a l l y a n d c o l le l e c t iv i v e l y o n t h e r e s u l t in i n g m a x i m u m u n i t w e i g h t a n d o p t i m u m m o i s tu tu r e content." In this study, all three test methods were utilized to evaluate t h e i n fl f l u e n ce c e o f m o l d si si ze ze o n m a x i m u m d r y d e n s i t y . I n a d d i ti ti o n , t h e t e s t p r o c e d u r e s i n c l u d e d a l l e i g h t s u b b a s e s o u rc rc e s . T h e e f f e c t o f a m p l i t u d e w a s in in v e s t i g a t e d o n l y w i t h M e t h o d I I b y u s i n g v ario u s amp litu d es o f v ib ratio n , w hich w ere 0 .0 1 8 6 in . (0 .0 47 cm), 0 .0 2 37 in. (0.060 cm), and 0.030 in. (0.076 cm). The surcharge pressures were varied in Methods II and III. With M et h o d I I, s u rch arg e p ressures of 0 , 1 p si (0. (0 . 0 7 k g /cm2 ), 2 p si s i (0 (0.. 1 4 k g / c m 2 ) , a n d 3 p s i ( 0 . 2 1 k g / c m~ m~) were applied, while with Method III, th e su rch arg e p ressures w ere 0.3 3 p si (0 .0 2 3 k g /cm~ ), 0 .6 6 p si (0 .0 4 6 k g/em ~ ), an d 1 .1 .1 7 p si (0 (0.. 0 8 2 k g/cm~ ). T h e e f fe f e c ts ts o f t h e d u r a t i o n o f v i b r a t i o n w e r e o n l y e v a l u a t e d w i t h M e t h o d I I I , a n d t h e s e l e c t e d p e r i o d s o f v i b r a t i o n w e r e 1 , 2 , 3, 3 , 4 , a n d 5 r ai ai n . Results and Discussion

Subbase Gradation--The e f f e c t o f v a r y i n g t h e p r o p o r t i o n o f m a t e r i a l p a s s i n g a N o . 4 s ie i e v e o n t h e m a x i m u m d r y d e n s i t ie i e s i s i l l u s t r a t e d i n F i g s. s. 1 a n d 2 . A d e f i n it i t e p e a k v a l u e f o r m a x i m u m d e n s i t y i s ac ac h i e v e d a t a

Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

CUMBE UMBERL RLE EDG DGE E AND CO M INSKY ON SU SUBBAS BBASE EM ATERI ATERIALS ALS 1 4 5

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vibrating ng 6-in. cylindrical cylindrical mold at O.030 O.030 -i -in. n. F I G . 2- -M a xi m um dry density obtained by vibrati

amplitude with 1-psi surcharge pressur pressuree and varying the per percent centages ages of + N o. .$ material of A m ity Ha ll grav gravel el..

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146

RELATIVEDENSITY INVOLVING COHESI RELATIVEDENSITY COHESIONLESS ONLESS SOILS

certain percentage of ~-No. 4 and -No. 4 material for both methods. This indicates that there is a ratio of coarse to fine material which should be utilized when obtaining the greatest dry density possible by either the impact or vibratory methods. Wi th lower percentages of fin fines es,, the aggregate experien experiences ces grain-to-grain contact. However, it is very difficult to compact such an admixture and, consequently, the density results can be quite variable. The aggregate with sufficient fines will encounter encounter grain-to-grain contact with increased resistance against deformation. This condition will result in an increase in density. The aggregate mixed with a large amount of fines will have

grain-to-grain contact destroyed and the aggregate will be "floating" in the fines, which can lead to a substantial decrease in density. R e p r o d u c ib i b i li l i ty t y o f T e s t s - - N o attempt was made to determine the reproducibility of the maximum dry densities obtained by Method III. Table 2 shows the reproducibilities of the maximum dry densities produced by Methods I and II. The best reproducibility is achieved with the vibratory table method and is ~-0.49 lb/ft3 lb/ft 3 (• kg/cm kg/ cm3). 3). Wit h the vibr ator y test, the application of a surcharge pressure of 1 psi (0.07 kg/cm~) kg/cm ~) gives the best reproducibility and the reproducibility of the test bec become omess better with increasing amplitude, that is, a decrease in the standard deviation (• lb /f t 3) about the mean value. The repr reproduci oducibilit bility y of • lb /f t 8 (• kg/c m 3) is probably due to the proper combination of surch surcharge arge pressu pressure re an d amplitude which prevent the soil particles from moving in an erratic motion. With this vibration of the tota l mass, mass, more unifo rmity in the system is is establis established, hed, thus resulting in a better degree of reproducibility. TABLE 2--Repr oducibility of tests tests perf performed ormed on A m ity Ha ll grave gravel. l. Test Methods Impact, 4-in. mold Impact, 6-in. mold Vibratory, 6-in. cylindricalmold cylindricalmold 0 surcharge, 0. 01860186-in. in. ampl amplitu itude de 0 surcharge, sur charge, 0.030-in. 0.0237-in. 0.0237 -in.amplitude amplitu ampl itude de 1 psi surcharge,0.0186-in 0.0186-in.. amplitude 1 psi surcharge, 0.02 0.0237-i 37-in. n. amplitude 0.030-in. in. amplitude amplitud e 1 psi surcharge, 0.0302 psi surcharge, 0.01 0.0186-i 86-in. n. amplitude 2 psi surcharge, 0.02 0.0237-i 37-in. n. amplitude 2 psi surcharge, 0.030-i 0.030-in. n. amplitude amplitud e 3 psi surcharge, 0.0186-in. amplitude 3 psi surcharge, 0. 0237-in. 0237-in. amplitude amplitud e 3 psi surcharge, 0.030-in. amplitude

Reproduci Repr oducibility bility,,lb lb/f /ftt3 • -4-0.80 • • • • • • • • • • • •

a

a Test method showing he h e best b est reproducibility.

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CUMBERLEDGE AND C O M I N S K Y ON SUBBASE MATERIALS

| 47

Statistically, however, when comparing the reproducibilities of the test r e s u l t s b e t w e e n M e t h o d s I a n d I I , t h e d i f fe f e r e n c e s a r e n o t s i g n i fi f i c an an t . T h e r e f o r e , f o r e n g i n e e r i n g p u r p o s e s , t h e r e p r o d u c i b il i l i ti ti e s o f t h e i m p a c t m e t h o d s a r e a s s a t i s fa fa c t o r y a s t h e v i b r a t o r y m e t h o d s . E ff f f e ct c t o f A i r - D r i e d a n d S a tu tu ra r a te te d M a t e ri ri a l o n M a x i m u m D e n s i t y - - I n g e n e ra r a l , w i t h s u b b a s e - t y p e m a t e r i a l, l, t h e r e s u l t i s t h a t m a x i m u m d e n s i t y i s a c h ie i e v e d w h e n t h e s p e c im i m e n is is v i b r a t e d i n t h e a i rr - d r ie i e d s t a te te . I n t h o s e f e w c a se s e s w h e r e t h e d e n s i t y o f t h e s p e c im i m e n is is g r e a t e r w h e n v i b r a t e d i n a s a t u r a t e d c o n d i t io i o n , s t a t is i s t i c a l a n a l y s i s i n d i c a t e s t h a t t h e d i f f er er e n c e i n m a x i m u m d e n s i t i e s i s n o t s i g n if i f i c an a n t [ 6] 6] . A t i n t e r m e d i a t e m o i s t u r e c o n t e n t s ,

t h e r e s u l t a n t d e n s i t ie i e s a r e s i g n i f ic ic a n t l y l o w e r . T h e r e f o r e , f o r t h e r e m a i n d e r o f t h e r e s e a r c h s t u d y , a l l sp s p e c i m e n s w e r e v i b r a t e d i n a n a i r - d r ie ie d c o n d i t i o n . Mold Size, Amplitude, Surcharge Pressure, and Duration of Vibration-T h e a n a l y s i s o f v a r i a n c e a p p r o a c h , u t i li li z in in g t h e F - t e s t , i s e m p l o y e d t o t e s t t h e v a r i a b l e s f o r s t a ti t i s t i c a l s i g ni n i fi fi ca c a n c e. e . T h e e r r o r t e r m f o r t h e s t a t i s t ic ic a l tests consists of a second order interaction variance estimate. The larger the F-value, the greater the probability that the variance of a particular factor is greater than the experimental error variance. When the F-value i s s o la l a r g e t h a t i t w o u l d h a v e a p r o b a b i l i t y o f o c c u r re re n c e b y c h a n c e o f 1 o r 5 p e r c e n t , th t h i s w o u l d ju j u s t i f y r e je j e c t i n g t h e n u l l h y p o t h e s is is t h a t t h e r e i s n o f a c to t o r e f fe fe c t o n m a x i m u m d r y d e n s i t y . I t t h e n c a n b e c o n c l u d e d t h a t th e v aria b le effect is real r eal an d sign ifican if ican t. T a b l e 3 s h o w s t h e r e s u lt l t s o f t h e s t a ti t i s ti ti c a l t e s t s p e r f o r m e d o n M e t h o d s I , I I , a n d I I I . F o r M e t h o d I , t h e t y p e o f s u b b a s e m a t e r i a l ( s p ec e c im im e n ) h a s a d e f i n it i t e e f f e c t o n m a x i m u m d e n s i t y a n d t h i s e f f e c t i s s i g n if i f i c an an t a t t h e 1 p e r c e n t l ev e v e l.l. T h e F - t e s t i n d i c a t es e s t h a t t h e i n t e r a c t i o n e f fe fe c t b e t w e e n m o ld size sizess an d sp ecim en s is no n sign ifican t. T h e s tatistical sig n ifican if ican ce o f t h e e f fe f e c t o f s p e c im i m e n s i n d i c a te t e s t h a t t h e m a x i m u m d e n s it i t ie ie s v a r y a m o n g the eight subbase materials. This should be expected even though the s a m e g r a d a t i o n i s e m p l o y e d fo f o r e a c h s p e c im i m e n . T h e v a r i a t i o n i n d e n s it it ie ie s c a n b e a t t r i b u t e d , a t l e a s t in i n p a r t , t o t h e v a r i a t i o n i n p a r t ic i c l e sh sh a p e a m o n g t h e s u b b a s e m a t e r i a ls l s . M o r e o v e r , t h e s l a g m a t e r i a l s c o n t a i n la la r g e q u a n t i t i e s o f v o id i d s p a c e w i t h i n t h e s o li li d m a t r i x w h i c h w i ll ll g r e a t l y r e d u c e t h e m a x i m u m d r y d e ns n s it i t y. y. Table 3 also shows that for Method 1, the maximum densities are statistically sig n ifican t w h en d ifferen t mo ld sizes are u tilized. T he 6-in . (15.2-cm) mold in Method I produced slightly higher densities for all of the subbase materials. These results are in contrast to the results found f r o m s i m i la l a r s t u d ie i e s c o n d u c t e d b y B u r m i s t e r [ 1] 1] a n d T o w n s e n d a n d D o h a n c y [ 7 ] . T h e s a m e c o m p a c t i v e e f f o r t ( 12 1 2 3 95 9 5 f t . l b s / f t a) w a s u t i li li z e d f o r th e 4 -i -i n . (1 0 .2 .2 -cm) an d 6 -in -in . (1 5 .2 . 2 -cm) mo ld s in th is stu d y . In d iv id u a l s p e c im i m e n s w e r e u s e d fo fo r t h e d e t e r m i n a t i o n o f e a c h p o i n t o n t h e m o i s t u r e d e n s i t y c u r v e e s t a b l i s h e d b y u t i li li z i n g a 4 - in in . ( 1 0. 0 . 22 - cm cm ) m o l d , w h e r e a s t h e s a m e s p e c i m e n w a s e m p l o y e d f o r e a c h p o i n t u s i n g a 6 - in in . ( 1 5. 5 . 22 - cm cm ) m o l d .

C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A  

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FIG. 3--G rad ation cur curves ves illustrating aggregat aggregatee breakdow n of a gravel gravel and slag sam p les. C o n s e q u e n t l y , t h e r e i s p a r t i c l e d e g r a d a t i o n w i t h t h e 6 -i - i n . ( 1 5 .2 .2 - c m ) m o l d , w h i c h re s u l t s in i n h i g h e r d e n s i t i e s d u e t o t h e g e n e ra t i o n o f e x t r a fin fi n e s (Fi g. g . 3 ). Table 3 illustrates that for Method II, all the first-order interactions are s ig i g n i fi f i c an an t a t t h e 1 p e r c e n t l e v e l e x c e p t f o r t h e a m p l i t u d e - s u r c h a r g e p r e s sure interaction, which is significant at the 5 percent level. When an intera c t i o n i s s t a t i s t ic i c a l l y s i g n if i f ic i c a n t, t , t h e c o r r e s p o n d i n g m a i n e f f e c ts ts ( a m p l i t u d e , s u r c h a rg r g e p r e s s u re r e , s p e c im i m e n t y p e ) c e a se s e t o h a v e m u c h m e a n in in g . T h e n a t u r e a n d m a g n i t u d e o f v a r i a t io i o n f o r p o s s ib i b l e i n t e ra r a c t io io n s s h o u l d b e k n o w n , t o s o m e de d e g r e e, e, b e f o r e a n d w h i l e t h e e x p e r i m e n t i s b e i n g p e r f o r m e d . T h e r e f o r e , i t is i s a l w a y s n e c e s s a r y t o i n v e s t i g a t e w h a t t h e s i gn g n i fi f i c an an c e o f t h e interaction represents. Referring to Table 3 for Method II, the significant interaction effect involving specimen type is to be expected, since the maximum densities w i ll l l v a r y g r e a t l y f r o m m a t e r i a l t o m a t e r i a l d u e t o t h e v a r i a t i o n o f s p e ci c i fi fi c g r a v i t y a n d p a r t i c l e s h a p e o f t h e m a t e r ia i a l s . F i g u r e 4 i l lu lu s t r a t e s t h e g r a p h i c a l p r e s e n t a t io i o n o f t h e m a x i m u m d e n s i t y i n te t e r a c t i o n e f f e ct ct b e t w e e n a m p l i t u d e s a n d s u r c h a r g e p r e s s u r e s . I n t h e a b s e n c e o f a n i n t e r a c t io io n , i t c o u l d b e e x p e c t e d t h a t t h e f o u r le l e v e l s o f s u r c h a r g e p r e s s u r e s h o u l d f o l lo lo w t h e s a m e t r e n d a s th th e t e s t p r o c e e d s f r o m o n e a m p l i t u d e o f v i b r a t i o n t o a n o t h e r . In other words, they should be nearly parallel or at least resemble one another in graphical form. T h e d i v e r g e n c e o f t h e l i n es e s in in d i c a t e s t h a t a n i n t e r a c t i o n i s t a k i n g p l a c e . A n i n t e ra r a c t i o n e f fe f e c t b e t w e e n a m p l i tu t u d e s a n d s u r c h a r g e p r e s s u r es es w a s assumed to be occurring during the tests since the loading was a "dead w e i g h t " t y p e . W h e n s u c h a lo lo a d i n g i s u s e d a n d t h e a m p l i t u d e o f v i b r a t i o n

C se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D oo pwynrliogahdt ebdy/p / pAr iSnTte t eMd bI nyt l ( a l l r i g h t s r e se ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c  

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increa ses, the "dea d weig ht" will rise a nd fa ll fro m the surfa ce o f the ma teria l [ 2 ]. C o n sequen tly , the surcha rg r g e pressure pres sure po ssibly tra n smits stresses to the ma teria l a nd ca uses a n increa se in density . Hence, the existence of the interaction implies that the effect of amplitude on the resultant density is markedly dependent on the level of the applied surcha rg e pre press ssure ure.. W hen quo ting the effect o f a mp lit litude, ude, it no w bec o m es necessa ry to specify the ma g nitude o f the a pplied surcha rg e pressure. I t i s i n t e re r e s t in i n g t o n o t e f r o m F i g . 4 t h a t t h e m a x i m u m d e n s it i t ie i e s i n c re re a s e up to a nd including th e a p plica tio n o f a 2-psi 2 -psi (0 .14 -kg /cm 2) surcha rg e press pre ssur ure. e. W ith the a pp lica tio ti o n o f a 3-psi (0.2 1- kg /c m 2) surcha rg r g e pressure, pressure, the m a x imu m densities a re lo wer .t .tha ha n tho se pro duced b y a p ply ing a 2 o psi psi

(0 .14 -kg /cm ~ ) pre press ssur ure. e. E v iden tly , the 3 -psi (0.2 1- kg /c m ~) surcha rg e pressure pro duces just eno ug h effectiv e stress befo re v ibra tio n tha t it is mo re difficult to reduc e the intergranular stresses sufficiently to pe rm it particl e movement to a more stable condition such as produced with the 2-psi (0 .14 -kg /cm ~ ) surcha rge rg e pressu pressure re.. A no ther ex pla na tio n fo r this o ddity is t h a t t h e v i b r a t o r a s s o c ia ia t e d w i t h t h i s p a r t ic i c u l ar ar a p p a r a t u s m i g h t n o t h a v e been a ble to h a ndle th e 3 -psi (0.2 1- kg /c m ~) surcha rge rge press pressure ure.. C o n seq u e n t l y , t h e a m p l i tu t u d e o f v i b r a t i on o n c o u l d h a v e d e c r e a s ed ed t o a l o w e r v a l u e ca using a reductio n in density . Hence, the effect o f decrea sing a mplitude, plus the reductio n fo r the test ma teria ls to ex perience v o lume cha ng e needed to a cco mplish a mo re sta ble pa rticle po sitio n, crea te a co mpo und effect. T his a g rees w ith simila si mila r findi finding ng s o f Ha rdin a nd P ettib o ne [8]. W hen no surcharge pressure is applied, the granular particles have a greater

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t e n d e n c y t o "float", p r o d u c i n g l o w e r d e n s i t i e s t h a n w h e n a s p e c i f i c s u r ch arg e p ressure is app lied . Essentially the same pattern of statistical results is established for M e t h o d I I I ( T a b l e 3 ) . O f p a r t i c u l a r i n t e r e s t is is t h e s ig i g n i fi f i c an an c e o f t h e i n t e r a c t i o n e f f e c t b e t w e e n t h e d u r a t i o n s o f v i b r a t i o n a n d s u r c h a r g e p re re ss- . s u re r e s . F i g u r e 5 i l lu l u s t r a t e s t h e i n t e r a c t i o n e f f e c t g r a p h i c a l ly ly . A s t h e s u r c h a r g e p r e s s u r e in i n c r e a s e s f r o m 0 .3 .3 3 p s i ( 0 .0 .0 23 2 3 k g / c m ~) to 1.17 psi (0.082 kg/cm~), greater densities are achieved. However, these densities are dependent on the duration of vibration, which implies that the significant i n t e r a c t i o n e f f e c t m u s t b e a c c e p t e d . T h i s c o n c e p t c o in i n c i d es es w i t h t h a t proposed by D'Ap polonia e t al [9], th at increasing the surcharge pressure r e q u i r e s l o n g e r p e ri ri o d s o f v i b r a t i o n t o a c h i e v e t h e t e r m i n a l d e n s i t y . Correlation and Regression Analysis--There w a s a v e r y h i g h d e g r e e o f c o r r e l a t io i o n ( R = 0 .9 .9 9) 9 ) b e t w e e n d e n s i ti ti e s p r o d u c e d b y e m p l o y i n g t h e t w o m o l d s i n M e t h o d I [ 6] 6 ] . I n a ll l l c as a s e s d u r i n g t h is is s t u d y , M e t h o d I p r o d u c e d higher densities than the vibratory methods. These findings are contrary t o s im i m i l a r w o r k s r e p o r t e d i n t h e l i te t e r a t u r e . T h i s a n o m a l y c a n b e e x p la l a in in e d , a t l e a st s t in i n p a r t , t o p a r t i cl cl e d e g r a d a t i o n w h e n e m p l o y i n g t h e i m p a c t m e t h o d s. s . H o w e v e r , t h e p r i m a r y c a u s e c a n b e a t t r i b u t e d t o i m p r o p e r a cc c c e l e r a ti ti o n o f v i b r a t i o n o f t h e v i b r a t o r y t a b l e. e . T h i s v a r i a b l e w a s n o t c o n s id id e r e d i n t h e i n v e s t ig i g a t i o n . M o r e o v e r , t h e f r e q u e n c y o f v i b r a t i o n w a s f ix ix e d a t 3 60 60 0 c p m a s sp s p e c if i f ie i e d i n A S T M D 2 0 4 9 -6 -6 9 . F e l t [ 5] 5] d e m o n s t r a t e d , h o w e v e r , t h a t maximum density occurred with different soils at different critical freq u e nc n c ie i e s . C o n s e q u e n t ly ly , t h e f r e q u e n c y o f v i b r a t i o n e m p l o y e d i n t h i s s t u d y m a y n o t h a v e b e e n t h e c r it i t ic i c a l f r e q u e n c y fo f o r t h e t y p e o f s u b b a se s e m a t e r ia ia l s evaluated. C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n  

152

RELATIVE RELATI VE DENSITY INVO LVING COHESIO COHESIONLESS NLESS SOIL SOILS S

To investigate and determine if any relationship existed between the i m p a c t a n d v i b r a t o r y t e s t s , li l i n e a r c o r r e l a ti t i o n a n d r e g re r e s s io io n a n a l y s e s w e r e c o n d u c t e d o n t h e d e n s i ty t y r e su s u l ts ts o f M e t h o d s I , I I , a n d I I I . T h e m a x i m u m d e n si s i ti t i e s r e s u lt l t i n g f r o m t h e i m p a c t m e t h o d s w e r e a s si s i g n ed ed a s t h e d e p e n d e n t Y-values, and the densities obtained by the various vibratory methods w e r e a s s ig ig n e d a s t h e i n d e p e n d e n t X - v a l u e s . The highest degree of correlation was established by employing the d e n s ity resu lts fro m v ib ra tin g a 6 -i -i n . (1 5 .2 .2 -cm) cy lin d rica l m old at 0 .03 .03 0-i 0-inn . (0 .0 76 0 -cm) amp litu de an d ap ply in g a 1 -p si (0 .0 7 k g /cm ~) su rc h arg e p re ss u r e. e. F i g u r e s 6 a n d 7 s h o w t h e s c a t t e r d i a g r a m s a n d t h e a s s o c i a t e d s t a t i s t i cal parameters. Perfect linear correlation is unity. Since the linear corre-

lation coefficient (R-value) in this particular case represents how well a g i v e n s t r a i g h t l i n e d e sc s c r i b es e s t h e r e l a t io io n s h i p b e t w e e n t w o t e s t m e t h o d s , i t can be inferred that there is a high degree of positive linear correlation b e t w e e n d e n si s i ti t i es e s . I t i s im i m p o r t a n t t o n o t e t h a t t h is is v i b r a t o r y t e s t a l s o p r o v i d e d t h e b e s t r e p r o d u c i b i l i t y ( T a b l e 2, 2 , -4- 0 .4 .4 9 l b / ft ft a ) . T h e r e m a i n i n g t e s t c o m b i n a ti t i o n s i n M e t h o d I I p r o d u c e d lo l o w e r R -v - v a lu l u e s. s. T h e t e s t c o m b i nations in Method III showed the lowest degree of correlation (average R = 0.57). T h e l i n e a r c o e ff f f ic i c i en e n t o f d e t e r m i n a t i o n ( R 2) i s d e f i n e d a s t h e s q u a r e o f t h e l i n e a r c o e ff f f ic i c i en e n t o f c o r r e l a ti t i o n a n d r e p r e s e n t s t h e r a t i o o f e x p l a in in e d v a r i a t i o n o f t h e t e s t t o t h e t o t a l v a r i a t i o n . F o r e x a m p l e , s q u a r i n g 0 .9 .9 7

14C

R2=0.94

0y ~

S2ylx : 2 2 2 8

130

.

