10-Shear-Strength-of-Soil.pdf

CEL 610 – Founda Foundation tion Enginee Engineerin ring g

Strength of different materials

Steel

Tensile

Concrete

Compressive

Complex

Soil

Shear 

Presence of pore water 

Strength of different materials

Steel

Tensile

Concrete

Compressive

Complex

Soil

Shear 

Presence of pore water 

Shear failure of soils Soils generally fail in shear  Embankment Strip footing

Failure surface Mobilized shear resistance

 At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength. s trength.

Shear failure of soils Soils generally fail in shear 

Retaining wall

Shear failure of soils Soils generally fail in shear 

Retaining wall

Mobilized shear resistance Failure surface

failure surface

The soil gra over each othe the failure surf ru

Mohr-Coulomb Failure Criter in terms of total stresses



  f 

 c    tan    Friction angle

Cohesion

f 

c



Mohr-Coulomb Failure Crite in terms of effective stresses



  f 

 c' ' tan  '  

’ Effective cohesion

 

c’

’

f 



=  pr

Effective r c on ang e



Mohr-Coulomb Failure Criterio Shear strength consists of two com onents: cohesive and frictional.



 f 

f  ’ c’

’ c’

’

  

'

' f 

frictional component

. ,

Mohr Circle of stress ’1

’ ’3 Soil element

’1 , ' 1

 

  

' 3

 

   

Mohr Circle of stress ’1

’ ’3

’3

Soil element

’1

 1     '                2

' 1

' 3

'

' 3

 1'   3' 2

Mohr Circle of stress ’1

’ ’3

’3

Soil element

’1

’,

 1     '                2

' 1

' 3

'

' 3

 1'   3' 2

Mohr Circles & Failure Envelo 

Failure surface

 Y X

Soil elements at different locations

 

 c ' ' tan

X

Mohr Circles & Failure Envelo The soil element does not fail if within the envelope

 c Y

c

c Initially, Mohr circle is a point



Mohr Circles & Failure Envelo  As loading progresses, Mohr circle becomes larger…



c Y

c c

Orientation of Failure Plane ’1

Failure envelo ’

’3

’3

’,

f 

 – ’1

’ ' 3

 

 1'   3' 2

PD = Pole w.r.t. plane

 

Mohr circles in terms of total & effective stre

v X

v’

h

=

X

effective stresses

u h’

+

X

total stresses

Failure envelopes in terms of total & effecti

v X

If X is on failure

v’

h

=

X

u h’

+

Failure envelope in terms of effective stresses

’ effective stresses

X

Failure terms of

total stresses

Mohr Coulomb failure criterion with Mohr cir

’v = ’1 X

Failure envelope in terms of effective stresses

’h = ’3

effectiv

’

Therefore,

c’

’

X is on failure

’

’3

’

’

’

’1 ’

Mohr Coulomb failure criterion with Mohr cir



'



' 1

  ' 1

' 1

'

  1'   3' 

    ' 3



' 1

  '

' 3

2

 

'



  

' 3

2

 

 

in '2c' os '

' 3

1  Sin ' 1  Sin '

  1'   3'  

'

'

'

Cos '

1  Sin '

'

Determination of shear strength paramet , ’ ’

specimens taken from representative undisturbed samples os common a ora ory es s to determine the shear strength parameters are, 1.Direct shear test 2.Triaxial shear test

. 2. 3. 4. 5. 6.

ane s ear es Torvane Pocket penetro Fall cone Pressuremeter  Static cone en

Laboratory tests Field conditions

A re resentative soil sample

z

vc hc

 vc

vc +  hc

hc vc

vc

Laboratory tests Simulating field conditions in the laboratory 0

vc 0

0

hc

0 Representative

hc





hc vc

 

Step 1 ep

Direct shear test c ema c

agram o

e

rec s ear appara us

Direct shear test rec s ear es s mos su a e or conso a e specially on granular soils (e.g.: sand) or stiff clays

plates

ra n

Direct shear test Preparation of a sand specimen

eve ng t e top sur ace

Pressu

Specimen prepara

Direct shear test Test procedure

P

ee

a

Pressure plate Porous plates S

Proving ri o measur shear forc

Direct shear test Test procedure

P

ee

a

Pressure plate Porous plates S

Proving ri o measur shear forc

Direct shear test Shear box

Dial gauge measure vert

Pro to sh

Loadin

frame to

Dial

au e

Direct shear test Analysis of test results

   Normal stress 

   Shear stress



 Normal force (P)

ear res stance eve ope at t e s

ng

Area of  cross section of  the sampl

Note: Cross-sectional area of the sample changes with the ho dis lacement

Direct shear tests on sands Stress-strain relationshi  ,   s   s   r    t   s   r   a   e    h    S