Sy.x =4172 >,,r v

/

~

f

12C

:= I10

E~

a I00 r

9o , 9O

I

i

I

i

i

I00 I10 120 130 Moximun Moxim unnn Dry Density ( P c f) - V i b r a t o r y

140

FIG. 6--S catte r diagram and regression regression li line ne for M ethod I (4-in. mold) and M ethod II

(6-in. mold).

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

CUMBE CU MBERL RLED EDGE GE AND CO MIN SK Y ON SUBB SUBBASE ASE MATE RIALS

140

~'x = 126. 126.88 88 + 0 90iX -118.59) R=096

0

R2= O 9 2 130

~o I

I10

/

S ~ 'x'x = 2 l ' 6 3 Sy x = 465

/ 0 /

J Q//X ~

/

153

~, ,oo

90 90

I000 I0 I10 120 130 Maximum Dry Density Pcf.)- Vibrotory

140

FIG. 7--Sca tter diagram diagram a nd re~ress re~ression ion li line ne for M ethod I (6 (6-i -in. n. mold) and Method I I

(a-in. mold).

( R - v a l u e f r o m F i g . 6 ) y i e l d s a c o e f fi f i c ie ie n t o f d e t e r m i n a t i o n o f 0. 0 . 9 4. 4. S t a t is i s t ic i c a l ly l y , t h is i s m e a n s t h a t 9 4 p e r c e n t o f t h e t o t a l v a r i a t i o n c a n b e e x p l a i ne ne d by the variables investigated. Six percent of the total variation remains unexplained. This could possibly be due to random fluctuation or to an additional variable, such as acceleration or frequency , wh ich has n ot be en co n sid ered . The standard error of the estimate (Sy.z) for the two diagrams are 4 .7 .7 2 lb /f t s (75 (7 5 .75 .75 k g /m s) an d 4 .65 .65 lb /f t 3 (7 (74. 4.66 3 k g /mS ), respectiv e ly . T h e d i f f e re r e n c e i n t h e s t a n d a r d e r r o r s is is n o t s t a t i s t ic i c a l l y s i g n if if ic i c a n t. t. T h e r e f o r e , either estimating equation can be employed with satisfactory results. H o w e v e r , t h e e s t i m a t i n g e q u a t i o n s a r e o n l y a p p li l i c ab ab l e f o r v i b r a t o r y t e s t apparatus used in this study, and they are also restricted to the subbase materials investigated. Moreover, the test conditions must be such that th e test sp ecim en is v ib ratin g at 0 .0 .0 3 0-i 0-inn . (0 (0.. 07 6-c 6-cm) m) am plitu d e, in a 6 -in -in.. (1 5 .2 -cm) mo ld w h ile ap p ly in g a 1 -p si (0 .0 7 kg /cm ~) su rc h arg e p ressu re. Conclusions

F r o m t h e r e s u lt l t s o f t h e d i f f e re r e n t t y p e s o f llaa b o r a t o r y t e s t s o n t h e m a x i mum dry density of cohesionless subbase materials the following conc lu l u s io io n s m a y b e d r a w n . (a) There is an "optimum" gradation ratio of coarse to fine material C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t ttoo L i c  

154

RELATIVE DENSITY INVO LVIN G COHES RELATIVEDENSITY COHESION IONLESS LESS SOIL SOILS S

which should be utilized when obtaining the greatest dry density possible b y e i th t h e r t h e i m p a c t o r v i b r a t o r y m e th th o d s . ( b) b) T h e r e p r o d u c i b i li l i t ie ie s o f t h e v i b r a t o r y m e t h o d s a r e a s s a t i s f a c t o r y a s the impact methods for engineering purposes. (c) The interaction effects of subbase type, mold size, amplitude of v i b r a t i o n , s u r c h a r g e p r e s s u r e , a n d d u r a t i o n o f v i b r a t i o n a r e h i g h l y s ig ig n i f ic ic a n t o n m a x i m u m d r y d e n s i t y . S i n c e a n i n t e r a c t i o n e f f e c t i m p l i e s a d i f fe f e r e n t ia i a l r e s p o n s e o f t h e v a r i a b l e , i t b e c o m e s n e c e s s a r y t o s t a t e e x p l i c it it l y t h e t e s t c o n d i ti t i o n s w h e n r e p o r t in i n g m a x i m u m d e n s i t y v a lu lu e s o f g r a n u l a r m a t e r ia i a l s a s d e te te r m i n e d b y v i b r a t o r y m e t h o d s . (d) The impact methods consistently produce greater densities for the s u b b a s e m a t e r i a l s i n v e s t i g a t e d . M o r e o v e r , th th e r e i s a v e r y h i g h d e g r e e o f

c o rre l a t i o n b e t w e e n t h e 4 -i -i n . (1 0 .2 . 2 -c m) a n d 6 -in -in . (1 5 .2 -cm) -c m) c y l i n d ri c a l m o l d s e m p l o y e d i n t h e i m p a c t t e s ts ts . (e) Even though the vibrating table test methods produce lower dens i ti t i e s t h a n t h e i m p a c t m e t h o d s , t h e r e i s a h ig i g h d e g r e e o f c o r r e l a ti ti o n b e t w e e n the methods, thus enabling the maximum density to be calculated from the vibratory test data. (f) The vibrating rectangular mold method is the least desirable test m e t h o d f o r d e t e r m i n in i n g m a x i m u m d e n s it it y . Acknowledgments

The authors express their appreciation to the Pennsylvania Department o f T r a n s p o r t a t i o n a n d t h e F e d e r a l H i g h w a y A d m i n i s t r a ti t i o n f o r t h e s p o n s o rrship and financial assistance which made this investigation possible; L. D. S a n d v i g , d i r e c t o r , W . C . K o e h l e r , e n g i n ee ee r o f t e s t s , W . L . G r a m l i n g , r e s e a r c h e n g in i n e e r, r , a n d R . K . S h a f f e r, r, r e s e a r c h c o o r d i n a t o r , o f t h e B u r e a u o f M a t e r i a l s , T e s t i n g a n d R e s e a r c h f o r a l l o tt tt i n g t h e t i m e a n d p e r s o n n e l t o conduct this study; and, especially A. C. Bhajandas for his helpful suggestions during the p repa ration of this paper. References

[I] B urmister, D. M ., "Environm ental Factors in S oil Com pacti paction," on," Symp osium on Com pact paction, ion, Sixty-Sev enth Ann ual Mee ting of the Am eric erican an Society for Te sting and M aterials, Philadelphia, Pa., Ju ne 196 1964. 4. [2]] and [2 D'A ppolonia, E., E"Beh avior ofCon Comference, pacted Fills," Fifteenth nnual Soil M echanics Foun dation ngineering Un iversity of M A innesota, Minneapolis, March 1967. [3]] F orsbladd, L., "Investigation of S oil Com paction by V ibration," Acta Polytechnica [3 Scandinavica, Civ il Eng ineering C ons truction Se ries 34, 1965. [4]] Johnson , A. W. and Sallberg, J. R ., "Factors Influenci [4 Influencing ng Com paction Test Resu lts, lts,"" Highw ay Research Board Bulletin 319 , 1962 1962.. [5] Felt, E. J., Symposium on Application of Soil Testing in Highway Design and Cons tr tr uc uc titi o n, n , A S T M S T P ~ 3 9 , Am erican Society for Testing and M aterials, 1958, pp. 83-110. [6]] Cum berle [6 berledge, dge, G., and Com insky, R. J., "M aximum Density Determination of Subbase M aterials," Pe nsy lvan ia Department of Transportation Transportation Research Report, Burea u of M aterials, Testing and Resea rch, Rese arch Project 67-15, M ay 1970 1970.. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFP E) Universidade Federal de Pernambu co) pursuant to License Agreement. No further repr  

CUMBERL CU MBERLED EDGE GE AND COM INSK Y ON SUBBASE SUBBASEMATERIALS MATERIALS

155

[ 7] 7] T o w n s e n d , D . , a n d D o h a n e y , W . , " R e l a t i v e D e n s i t y T e s t s o n S o m e O n t a r i o S a n d s , " O n t a r i o J o i n t H i g h w a y R e s e a r c h P r o g r a m , O n t a r io io D e p a r t m e n t o f H i g h w a y s , R e port 20, Aug. 1963. [ 8] 8] P e t t ib i b o n e , H . C . , a n d H a r d i n , J ., ., " R e s e a r c h o n V i b r a t o r y M a x i m u m D e n s i t y T e s t f o r C o h e s io i o n l e ss s s S o i l s, s , " S y m p o s i u m o n C o m p a c t i o n o f S o i ls ls , S i x t y - S e v e n t h A n n u a l M e e t i n g o f t h e A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , C h i c ag a g o , I l l .,., 1 9 64 64 . [ 9] 9] D ' A p p o l o n i a , E . a n d D ' A p p o l o n i a , D . J . , " D e t e r m i n a t i o n o f t h e M a x i m u m D e n s i t y of Cohesionless Soils," Third Asian Regional Conference on Soil Mechanics and Foundation Engineering, Haifa, Israel, Sept. 1967.

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

R i c a rd o D o b r y ~ a n d R . V . W h i t m a n 2

C o m p a c t io i o n o f S a n d o n a Ve V e r t ic ic a ll y Vibrating Table

R E F E R E N C E . " D o b r y , R i ca c a rd r d o a n d W h i tm tm a n , R . V . , " C o m p a c t i o n o f S a n d t i c a l ly l y V i b r a t in i n g T a b l e , " Evaluation of Relative Density and Its o n a V e r ti

Role in Geotechnical Geotechnical Projects Projects Involving Involving Cohesionless Cohesionless Soil Soils, s, A S T M S T P 5~8, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 7 3 , 15 1 5 6 -1 -1 7 0. 0.

A B S T R A C T : A d e t a i le l e d s t u d y h a s b e e n m a d e o f t h e f a c to t o r s c o n t r i b u t in in g t o d e n s i fi f i c a ti ti o n o f d r y s a n d o n a s h a k i n g t a b l e . T h e v a r i a b l e s c o n s i d e r e d w e r e t h e frequency of vibrations, amplitude of vibrations, and size and shape of cont a i n e r . N o s u r c h a r g e w a s u s e d i n a n y t e s t . T h e d i f fe f e r e n t p r o c e ss s s e s a f f ec e c t in in g t h e achieved density were found to b e: (1) rep eated change in vertical stress o w i n g t o i n e r t i a f o r ce c e s w i t h i n t h e s a n d w h e n t h e p e a k a c c e l e r a t io i o n is is l e ss ss t h a n 1 g ; ( 2 ) r e a r r a n g e m e n t o f p a r t i c l e s d u r i n g f r e e f a ll l l , w h e n t h e p e a k a c c e l e r a ti ti o n j u s t r e a c h e s 1 g ; ( 3 ) i m p a c t a c t i o n a t t h e e n d o f f r ee e e fa fa l l, l, w h e n t h e p e a k a c c e l e r a ti t i o n ex e x c e e d s 1 g; g ; a n d ( 4 ) s p a l l in i n g o f t h e s u r f ac ac e l a y e r b y s t r e s s w a v e r e f le le c t i o n s , w h e n t h e p e a k a c c e l e r a t i o n s r e a c h s e v e r a l g ' s . KEY

W O R D S : cohesionless softs, tests, soil compacting, vibratory compact-

ing, sands, density (mass/volume)

V e r t ic i c a l v i b r a t i o n o n a s h a k i n g t a b le le i s t h e m o s t w i d e l y u s e d m e t h o d f o r d e t e r m i n i n g t h e m a x i m u m d e n s i t y o f a s a n d . T h e t e s t i n c lu l u d e d in in t h e ASTM Standard for Relative Density of Cohesionless Soils (D 2049-69) is of this typ e. Ho wev er, until a few years ago, the results of this kin d o f t e s t a s r e p o r t e d b y d i f f e re r e n t a u t h o r s o f t e n w e r e c o n t r a d i c t o r y [ 1 ]. ].s O n l y r e c e n t l y h a s a c l e a re r e r p i c t u r e e m e r g e d o f t h e m e c h a n i s m s i n v o lv lv e d i n t h e t e s t [ 2 -6 -6 ] . S u c h b e t t e r c o m p r e h e n s i o n i s e s se s e n t ia i a l i n o r d e r t o s e l ec ec t , o n a r a t i o n a l b a si s i s, s , t h e c o r r e c t c o m b i n a t i o n o f a cc c c e l e r a ti ti o n a n d f r e q u e n c y o f vibration, type and size of mold, moisture content, use of surcharge, and tim e of vibration. 1 P r o f e ss ss o r , S o i l M e c h a n i c s , I n s t i t u t o d e I n v e s t i g a c i o n e s y E n s a y o s d e M a t e r i a l e s , U n i v e r s i t y o f C h i l e , S a n t ia ia g o , C h i le le . 2 P r o f e ss s s o r , C i v i l E n g i n e e r in in g , M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , C a m b r i d g e , Mass. 02139. 8 T h e i t a l i c n u m b e r s i n b r a c k e t s r e f e r to t o t h e l i s t o f re re f e re re n c e s a p p e n d e d t o t h i s p a p e r . 156

opyright by AST M Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Copyright9 ed byby ASTM Inter International national ww w.astm.org Dow nloaded/print nloaded/printed (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

DOBRY AND W HITM AN ON A VER VERTI TICAL CALLY LY VIBRATING TABL TABLE E

1.72

LT"~

l

(~v)p

/,'.e

j2,~ =,-/.-~=

/

2.0

9

/.0

1.6.

o

1.60

o

I

I

I

I

I

I

I

I

I

| 57

4o

80 Frequ e,~c/

120

160

s

f~ cps

FIG. 1--Selig's densificatlan results: dry sand (Ref. 8). M o s t r e se s e a r ch c h e r s h a v e c o n c l u d e d t h a t t h e f in i n a l d e n s i t y i s c o n t ro ro l l e d primarily by the acceleration. Barkan [7] thought it to be the sole controlling factor, but experimental results obtained by Selig [ 8] indicated t h a t b o t h a c c e le l e r a ti t i o n a n d f r e q u e n c y m u s t b e c o n s i d e re r e d (F ( F i g. g . 1 ). ). A m a j o r step was the discovery that an important transition occurs when the a c c e le l e r a ti t i o n re re a c h e s 1 g . T h i s f a c t , o f t e n m a s k e d b y i m p e r f e c t e x p e r i m e n t a l t e c h n i q u e s , w a s s h o w n b y d a t a p r e s e n t e d in i n 1 96 9 6 7 b y D ' A p p o l o n i a e t a l [ 9 ]. ]. Since then, an impressive amount of evidence has accumulated showing t h a t t h e d e n s i ti t i c a ti t i o n p r o c es e s s s t a r t s a t I g , w i t h v e r y l i t tl tl e o r n o c o m p a c t i o n p r o d u c e d be b e lo l o w t h is i s v a l ue u e . T h i s i s t r u e f o r b o t h d r y a n d m o i s t sa sa n d s w i t h n o s t a t i c s u r c h a r g e, e , a n d i t s u g g e s t s t h a t i m p a c t s b e t w e e n t h e s o il il a n d t h e m o l d b a se s e a r e t h e m a i n c a u s e o f c o m p a c t i o n [ 2, 2, 5 , 6] 6] . This paper presents the results of a detailed study made of the compaction behavior of a dry sand on a vibrating table. Only one soil was tested, but the influence of all factors thought to be important, with the exception of surcharge, was verified. Although some tests were also performed using moist and saturated samples, they are not discussed here. T h e o r e t i c a l w o r k a i d e d t h e i n t e r p r e t a t i o n o f e x p e r i m e n t a l r e s u lt lt s o b t a i n e d b o t h b y t h e w r it i t e rs r s a n d b y o t h e r a u t h o rs r s . A d d i t i o n a l d e ta t a il il s m a y b e f o u n d in th e origi original nal rep ort [ 5]. 5] .

E x p e r i m e n t a l P ro r o c ed e d u re r e s a n d T e s t i n g P r o gr g r am am T h e t e s t e q u i p m e n t i n o p e r a ti t i o n d u r in i n g a t e s t w i t h m o i s t s a n d i s sh sh o w n i n F i g . 2 . T h e s h a k i n g t a b l e p r o d u c e s v e r ti t i c a l o s c il i l la l a ti t i o ns ns o f a p p r o x i m a t e l y sinusoidal shape, double amplitude 2y~ up to 0.15 in. within a range of frequencies,, f = 10 to 60 Hz. T he am plit ud e is fi frequencies fixed xed before each test, b u t f c o u l d b e c h a n g e d d u r i n g o p e r a ti ti o n . I n d e e d , t h e m a c h i n e w a s a l w a y s C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFP E) Universidade Federal de Pernambuco) pursuant to License A  

1 .$8

RELATIVE RELATI VEDENSITY DENSITY INV OL OLVIN VIN G COHESIONLESS SOILS

s t a r t e d a t 1 0 H z , a n d t h e f r e q u e n c y w a s t h e n r a p i d l y i n c re r e a s ed ed , m a n u a l l y , to the desired value. Th e nom inal pea k acceleration ap is ap = 0.0511(2y~)J ~

(1)

w h e re a p i s i n g , 2 y~ y ~ i s i n i n c h e s , a n d f i s i n h e rt z . D i re c t m e a s u re m e n t s w e r e m a d e o f a ~ b y p l ac a c in in g a n a c c e l e r o m e t e r o n a p e d e s t a l a t t a c h e d t o t h e m o l d a s s h o w n in i n F i g . 2 . M e a s u r e d v a l u e s a g re re e d w i t h E q . 1 w i t h i n a 10 percent error. Accelerations reported in this paper are the nominal peak a c c e l e ra t i o n a ~. ~. T h r e e c y l in i n d r i c a l m o l d s w e r e u s e d : ( a) a ) a s t e e l P r o c t o r m o l d , 6 i n. n. d i a m e t e r a n d 6 i n. n . h i g h ; (b (b)) a c o ll l l a r mo l d c o n s i s t i n g o f a m a x i m u m o f 12 1 2 s t e e l c o l la l a rs ,

e a c h 1 i n . h i g h a n d 1 ~ i n. n . th th i c k , l i n k e d t o g e t h e r t o s h a p e a c o n t a i n e r o f 6 .2 . 2 5 i n. n . d i a m e t e r a n d o f v a r i a b l e h e i g h t ; a n d ( c ) a lu lu c i t e m o l d ( s h o w n i n Fi g . 2 ) 5 in in . d i a m e t e r a n d 4 5/ 5 / ~ i n . h ig ig h . S i n c e a l l m o l d s h a d c o m p a r a b l e d i m e n s i o n s , t h e i m p o r t a n c e o f m o l d m a t e r i a l c o u l d b e s t u d i e d . T h e c o ll ll a r m o l d w a s u s e f u l f o r s t u d y i n g t h e i n fl f l u e n c e o f s a m p l e h e i g h t. t. All recording instruments appear in Fig. 2: an accelerometer; a cathode f o l lo l o w e r t o a m p l i f y t h e a c c e l e r a t io i o n s i g n a l; l ; a n d a t w o - b e a m o s c il il lo lo s c op op e . In a typical test w ith dry sand, the am plitude control dial of the shaking table was placed at the test value, and the mold was fixed to the table with the accelerometer attached. First, the empty mold was vibrated at

operation, on, including including rec recordi ording ng instruments. instruments. FIG. 2---Equipment in operati Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/ printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agree  

DOBRY AND W HITMAN O N A VERT VERTIICA CALL LLY Y VIBRATING TABLE

TABLE 1 - - F a c t o r s

159

studied.

Factor Studied

Values Cited

Peak accelerationap Double amplit amp litude ude 2yp 2yp Mold type Sample Samp le height

Oto3g o. 025, 025, o. 050, and 0.150 in. Lucite, Proctor, and collar 3, 6, and 10 in.

the test freque frequency, ncy, and a photograph was take n of the acce accelerat leration ion vers versus us time display on the oscilloscope. Then the shaking was stopped and the mold was filled with ovendried sand using a large scoop; this procedure

placed the so placed soil il at an initial density of about 1.3 1.39 9 g/ cm cm3 3, slightly above th e minimum density. The vibrator was turned on again, and the frequency was increased as rapidly as possible to the desired steady-state value. During the test a second photograph of the display was taken (see Fig. 3). The test was stopped by turning off the switch, usually after 10 rain of vibration. The mold was then taken off the platform, the upper collar(s) removed, the top surface of the sand levelled, and the mold weighed to givee data for computing the density. giv About 200 tests were performed. In this way the influence of the factors indicated in Table 1 was studied. P r o p e r t ie ie s o f S a n d

The soil selected was a quartz sand of subangular grains. The particle sizes ranged between 0.25 and 2 ram, and the uniformity coefficient was 1.7. The specific gravity of particles was 2.64, and the minimum density, obtained by carefully pouring sand from a spoon, was 1.388 g/cm 3. A series of tests was performed with a Harvard miniature mold using different compaction techniq techniques, ues, to obtain independent information on th e maximum density of the sand. The value estimated from these these results was was 1 . 6 4 g / c m 3. 3. T e s t R e s u l ts ts

One of the first conclusions of the research was that the mold type was relatively unimportant as compared with the influence of the amplitude for a v > 1 g. Therefore, results obtained obtain ed wit h an y mol d can be ta ke n as being representative for all molds. Figure 4 shows the three plots of final density -y versus ap obtained with the lucite mold. The most distinctive features of these graphs are: (a) Below 0. (a) 0.9 9 g there is little densification, and most of the densification is produced in the range 0.9 to 1.1 g. (b) In all cas cases es ther e is a well defined peak den densit sit y ~v an and d a corresponding cor responding Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to Lice  

160

RELATIVE RELATI VE DENSITY INV OLV ING COH COHESI ESIONL ONLESS ESS SOI SOILS LS

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreem  

v0

z 0z

  <

  0 i

z h a o o e

g 5 ~

h u N

a 9 0

m e

=

A

a

w b

c L o

as

u p

h w a h w d r o a e A 3 G F

m n

2 E 0 1 1 1 a M F v e s g a l n   b Me n A p b g o

P d a F d v U U

m n P d a F d v U

w C D U (

 

162

RELATIVEDENSITY RELATIVE DENSITY INV OLV ING COHESI COHESIONLES ONLESS S SOILS

o p t i m u m a c c e l e r a t i o n (a~)opt ~> 1 g; (ap)opt ra n g e s fro m 1 .1 t o 1 .3 g . T h e l o o se s e n i n g o f t h e s a n d a f t e r t h e p e a k i s n o t l a rg rg e a n d t h e s a n d r e m a i n s i n a dense condition. ( c ) A t s o m e p o i n t b e t w e e n 1 .3 .3 a n d 2 g t h e l o o s e n i n g p r o c e s s s t o p s , a n d e i t h e r t h e d e n s i t y s t a b i l i z e s o r i n c re a s e s a g a i n . O t h e r o b s e r v a t i o n s c o n f i r m e d t h a t t h e b e h a v i o r o f t h e s a n d is is d i f f e r e n t b e l o w a n d a b o v e 1 g. g. T h e f ir ir s t o b s e r v a t i o n a r o s e f r o m t h e f a c t t h a t , i n m o s t t e s t s , t h e d e s i r e d ap ap w a s a c h i e v e d b y i n c r e a s in in g t h e f r e q u e n c y a f t e r s h a k i n g started. Observing the sand as the acceleration was thus increased, there w a s n o m a j o r c h a n g e i n t h e s a n d u n t i l av ~ 1 g ; t h e n , i n a fe w s e c o n d s the surface settled appreciably. The second observation was that, for a v / > 1 g , t h e n o i s e o f i mp a c t s w a s c l e a rl y h e a rd , e s p e c i a l l y w h e n w i t h

one's ear near the mold. As will be discussed subsequently, these impacts o c c u r r e d b e c a u s e t h e s a n d j u m p e d f r ee e e o f t h e m o l d a n d t h e n f el ell b a c k a g a i n s t t h e m o l d . T h e d e c i s iv i v e p r o o f o f t h e e x i s te te n c e o f i m p a c t s c a m e w h e n u s i n g t h e l u c i t e m o l d . O w i n g t o t h e f le l e x i b il i l it it y o f t h i s m o l d , t h e i m p a c t s w e r e p i c k e d u p b y t h e a c c e l e r o m e t e r . T y p i c a l o s c i ll ll o s co co p e d i s p l a y s showing the impacts are presented in Fig. 3; the impacts appeared at prec is i s e ly ly 1 g a n d t h e y w e r e n o t p r e s e n t w h e n t h e m o l d w a s v i b r a t e d e m p t y . T h e a m o u n t o f d e n s if i f ic i c a ti t i o n p r o d u c e d b e l o w 1 g v a r i e d w i d e ly l y fr fr o m o n e s e r ie ie s o f t e s t s t o t h e n e x t . T h i s d e n s i f i c at a t io io n d e p e n d s m a i n l y o n t h e i m p o r t a n c e o f h i gh g h f r e q u e n c y v i b r a t i o n s s u p e r im i m p o s e d t o t h e m a i n s in i n u s o id id a l s h a k i n g . In Fi g . 5 a l l d e n s i t i e s me a s u r e d fo r a v = 0 .93 .9 3 g h a v e b e e n p l o t t e d , and they range from 20 to 70 percent relative density. Conversely, the r e l a t i v e d e n s i t y f o r a v = 1 .1 .1 1 g w a s 8 3 • 3 p e r c e n t , w i t h t h e e x c e p t i o n o f o n e p o i n t. t . T h i s m e a n s t h a t t h e d e n s i t y r e a c h e d i m m e d i a t e l y a f te te r i m p a c t s began was notably constant, being independent of mold type and height 9 Zuc /~e / Io/ o' ~r y -~ no '

-- ~o

2y~ =0.02~ =0.02~"" 2 y p = 0.o~o Z yp = O. /~ o

X6~

7,-.

q /3 5

i

i

/

o

FIG.

i

i

2 A c - z 2 e / ~ r o~ o~ / o f ) j 9 ~

~k

i

i

3

4 - - T y p i c a l r e su s u l ts t s f o r d e n s i ty t y a s f u n c t i o n o f ac a c c el e l er e r at a t io io n .

C o p y r i g h t b y A S T M I n t l ( a l l r ig ig h t s r e s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n te te d b y (UFPE) U niversidade Federal de Pernambuco ((UF PE) Universidade Federal de Pernambuco) pursuant to License Agre  

163

DOB RY AND W HITM AN ON A VE VERTI RTICAL CALLY LY VIBRATING TABLE

D

-

Ib

&

ap

=

0 . 9 59 59

Cq%,

I

.4 .~0

~ ' ~ ' O p = ZI I 9

\

\

/

/

/

/

/

/

/

0

1

O L~

i

i

I

I

I

i

Luc/fe Hold H=6 ~

P/-oc~ H=6

FIG.

5--Equilibrium

i

~o/d

C o / Lo Lo t " M o l d 14= 6"

~

density for up =

i

/4=/0"

1.1 g.

a n d o f v i b r a t i o n a m p l i t u d e . T h i s c o n s t a n t d e n s i ty t y ( ~ = 1 . 59 59 3 g / c m 9 i s c a l le le d t h e e q u i l i b r i u m d e n s i t y . Theoretical Models The simplest model for the behavior of the sand is [8, $, 5] a rigid block sitting on a rigid table, as shown in Fig. 6. The table represents the mold base; it oscillates vertically with a sinusoidal movement. Two situations are possible for the b lock: ( a ) I f a~ a~ < whole cycle of (b) If a~ > the cycle, an d

1 g, the block displaces together w ith the table during the vibration. 1 g, the bloc k displaces w ith the table only during part of t h e r e i s a p e r i o d o f fr fr e e fa fa l l f o l lo lo w e d b y a n i m p a c t .

In either case, the whole history of displacements, velocities, and accelera t i o n s o f t h e b l o c k i s c o m p l e t e l y d e t e r m i n e d i f a ~ a n d ~ --- 2~ 2~ rf rf o f t h e t a b l e are specified. A detailed study has been made using this model [5]; some result s will b e p resent ed here. T h e r e a r e t w o i n s t a n t s T 1 a n d T ~ w h i c h c o r r e s p o n d t o t h e t a k e - of of f a n d t o t he end o f t he f ree f a ll o f t he b lo ck. I f T 1 a nd T ~ a re def ined in ra dia ns ( T = ~t = 2vf t, where t is in seconds) and measured from the beginning of the cycle, they depend only on a~/g: sin T 1 = - g a~

(2 )

~ [ s in in T 1 - - s i n T ~ + ( T ~ - - T 1 ) c o s T1 T1 ] - - ~ ( T ~ - - T , ) ~ = 0 g

(3)

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/ printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agree  

164

RELATIVE RELATI VE DENSIT DENSITY Y INVO LVIN G COHESIONLESS COHESIONLESS SOI SOILS LS

////

////

l

FIG. 6- -R igi d body model: model: ske sketc tch. h.

T1 and T~ hav e been p lotted v ersus a p /g in Fig. 7. To check the model, a s e ri r i es e s o f s p e c ia ia l t e s t s w i t h d r y a n d m o i s t s a n d w e r e p e r f o r m e d a n d T ~ was carefully measured in photographs such as those shown in Fig. 3. T~ was defined as the distance be tw een the beginning of the cycle and the f i rs r s t s p i k e o f t h e i m p a c t . T h e e x p e r i m e n t a l r e s u l ts ts h a v e b e e n s u p e r i m p o s e d i n F ig ig . 7 , a n d t h e y s h o w t h e s a m e t r e n d a s t h e t h e o r e t i c a l c u r v e , w i t h t h e me a s u re d v a l u e s b e i n g s l i g h t l y s ma l l e r, e s p e c i a l l y fo r h i g h a c c e l e ra t i o n s . A n o t h e r u s e f u l p a r a m e t e r c o m p u t e d f r o m t h e r i gi g i d b lo lo c k m o d e l w a s t h e v e l o c i t y o f i m p a c t A v, v, t h a t i s, s , t h e a l g e b ra i c d i ffe re n c e i n v e l o c i t ie ie s b e t w e e n the block and the table at the time T~. AV = a~ (co s T~ -- co s T1) -~ -g -g (T~ O~

OJ

~e

NIoLS~

(4)

T1)

5o~d

8

I

6'

/

f 0

T2 (thtore~,cQO

o

2~

Q

e

2

Peo k

Ar

,, 9 ~

FIG. 7 - - T i m e s T , a n d T ~ v er er su su s ap: theoretical and measured. C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFP E) Universidade Federal de Pernambu co) pursuant to Lic  

DOBRY DOBR Y AND WHIT WHITMAN MAN ON A VE VERT RTIC ICALL ALLY YVIBRATING TAB TABLE LE

5.0

2.5

~

2.0

-~0

20

/6

/2

165

K5

go 0

20

~+O

60

80

120

I00

Ig*O

/ 60

FIG. 8--Rela~ ion amo ng acceleration, acceleration, frequency, an d imp act velocity. velocity.

As both T1 and T~ depend only on a~, hv is a function of two variables: frequency and acceleration. This function has been plotted in Fig. 8 as a family of curves on a graph of acceleration versus frequency. The rigid block model provides useful kinematic information, but does not tell what happens inside the sand mass. An additional insight comes from assuming that the block actually is deformable. Then, according to elastic theory, the maximum impact stress at the bottom is proportional to Av: ,~ = pCA v (5) w h e r e a~ a ~ = i m p a c t s t r e s s , p = m a s s d e n s i t y o f m a t e r ia ia l , a n d C = l o n g i t u d i n a l w a v e v e l o c i ty t y o f m a t e r ia i a l . T h i s i m p a c t s t r e ss s s is is t r a n s m i t t e d u p wards as a compressive stress wave, and reflects from the top surface as a tensile stress wave of equal magnitude. There are subsequent reflections, but the stresses become smaller and finally disappear because of the dam ping properties of the sand. T h u s , t h e i m p a c t s a t t h e e n d o f f r e e f a ll l l i n d u c e d y n a m i c t e n s i l e s t re s s e s p r o p o r t i o n a l t o pChv. O n t h e o t h e r h a n d , t h e r e i s a t a n y d e p t h z o f t h e column a static compressive stress ~g = pg z due to the weight of the material. Dry sand has no tensile strength, and whenever a net tensile s t re r e s s a p p e a r s i n s id i d e t h e m a s s , . th t h e p h e n o m e n o n o f " sp s p a l li li n g " i s p r o d u c e d ; that is, the grains separate. It is reasonable to assume that the loosening C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuco ((UFP E) Universidade Federal de Pernambuco) pursuant to License A  

166

RELATIVE RELAT IVE DENS ITY INVO LVIN G COHESIONLESS SOILS

TABLE 22--O -Opt ptim imum um acceleration measured and predicted using the equation (AV )p = 0.2MH. M o ld ld T y p e

S a m p l eH eH eight, in.

2yp, in.

Optimum Accelerat Acceleration, ion, g Predicted

Measured

Lucite Proctor Collar Lucite Lucit e Proctor

6 6 6 6 6 6

0.025 0.025 0. 02 025 5 0.050 0.150 0.150

1.24 1.24 1.24 1.18 1.13 1.13

1.31 1.23 -1.3 1 1.23 1.24 1.10 1.10

Collar Collar Collar

6 3 3

0.150 0.025 0.150

1.13 1.12 1.06

1.10 1.10 • 1.10

Collar

10

0. 02 025 5

1.37

Fla t cur/'e cur/'e~ ~

There is a small peak for ap ~ 1.40 g, with a value of the d en sity slightl slightlyy larger larger tha n for the rest of the curve. o f t h e s a n d a f t e r t h e p e a k ( a p > ( a p) p) o pt pt ) i s c a u s e d b y s p a l l i n g w i t h i n a s u b s t a n t i a l f r a c t io io n o f t h e t o t a l d e p t h H . I f H / 2 i s t a k e n a s a r e p r e s e n t a t i v e d e p t h , i m p a c t s w i ll l l b e g i n t o lo lo o s e n t h e s a n d w h e n t h e n e t s t r e s s i s z e r o at z = H/2: ~ -- oo-, = l ~p gH -- BpC( Av )p = 0 (6) and (,~v (, ~v)~ )~ -

g H 2BC

(7)

w h e r e B < 1 i s a c o e ff f f ic i c i en en t i n c o r p o r a t i n g a m u l t i t u d e o f u n c e r t a i n f a c t o r s which tend to reduce a~ (imperfect rigidity of the base, damping of the s t re r e s s w a v e , e t c . ). ) . ( 5 v) v ) ~ s h o u l d b e t h e c r i ti ti c a l v a l u e o f t h e i m p a c t v e l o c i t y a s s o c i a t e d w i t h ( a~ a~ )o ) o pt p t ; t h a t i s , A v = ( A v ) ~ w h e n a p = ( a~ a~ )o ) o pt pt. A c c o r d i n g t o t h i s i n t e r p r e t a t i o n , ( hv h v )~ )~ i s t h e l i m i t b e t w e e n t w o s i t u a t i o n s : f o r 5 v < ( 5v 5 v )~ ) ~ i n c re r e a s i n g i m p a c t s d e n s i f y t h e s a n d a n d f o r A v > ( hv h v )p )p i n c r e a s i n g impacts loosen the sand. By combining Eqs 2, 3, 4, and 7, it would be possible to solve for the o p t i m u m a c c e l e ra r a t io io n a s a f u n c t i o n o f y~ a n d H , p r o v i d e d t h a t t h e q u a n t i t y g/2BC is know n. To test this theory, the following proced ure w as adopted . F i r s t , u s i n g t h e ( a ~) ~ ) o pt p t o b s e r v e d f o r t h e f i r s t e i g h t s e r i es es o f t e s t s i n T a b l e 2 , ( 5 v) v)p w a s c o m p u t e d f r o m E q 4 a n d t h e n g / 2 B C w a s c o m p u t e d f r o m E q 7. The resulting values of g/2BC were averaged, giving the value 0.241. Thus, E q 7 became (Av)pp = 0.2 41 H (Av) (8)) (8 w h e r e H i s i n c e n t i m e t e r s a n d ( A v )p )p i s i n c e n t i m e t e r s p e r s e c o n d. d. T h e n ,

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s rree s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o  

DOE, DO E, RY AND W HIT M AN ON A VERTIC VERTICAL ALLY LY VIBRA TING TA TABLE BLE

167

this a v era g e result w a s used to ba c kc o m pu te (a (a~)o ~)opt pt fo r ea ch test, g iv ing the results listed in Table 2. It may be seen that the theory correctly predicts the observed trends; that is, the theory correctly predicts the cha ng e in (ap)opt c a u s e d b y c h a n g in i n g 2 yp yp an an d H . The data by Selig [8] appear to provide further confirmation of the theo ry . T he (a (ap)o p)opt pt fro m o n e o f Selig Selig's 's dens ity v ersus a ccelera tio tio n, curv es w a s u s e d t o d e t e r m i n e ( ~ v ) ~ = 1 2 .3 .3 c m / s ( t h e c o r re r e s p o n d in in g v a l u e o f g /2B C - 0.44 ). Since H w a s the sa m e (11 in.) in.) in a ll o f Seli Seligg 's tests, (Av )~ )~ s h o u l d b e t h e s a m e f o r a ll ll te t e s t s . T h i s v M u e o f ( A v) v) ~ h a s b e e n p l o t t e d i n Fig . 1, a nd this "line o f spa lling " do es indeed a ppea r to define the co mbinations of frequency and acceleration giving maximum density.

e) o- = O COMPACTION

F]:/j

Send oriqinally loose

Little energy needed R a p i d p r o c e s s ( i . e . o c c u r s in in r e l a tit i v e l y smell number of cycles)

FIN AL DENSITY DENSITY INDEPENDE INDEPENDENT NT ON ENER GY INPUT

b)

i~

IMP A C T C OMP A C TION

Send originally dense Much energy needed S l o w p ro r o c e s s ( i .e .e . r e q u i r e s l a r ge ge n u m b e r o f c y c l e s )

reletively

FI NA L DENSI DENSITY TY DEPENDENT ON ENERG Y INPUT

FIG.

9~"~

= 0"

an d i mpact com paction pr pr oce ocesses. sses.

Copyright by A STM Int l (all rrights ights reserved); reserved); Fri Mar 11 16:13:06 EST 2016

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168

RELATIVE RELATI VE DENSITY INVO LVIN G COHESIONLESS SOIL SOILS S

I n t e r p r e t a t i o n o f D e n s i f i e a t io io n P r o c e s s e s

T h e r e a p p e a r t o b e t w o p r o ce c e s se s e s w h i c h l e a d t o d e n s i f i c a ti ti o n o f s a n d o n a v ertically vibra ting table. F i r s t , w h e n a p ~ 1 g t h e r e i s r a p i d d e n s i f ic ic a t io io n , a n d t h e r e s u l t i n g d e n s i t y (the equilibrium densityuabout 80 percent relative density for the sand tested in this program) is independent of initial density, frequency, and sample height. This densification occurs, apparently, because the initial i n t e r g r a n u l a r s t r es e s s e s a r e r e le le a s e d d u r i n g a p o r t i o n o f e a c h c y c l e o f m o t i o n , t h u s a l lo l o w i n g t h e p a r t ic i c l e s t o r e a r r a n g e t h e m s e l v e s i n a d e n s e r p a c k in in g . I t s e e m s r e a s o na n a b l e t o a s s u m e t h a t t h e e q u i li li b ri r i u m d e n s i t y re r e p r e s e n ts ts t h e densest possible packing which the grains can attain simply by releasing t h e i r p o t e n t i a l e n e rg rg ie i e s . T h i s p r o ce c e s s, s , w h o s e e n d p r o d u c t i s t h e e q u i l i b r iu iu m d e n s i t y , h a s b e e n c a l l e d "~ = 0 C o m p a c t i o n " b y t h e a u t h o r s , a n d i t i s

d ep icted in F ig . 9 a. T h e o b v i o u s c o n t i n u a t i o n o f th t h i s p i c t u r e f o r a~ a~ > 1 .1 .1 g i s t h a t f u r t h e r d e n s i f ic i c a t io i o n o c c u r s b e c a u s e o f in i n c r e a s in in g i n t e n s i t y o f t h e i m p a c t s , w h i c h provide the stresses needed to overcome the friction resistance from surrounding grains. This process will then continue either until maximum d e n s i t y is is r e a c h e d o r u n t i l s p a l li l i n g a p p e a rs r s . T h e c o m p a c t i o n is is n o w s l o w e r , with particles advancing a little bit in each cycle. This process has been c a l le le d " i m p a c t c o m p a c t i o n " a n d i s d e p i c t e d i n F i g . 9b 9b . D u r i n g i m p a c t c o m p a c t i o n , i t w o u l d b e e x p e c t e d t h a t t h e d e n s i t y w o u ld ld b e d e t e r m i n e d b y t h e i m p a c t s t re r e s s, s , w h i c h is is i n t u r n r e l a t e d t o h r . T h e experim ental curves for ~ = 1.69, 1.74, and 1.75 g/ cm 3 in F ig. 1 appear very similar to the theoretical curves of Fig. 8. By computing the values o f h v c o r r e s p o n d i n g to to t h e c o o r d i n a t e s ( a p , f ) o f e a c h p o i n t a l o n g t h e /78

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e x p e r i m e n t a l c u r v e , it i t w a s f o u n d t h a t t h e y a r e in in d e e d c u r v e s o f c o n s t a n t ~ v. v . T h e A v n e c e s s a r y t o a c h i e v e d i f f e re r e n t d e n s it i t ie ie s h a v e b e e n p l o t t e d i n Fig. 10. F i g u r e 1 1 t h u s d e s c r i b e s t h e d e n s i fi f i c a ti ti o n b e h a v i o r o f d r y s a n d i n a vmaor lydi nsgu bojne ec t pe ad r at om evteerrt,i csaul cvhi bas arsa tfire roe nq uaenndc ywoi tr h a nmop lsi ut ur cdhe a rogf ev. i bTrhaeti t i oe nf f, e cmt aoyf be predicted by superimposing on Fig. 11 a trajectory describing the test c o n d i ti t i o n s . F o r e x a m p l e , a s e r ie ie s o f t e s t s w i t h c o n s t a n t f r e q u e n c y w i ll ll p l o t a s a v e r t i c a l s t r a i g h t l in i n e a n d a s e ri r i es es o f t e s t s w i t h c o n s t a n t a m p l i t u d e a s a p a r a b o l a . T h e c o n d i ti t i o n s g iv i v i ng n g t h e p e a k d e n s i t y w i ll ll b e i n d i c a t e d b y t h e i n t e r s e c t io i o n o f t h e t r a j e c t o r y a n d t h e l in i n e o f s p al a l li li ng ng . F o r m e d i u m - c o a r s e , u n i f o r m q u a r t z s a n d s , a v a l u e o f g / 2 B C = 0.30 ss- 1 i s r e c o m m e n d e d f o r p r e l i m i n a r y e s t i m a t e s o f t h e l in i n e o f s p a ll l l in in g . Conclusions

1 . A t h e o r e t i c a l m o d e l h a s b e e n d e v e l o p e d t o e x p l a in in t h e c o m p a c t i o n bs ue rhcahvai rogre .o fT hd ri sy m s aondde li ni s a s ummom l da rsiuz be dj e cbtye d F ti og . v 1e 1r t iacnadl vc ihbercakt si o rnesa saonnda bnloy w e l l w i t h t e s t r e s u l ts t s . T h e m a i n f a c t o r c o n t r o ll l l in i n g t h e f in in a l d e n s i t y o f t h e sand is the inten sity of imp acts which occur wh en the acceleration is larger tha n 1 g. 2 . F o r a t e s t s e r ie i e s w i t h d r y s a n d , t h e p e a k d e n s i t y w i ll l l o c c u r a t t h e l in in e o f s p al a l l in in g , w h i c h m a y b e c o m p u t e d w i t h E q 7 . F o r m e d i u m q u a r t z s a n d , a v a l u e o f g / 2 B C = 0.30 ss - ~ c a n b e u s e d f o r p r e l im im i n a r y e s t i m a t e s . 3. Peak density may coincide with or may be lower than maximum d e n s i ty t y . T h e t h e o r e t ic i c a l p i c t u r e s u g g e st st s t h a t s a t u r a t i n g t h e s a n d a n d C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i  

170

R E L A T I V EDENSITY E DENSITY INVOLVING COHESIONLESS SOILS

a d d i n g a s u r c h a r g e w e i g h t o n t o p o f i t c o u l d i m p r o v e t h e e f fi f i c ie ie n c y o f t h e t e s t b y r e d u c i n g s p a ll l l in i n g . T h i s s u g g e s t i o n a ggrr e e s w i t h p a s t e x p e r i e n ce ce (ASTM D 2049-69).

Acknowledgments T h i s w o r k w a s ca c a r ri ri e d o u t u n d e r t h e M . I . T . I n t e r - A m e r i c a n P r o g r a m i n C iv i v i l E n g i n e e r i n g , a n d t h e f i na n a n c i al al s u p p o r t o f t h e F o r d F o u n d a t i o n a n d o f t h e U n i v e r s i t y o f C h i le le a r e g r a t e f u l l y a c k n o w l e d g e d . V a r i o u s s t u d e n t s c o n t r i b u t e d t o t h i s s t u d y t h r o u g h s p e ci c i a l p r o j e c t s a n d t e r m p r o je je c t s , e s p e c ia i a l ly l y J o s~ s ~ P a n i a g u a , D a v i d D r i sc s c o ll ll , a n d R a l p h M i t t e l b e r g e r .

References [1 ] Lu s ch er , U ., O r tig o s a, P ., R o ck er , K ., an d W h itman , R . V., " R ep eated Lo ad an d V ib r atio atio n Tes ts u p o n S an d , P r o g r es s R ep o r t N o . 1 ," R es ear ch R ep o r t R 6 77 - 29 29 o f th e

[2]] [2 [3] [4 ] [5]] [5 [6]

De pt. of Civ Civil il Engineering, M.I.T ., 196 1967. 7. O r tig tig o s a D e P ab lo , P ., " D en s if icatio icatio n o f S an d b y V er tical tical V ib r atio atio n s w ith A lmo s t Constant Stresses," Master thesis, Dept. of Civil Engineering, M.I.T., 1968. Whitman, R. V. and Ortigosa, P., "Densification o f S an d b y V er tical tical V ib r atio atio n s ," Technical Paper T68-5, Soils Publication 222, Dept. of Civil Engineering, M.I.T., 1968. Lamb e, T. W . an d W h itman , R . V. in Soil Mechanics, Wiley, 1969. D o b r y , R . an d W h itman , R . V ., " D en s if if icatio icatio n o f S an d b y V er tical tical V ib r atio atio n s in 'Standard' Molds," Research Report R70-05, Soils Publication 251, Dept. of Civil Engineering, M.I.T., 1969. Krisek, R. J. and Fernandez, J. I., Journal of the Soil Mechanics and Foundations, Am erican So ciety of Civil Engin eers, V ol. 97, No. SM 8, Au g. 1971 , pp. 10691069-1079. 1079.

[7] in Dynamics 2of and ican Foundations, [8] Barkan, Selig, E.D.T.,D. Proceedings, n dBases P an amer C o n f er enMcGraw-Hill, ce o n S o il M1948. ech an ics an d Fou nda tion Engineering, V ol. 1, 1963, pp. 129 129-1 -144. 44. [9] D'Appolonia, 1). J. and D'Appolonia, E. in Proceedings, 3d Asian Regional Conference on Soil Soil Mechanics an d Fou nda tion Engineering, 196 1967, 7, pp. 266266-268 268..

Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

A . I . J ohn son ~ a n d D . A . M o r r i s 2

V i b r a t o r y C o m p a c t io i o n iinn th t h e La b o r a t o r y o f G r a n u l a r M a t e r ia i a l s i n Lo L o n g Co l u m n s *

to r y C o m p a c t i o n R E F E R E N C E : J o h n s o n , A . I . a n d M o r r i s , D . A . , " V i b r a to i n t h e L a b o r a t o r y o f G r a n u l a r M a t e r ia i a l s i n L o n g C o l u m n s , " Evaluation

of Relative Density Density and It Itss Role in Geotechnic Geotechnical al Projects IInvolving nvolving Cohesionless Cohesionless Soils, ASTM STP 523, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i al a l s , 1 97 97 3, 3, pp. 171-181. A B S T R A C T : F o r a l a b o r a t o r y s t u d y o f t h e d r a i n ag ag e o f l o n g c o l u m n s o f p o r o u s m e d i a , a m a x i m u m d e n s it i t y , u n i fo f o r m l y d i s t ri ri b u t e d t h r o u g h o u t t h e c o l m n n , was required. Research resulted in the development of a mechanical technique for the packing of drainage columns, as much as 60 in. long, with glass beads and natural sands of various particle sizes. A vibratory packer used to pack these columns, which are 1 to 8 in. in diameter, provided good reproducibility of dry u nit weight and porosity betw een duplicate columns as well as a v e r t ic ic a J u n i f o r m i t y o f t h e s e p r o p e r t i e s w i t h i n t h e s a m e o r d u p l i c a t e c o l u m n s . T o d e v e l o p t h e s t a n d a r d m e t h o d o f p a ck c k i n g c o lu lu m n s , a s t u d y w a s m a d e o f t h e e f fe f e c ts ts o f t i m e , a m p l i t u d e , a n d s u r c h a r g e w e i g h t o n t h e u n i f o r m i t y a n d r e p r o d u c i b i l i t y o f r e s u lt l t s . T h e t e c h n i q u e w a s s ta t a n d a r d i z e d a t a p a c k i n g p e r i o d o f 10 10 s a n d a v i b r a t o r y a m p l i t u d e o f 0. 0 . 09 09 c m .

K E Y W O R D S : d e n s i t y ( m a s s / v o l u m e ) , c o m p a c t i n g , p o r o s i ty ty , v o i d r a t i o , s p e c if i f i c y i e l d , p o r o u s m a t e r i a l s , t e s t s , d r a i n a g e , c o h e s i o n l e ss s s s oi o i ls ls

A s p a r t o f a c o o p e r a t iv i v e r es e s e a r ch c h p r o j e c t b e t w e e n t h e C a l if i f o r ni ni a D e p a r t m e n t o f W a t e r R e s o u r c e s a n d t h e U . S . G e o lo l o g i c al a l S u r v e y , s p e c if if ic ic y i e l d ( th t h e v o l u m e o f w a t e r d r a in in e d b y g r a v i t y f r o m s a t u r a t e d p o r o u s m e d i a ) w a s s t u d i e d i n t h e l a b o r a t o r y a n d i n t h e f ie i e ld l d b y t h e a u t h o r s [ 1] 1] 3 O n e phase of this study was the laboratory drainage of columns of porous m a t e r ia i a l s. s . T o p e r m i t a c c u r a t e c o m p a r i s o n o f d r a in in a g e d a t a f r o m t h e s e c o lu l u m n s , a m a x i m u m , b u t u n i f o r m l y d i s t ri r i b u t e d , d e n s i t y w a s r e q u ir ir e d throughout the porous media. Although the research reported in this * Publication authorized by t he Director, U . S. Geological Survey. 1 A s s i s t a n t c h i ef e f , O ff f f ic ic e o f W a t e r D a t a C o o r d i n a t i o n , U . S . G e o l o g i c a l S u r v e y , W a s h i n g ton, D. C. 20242. 2 Assistant district chief, U. S. Geological Survey, Anchorage, Alaska. 3 Th e italic num bers in brack ets refer to the list of references append ed to this paper. 171

opyright by AST l (all reserved); Fri 11 .as 16:13:06 Copyright 9 M Intby ASrights TM Int Internat ernationa ional l Mar www .astm.or tm.orgg EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

172

RELATIVEDENSITY RELATIVE DENSITY INVOLVING COHESI COHESIONLESS ONLESSSOI SOILS LS

FIG. 1--Ca m-a ctuated packer used used fo r packing disturbed disturbed specimens specimens of granul granular ar m aterials.

p a p e r w a s n o t i n v o l v e d w i t h a s t u d y o f r e l a t i v e d e n s i t y , i t is is b e l i e v e d t h a t t h e d a t a o b t a i n e d a n d t e c h n iq i q u e s d e v e l o p e d w il il l b e o f i n t e re re s t t o t h o s e i n v o l v e d in i n t h a t s u b j e e t. t. In the U. S. Geological Survey's laboratory at Denver, Colo., a camactivated packer, (Fig. 1) designed by the senior author, had been used s i n ce c e 1 9 49 4 9 a s a s t a n d a r d m e t h o d o f p a c k i n g s m a l l c y li li n d e r s o f d i s t u r b e d s p e c i m e n s o f g r a n u l a r m a t e r i a ls l s [ 2] 2] . H o w e v e r , t h i s e q u i p m e n t w a s n o t l a r g e e n o u g h t o h a n d l e d ra i n a g e c o l u m n s 6 0 i n . i n le le n g t h a n d 1 t o 8 in . i n d i a m e t e r , w h e n f i ll ll ed ed w i t h p o r o u s m e d i a . sitdset aogfe tsh oe f ct oh el u rme ns es a w r ciht hin i na t hr ue blbaebro rm a taol rl ye t, m b y Dt ua pr ipnign gt h teh ef i rsst d id i ad n nu oa tl pp ar co kv iindge u n i f o r m p o r o s i t y ( t h e p e r c e n ta ta g e o f t h e t o t a l v o l u m e o f t h e m e d i a t h a t i s occupied by voids) throughout columns of porous media or reproducible porosity in different cylinders of the same porous media. Porosities within a c o l u m n v a r i e d b y a s m u c h a s 1 0 p e r c e n t - - t o o g r e a t a ra ra n g e f o r t h e r e s e a rc rc h . T h u s , a s e a r c h w a s m a d e f o r a m e c h a n i c a l m e t h o d o f p a c k i n g that would provide both uniform and reproducible porosities in columns of porous media. A r e v i e w o f l i t e r a t u r e p r o d u c e d li l i t tl tl e i n f o r m a t i o n o n m e c h a n i c a l p a c k i n g Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agre  

JOHNSON AND M ORRIS ON COM PACTION OF GRANULAR GRANULAR M ATERI ATERIALS ALS

173

m e t h o d s f o r c o lu l u m n s o f p o r o u s m a t er e r ia i a l s, s , b u t s o m e in in f o r m a t i o n w a s f o u n d on related techniques. Pauls and Goode [3] used a vibrating table to pack o v e n - d r y m a t e r i a ls l s a n d c o n c l u d ed e d t h a t 2 0 ra r a in in o f v i b r a t i o n w a s a d e q u a t e t o o b t a i n m a x i m u m d e n s i t y in i n t h e m a t e r ia ia l s. s. B a r t e l l a n d A l b a u g h [ $] investigated th e use of vibrational m ethods for packing small volum es of p o w d e r t o m a x i m u m d e n s it i t y a nd n d f o u n d t h a t t h e v i br b r a ti t i o n al al m e t h o d p r o v i d e d u n i f o r m a n d r e p r o d u c i b le l e p a c k i n g w i th t h i n a r e a s o n a b l e ti ti m e . C u s e n s [ 5] 5] s tu t u d i e d t h e v i b r a t o r y p a c k i n g i n t h e l a b o r a t o r y o f 2 6 0 00- g s p e c im i m e n s o f d r y -m - m i x c o n c r e te t e a n d f o u n d t h a t a f r e q u e n c y o f 3 00 00 0 c o u n t s p e r m i n a n d a n a m p l i t u d e o f 0 .0 . 0 0 4 i n. n . p r o v i d e d o p t i m u m p a c k i n g . F e l t [ 6] 6] p r e s e n t e d t h e r e s u l ts ts o f a c o o p e r a t i v e s t u d y o f p a c k i n g m e t h o d s f o r p r o ducing maximum density in six different granular materials. One free-fall p a c k e r u s e d 3 0 fre e fa ll l l s o f 1 8 i n . a n d a s u rc h a rg e o f 4 .2 p s i fo r p a c k i n g . Also used were four vibratory packers with amplitudes of 0.01 to 0.02 in.,

fre q u e n c i e s o f 3 5 00 00 , 3 6 0 0 (tw (t w i c e ), a n d 7 2 0 0 c o u n t s p e r ra in i n , a n d v i b ra t i o n t im i m e s o f 10 1 0 t o 4 5 ra ra in in . T h e y c o n c l u d ed e d th th a t t h e v i b r a t o r y m e t h o d w i t h a s u r c h a r g e o f 2 to t o 3 p si si p r o v i d e d o p t i m u m p a c k i n g . T h e E a r t h M a t e r i a ls l s L a b o r a t o r y o f t h e B u r e a u o f R e c l a m a t i o n [ 7, 7, 8 ] s t u d i e d t h e u s e o f m e c h a n i ca c a l v i b r a t o r s a s a p p l ie ie d t o d e t e r m i n a t i o n o f t h e m a x i m u m d e n s i t y o f s oi oi l s . T h i s s t u d y i n d i c a t e d t h a t a m e c h a n i c a l v i b r a t o r mounted under the container produced a more symmetrical vibration than that of several vibrators attached to the sides of the container being vibrated. This study also indicated that better reproducibility was obtained by completely filling the packing container rather than filling and vibrating by increments, and that higher densities were obtained by using oven-dry media and surcharge weights. T w o m e t h o d s o f t e s t fo fo r m a x i m u m a n d m i n i m u m d e n s i t y o f g r a n u l a r materials were suggested by Burmister [9] and Jones [ 1 0 ] in American S o c i e t y f o r T e s t i n g a n d M a t e r i a ls l s ( A S T M ) p u b l i c at a t io io n s . B u r m i s t e r ' s m e t h o d u s e d a v i b r a t i n g o r d r o p -w - w e i g h t ta ta m p e r , a n d J o n e s ' m e t h o d u s e d a foundry-type vibrator. F o l l o w i n g t h e l ib i b r a r y s e a rc rc h , t h e a u t h o r s c o n c l u d e d t h a t a d d i t i o n a l l a b o r a t o r y r e s e a r c h w a s n e e d e d t o e v a l u a t e t h e p o s s ib i b l e a p p l ic i c a t io io n o f m e c h a n i ca c a l v i b r a t in i n g e q u i p m e n t t o t h e p a c k i n g o f l o n g c o lu lu m n s o f g r a n u l a r materials. Throughout the study, porosity was used as the property to indicate the qua lity of packing. D e s c r i p t i o n a n d O p e r a t i o n a l C h a r a c t e r i s t ic ic s o f P a c k e r

A f t e r a p r e l i m i n a r y s t u d y o f s e v e r a l c o m m e r c i a l p a c k e r s , i n c lu l u d i n g j o l t in in g a s w e l l a s o s c i ll l l a to to r y e q u i p m e n t , t h e S y n t r o n V P - 6 0 v i b r a t o r y p a c k e r 4 ( F ig ig . 2 ) w a s c h o s e n a s m o s t s u i t a b l e f o r t h i s s t u d y . T h i s p a c k e r h a s a r h e o The use of brand brand names in in thi thiss report does not imp ly endor endorsement sement by the U. S. Geologi Geol ogical cal Survey. The ir equivalents equivalents may be used for the same processes. Copyright by AS TM Int l (all rights rights res reserved); erved); Fri Mar 11 16:13:06 EST 2016

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174

RELATIVE DENSITY INVO LV ING COHES RELATIVEDENSITY COHESION IONLESS LESS SOI SOILS LS

FIG. 2--V ibra tory packer and rheost rheostat, at, with column clamped on packer packer platform. platform.

s t a r c o n t ro r o l f o r a m p l i t u d e a d j u s t m e n t a n d a f i xe xe d f r e q u e n c y o f 6 0 v i b r a t i o n s p e r s e c o n d ( o r l in i n e f r e q u e n c y ) . I t i s m o u n t e d o n r u b b e r , h a s a l o w n o is is e l e v e l, l , a n d i s b u i l t f o r lo l o a d s u p t o a p p r o x i m a t e l y 3 0 0 lb l b . I t c o n s is is t s o f a d e c k or platform rigidly attached to an electromagnet. As a-c current energizes the electromagnet, the platform is alternately attracted and repelled by a permanent magnet rigidly attached to the base. T h e a m o u n t o f m o v e m e n t o f t h e u n l o ad a d e d v i b r a to to r p l a t f o r m w a s d e termined at five different settings of the rheostat by use of the General Electric vibrometer shown in Fig. 3. This instrument, also used to determine all vibrational amplitudes reported in this study, has a mechanical amplification in a linkage between the vibration sensing element and the stylus for the recording chart. The amplification factor was 10.5 for the i n s t r u m e n t u s e d in i n th t h i s s t u d y . A l l r e p o r t e d a m p l i tu tu d e s h a v e b e e n c o r r e c t e d

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JOHNSON AND M ORRIS ON COM PACTION OF GRAN GRANULAR ULAR M A TE TE R I A L S

| 75

f o r th t h i s a m p l if i f i c at a t io io n . T a b l e 1 s h o w s t h e v a r i a t i o n s i n a m p l i t u d e o b t a i n e d in this study. T h e c h a n g e i n a m p l i t u d e o f t h e p a c k e r p l a t f o r m a t a n a r b i t r a r il i l y c h o s en en r h e o s t a t s e t t in in g ( B ) , w i t h t h e c h a n g e o f w e i g h t o n t h e v i b r a t o r p l a t f o r m , w a s t h e n s t u d ie ie d . T h i s w a s d o n e t h r o u g h o u t t h e c a p a c i t y o f t h e p a c k e r b y adding the porous medium in 4.5-kg increments to a large cylindrical tube w h i c h w a s a t t a c h e d r i g id i d l y to t o t h e p a c k i n g p l a t f o r m . A d e c r e a s e o f 0 .0 .0 5 5 c m i n a m p l i t u d e o c c u r r e d a s t h e l o a d w a s in i n c r e a s e d f r o m 6 t o 1 35 35 k g . S e v e n t y f iv i v e p e r c e n t o f t h e c h a n g e i n a m p l i t u d e t o o k p l a c e in i n t h e f i rs rs t 3 5 k g o f l o ad a d i n g . O n l y 1 5 p e r c e n t a d d i t i o n a l c h a n g e t o o k p l a c e o v e r t h e 3 5 to to 8 0 - k g interval, a nd the rem aining 10 percen t change took place be yo nd 80 kg. E f f e c ts t s o f T i m e o f V ib ib r a ti on a n d P a c k i n g M e t h o d

The effect of length of time of vibration on porosity was studied using

c o l um u m n s a b o u t 2 .5 . 5 c m i n d ia i a m e t e r a n d a b o u t 1 20 20 c m i n h e ig i g h t. t. T w o c o l u m n s of 0.120-mm glass beads and one column of 20-mesh Del Monte sand (Fig. 4) were filled by letting the beads and sand drop freely from the top o f t h e c o lu l u m n . T w o o t h e r c o l u m n s o f g la la s s b e a d s l o a d e d w i t h a t r e m i e t u b e w e r e u se s e d . T h e c o l u m n s , r ig ig i d l y a t t a c h e d t o t h e d e c k o f t h e v i b r a t o r ( F ig i g . 2 ) , w e r e t h e n v i b r a t e d f o r 30 3 0 0 s. s. A l t h o u g h t h e i n i ti t i a l p o r o s i t y o f t h e c o l u m n s f il i l le le d w i t h a t r e m i e w a s considerably higher than the porosity of those loaded by free fall, this s t u d y i n d i c a t e d t h a t a f t e r 1 0 s o f v i b r a t i o n t h e p o r o s i t ie i e s in in a l l t h e c o l u m n s closely approximated their final porosity. Because the columns filled by the free-fall method and the columns filled with the tremie reached their minimum porosity at about the same time, the tremie technique was

FIG. 3--Vibrom eter used to m easure am plitude of vibrations of packer~

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176

RELATIVEDENSITY RELATIVE DENSITY INVOLVING COHESI COHESIONLESS ONLESSSOI SOILS LS

T A B L E 1- -A m pli tu de of vibr vibrati ation on for unloaded vibr vibra~ry a~ry packer. Rheostat Setting Minim um A B C D

I00

90

A m p l i t u de de , e m 1 st st R u n

2d Run

3d Run

4th Run

0.04 0.07 0.09 0.13 0.18

0.04 0.07 0 .09 0 .13 0.18

0.04 0.06 0.09 0.12 0.19

0.04 0.06 0.09 0.12 0.18

j

8 0 - -

8 o

70

z

:

t30

~ 120 I--

/

U.I I..-

I10

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/

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:

o

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120

9 X X 9 9 ~/

9

x/ /

/

/ 130 130

/

xx,,'.:

9

9

9

../

/

-X ---% F V I B R A T E D TEST DENSITY

140

M E A S U R ED ED D R Y D E N S I T Y - C O M P A C T E D

FIG. 5---Sound

/

~ " / /. , , ,

x

/x

/

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~

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o/ /9

/

//

lOOi I10

/

./ /

m

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150 150

160

F I LL LL , I b / f t 3

fresh quartzite density data.

t i m e . I n d e e d , t h i s w a s t r u e i n a ll l l b u t f o u r s e t s o f t e s t s d u r i n g t h e p r o g r am am . Therefore, relative density computations in the usual manner (ASTM D 2 0 4 9 - 6 9 ) w e r e n o t m a d e b e c a u s e r el e l a ti ti v e d e n s i t y v a l u e s a b o v e 1 0 0 p e r cent were not considered appropriate.

Since relative density values above 100 percent were undesirable, the ratio of each compacted rockfill density to the corresponding vibrated test density was expressed in percent. In general, the density of the compacted f il il l w a s b e t w e e n 1 0 0 a n d 1 3 0 p e r c en e n t o f t h e m a x i m u m v ib i b r a t e d t e s t d e n s i t y. y. T h i s i s s h o w n g r a p h i c a ll ll y i n F i g s . 5 , 6 , 7 , a n d 8 w h e r e t h e d a t a i s s u m m a r i z e d ~

140

>.,-

t,,D Z hi 0 >,-

L E G E N D FOR VIBRATING ROLLERS X I0 - TON 9 15 - TO N

t30

Q: 120 Q

//-

I'.(/) LIJ

o I10 i W I-.-

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,~ /

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(n

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140

130

120

OF VIBR ATED TEST DENSITY

160

150

M E A S U R E D D R Y D E N S I T Y - C O M P A C TE TE D F I L L , I b / f t 3

weathered quartzite density data.

FIG. 6----Slightly

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STEPHENSON STEPH ENSON O N RELA RELATIVE TIVE DENSI DENSITY TY TESTS O N ROCK FI LL

i,qn,* 120 E3 I-oO U,.I I-Q II0 ILl El

/

/

I00 9 I 0

/ /

/

9

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243

x VI BRA TED

TEST DENSITY

I

150

160

M E A S UR UR E D D RY RY D E N S I T Y - C O M P A CT CT E D F I L L , I b / f t 3

ea th th ered ered,, qua rr y r un ro ck densi densi ty data. F I G . 7 --M o dera tely w ea for each type of material. These figures also show the range of the data, and indicate each type of roller used for compacting the rock fill was equally effective in obtaining densities above the vibrated maximum test

density.

G r ain Size A naly nalyse sess T h e g r a in i n s iz i z e d i s tr tr i b u t i o n w a s d e t e r m i n e d f o r e v e r y s p e c i m e n t a k e n f r o m t h e c o m p a c t e d fi f i l l , w h e t h e r o r n o t t h e m i n i m u m a n d m a x i m u m v ib ib r a t e d 140

FILL COMPACTE COMPACTED D BY 4 PASSES OF 50-TON RUBBER TIRE ROLLER

..Q B

1-- 130

120

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/

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120

130

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-)('-% OF VIBRATED TEST DENSITY

f

140

150

160

M E A S UR U R E D DR DR Y D E N S I T Y - C O M P A C T E D F I L L , I b / f t 3

FIG.

8---SpaUs and weathered rock density data.

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244

R E L A T IV IV E

DENSITY

INVOLVING

CO HESION LESS

S O IL S

I' COBBLES I GRAV RAVEL EL I SAND ] u.S .S.STANDARDSIE IEVE VEOPENNGSN U.S.STANDARDSIE IEVE VENUMBERS

I00_ ~ 12

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500

I00

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FIG.

I0 5 I 0.5 G R A I N S I Z E , MI L L I ME T E R S

O.I

9--Sound fresh quartzite gradation curves.

0. 05

m

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20

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I00 0.01

I CO BBL ES

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FINES

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U.S. STANDARD SIEV E OPENINGS, IN. U. S STANDARD SIEV E NUMBERS

, o

o

12 6 :3 :3 . . . , . . ,

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20 , ,

40

I00 ,

20 0

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~ 60 ~_

n

20

0

~

80

50 0

I00

50

IO 5 I 0.5 G R A I N S I Z E , MI L L I ME T E R S

FIG.

lO--Slightly weathered quartzite gradation

IOO o. ol

IJ_LI 0. 05

0.11 0.

curves.

Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant  

I

I CO BBLES

STEPH ENS ON

ON

GR AVEL

I

R E L A T IV E

D E N S IT Y

T E S TS

ON

SAN D

R OC K

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F IL IL L

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FINES

U.S. STANDARD SIEVE OPENINGS, N U.S. STANDARD SIEVE NUMBERS I00

l'-T (.9

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20 ,

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0

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20

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500

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I0 0

FIG.

50

0 5 I 0.5 GRAIN SIZE, MILLIMETERS

0. I

0.05

l l - - M o d e r a t e l y w e at a t he he re re d, d , q u a r r y r u n r o c k g r a d a ti t i o n cu c u rv r v es es .

I I00 0.01

~

I CO BBLES

I

GR AVEL

I

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SAN D

FINES

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U.S. STANDARD SI SIEVE EVE OPENINGS, N. U.S STANDARD SIEVE SIE VE NUMBERS I00

12

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lO ,

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60

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40

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FIG.

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I I I 50

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llllll~ ll I I IIII III I I0 .5 I 0.5 GRAIN SIZE, MILLIMETERS

I

IIII IIl l I 0.1 0.0 5

I

I00 0.01

1 2 --S p ~ lls a n d w ea th ered ro ck g ra d a $io n cu rves.

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246

RELATIVE DENSITY INVOLV ING COHESIONL COHESIONLESS ESS SOILS

dwehni sc iht y a t ecsot m s pwl ee tree ps ee rr ifeosr moefd .d eTnyspi it yc a lt egs rt as d w a tei roen pc eu rrfvoersm feodr as rpee csi hmoewn ns oi nn Fi g s . 9 , 1 0 , 1 1 , a n d 1 2 . T h e s e p a rt i c u l a r c u rv e s a l s o re p re s e n t t h e g ra d a t i o n "band" obtained for alI the specimens taken from each embankment zone during construction. Discussion

Tes t Equi pment Since the vibrated test densities were less than the compacted rock fill d e n s i ty ty , t h e r e i s s o m e q u e s t i o n a b o u t t h e a d e q u a c y o f t h e s p e c i m e n c o n tainer and the vibrating table. During vibration, the material tended to " r o t a t e " d o w n o n e s id i d e of o f t h e c o n t a in i n e r a n d u p t h e o t h e r i n s t e a d o f co co n s o l i d a ti t i n g v e r t i c a l ly l y u n d e r t h e s u r c h a r g e . I t h a s b e e n s u g g e s t e d th th e s p h e r i c a l s h a p e d b o t t o m o f t h e c o n t a in i n e r c a u s e d t h is i s ; h o w e v e r , th th e v i b r a t o r y m otion of the vibra ting tab le could have be en the m ajor cause. If a fiat bottomed container were used, inaccuracy would probably arise from the i r r e g u la l a r s u r f a c e e f f e ct c t s i n t h e i n s id i d e c o r n e r s o f t h e c o n t a in in e r , p a r t i c u l a r l y when the specimen contains particle sizes as large as those involved in these tests. A limited amount of data indicates no significant increase in density would result with a larger container that would provide a higher r a t i o o f c o n t a i n e r d i a m e t e r t o m a x i m u m p a r t i c le l e s iz iz e. e. D u p l i c a t e t e s t s w e r e

performed on some of the specimens after removing the larger sizes to e v a l u a t e t h i s e ffe c t . H i g h e r v i b r a t e d t e s t d e n s it i t ie ie s c o u l d p r o b a b l y h a v e b e e n o b t a i n e d i f t h e frequency and amplitude of the vibrating table could have been varied. Equipment with these features and the required load capacity was not a v a i la l a b l e fo f o r t h is i s t e s t p r o g ra r a m . I t w a s l a t e r d e t e rm rm i n e d t h a t t w o r o t a r y eccentric vibrators operating in perpendicular directions on the vibrating t a b l e w o u l d e l im i m i n a t e t h e e l l ip i p t ic i c a l m o t i o n a n d p r o d u c e a s i n u so so i d a l m o t i o n . This would compare more favorably with the motion produced by electrom a g n e t i c v i b r a t o r s ( A S T M D 2 0 4 9 -6 - 6 9 ) a n d p r o b a b l y in i n c r ea ea s e t h e m a x i m u m v i b r a t e d d e n s it i t ie i e s o b t a in in a b l e .

Test Procedures In the early tests a mortar of fire clay was prepared to smooth the el us mi ne t m h ee adseunr se m i t ye nht os .l eTbheifso rr ee qli lui ni rin ine dg ci ta rwe fi ut hl tmheea spul ar isnt ic igc omf et hmeb fr ir tchr ee vvi co es iarne ec lfaoyr and correcting for it in the computations. It was soon discovered the same results could be obtained by smoothing the sides of the density hole as m u c h a s p o s s i b l e d u r i n g e x c a v a t i o n a n d c a r e f u l ly l y p la la c i n g t h e p l a s t i c m e m b r a n e t o f o l lo l o w t h e r e m a i n i n g i r r e g u la l a r s u r fa fa c e s . T h i s n o t i c e a b l y r e d u c e d the labor and the time required for the equipment to be set up on the d e n s i t y h o le l e s it it e. e . A n y t h i n g t h a t s h o r t e n e d t h e t i m e r e q u i re r e d f o r th th e e q u i p C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernambuc o ((UFPE) Universidade Federal de Pernambuco) pursuant to Licens  

STEPHEN STE PHENSON SON ON RELA RELATI TIVE VE DENSITY TESTS ON RO CK F ILL

247

ment at the test site pleased the project and contractor personnel as well as the technicians performing the tests. For the minimum density tests, no "refinements" in the method of placing the material in the specimen container were investigated to det e r m i n e t h e e f fe f e c t,t , i f a n y , o n t h e m i n i m u m d e n s i t y v a lu lu e s . D u e t o t h e n a t u r e o f t h e r o c kf k f il i l l m a t e r i a l a n d t h e p r e v a i li l i n g f i el e l d c o n d i ti ti o n s , t h i s w a s n o t c o n s i d e re r e d f e a s ib i b l e o r j u st s t if i f i a b le le . T h e m a t e r i a l w a s c o n s i s t e n t l y s h o v e l e d into the container from the density hole or from the floor of the field laboratory if it had required air drying as described previously. In the l a t t e r i n s ta ta n c e , c a r e w a s t a k e n t o a v o i d s e g r e g a t i o n o f t h e p a r t i c l e s w i t h re s p e c t t o g ra i n s i z e . L i m i t e d s t u d i e s w e r e m a d e t o d e t e r m i n e t h e e f fe f e c ts t s o f i n cr c r e as a s in in g t h e sDuur pc hl iacrg ragtee at ensdt sl ewnegrteh poefr fo t essut rs. s-. fvoi rbmr aetdi oonn i nt h et h es a m m ea xsipme uc m i m evni bwr ai tt eh di ndcernea e sa istin iyn gte c h a r g e s u p t o 2 5 p s i.i . A n o t h e r s e ri r i es es o f t e s t s w e r e r u n i n w h i c h t h e l e n g t h o f v i b r a t i o n w a s i n c r e a s e d u p t o 6 0 m i n . N e i t h e r i n c r e as as i n g t h e s u r c h a r g e n o r i n c re r e a s in i n g t h e l e n g t h o f v i b r a t i o n p r o d u c e d a n i n c re re a s e i n t h e v i b r a t e d test density.

Conclusions A l t h o u g h t h i s te t e s t p r o g r a m a t C a r t e r s D a m w a s n o t e s t a b l is is h e d f o r c o n s t r u c t i o n c o n t r o l, l , s o m e o f t h e t e s t r e s u l t s w e r e v e r y h e l p f u l fo fo r c o m -

parison with the design assumptions. The minimum density and maximum v i b r a t e d t e s t d e n s i t y r e s u l t s w e r e o f l it i t t le le v a l u e o n t h i s p r o j e c t . I t i s o b v i o u s t haast n iont tchais ips a bt el es t o fp rpor og dra r aumc i nt gh ed emn sait w ixt ie iiems ucmo mvpi abrraabt el ed t od et nh soistey atcehsite va epdp abrya ttuhse compaction equipment in the rock fill. These tests, however, do provide b a c k g r o u n d i n f o r m a t i o n f o r n e c e s s a r y i m p r o v e m e n t s in in e q u i p m e n t a n d p r o c e d u r e s f o r t e s t i n g r o c k f il il l t h a t c o n t a i n s m a t e r i a l c o a r s e r t h a n t h e 3 - in in . particle size. T h e m o s t r el e l ia i a b le le a n d u s e f u l i n f o r m a t i o n d e r i v e d f r o m t h i s p r o g r a m w a s the gradation data. As often happens, the rock did not quarry with the gradations anticipated and originally specified. Yet, the gradation tests provided accurate information regularly for the material being placed in e a c h z o ne ne o f t h e e m b a n k m e n t .

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by (UFPE ) Universidade Federal de Pernamb uco ((UFPE ) Universidade Federal de Pernamb uco) pursuant to Lic  

Correlati Correl ation on Betw een Relati Relat i ve Density Densit y and

Measured Performa Pe rformance nce or Proper Propertties of Granular Soils

Copy right by ASTM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement.  

Yves Lacroix 1 and H. M . H orn s

Direct Determination and Indirect Evaluation of Relative Density and Its Use on Earthwork Construction Projects

r o i x, x, Y v e s a n d H o r n , H . M . , " D i r e c t D e t e r m i n a t i o n R E F E R E N C E : L a c ro a n d I n d i r e c t E v a l u a t i o n o f R e l a t iv e D e n s i t y a n d I t s U s e o n E a r t h w o r k C o n s t r u c t i o n P r o j e c t s , " Evaluation of Relative Density and Its I ts Role in GeoGeo-

technical Projec technical Projects ts Involvi Involving ng Cohesionles Cohesionlesss Soil Soils, s, A S T M S T P 523, A m e r i c a n S o c i e t y f o r T e s t i n g a n d M a t e r i a l s , 1 9 7 3 , p p . 2 5 1 -2 -2 8 0 .

A B S T R A C T : R e l a t i v e d e n s i t y is is o f te te n u s e d a s th t h e c r i te t e r i o n f o r c o n tr t r o l li li n g t h e q u a l i t y o f c o m p a c t e d g r a n u l a r f il il l.l. T h e d i r e c t a n d i n d i r e c t m e t h o d s ~ v a i l a b l e t o d e t e r m i n e in situ r e l a t i v e d e n s i t y a r e c o n s i d e r e d a lo l o n g w i t h t h e d i ff f f ic i c u l ti ti e s a s s o c i a te te d w i t h t h e s e m e t h o d s . D a t a a r e p r e s e n t e d w h i c h i n d i c a t e t h e d e g r e e o f er e r r o r t h a t c a n b e e x p e c t e d w h e n m a k i n g in situ d e t e r m i n a t i o n s o f r e l a t i v e

d e n s i t y . C o r r e l a t i o n s a re r e p r e s e n t e d w h i c h r e l a t e in situ d a t a o b t a in in e d b y t h e m o s t c o m m o n l y u s e d f ie ie l d t e c h n i q u e s e m p l o y e d in in t h e d e t e r m i n a t i o n o f r e l a t i v e density. density (mass/volume), earthwork, soft compacting, earth fill fi lls, s, co nstru ction , c ohesionless soils soils KEY

W O R D S:

C o m p a c t e d f ilil l h a s w i d e s p r e a d a p p l i c a t i o n i n c o n s t r u c t i o n , s u c h a s c o n struction of dikes, dams, building subfoundations, and highway embankm e n t s . T h e p r o p e r ti t i e s o f c o m p a c t e d fi fill t h a t a r e o f m o s t c o n c e r n t o t h e d e s i g n e r a r e t h e e n g i n e e r i n g p r o p e r t i e s ; t h a t i s , c o m p r e s s ib i b i l it it y , s h e a r s t r e n g t h , a n d p e r m e a b i l it i t y . D i r e c t i n s i t u d e t e r m i n a t i o n o f t h e s e p r o p e r ti ti e s i s t i m e - c o n s u m i n g a n d c o s tl t l y , a n d , c o n s e q u e n t ly ly , t h e i r d i r e c t m e a s u r e m e n t i s n o t a n a p p r o a c h g e n e r a l l y u s e d t o c o n t r o l t h e q u a l i t y o f c o m p a c t e d fi fi l l . I n m o s t c a se s e s, s , t h e e n g i n ee e e r in i n g p r o p e r ti ti e s a r e r e l a t e d t o t h e c o m p a c t i o n characteristics of the fill material by means of laboratory or field tests, a n d s o m e m e a s u r e m e n t o f c o m p a c t n e s s is is u s e d a s t h e c r i te te r i o n f o r q u a l i t y c o n t r o l o f t h e c o m p a c t e d fi f i l l . W h e n p r e d o m i n a n t l y g r a n u l a r s oi oi l s a r e e m 1 D i r e c t o r , W o o d w a r d - C l y d e C o n s u l t a n t s , N e w Y o r k , N . Y . 1 00 0 0 01 01 . A s s o c i a t e , W o o d w a r d - M o o r h o u s e & A s s o c i a t e s , I n c . , C l i ft f t o n , N . J . 0 7 01 01 2 . 251

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252

RELATIV RELA TIVE E DENS DENSITY ITY INVOLVING C O H E S I O N L E S S SOILS

TABLE 1--D efinitio ns of relative relative densi density, ty, densi density ty rati ratio, o, and degree of compaction. Relative Density (Dr) Dr

emax

--

emax --

en

'Ydm ax

em in

"Ydn

~

"Ydn --

" Y d ma ma x - -

"Ydmin "~dmln

Density Ratio (Rr) Rr

=

")'tin ~

'Ydmax --

*Ydmin 'Ydmin

Degree Degr ee of Compaction (Dc) De =

where:

en, e m a x , e m i n "[dn,

"fdmal,

~fdmin

" Yd Ydn, n, =~R r

~a~x Dr are the in situ, maximum, and minimum vo void id ratios,

respectively; and, are the in situ, maximum,and minimum minimumdry dry unit weights, respectively.

NOTE~Dr NOTE ~Dr and D c are freq frequen uently tly expressed expressed as percentage percentages. s. ployed as fill material, relative density is frequently specified as the basis for compaction control. Other measurements of compactness that are commonl y used are "degree of compa ctio ction" n" for cohesi cohesive ve so soil ilss and "d "den ensi si ty ratio" for cohesionless soils; definitions of the above are given in Table 1. It should be recognized that the three methods of defining compaction previously cited cited are quite diffe different, rent, although th e terms are too often used

interchangeably. The concept of relative densi d ensi ty is being used successful successfully ly by engineering firms defineand andWoodward control the [I]3). quality of compacted fills (for example,toLeafy Our experiencesgranular have taught us that relative dens ity, while simpl simplee in concept, is a tool, the application of which requires considerable care and judgment to obtain the desired quality without imposing overly stringent and sometimes unfair or arbitrary restrictions on the earthwork contractor. Difficulties with the use of relative density as a control criterion are associated with both the determinations of the maximum and minimum dry unit weights (the reference densities) of the fi fill ll materia material, l, an d with th e d eterminati on of the i n s i t u density of the compacted fill. In some applications, the use of correlations between relative density and some indirect measurement, such as static or dynamic penetration resistance, have been used successfully; but, again, such approaches involve difficulties at to mus t be recog recognized coped d with. The pur purpos poses es ofdiffic this ulties paperthare indicate the nized directand andcope indirect methods that are being used to determine i n s i t u relative density; present correlations between results obtained by several of these methods; and present data which indicate the reliability of these methods. Only by recognizing thee degree of error involved with a measuremen t procedure, can a reasoned th 3The italic numbers in brackets brack ets refer to the list of referen references cesappended to this paper.

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LACROI LAC ROIX X AND HORN ON EART EARTHWORK HWORK CONS CONSTRUC TRUCTIO TION N PROJ PROJECTS ECTS 2 5 3

judg ment be ma de co ncerning its a pplica bility a s a qua lity co ntro l dev ice. Descriptions of how relative density has been used to control compaction o f g ra r a nula r fill fill o n m a jo r ea rthw o rk pro jec ts a re presented else elsew w here [1] [1].. Factors Affecting Relative Density The earliest research of the factors affecting maximum and minimum dry un it we ig hts o f g ra r a nula r so ils ils w a s ca rri rried ed o ut b y B urm ister [~ ]. Since t h e s e u n i t w e i g h t s , a l o n g w i t h t h e in situ d r y u n i t w e i g h t , d e f i n e t h e r e la la tiv e density o f a co mpa cted so il, tho se fa cto rs a ffecting their determina tio n must be reco g nized befo re the difficulties inv o lv ed in the direct determina t i o n o f in situ r e l a t i v e d e n s i t y c a n b e a p p r e c i a t e d . B u r m i s t e r f o u n d t h a t b o t h m a x i m u m a n d m i n im i m u m d r y u n i t w e i g h t s w e r e f u n c t io i o n s o f g ra r a d a ti t i on on a s we ll a s pa rticle rti cle sha pe. T hese fa c to rs will no w b e co nsidered. Gradat i on Type

15G

C

f

i

CD~L D, SD S

"~ 130

_-

~

/~

.I

....

I

[

ES,ED E

-'= t20

I//-I

b

E

C u r v e s o r e f o r s u b o n g u la la r s a n d a n d w a t e r w o r n g r o v e l . S p e c i f ic ic g r a v i t y

/#'

2.67

taken to be

R ef erence: Burrn i st er, 196 2

I00

0

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2

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4

5

6

7

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E f f ec t i v e Groi n S ize ize R ang e, C exp ress ed b y M ean S lop lop e i n S oi l F ract ract i ons ab ove 0 10 10

'2 ~

~ U llll

,o o ~

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Effective Groin Size, Dsoin M i l l i m et ers

0.06

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0006

R ef erence; Burm i st er, 1962

1--C orr el elat ations ions bet etwe ween en maxim um and min im u m dr y u n i t we weig ig ht htss and grain -siz -sizee charact cha racteristics eristics of g ranu la larr soils soils.. FIG.

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254

RELATIV RELA TIVE E DENS DENSITY ITY INVOLVING COHE COHESIO SIONLES NLESS S SOI SOILS LS

Influen ce of Gradation on R efer eference ence Densities Densities Maximum Dry Unit Weight--Burmister [ ~ ] proposed that maximum d r y w e i g h t ( ~ d= d = ,.,. ) is is p r i m a r i l y a f u n c t i o n o f t h e r a n g e o f p a r t i c l e si s i z es es a n d t h e s h a p e o f t h e g r ai a i n -s - s iz i z e d i s tr t r i b u t io io n c u r v e . H e p r e s e n t e d c u r v e s w h i c h c o r r e l a t e d ~ d. d .~ = w i t h c o m b i n a t i o n s o f r a n g e o f p a r t i c l e s iz iz e a n d t h e s h a p e o f t h e g r a in i n - s iz i z e d i s t r i b u t i o n c u r v e . T h e s e c o r r e la l a t i o n s, s, w h i c h a r e g i v e n i n F i g . 1, 1, i n d i c a t e t h a t ~ . c a n v a r y f r o m a b o u t 1 00 0 0 l b / f t 3 f o r r e l a t iv iv e l y f in i n e , u n i f o r m l y g r a d e d g r a n u l a r s oi oi l , t o 1 4 6 l b / f t 3 f o r w e l l - g r a d e d g r a n u l a r 135

130

125

120

x~

[

I

I

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I

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110

i"

E

9

NOTE: Data ploffed are fro m the Ludingloo

,,p~,

9 ,,..

Projec t and Co ope r Stofion and

9l % ~

from th e following sources: D' Appolon io el ol~ ol~ 1969 Koerner ~ 1970

105

I 00

95

i

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t

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2

i

3

~

4 Coefficient ofUnifo rmity.

I

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5

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6

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B

Cu

2--C orr el elat ation ion bet etwe weeen maxi mu m dry un it we weig ig ht and coe~cle coe~clent nt of un ifor mi ty of gr anular soils. soils. FIG.

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LACROIX AND HORN ON EARTHWORK CONSTRUCTION PROJECTS

I

120

I

I

I

J

i

l

l

255

/

il5 c E

E~IIO

medi um to finesand, w i t h n o n - pl p l a st st i c i n e s Z. " Fines" efers to particles assing I.

o

Soi l is o

N o2 0 0

sieve

Eo E

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Fines Content,

FIG. 3--C orr ela elations tions be b etwe weeen maxi mu m and mi ni mu m dr y un it weight weightss and fin es cont c onteent

for a glacial sand at the the L uding ton Pr oje oject ct.. so ils ha vcoing wide ng engoula f pa B urmister's rrela tio ns a pply to so ils mpoa sed o f ra suba r rticle sa nds sizes. o r wa ter-wo rn g ra vco els. Po ulo s a nd Hed [3] ca rried o ut a n ex tensiv e inv estig a tio n o f the density cha ra cteristics cteristics o f hy dra ulica lly pla ced clea n sa sa nd. T hey fo un d tha t the maximum dry unit weight correlated quite well with the coefficient of unifo rmity (C ~ = Ddo/D~o). T h i s fi fi n d in in g i s i n a g r e e m e n t w i t h d a t a w h i c h have been collected by the authors on two projects; namely, Cooper Nuclear Station near Brownville, Neb. (alluvial medium to fine sand), and Ludington Pumped Storage Project, near Ludington, Mich. (glacial outwash sand containing less than 7 percent fines, by weight). The data ref e rr rr e d t o a r e p l o t t e d i n F i g . 2 a l o n g w i t h t h e c u r v e s o f P o u l o s a n d H e d co rrelating rrela ting ~ x w ith C a. a. T his fi figg ure ure a lso includes da ta o bta ined in i n studies [i~t h] atnhde Ke xo ce er pnteiro n[ 5 ]. ]o. fI tKsoheorunledr 'bs e, n rbeys uDl 'tA s prpe foel ro rnei da et ot ,a lw[~ i novt oe dl v et hd a st aanldl so ft ht ha et w e r e d e p o s i t e d e i t h e r b y f l ow o w i n g w a t e r o r b y w i n d , a n d i t i s li li k e ly ly t h a t t h e g ra in-size distributio n curv es ha d simila r, mo re-o r-less, S-sha pes. C o nsequently , befo re using co rrela tio ns such a s sho wn in Fig . 2 , the g ra in-size distributio n cha ra cteristics sho uld be co nsidered; B urmister's finding s indica te tha t the sha pe o f the g ra in-size distributio n curv e ha s a la rg e influence o n ~ a ~x w hen th e so il ha s a w ide ra ng e o f pa rticle sizes. sizes. Copyright by AST M Int l (all (all rights rights re se rved); rved); Fri Ma r 11 16:13:06 E ST 2016 Downloa de d/printe d/printe d by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement.  

256

RELATIVE RELATI VE DENSIT DENSITY Y I NVO LVIN G COHESIO COHESIONLESS NLESS SOI SOILS LS

T A B L E 2---Influen ce of gradation gradation on reference reference densit densities ies of clean clean sand at Cooper Station.

( 1) 1) ( 2) 2) ( 3) 3) ( 4) 4) ( 5) 5)

To tal specimen Fractio n retained on No. 20 sieve Frac tion passing No. 20 sieve A verag e of values for both fractions D i f f e r e n c e b e t w e e n ( 1 ) a n d ( 4) 4)

~'~, ~' ~,.* .**, *, l b / f t 3

~'~mi ~' ~mio, o, l b /f t a

123.5 115.4 116.0 115.7 7.8

109.5 102.5 100.5 101.5

8.0

M i n i m u m D r y U n i t W e i g h t -- - B u r m i st s t e r [ 2] 2] a ls ls o i n v e s t i g a t e d t h e r e l a t i o n b e t w e e n m i n i m u m d r y u n i t w e i g h t (~ 'd ~ in ) a n d g r a i n -s - s i z e c h a r a c t e r i s t ic ic s . H e f o u n d t h a t ~ d m in in c o u ld l d b e c o r r e l a te te d w i t h c o m b i n a t i o n s o f D ~ a n d t h e r a n g e o f p a r t i c l e s iz iz es es ( se s e e F i g . 1 ) . P o u lo l o s a n d H e d [ 3] 3] f o u n d t h a t t h e dif fere nc e ~ x - ~'~ml mlnnw a s e s s e n ti t i a ll ll y c o n s t a n t t h r o u g h o u t t h e t w o d e p o s it i t s o f h y d r a u l i c a l l y p l a c e d fi f i l l t h a t t h e y i n v e s t ig ig a t e d . T h e y p o i n t e d o u t t h a t a l th t h o u g h a r e la l a ti t i o n sh sh i p b e t w e e n m a x i m u m a n d m i n i m u m d r y u n i t w e i g h t s m a y e x i st s t fo f o r a g i v e n s oi o i l d e p o s i t, t , t h e s a m e r e la la t i o n s h i p c a n n o t b e e x p e c t e d t o b e o b t a i n e d w i t h a l l d e p o s it it s . It should be noted that a unique relationship between maximum and m i n i m u m d r y u n i t w e i g ht h t s w a s n o t f o u n d i n t h e c a se s e o f t h e g l ac a c ia ia l s a n d s a t the Ludington Project referred to earlier. For these sands, the difference increased with increasing percentage of fines (see Fig. 3). Burmister's

s t u d i e s s u g g e s t t h a t t h e s h a p e o f t h e g r a in i n - s iz i z e d i s t r i b u t i o n c u r v e , w h i c h is is governed by the depositional process, determines the relationship between ~d~x and Ydmi.. Relative Density of Natural Deposits--Many cohesionless natural deposits are reasonably uniform over distances of several tens of feet, but m a y b e c o m p o s e d o f m a n y d i f f e r en e n t l a y e r s o f s a n d o r g r a v el el . E a c h s u c h layer has its own in situ dry unit weight and its own values of ~'d~ and ~/gm~.. M i x in i n g l a y e rs r s t o g e t h e r d u r i n g s a m p l i n g o r p r e p a r a t i o n o f t e s t s p ec ec i m e n s c a n p r o d u c e a s o ilil h a v i n g d e n s i t y c h a r a c t e r is i s t i cs c s w h i c h b e a r n o r e l aationship to those of any of the individual layers. This is illustrated in T a b l e 2 , w h i c h is b a s e d o n t e s t d a t a o b t a i n e d a t C o o p e r S t a t i o n . The previous example demonstrates the importance of sampling only i n d i v id i d u a l l a y e rs r s a n d o b t a i n in in g e n o u g h m a t e r i a l t o d e t e r m i n e n o t o n l y t h e in situ dry unit weight, but also enough for determinations of ~/d~. and ~ 'd 'd ~. ~ . . I t s h o u l d a ls l s o b e r e c o g n iz iz e d t h a t i n s o m e n a t u r a l d e p o s i t s , i n d i v i d u a l l a y e r s m a y b e o n l y a f e w g r a i n s i n th t h i c k n e s s a n d t h a t , i n s u c h c a se se s , d e t e r m i n a t i o n o f r e la l a t i v e d e n s i t y m a y b e i m p o s si s i b le le b y c o n v e n t i o n a l m e t h o d s . Influenc e of Particle" Particle" Sh ap e on Reference Densities Densities B u r m i s t e r [ 2] 2 ] r e c o g ni n i z ed e d t h a t p a r t ic i c l e s h a p e i n f lu lu e n ce ce s t h e m a x i m u m and minimum dry unit weights. His work indicated that granular soils Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

LACROIX AND HORN ON EARTHWORK CONSTRUCTION PROJECTS

257

c o m p o s e d o f h i g h l y a n g u l a r p a r t i c le l e s h a d v a l u e s o f ~ dm dm ~ t h a t w e r e 1 0 l b / f t a t o 1 5 l b / f t ~ l o w e r t h a n t h o s e o f s oi o i ls ls m a d e u p o f s u b g r a n u l a r g r a i n s; s; n o q u a n t i t a t i v e e s t i m a t e w a s m a d e o f t h e i n fl u e n c e o f a n g u l a ri t y o n ~/ ~/dmint I o l u b e c a n d D ' A p p o l o n i a [ 6] 6] h a v e s h o w n t h a t i n c re r e a s in i n g p a r t i c le le a n g u l a r i t y d e c r e a s e s ~ m ~ a r e l a t i v e l y sl s l ig i g h t a m o u n t , b u t c a n d e c r e a s e ~dm in in s u b s t a n t ia i a l ly l y . E q u a l l y a s i m p o r t a n t , t h e y p o i n t o u t t h a t s oi oil s h a v i n g t h e s a m e g e n e r al a l r a n g e o f p a r t i c le l e s i ze z e s a n d t h e s a m e r e l a t iv iv e d e n s i t y , b u t w i t h d i f f e re r e n t p a r t i c le l e s h a p e s , c a n h a v e d r a s t i c a l ly l y d i f f e r e n t c o m p r e s s i b i l it it y a n d s t r e n g t h c h a r a c t e r is i s t ic i c s . T h e i n fl f l u e nc nc e o f p a r t i c l e s h a p e o n t h e r e f e r e n c e densities should be recognized before using correlations such as those in Fig. 1 and 2. For similar reasons, published correlations between angle of s h e a r in i n g r e s is i s t a n c e , o r c o m p r e s s i b il i l i ty ty , a n d r e l a t i v e d e n s i t y s h o u l d b e u s e d w i t h c a u t io i o n . R e s u l t s o f sm s m a l ll - sc s c a le l e t e s t s b y H o l u b e c a n d D ' A p p o l o n i a [ 6] 6] s u g g e s t t h a t t h e r e s u lt l t s o f d y n a m i c p e n e t r a t i o n t e s t s a r e a l so s o a ff f f e c te te d b y particle shape. W h i l e t h e i m p o r t a n t i n fl f l u e n ce ce s o f p a r t i c l e s h a p e o n t h e r e f e r e n c e d e n s i t i e s a n d e n g i n e e r in i n g p r o p e r t i e s a r e r e c o g n iz iz e d , d i r e c t m e t h o d s o f m e a s u r i n g a n d d e fi f i ni n i ng n g p a r ti t i c le l e s h a p e a r e c u m b e r s o m e . H o l u b e c a n d D ' A p p o l o n i a [ 6] 6] s u g g e s t t h e u s e o f i n d ir i r e c t m e t h o d s , s u c h a s t h a t b a s e d o n p e r m e a b i l it it y m easurem ents, as a me ans of arriving at a m easure of particle shape. D i r e c t D e t e r m i n a t i o n s o f I n Si tu iv e D e n s i t y tu R e l a t iv

I n f a c t , t h e r e is n o d i r e c t m e t h o d o f d e t e r m i n i n g i n s i t u r e l a t i v e d e n s i t y . Direct determination, as used in this paper, refers to direct measurement t iuvsee dd et no s m i t ye a fsruorm int as int du tohfei nr esfietrue ndcr ey duenni st i w t i ee si g. hMt eatnhdo dcso tmh pa tu taartei ogne noefr rael ll ya ti e iit d r y u n i t w e i g ht h t a r e t h e w a t e r b a ll l l o on on m e t h o d , A S T M T e s t f o r D e n s i t y o f Soil in Place by the Rubber-Balloon Method (D 2167-66), and the sandc o ne n e m e t h o d , A S T M T e s t f o r D e n s i t y o f S o il i l i n P la la c e b y t h e S a n d - C o n e M e t h o d ( D 1 55 5 5 66- 6 4) 4) ; t h e W a s h i n g t o n D e n s o m e t e r 4 m e t h o d , i s a c o m m o n l y used type of water balloon test. Our firm has used both the Washington D e n s o m e t e r a n d t h e s a n d - c o n e m e t h o d s o n s e v er e r a l m a j o r p r o j e c ts t s in i n v o l v in in g compacted granular fill. Both methods give about the same result when u s e d p r o p e r l y ( s ee e e F i g . 4 ). ). T h e W a s h i n g t o n D e n s o m e t e r m e t h o d h a s , h o w ever, significant advantages over the sand-cone method. In thinly layered deposits, the Washington Densometer method is more ss aa tmi sef avcot lour m y et h aonf ht hoele o naes hmi en tght oo dn . T a seot ne rf oprr ot hvis iid l e s, a tnhde- cW D he ne sroem isd ei ss t ho an te, tfhoar t t hies shallower than that required by the sand-cone method. Therefore, it is e a s i e r t o k e e p t h e h o l e in i n a s in i n g l e l a y e r o f t h e d e p o s i t . In a n a l l u v i a l d e p o s i t o f t h e M i s s o u r i R i v e r , c o n s i s t in i n g o f t h i n l y l a y e r e d m e d i u m t o f in in e s a n d , t h e r e l a t i v e d e n s i t y o f t h e i n s i t u s oi o i l , a s d e t e rm rm i n e d b y t h e s a n d - c o n e m e t h o d , 4 M anufactur anufactured ed by D. G. P arrot & Son, Olympia, W ashi ashington, ngton, M odels 15 and 30.

Copyright by AS TM Int l (all rights rights res reserved); erved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/printed nloaded/printed by (UFPE) U niversidade niversidade Federal de Pernambuco ((UFPE) Un iversidade iversidade Federal de Pernambuco ) pursuant to to License Agreem ent. No further r  

258

RELATIVE RELATI VE DENSIT DENSITY Y INVO LVING COHESIONLESS SOI SOILS LS

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F I G . 4 - - C o m p a r i s o n o f re re su su lt lt s o f i n s i t u dry u nit weight dete determinat rminations ions in compacted

granular granul ar fill by W ashing ton densomet densometer er and san d co ne methods.

w a s fo f o u n d t o b e l ow o w e r t h a n t h a t d e t e rm r m i n e d b y t h e W a s h i n g to to n D e n s o m e t e r m e t h o d . T h e in situ d r y u n i t w e i g h t s w e r e a b o u t t h e s a m e b y b o t h methods. However, both the maximum and minimum dry unit weights determined on the soil excavated from the sand-cone hole were about 0.6 l b / f t a h i gh g h e r t h a n t h o s e d e t e r m i n e d o n t h e s oi o i l e x c a v a t e d f r o m t h e W a s h in in g ton Densometer hole. Careful observation showed that the samples from the sand-cone holes were relatively well graded because they consisted of a m i x tu t u r e o f s e v e r al a l s a n d l a y er e r s , w h e r e a s t h e s a m p l e s f ro ro m t h e W a s h i n g t o n D e n s o m e t e r h o le le s w e r e m o r e u n i f o r m l y g r a d e d . On earthwork construction projects involving cohesionless soils that were compacted with vibratory rollers, the sand-cone method has several d i s a d v a n ta t a g e s . V i b r a ti t i o n s c a u s e d b y c o n s t r u c t i o n e q u i p m e n t a r e s u ff f f ic i c ie ie n t t o i n c r e a s e t h e u n i t w e i g h t o f t h e c a l i b r a t e d s a n d w h e n i t is is p o u r e d i n t h e sand-cone holes; this leads to calculated dry unit weights lower than the C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si si d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o  

LACROIX LACRO IX AND HOR N ON EART EARTHWORK HWORK CONS CONSTRU TRUCTI CTION ON PROJE PROJECTS CTS 2 5 9

in situ values. Rainwater, or even condensation water, are sufficient to wet t h e c a l i b r a t e d s a n d a n d g i v e i t a d i f f er er e n t u n i t w e i g h t t h a n w h e n d r y . I n a d d i t i o n , a s ig i g n i fi f i c an an t p o r t i o n o f t h e c a l i b r a t e d s a n d m u s t b e w a s t e d a t each sand-cone tes t location; the c ost of replacem ent of the sand is no t negligible. Tests made with the Washington Densometer and by the sand-cone m e t h o d r e q u i r e a b o u t t h e s a m e a m o u n t o f t im i m e . C o n s i d e r a b le le c a r e m u s t b e e x e r c is i s e d b y t h e o p e r a t o r w h e n u s i n g e it i t h e r o f t h e m e t h o d s . O u r f ir ir m ' s e x p e ri r i en e n c e h a s s h o w n t h a t r e a d in i n g e r r o rs rs a r e s o m e w h a t m o r e f r e q u e n t w i t h t h e W a s h i n g to t o n D e n s o m e t e r m e t h o d t h a n w i t h t h e s a n dd - c on on e m e t h o d . Re laxation of horizontal stresses tha t occurs when a hole is dug induces a s m a l l r e d u c ti t i o n i n t h e v o l u m e o f t h e h o le le . T h e s a n d - c on on e m e t h o d c a n n o t correct for this reduction, whereas a reasonable correction can be made w h e n u s in i n g t h e W a s h i n g t o n D e n s o m e t e r m e t h o d [ 1] 1 ] . T h e c o r r e c ti ti o n i s m a d e b y i n c re r e a s in i n g t h e w a t e r p r e s s u r e i n t h e b a l l o o n u n t i l i t is is e q u a l t o t h e v a l u e of horizontal stress estim ated to hav e existed prior to m aking th e hole. I n d i r e c t E v a l u a t i o n o f R e l a t iv iv e D e n s i t y b y M e a n s o f t h e S t a n d a r d Penetration Test

T h e s t a n d a r d p e n e t r a t i o n t e s t ( S P T ) c o n si s i st s t s o f a b o r in i n g a n d s a m p l in in g technique which allows measurement of the penetration resistance of a s t a n d a r d i z e d s a m p l i n g s p o o n d r i v e n b y a s p e c if i f ie ie d i m p a c t e n e r g y . T h e s t a n d a r d p e n e t r a t i o n r e s is i s ta t a n c e ( N ) i s eq e q u a l to to t h e n u m b e r o f b l o w s r e -

q u i re d t o d ri v e a 2 -i - i n . o u t s i d e d i a m e t e r, 1 -3 -3 /~ /~ -i - i n . i n s i d e d i a m e t e r, s p l i t s p o o n 1 f t i n t o t h e s o i l a f t e r a n i n it i t ia i a l p e n e t r a t i o n o f 6 in in . T h e d r i v i n g e n e r g y i s d e l i v e r e d b y a 1 4 0 -1 - 1 b h a m m e r f a ll l l in i n g f r e e l y a h e i g h t o f 3 0 in in . T h e t e s t p r o c e d u r e is i s s p ec e c if i f ie i e d b y A S T M P e n e t r a t i o n T e s t a n d S p l it it B a r r e l S a m p l i n g o f S o il i l s ( D 1 58 5 8 66 - 67 67 ). ). T h e u s e a n d a b u s e o f t h e S P T a n d a thorough analysis of its various aspects have recently been reported [7, s]. Factors Influencing Standard Penetration Resistance ( N )

E v e n w h e n A S T M D 1 58 5 8 66 - 67 67 i s s c r u p u l o u s l y f o l lo l o w e d , t h e r e a r e s t il il l a n u m b e r o f f a c t o r s n o t s p e c i fi f i e d w h i c h h a v e c o n s i d e r a b l e e f f e ct ct o n N . T h e p r i m a r y s u c h fa f a c t o r is is t h e " b o r i n g t e c h n i q u e . " V a r io io u s m e t h o d s o f a d vancing the boring are commonly used; namely, wash boring (using a chopping bit in combination with wash water pumped down the drill rod and through the bit; 2.5-in. diameter casing being used as necessary); h o l l o w - s t e m a u g e r ; r o t a r y d r il i l l u s in i n g w a t e r o r m u d a s t h e d r i ll l l in in g f l u i d ; e t c . Data obtained at Cooper Station, and presented in Fig. 5, demonstrates t h e s u b s t a n t i a l e f fe f e c t t h a t b o r i n g t e c h n iq i q u e c a n h a v e o n t h e r e s u l ts t s o f th th e S P T . F o r p r o j e c t s w h e r e r e p e a t a b l e v a l u e s o f N a r e im i m p o r t a n t , o u r f ir ir m s p e ci c i fi f i es e s t h a t t h e b o r i n g s b e m a d e w i t h a r o t a r y d r il i l l u s i n g d r il i l li li n g m u d , and that N-size rods be used for the drill stem. Although the type of drill C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d /p / p r i n te te d b y ( U F P E ) U n i v e r si s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A g r  

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r e s i s ta n c e .

]

ro d is no t v ery sig nifica nt fo r sha llo w ho les (tha t is, less tha n 50 ft), it is impo rta nt fo r deeper ho les. In g enera l, it ca n be sa id tha t mo dern techniques o f a dv a ncing bo ring s lead to higher standard penetration resistances than those obtained when using the o rig ina ina l (w a sh bo ring ) techn iques [9]. Th is, o f co urse, urse , a ssumes tha t impro per metho ds a re no t used, such a s using a drill bit with stra ig ht downward discharge holes, or inadequate cleaning of the bottom of the h o l e p r io io r t o t h e S P T . Another major factor affecting results of the SPT is the "effective confining stress," which is influenced by the unit weig ht o f the so ft, depth be lo w g ro und surfa ce, stress stress histo ry , a nd the g ro un dw a ter lev el. el. It ha s been suggested that N be corrected when obtained below the water table to take into account the reduction in effective stress due to pore-water pressure. The qua ntita tiv e influence o f v ertica l effectiv e stress o n SPT resista n c e h a s b e e n s t u d i e d i n t h e l a b o r a t or o r y [ 1 0 ] a n d w a s f o u n d t o b e s u b s t a n t ia ia l . The effect o f a decrea se in the v ertica l effectiv e stress o n SPT resista nce is illustra ted by da ta o bta ined a t C o o per Sta tio n (see Fig . 6). At tha t site, sta nda rd p enetra tio n te sts w ere ma de in 15 b o ring s dril dr ille led d fro m the o rig ri g ina l ground surface. An excavation was then made, and when it had reached a depth of 26 ft, standard penetration tests were made in nine borings

Copyright by A ST M Int l (a ll rights re se rve d); Fri Ma r 11 16:13:06 E S T 2016 Downloa de d/printe d by (UFPE ) Un ive rsida de Fe de ra l de Pe rna mbuc o ((UFP E ) Unive rsida de Fe de ra l de Pe rna mbuc o) pursua nt to L ic e nse Agre e me n  

LACROIX AND HORN ON EARTHWORK CONSTRUCTION PROJECTS

261

drilled from the bottom of the excavation. The average values of N are plotted in Fig. 6 as functions of depth for conditions before and after excavation. V alues of N determined after excav ation were found to be ab out 10 blows/ft lower than those made at the same elevation prior to excavation. Similar findings have been reported by Mansur and Kaufman [11], w h e r e in i n t h e r e m o v a l o f 5 0 f t o f o v e r b u r d e n r e d u c e d N b y a h a lf lf . R a t h e r t h a n c o n s i d e r in i n g t h e i n fl f l u e n c e o f v e r t i c a l e f f e c t iv i v e s t r es es s a t t h e l o c a t i o n o f th t h e S P T , t h e a u t h o r s s u g g e s t t h a t t h e h o r i z o n t a l e ff f f e c t iv i v e s t r e ss ss b e c o n s i d e r ed e d a s t h e p r i m a r y s t r e ss ss f a c to t o r i n fl fl u e n c i n g N . T h i s a l l o w s t a k i n g into account high horizontal stresses, such as those existing in overcons o l i d a t e d d e p o s i t s o r h e a v i l y c o m p a c t e d f il ls . Another major factor affecting the results of the SPT is the "type of s o i l; l; " t h a t i s , t h e g r a d a t i o n a n d t h e s h a p e o f g r ai a i n s. s. F o r e x a m p l e , t h e p r e s ence of gravel will result in values of N that are higher than those that would be measured in a soil having the same relative density but which does not contain gravel. A high degree of angularity has the same effect on N. A n o t h e r f a c t o r a ff f f e c t in i n g N i s t h e l o c a t i o n o f t h e " g r o u n d w a t e r l e v e l. l. " I n the case of compact silty fine sand, N measured below the water table is O rir i g i n a l g r o u n d s u r f a c e I

Cooper Station

Al lu lu v i a l m e d i u m o f i n e S AN AN D tO

%.-

7" = 133 133 Ib /ft 3

WT

7'=7' 0 tb/ft 3

NOTE:

Re a t i v e d e n s i t i e s ~ Dr ~ in d icated w er e

d e t e r m i n e d b y G ib ib b s a n d H o ltlt z 's 's M e t h o d

2O

Gr Ou Ou n d s u r fac e r excavation

.T-

3O .__

~=73

40

500

~ ,

k ~

~ \

Ave o f 9 bo r in gs / after excavationJ

I

I0 Stand ard

~73

"~/---Avei

\

~e73 t

20

of '5

borings before exccvation

74~1 I

30

40

P e n e t r a tit i o n Re Re s i s ta ta n c e N, b l / f t

F I G . 6---Effect of decrease of vertical effective stress on standa r d penet enetrr at ation ion r esistance. Copyright by A STM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Dow nloaded/print nloaded/printed ed by (UFPE ) Universidade Federal de Pernambu co ((UFPE) U niversidade Federal de Pernambuc o) pursuant to to License Agreemen t. No  

262

RELATI RELA TIVE VE DENS DENSITY ITY INVOLVING COHE COHESIO SIONLES NLESS S SOI SOILS LS

greater than that which would be determined above the water table in an otherwise similar soil, because of negative pore water pressures resulting from dilatancy; a correction equation has been proposed [ 1 2 ] to account for such a condition. Conversely, the measured N of a loose medium to fine sand located below the water table will be less than if the same soil had bee been n located located at the same depth, b ut above the ground-water leve level. l. The reason for for this is th at such a sand wi will ll ten d to liquefy under the influ influenc encee of the vibrations and stresses induced by driving and, thereby, lose much of its its shear strength. Equations relating N to soil properties may be misleading if the factors cited previously are not taken into account, as well as the effects of the presence of substantial numbers of large particles (for example, gravel or cobbles), a collapsible soil structure (for example, loess), and cementation between soil grains. Charts have been proposed in which the influence of gradati on on the relationship relationship between between relative relative density and N is tak en in to account [2]. C o r r el e l a ti t i o n s B e t w e e n R e l a t iv iv e D e n s i t y a n d S t a n d a r d P e n e t r a t i o n R e s i s t a n c e

Ind irec t ev aluati on of th Indirec thee re lative dens ity of cohe cohesi sion onle less ss so soil ilss can b e made reasonably well by means of the standard penetration test. Initially

% o~

a

~0

I0

20

30

40

S t a n d a r d P e n e f r o t io io n R e s i s t a n c e

5 0

0

60

80

N , b l / fl fl

FIG. 7--C orre lation betwee betweenn rel relati ative ve density an d standard penet penetrat ration ion resi resistanc stancee i n accordanc cor dancee with Gibbs and Ho ltz [10]. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed Downloaded/p rinted by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. No further reprod  

LACROI LAC ROIX X AND HORN ON EAR EARTHWORK THWORK CONS CONSTRUC TRUCTIO TION N PROJ PROJECTS ECTS 2 6 3

uJ

~

v

0

I0

20

30

~0

50

60

70

80

Stondord Stond ord Penetrof PenetrofionRe ionResistQ sistQnce nce N, bl /f t

FIG. 8 --Co mp ariso ns of several corre correlat lations ions between between rel relati ative ve densit densityy an d standar standardd pene-

tration trati on resist resistance. ance.

correlated q ualitat ively with values of N ob[13], relative density was correlated

tained in borings that had been generally made for conventional soil investigations and for the desi design gn of shallow shallow foundations. Later, the infl influenc uencee of the effec effective tive confinin confining g stress was recognize recognized d and a qu ant it ati ve correlacorrelation between relative density and N was established which took into accountt th e vertical coun v ertical effec effective tive stress [10]. This correlation was based prima rily on the results of a laboratory investigation, but was checked on U.S. Bureau of Reclamation (USB (USBR) R) proje projects. cts. ~ Figure 7 is a chart replotted from the Gibbs and Holtz cha rt published by t he USBR [1~ 1~]] and inclu includes des both interpolations and extrapolations. Figure 6 illustrates illustrates th at in a natu ral alluvia alluviall deposit deposit consisting consisting of medium to fine sand (Cooper Station), the influence of verticM effective stress is accounted for quite well by the method proposed by Gibbs and Holtz. At an elevation corresponding to a depth of 35 ft before excavation, the average stand ard penetrati on resista resistance nce was N = 26 blow s/ft prior to exca excavavation, and N - 15 bl ows /ft after excavation. The relative densities calc calcuulated by the Gibbs and Holtz method for conditions before and after excavatio n were were the same, which is as th ey shoul d be. be. Figure 8 shows a compa comparison rison between relative density charts prepared b y Personal communicationwith" communicationwith"H. H. J. Gibbs, 1968. Copyright by ASTM Int l (all rights reserved); Fri Mar 11 16:13:06 EST 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. No further re re  

264

RELATIVE DENSITY INVOLVING COHESIONLESS SOILS

St o n d o rd Pen et rat i o n R esi st an ce N,b l/ft

00

50

I00

1500 15

200

250

A

CooperStati Cooper Static__._ I0

p ~

~

C o m p a c t e d m e d i u m t o f in in e

~

1"5 1" 5 -3 ~176 in ines' es' u = I 5 - 3

~C~

20

E~

LE GE N D

~.~ '--0. ~. z~ ~

[] N

~

[~ ~ rnr~ ~ ~""-- []~

~.~"

30

SAND

_~ E~

" ~

S t a n d a r dpen d pen et rat io io n resi st an c e c a l c u l a t e d f r o m r e l a t i v e d e n s i ty ty determin determ ined ed on u n d i s t u r b e d D e n i s o n s a m p l e s u s i n g Gi b bs bs a n d H o l t z, z, s method

0 NB

.~ v

~

~

_"~

C~.~ ..~ ~

S t a n d a r d p e n e t r at i on resistance calculated from relative

d e n s i t y e t er er m i n e d o n u n d i s t u r b e d De n i s o n s a m p l e s u s i n g B a za za r a o , s method

~'ghhtouge bor'ng ~'g

40

50

{

I

I

{

ibbss an d H oltz oltz,, a n d B azara a corr el elat ations ions bet etwe ween en relat relative F I G . 9 - - C o m p a r i s o n o f the G ibb

den si ty an d standa r d pene enetrat tration ion resista resistances. nces. sev era l inv est ig a t o rs [ 9 , 1 4 , 1 5 , 1 6 ] . C a s a g r a n d e ' s c o r r e la l a t io io n w a s p r e p a r e d f o r a rela t iv e densit y o f 8 5 p ercent f o r a sp ecif ic p ro ject , a nd co nsidered t he lowest values of N obtained in conjunction with several drilling methods. All of the correlations are reasonably consistent at low relative densities, b u t div erg e sig nif ica i ca nt ly a t hig h rela t iv e densit ies. Figure 9 presents a comparison between the Gibbs and Holtz method of analysis and the Bazaraa method of analysis, using the data obtained at C o o p e r S t a t i o n , a n d r e p o r t e d i n F i g . 5 . T h e r e l a t iv i v e d e n s i t ie ie s o f s a n d s a m ples obtained by means of a Denison sampler were determined directly. The corresponding values of N were calculated using both the Gibbs and ttoltz, and the Bazaraa methods of analysis. These standard penetration resistances are compared with values measured in a boring drilled in the dry wit h a so lid f lig ht a ug er. Our experience is that the Gibbs and Holtz method of analysis yields r e l a t iv i v e d e n s i t ie i e s t h a t a r e t o o h i g h fo f o r h e a v i l y c o m p a c t e d f il il l ; t h i s h a s a l s o been noted by others [ 1 7 ] . The probable reason is that increases in values o f N a re no t essent ia lly du e t o increa ses in v ert ica l ef f ect iv e st ress, ress, b u t a re, ra t her, t he result o f a n increa se in t he ho rizo nt a l ef f ect iv e st ress. I f t his

C o p y r i g h t b y A S T M I n t l (a ( a l l r i g h ts t s r e s e r v e d ); ); F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e A  

LACROIX AND HORN ON EARTHWORK CONSTRUCTION PROJECTS

265

concept is correct, and if it is assumed that the coefficient of horizontal earth pressure (K) was 0.4 in the laboratory investigation by Gibbs and Holtz, and in the natural deposits where their method works well (for e x a m p l e , F i g . 6 ) , w e c o n c l u d e t h a t t h e v e r t i c a l e f f e c t iv i v e s t r e s s s h o u ld ld b e m u l t i p l i e d b y t h e f a c t o r K/0.4 b e f o r e e n t e r i n g t h e c h a r t s h o w n i n F i g . 7 . T h e a u t h o r s r e c o m m e n d t h e u s e o f t h is i s m o d i fi f i c a ti ti o n w h e n e v a l u a t i n g r e l a ti t i v e d e n si s i ti ti e s b y t h e G i b b s a n d H o l t z m e t h o d . F o r e x a m p l e , a t a d e p t h o f 1 5 f t i n a d r y n a t u r a l s a n d d e p o s i t w i t h a u n i t w e i g h t o f 1 2 0 l b / f t 8, t h e v e rt i c a l e ffe c t i v e s t re s s is is ~ = 1 .8 .8 k i p s / ft 2. If N i s 3 5 b l o w s / f t , t h e re l a t i v e density would be estimated to be 95 percent on the basis of Fig. 7. Cons i d e r a s e c o n d c a se s e , si s i m i la l a r t o t h a t r e f e r r e d t o a b o v e , e x c e p t t h a t i t in in v o l v e s a h e a v i l y c o m p a c t e d s a n d f il i l l . M e a s u r e m e n t s [ 4] 4] h a v e s h o w n t h a t s a n d f il ills c o m p a c t e d t o h i g h r e l a t i v e d e n s i t ie i e s h a v e h i g h c o e ff f f ic i c i en en t s o f h o r i z o n t a l e a r t h p r e s s u re r e ; a s g r e a t a s 2 t o 3 , b u t w i t h v a l u e s ty ty p i c a l l y b e i n g a b o u t 1 .5 .5 . I f t h e s e c o n d d e p o s i t h a d a c o e ff f f ic i c i en en t o f h o r i z o n t a l e a r t h p r e s s u r e o f 1 .2 .2 , w e w o u l d m u l t i p l y t h e v e r t i c a l e f f e c t i v e s t r e s s b y t h e f a c t o r 1 . 2 / 0 . 4 = 3 b e f o r e e n t e r in in g F i g . 7 . U s i n g t h i s a p p r o a c h , t h e r e s u l t i n g e s t i m a t e d r e l a t i v e d e n s i t y i $ 7 1 p e r c e n t . C o n v e r s e l y , i f th t h e e s t i m a t e d c o e ff f f ic i c i en en t o f h o r i z o n t a l e a r t h p r e s s u r e h a d b e e n 0. 0 . 3 , t h e v e r t i c a l e f f e c ti ti v e s t r e s s w o u l d h a v e b e e n m u l t i p li l i e d b y 0 . 3 / 0 . 4 = 0 .7 .7 5 b e f o r e e n t e r i n g t h e c h a r t . T h e u n m o d i fi f i e d G i b b s a n d H o l t z re r e l at a t io i o n s h ip ip b e t w e e n N a n d v e r t i c a l e f f e c ti t i v e s t r e s s fo f o r a r e l a t i v e d e n s i t y o f 1 00 00 p e r c e n t h a s b e e n p l o t t e d i n Fig. 10, along with m easured v alues of N obtained in a test prog ram in-

v o l v i n g t h e h e a v i l y c o m p a c t e d s a n d fill a t C o o p e r S t a t i o n . A l s o i n c l u d e d i s t h e r e l a ti t i o n sh sh i p p r o p o s e d b y B a z a r a a . A s p a r t o f t h a t p r o g r a m , d e t e r m i n a t i o n s o f in situ r e l a ti ti v e d e n s i t y w e r e m a d e o n t h e b a s i s o f W a s h i n g t o n D e n s o m e t e r r e s u lt l t s a s w e ll l l a s b y m e a n s o f t e s t s c a r r ie ie d o u t o n u n d i s t u r b e d s a m p l e s o b t a i n e d w i t h a D e n i s o n s a m p l er e r . A n e v a l u a t i o n o f t h e r e s u l ts ts o f t h e s e t e s t s i n d i c a t e d t h a t t h e f ilil l h a d a n a v e r a g e r e l a t i v e d e n s i t y o f M m o s t 1 00 00 p e r c e n t ; n a m e l y , 9 7 p e r c e n t . E x a m i n a t i o n o f F i g . 1 0 r e v e a l s t h a t t h e u n m o d i f i e d G i b b s a n d H o l t z r e la l a t io i o n s h ip i p g r e a t ly ly u n d e r e s t i m a t e s t h e v a l u e s o f N c o r r e s p o n d i n g t o 1 00 00 p e r c e n t r e l a t i v e d e n s i t y , o r c o n v e r s e l y , o v e r e s t i m a t e s t h e r e l a t i v e d e n s i t ie ie s a s s o c i a t e d w i t h t h e s e t o f N v a l u e s . O n t h e other hand, Bazaraa's relationship is in good agreement with the N-value data. Average values of N have been computed for the Cooper Station data, a n d a re p l o t t e d i n Fi g . 1 1 a s a fu n c t i o n o f v e rt i c M e ffe c t i v e s t re s s . A l s o shown are the Bazaraa relationship and the unmodified Gibbs and Holtz relationship for relative densities of 100 percent. The excellent agreement b e t w e e n t h e a v e r a g e v a l u e s o f N a n d t h e B a z a r a a r e la l a t io i o n s h ip i p w il ill b e n o t e d . Figure 11 also contains the relationship between coefficient of horizontal e a r t h p r e s s u r e a n d v e r t i c a l e f f e c ti ti v e s t r e s s r e q u i r e d t o o b t a i n a g r e e m e n t b e t w e e n t h e a v e r a g e v a l u e s o f N a n d t h e G i b b s a n d H o l t z r el e l a ti t i o n s h ip ip

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s re re s e r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r in in t e d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i c e n s e  

266

RELAT IVE DEN DENSI SITY TY INV OLV ING COHESI COHESIONL ONLESS ESS SOI SOILS LS

modified as describ described ed previously. The coe coeffic fficient ient of horizontal ear th pressure would have to decrease from a value of between 2.0 and 2.5 near the surface, to a value of about 0.5 at a depth of several tens of feet. These values, value s, and the shape of the K ve rs us /5 , relat relationship ionship in Fig. Fig. 11 11, are reas reasononable. abl e. Th e higher values values are in agreement with the measureme measurements nts made by D'Appol onia et al [4] at shallow depth depthss in heav ily compacted sand fi fill ll.. The decrease decre ase of K with depth, d epth, becoming asym pto ptotic tic with a val ue of K corresponding to an " a t rest" condition, is consistent with what would be expected for a heavil y compacted fill. fill. Standard

Penetration

50

I00

I

I

Resistance

m

D

w

-.-. N

150 I

N, blows/ft 200

250

I

I

300

000 |

00

59

~>

9

N

o~

09

oo

IP

Dr = 100%

8, H U nm o di f i e d Dr : 100% I

I

l

,I

F I G . lO --S tan da rd penetration resi resist stance ancess of a heavily com com pacted pacted sa nd fill fill at C ooper ~tation.

Copyright by A STM Int l (all rights reserved); Fri Ma r 11 16:13:06 EST 2016 Downloaded/printed by (UFPE ) Universidade Federal de Pernam buco ((UFPE ) Universidade Federal de Pernam buco) pursuant to License Agre  

LACROIX LACROI X AND HORN O N EART EARTHWORK HWORK CONSTRUC CONSTRUCTION TION PROJEC PROJECTS TS Calculated Coefficienfof Horizontal Earth Pressure(K) 0 I

0

0

05

1.00 1.

I

1.55 1.

I

50

I

O

+ / 2

N

3

/

/

2. 5

3.0

200

250

300

i

N, bl/ft 150

100

2.0

J§

I

,J+

/+

-4- Q

03 4 ~" ~ ( ~ 5

LEGEND 0 Average N 4 " C a l c u l a t e d v a l u e of K u s i n g M o d i f i e d Gibb., Q 81Holtz e l a t i o n s h i p

l

267

6 /

~

/-- .Bazaraa Or=lOO% Or=l OO%

7

~

~p-~ G ~ H Unmodified Dr : 100%

F I G . l l-l --Va Vari riat atio io n of cal calcula culated ted coe~c coe~cient ient of horizontal horizontal earth press pressure ure required required to obtain obtain

agreement between modified Gibbs and Holtz analysis and dat data a obtained at Cooper Station.

T h e r e l a t io i o n s h i p b e t w e e n K a n d #~ i n F i g . 1 1 i s n o t m e a n t t o a p p l y t o a l l h e a v i l y c o m p a c t e d g r a n u l a r f ilil l s , b u t r a t h e r ~ i s p r e s e n t e d t o d e m o n s t r a t e that the high horizontal stresses built into such fills provide the likely e x p l a n a t io i o n o f w h y t h e G i b b s a n d H o l t z r e l a ti t i o n s h ip i p g r e a t l y o v e r e s t im im a t e s th e relativ e d en sities o f th ese fill fill s. Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

268

RELATIVEDENSITY RELATIVE DENSITY INVOLVING COHESIONLESS SOILS

Correlation Between Nonstandard Penetration Resistance N1 and Standard Penetration Resistance N

It is sometimes necessary to estimate standard penetration resistance from a penetration resistance N1, obtained with a nonstandard split spoon o r a s o li l i d c o n i c al al p o i n t ; i n a d d i t i o n , t h e d r i v i n g e n e r g y a n d d e p t h o f p e n e t r a t i o n m a y b e n o n s t a n d a r d . I n s u c h c a se se s , a n d w h e n a n a p p r o x i m a t e c o r r e l a ti t i o n i s a c c e p t a b l e , w e b e l ie ie v e t h a t i t i s s a t i s f a c t o r y t o a s s u m e t h a t the number of blows (n) required to drive the split spoon or conical point t o a p e n e t r a t i o n d e p t h ( L ) i s d i r e c t ly l y p r o p o r t io io n a l t o t h e s q u a r e o f t h e o u t s i d e d i a m e t e r ( D ) o f t h e s p l i t s p o o n o r c on o n i ca ca l p o i n t a n d t h e d e p t h o f p e n e t r a t io i o n , a n d i n v e r s e ly ly p r o p o r t i o n a l t o t h e e n e r g y p e r b l o w ( W H ) ; that is, n ~ --- D - -~ L WH

( 1)

T h e r e f o r e , N m a y b e e s t i m a t e d f r o m N 1 in i n t h e f o ll l l o w in in g m a n n e r : N--

// 2 in.~ ~ //2 12 in. W1 H~ 2 N~W~H~ N lk, D~ ] X ~ X 1 4 0 1 b X 3 0 i n . - 1 7 5D 5 D l ~L ~L ~

w h e r e t h e f o ll l l ow ow i n g a p p l y t o t h e n o n s t a n d a r d t e s t : D ~ = t h e o u t s i d e d i a m e t e r o f t h e s p l i t s p o o n o r c o n i c al al p o i n t i n inches, L ~ = t h e d e p t h o f p e n e t r a t i o n i n i n c h es es ,

(2 )

W1 = the weight of the ham m er in pounds, and H 1 = t h e h e i g h t o f f r e e f a ll l l o f t h e h a m m e r i n in i n c h e s. s. I t s h o u l d b e r e c o g n i ze z e d t h a t t h i s is i s c o n s i d e r e d a n a p p r o x i m a t e c o r r e la la tion and that, when possible, correlations should be developed for the p a r t i c u la la r n o n s t a n d a r d e q u i p m e n t o r m e t h o d s b e i n g u s e d , a n d f o r t h e p a r t i c u l a r s o il il d e p o s i t b e i n g i n v e s t i g a t e d . E x a m p l e o f A p p l i c a t i o n o f C o r re r e la l a t io i o n to t o R e s u l t s o f T e s t s In In v o l v i n g a C o n e D r i v e n W i t h a L i g h tw tw e i g h t H a m m e r

There is frequently need to evaluate the relative density of cohesionless s o il il s i n s i t u a t i o n s w h e r e t h e u s e o f s t a n d a r d e q u i p m e n t i s e i t h e r t o o e x p e n s i v e o r c u m b e r s o m e . S u c h a n e x a m p l e o c c u r s w h e n i t is i s d e s ir ir e d t o e v a l u a t e t h e r e l a t iv i v e d e n s i t y o f a d e p o s i t of o f n a t u r a l s a n d l o c a t e d b e l o w th th e b o t t o m o f a f o o t i n g e x c a v a t io i o n b e f o r e th t h e f o o t in i n g c o n c r e t e is i s p la la c e d ; t h e d e p t h o f i n t e r e s t i s u s u a l l y 5 t o 1 5 f t . I n s u c h c a se se s , t h e w o r k i n g a r e a i s o f t e n c o n s t r i c te t e d a n d t h e u s e o f l ig ig h t w e i g h t e q u i p m e n t is a d v a n t a g e o u s . The authors have found that it is practical and economical to obtain t h e d y n a m i c c o n e p e n e t r a t i o n r e s is i s t an an c e o f n a t u r a l l y d e p o s i t e d o r c o m pacted cohesionless soils with lightweight equipment. The equipment we h a v e u s e d is is m a n u f a c t u r e d b y t h e A c k e r D r il i l li l i n g C o m p a n y ( si s i m il i l ar ar e q u i p m e n t i s m a n u f a c t u r e d b y o t h e r s ) . A 6 0 - d e g , 1 -5 -5 /~ /~ 66 - in in . o u t s i d e d i a m e t e r

C o p y r i g h t b y A S T M I n t l ( a l l ri r i g h t s r e s e rv rv e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 D o w n l o a d e d / p r i n te te d b y ( U F P E ) U n i v e r s id id a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t t o L i  

LACROIX LACR OIX AND HORN ON EART EARTHW HW ORK CONSTRUC CONSTRUCTIO TION N PRO JECT S

269

steel cone is screwed on to the lower end of an E-rod. An attachment is p l a c e d o n t h e u p p e r e n d o f th t h e E - r o d w h i c h a l l o w s d r iv iv i n g o f t h e r o d w i t h a 3 4 -1 - 1 b h a m m e r f a l l in in g t w o f e e t . T h e n u m b e r o f b l o w s r e q u ir ir e d t o d r i v e t h e cone 4 in. is recorded. The test can be done manually. However, a small p o w e r w i n c h a n d a li l i g h t t r ip i p o d a r e a d v is is a b l e w h e n m a n y o f t h e s e t e s t s a r e required. O u r f ir i r m h a s c o r r e la la t e d t h e d y n a m i c p e n e t r a t i o n r e s i s t a n c e N d ( b l o w s / 4 in.) obtained with this lightweight equipment with the standard penetration resistance N of cohesionless soils at several construction sites. The cohesionless soils ranged from silty sand to coarse sand, and included both natural deposits and compacted fills. T h e c o r r e la l a t io io n w e u s e i s :

N = Nd,

N = 20 + 0 .5 (N d- -

20)

for N d < 20 f O r N d > 20

(a ) (b )

E q u a t i o n 2 , g iv i v e n i n t h e p r e c e d i n g s u b s e c t i o n , y ie i e l d s a c o r re r e l at a t io io n N 1.33 Na.

A

(3 ) =

.o z 40

N=135Nd(E q 2)

I

z~

~ z~

t,

z1

f A

J

C

.:_o

=20*O.5(Nd-20)

o

/

&

~ 0

0

NOTE : Tesl s w er e co n d u ct ed in o very d ense , heav ililyy co m p act ed f i l l

N = Nd Nd ( E q 3 a } I 10

I 20

I

30

I

I

40

50

60

Dynam ic Cone Cone Penetration Penetration Resistance Nd, bl/4in.

FIG. 12--C or r elat elation ion bet etwee weenn standard penetration penetration r esistance

cone penet enetrr at ation ion r esistance.

and a

light weight weight dynam dynam ic

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270

RELATIVE RELATI VE DENSIT DENSITY Y INVO LV ING COHESI COHESIONLESS ONLESS SOIL SOILS S

The correlation represented by Eq 3 is is considered considered to be more satisf acto ry for loose loose to mediu medium m relative densities than th an for very high relative relativ e densities. densities. The lightweight equipment described should not be used for very dense compacted fill or for depths exceeding about 15 ft because of excessive friction on the E-rod. An improvement m ight involve using using an expend expendable able cone with a diameter d iameter sli ghtly greater t ha n t he E-rod E-ro d [1 [18] 8];; our firm has h ad success in using such an approach. If this is done, it is recommended that a conical point be used which has a 60-deg angle and a base area of 10 cm2 cm 2, which is the shape and area of the cone used in the standard static cone penetration test. Figure 12 shows a rather poor correlation between Eq 3 and penetration test resul results ts obtained during the construction of a ve ry dense heavily comcompacte d fill; the correlation represented by Eq 2 is als also o given. given. Be tt er corre correlalations have been obtained with Eq 3 when dealing with natural deposits, and when the relative densit y was was le less tha n about 70 perc percent. ent. I n d i r e c t E v a l u a ti o n P e n e t r a t io n

o f R e l a t iv e D e n s i t y b y M e a n s

o f S t a ti c C o n e

Tests

Standard Stand ard Static Cone Penet Penetration ration Test (S (SCP CPT) T)

Static con conee penetrat ion tests are used widely in Europe to evaluate in an indirect manner the in situ properties of deposits of soils. Much of the development of the equipment and procedures used in such tests has been carried out in Holland, and when mention is made herein to the standard static cone penetration test, we are referring to the test made with the

"D ut ch friction jacket cone" shown in Fig. 13. The stand ard stati c cone penetrometer is a sounding apparatus. A cylindrical rod with a conical poin pointt ~tt ~tt the lower end is pushed i nto t he so soil il.. T he cone has a 60-deg point and a base with an area of 10 cm 2. A sleeve a few inches above the conical point can be advanced simultaneously with the point, or left statio nary. The resistance resistance to penetratio n is read read on a gage as as the cone is pushed into the soil at a rate of penetration of about 2 cm/s. Another method that gives somewhat lower but more repeatable values involves reading the gage as the rate of penetration is decreased from 2 cm/s to zero. The standard cone penetration resistance R, is equal to the vertical force required to push the cone divided by b y t he cone area (namely, 10 cm2 cm2). ). R, is usual us ual ly expressed expressed in kg/cm2,e Correlation Between Standard Penetration Resistance and Standard Static Cone Penetration Resistance

Stand ard penet ration resista resistance nce N and stan dard static cone penetrat ion resistance resis tance R, have been correlated correlated to one another by investigators in ma ny e I n W est estern ern E uro p e this unit is no w ref referre erred d to a s " b a r" .

Copyright by A STM Int l (all rights reserved); reserved); Fri Mar 11 16:13:06 ES T 2016 Downloaded/printed by (UFPE) Universidade Federal de Pernambuco ((UFPE) Universidade Federal de Pernambuco) pursuant to License Agreement. N  

LACROI LAC ROIX X AND HORN O N EART EARTHW HW ORK CONSTRUCTI CONSTRUCTION ON PROJECT PROJECTS S 271

Push outer rod

iPush

inner

od

Conhnu e inner rod push

_1

Cone

only o d v o n c e s

for beoringcopocify Cone and jack jacket et both odvonce for beoring capa capacity city e fricti on

F I G . 13---D utch friction j acket cone cone.. p a r t s o f t h e w o r ld l d f o r m a n y y e a r s . U n f o r t u n a t e l y , d e t a i le le d i n f o r m a t i o n c o n c e r n in i n g t h e p r o c e d u r e s a n d e q u i p m e n t u s e d in i n th th e s e t e s t s a r e a l m o s t always missing. O u r f i rm r m h a s s t u d i e d c o r r e la l a t io i o n s r e p o r t e d i n th t h e l i t e r a t u r e ( fo fo r e x a m p l e , T A B L E 3--C o rrelation bet betw w een standard pen etration resi resist stance ance N and stand ard static cone penetration resis resista tance nce Rs as a fun ctio n of soil description, description, R . (kg cm ~) = C N (blows ft). Soil Descript Description ion

Correlati Correl ation on Fa cto r C

Clay Silt Sand Grav el l y San Sandd San d y Grav el

1- 2 2- 4 4- 6 6- 8 8 -1 0

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e se se r v e d ) ; F r i M a r 1 1 1 6 : 1 3 : 0 6 E S T 2 0 1 6 Downloaded/printed by ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ( ( U F P E ) U n i v e r s i d a d e F e d e r a l d e P e r n a m b u c o ) p u r s u a n t to to L i c e n s e A g r  

272

RELATIVEDENSITY RELATIVE DENSITY INVOLVING COHESIONLESS SOILS

Penetration

00

IO .=-

s'o

I0 I

i

Resistance

,;o

20I

50

I

N

bllft

20 0 RS RS,, kg/cm z

Ludington Project Glacial deposits consisting of sand and silty sand 0 Avera ge N fo ; 152b::~:dgin 152b::~:dgings gs

c~ 15

20

25

Rs=6"25N

I

T

I

I

I

I

FIG. 1 4 ---E xa m p le o f a site co rrel rrelaa tio tio n b etw etw een sta n d a rd p en etra tio n resis resista tann ce N a n d sta n d a rd sta tic co n e p en etra tio n resista n ce R ~ .

Sanglerat , [1 [19] 9])) and those developed by us for various so soil il deposits. deposits. Based on these evaluations, we suggest the follow following ing correlation (Table 3). The correlation factor C appears to increase with depth. We suggest th at this correlation be limited to a dep th range of 10 10 to 50 ft. F urth ermore, th e correlation should be used only as a guide. guide. I f warranted, a bet ter cor cor-relation can be generally developed for a specific project by means of a testing program. For example, Fig. 14 shows a very good correlation obtained in glacial deposits consisting of sand and silty sand at the site of th e Lud ing ton Proj ect; the correlation is R8 = 6. 6.25 25 N. The correl correlation ation factors factors given in Table 3 are somewhat greater th an those proposed by other American investigators. For example, the correlation factors suggested by Sch Schmert mert man mann n [20] [20] have t he follow following ing tre nd (Table 4). TABLE 4 - - C o r r e l a t i o n f a c t o r s s u g g e s t e d b y S c h m e r t m a n n [20]. Soil Description

Correlation Factor C

Silt, and sand-silt mixtures Fine to t o mediumsand Coarse sand and gravell gravelly y sand Sandy gravel and gravel

2.0 3.5 5.0 6.0

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L A C R O IX

AND

HO R N

ON

EARTHW ORK

C O N S T R U C T IO N

P R O JE C T S

273

I n d i re r e c t D e t e r m i n a t i o n o f Dr Dr y U n i t W e i g h t b y M e a n s o f N u c l e a r Devices Nuclear devices can be used to make indirect determinations of in situ total unit weight or water content. Gamma ray sources are used for determination of total unit weight and neutron sources for determination of water content. Either direct transmission or backscatter techniques are employed, although direct transmission techniques generally give better results. resu lts. Th e composition of of the so soil il affe affects cts the deter minat ion of both tota l unit weight and water content. The total unit weight also affects the determination of water content. The air-gap technique theoretically eliminates the effec effectt of soi soill compositi composition. on. It consi consists sts of making a measur ement at the soil surface and another at a fixed distance, usually 1 or 2 in., above th e surface of the so soil il.. Nuclear surface devices devices are designed designed to be used on t he so soil il surface or at 125

I

I

0

I

I

I

0 12 0[

9

O

Q

D

I~

go 9

00

O

go

O O

O

9

6) ID

9

O

0

Q OiD

9 OO

O

9

OQ

~

~

~" ~

9

~ 176

_ ----= E

9

o~

~

ooQ~

c8

o~ o o ~

0 (~

0

-

0

0

~'-~ I01 "~ ~

0

0

Oo

-

0

0

0 Oo

O

0

9

9

O

0

O

O Com pacted Me Medi diumO u mO o Fine SAND

oO

9 I% fines , Dio Dio=O. =O. 17 17mm mm,, Cu= l.6 0 3% fine s, DI DIO O= O. 33mm,Cu=2.8

O IOO

o

0

0

= Ee Ee''

o

O

O 0

95 95

I I0 0

0 O NOTE: NOT E: All water contents obtained by means mea ns of AST M Design ation I 1 D 221 6-6 6 105 I lO 1155 11 120 125 Dry Un Unit it Weight, Ib / ft 3 N u c l e a r M o i s t u r e - D e n s i ty

M eter

15--Laclr of correlation correlation between dry unit un it weights obtained wit with h Washin Was hing~m g~m densometer and those obtained with a portable surface nuclear dev device ice.. FIG.

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274

RELATIVE RELA TIVE DENSI DENSITY TY INV OL V IN G COHES COHESIONL IONLESS ESS SOI SOILS LS

the bottom of a test pit. Nuclear probe devices are designed to be placed or pushed into a hole, a few inches to about 2 ft below the soil surface. Nuclear devices, portable by hand, have a small radioactive power source of two to five milli millicurie curiess (mc); larger nuclear devi devices ces are are available th at can be mounted on a small panel truck and which have a radioactive power source of 300 to 500 mc. Our firm's experience with several types of portable nuclear surface devices which operate on the backscatter principle has been so poor that our use of them has been discontinued. Even calibration of such devices for each type of so soil il at least twice twice every da y d id n ot signif significantl icantly y improve the results. T h e effect effect of soi soill composition cannot be eliminated when using nuclear devices havi ng small power sour source ces. s. In additi on, t he effe effect ct of surface irregularities is very significant when using portable surface devices because the depth interval of measurement is very small, about 2 in. for tota l uni t weight, weight, and ab out 5 in. for water conten t determinations. On several major earthwork projects requiring compaction of sand or silty sand, the st anda rd deviation was was found to be • 10 lb /f t 3 for an average unit un it weight of 13 130 0 l b/ ft 3 when portabl p ortabl e nuclear surface devices were were used. Figure 15 shows the lack of correlation between dry unit weight calculated from total unit weights determined by means of a portable nuclear surface device, and those determined with the Washington Densometer. In both cases, water contents were determined in accordance ~,- r so

C~ "5 125 Z

5 N

120

N 115

7

I

/2"" o

115 150 r20 125 Total Unit Unit Weig Weight ht from Washi Washingt ngton on Densom eter, Ib /ft 3

f35

totall un unit it weights obtained with the Troxler 2401 portable FIG. 16--Correlation between tota probe nuclear device and those obtained with the Washington Washingto n densometer densometer..

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LACROIX LACROI X AND HORN ON EARTHWORK CONSTRUCTI CONSTRUCTION ON PROJECTS

GommomyRoye myRoye,ecorsDetectors v~ u

/ f

Oelectors Oele ctors ~

/J

Probe

275

~\~

~

h

I

Nuctear Sources

I

lOrnc forfor garnrno garn rno roys~ 300 mc neutron neutrons s]

FIG. 1717--Sk -Sketc etch h of the truck-mounted truck-mounted French A GS probe nuclear device. device.

with ASTM Laboratory Determination of Moisture Content of Soil (D 2216-66). Wate r content determinations with portable nuclear surfac surfacee device devicess are even more erratic than total unit weight determinations. For cohesionless soil so il,, the water cont ent can be effici efficiently ently determ ined w ith suffi sufficient cient accuracy by means of either the Speedy Moisture Tester Model MC3207 (water contained contain ed in a small so soil il specime specimen n is quickly absorbed by h yd ydra ra ti on

of calcium calcium chlor chloride) ide) or by dry drying ing the so soil il specime specimen n on a hot plate. Extensive field testing conducted by our firm shows that portable nuclear probe p robe device devices, s, for example, th thee Trox Troxler ler Model 2401 nucl nuclc~ c~ar ar probe, 8 are sufficientl sufficiently y rel reliab iable le for the determi nation of tot al u nit ~eight . The sta nda rd devia tion was found fou nd to be -4-2 lb /f t 3 (s (see ee Fig. 16 16). ). For control of a cohe cohesi sion onle less ss emb embank ankmen mentt compacted ,by moder n met hods, od s, namely, heavy vi brato ry compactors, compactors, the i n s i t u unit weight must be determ ined at a dep th of 1.5 1.5 to 2 ft below the surface of th e fill fill.. The exc excaavation of a test pit to that depth without disturbance of the bottom of the pit takes 15 to 30 min. After completion of the test pit, a nuclear test will take 15 min to make, whereas the Washington Densometer test will tak e 30 min. Therefore, the overall saving of time using the nuclear device is not very significa significant. nt. In both case ses, s, the water con tent mu st be determined by direct methods. Truck-mounted, more powerful nuclear surface or probe devices appear promisin prom ising. g. New York St ate Depa rtme nt of Public Works [2 [21] 1] reports satisfactory use use of the Road-Logger Road-Logger9 9 which is a nuclear n uclear surface device with wi th 7 Manufact ured b y th e Alpha-Lux Co., Inc., Philadelphia, Pa. s Manufactured by Troxler Electronic Laboratories, Inc. Raleigh, N. C. 9 Developed by Lane-Well Lane-Wells, s, Houst on, Texas.

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4 -

<

e s w a hm r d b a c d o p e n h w o n m e d g

Z

O

S

O

z

s

e

T o

m o

2

6

4

N s o a D d a S

b ~

6 1

8 1

8 2

D o n h a W h w

% ~

4 0

0 1

8 1

s Ug b y e D W7

e e % a W ~ C

1

1

1

1

1

1

9 3

9 3

1 3 n

h m e d h o n L a h m

z

u v h o m c m h a h m o h m e n h b n m e d u

h a o o e h u N m e A c L o u p

m n P d a

w u d a e c e w w b

c s e a

a g

C

s y s

S

s n o

c

o

ms m u y a mt s s

e o G P e 1 a o o T m a eu S e F a mm mP Do P s h o Cd n 1 A t MG L U An 1

m p

os

E

m C 5

a e S

A T

s h o a m s

m u

v o o a

2

d o

1

v

1 a M

U

w

m e n

h

n

E 0 1

F v

d h s m e o d a e d h d h s d b C a S M s nm h A T e N m d

n 6 =

m

m e u m oh d

e s g

F d

U

m n P d a

a l F n   b Me n d A p v b U g o w C D U (

 

LACRO LA CROIX IX AND HORN ON EAR EARTHWORK THWORK CONS CONSTRUC TRUCTIO TION N PROJ PROJECTS ECTS 2 7 7

a 43 430 0 mc gamma- ray source source.. Repeat abili ty of 44-0.8 0.8 lb /f t a is reported w ith the Road-Log Road-Logger. ger. Electricite Electricite de France used a t ruck- mount ed nuclear probe probe device for compaction control of Mr. Cenis Dam. Figure 17 is a sketch of th e AGS devic devicee 1~used at Mr. Ceni Ceniss Dam. Table 5 presents c omparative results obtained with the Troxler portable nuclear probe device and the AGS device. Indirect Plate

Evaluation

Load

of

R e la t iv e

D e n s i ty

by

M eans

of

Standard

Test

The stan dard plate load test (SPLT) con consis sists ts of of loading, in increments, increments, a rigid steel plate, one foot square, located at the bottom of a test pit which is at least five feet square. The settlement under each load is measured. The results represent represent t he loading pressure-settleme pressure-settlement nt characteristics characteristics of the so soil il within a dept h interval of approximately 1. 1.5 5 ft below the plate. The loading pressure-settlement characteristics have been correlated qualitativel y with relative relative density [13] for use use in set tlement estimates required required in shal shallow low founda tion design. design. Our firm has conducted an extensive field test program at several sites in an attempt to correlate relative density with settlement of a one-footsquare plate under a loading press pressure ure of 3 to ns /f t 2. Fig Figure ure 18 shows a te nt ative corre correlation lation between relative density and se ttlement during a s tand ard

12~

"

-

-

/ / ~, - I - I l l i p [ [

i l'

l I [ Ti -r-rr-r--,-,,,:

- - Ij