Dense sand/  c ay

f  f 

Loose sand/ NC clay

Shear displacement    t    h   g    i   e   e   l    h   p   n

  n   o   s   n   a   p   x    E

Dense sand

Direct shear tests on sands

 ,   s   e   r    t   s   r   a    h    S

Normal stress =

3

Normal stress =

2

= f2

f1

f3

   f

 ,   e   r   u    l    i   a    f    t   a   s

Shear displacement

Mohr – Coulomb failure enve

Direct shear tests on sands

Sand is cohesionless hence c = 0

drained and pore water  pressures are , Therefore, ’=

and c’

Direct shear tests on clays In case of clay, horizontal displacement should be applied slow rate to allow dissipation of pore water pressure (there

Failure envelopes for clay from drained direct shear tests    f

Overconsolidated clay (c’

 ,   r   u    l    i   a    f    t   s   s   e   r    t   s   r

Normally consolidated clay

’

Interface tests on direct shear apparatus n many oun a on es gn pro ems an re a n ng wa pro is required to determine the angle of internal friction betw and the structural material (concrete, steel or wood) P

Soil

Foundation material

S

Triaxial Shear Test

Piston (to apply deviatoric stre

Failure plane

O-ring impervious membrane

sample

at failure Perspex cell

Porous stone Water 

Triaxial Shear Test Specimen preparation (undisturbed sample)

Triaxial Shear Test Specimen preparation (undisturbed sample)

Triaxial Shear Test Specimen preparation (undisturbed sample)

Triaxial Shear Test Specimen preparation (undisturbed sample) Provin rin to measure the deviator load Dial gauge to measure vertical displacement

Types of Triaxial Tests c

Step 1

deviatoric =

Step 2

c

c

c

c

+ c Under all-around cell pressure Is the drainage valve open?

c

Shearing (loading)

Is the drainage valve o

Types of Triaxial Tests Step 2

Step 1 -

u

u

c

Is the drainage valve open? yes

Consolidated sam le

ear ng oa ng

Is the drainage valve o

no

Unconsolidated

Drained oa ng

CD test

UU test

Und

Consolidated- drained test (CD Test) ,

,

Step 1: At the end of consolidation ’

hC

= ’hC

0

hC

Step 2: During axial stress increase VC +

Drainage

V

=

VC +

’1 hC

0

h

=

Consolidated- drained test (CD Test)

=

3=

Deviator stress (q or

)

hC

Consolidated- drained test (CD Test) Volume chan e of sam le durin consolidation

  e    h    t    f   e   g   n   a    h   e   l   e   m  p   u   m    l   o   a

  n   o    i   s   n   a   p    E

Time   n   o    i   s   e   r   p   m   o    C

Consolidated- drained test (CD Test) Stre res sss-s stra rain in re rela lati tio ons nsh hi du duri rin n sh she ear arin in    d

 ,   s   e   r    t   s   r   o    t   a    i   v   e

Dense sand d)f  d)f 

Loose sand or NC Clay

Axial strain   e   g   e   n   l   a   p

  n   o   s   n   a   p   x    E

Dense sand or OC cla

CD tests

How to determine strength parameters c and 1

 ,   s   s   e    t   s   r   o    t   a    i   e    D

Confining stress =

on n ng s ress = Confining stress =

d)fb

d fa

Axial strain

 ,   s   s   r    t   s   r   a

3c

Mohr Mo hr – Co Coul ulom omb b

3b 3a

CD tests reng

parame ers c an

Since u = 0 in CD , = ’

o

a ne

ro m

es

Therefo re, c = c’ Therefore, and = ’

cd and d are to denote th

CD tests Failure envelopes For sand and NC Clay, cd = 0

 ,   s   e   r    t   s   r   a   e    h

d

o r – ou om failure envelope

3a

1a d fa

CD tests Failure envelopes For OC Clay, cd ≠ 0

3

1

c

Some practical applications of CD analys

1. Embankment constructed very slowly, in layers over a sof deposit

Soft clay

= in situ dra shear stre

Some practical applications of CD analys 2. Earth dam with steady state seepage

Core

= drained shea

Some practical applications of CD analys 3. Excavation or natural slope in clay

= In situ drained shear strength

Consolidated- Undrained test (CU Test) ,

, ’

Step 1: At the end of consolidation ’

hC

= ’hC =

0

hC

Step 2: During axial stress increase ’V

VC +

No drainage

hC

± u

VC

h

=

hC

Consolidated- Undrained test (CU Test) Volume chan e of sam le durin consolidation

  e    h    t    f   e   g   n   a    h   e   l   e   m  p   u   m    l   o   a

  n   o    i   s   n   a   p    E

Time   n   o    i   s   e   r   p   m   o    C

Consolidated- Undrained test (CU Test) Stress-strain relationshi durin shearin    d

 ,   s   e   r    t   s   r   o    t   a    i   v   e

Dense sand d)f  d)f 

Loose sand or NC Clay

Axial strain

   +

Loose sand  /NC Clay

  u

CU tests

How to determine strength parameters c and =

 ,   s   s   e    t   s   r   o    t   a    i   e    D

 ,   s   s   e   r    t   r   a   e    h    S

Confining stress =

3b 3a

d fa

Total stresses Axial strain Mohr – Coulomb failure envelope in terms of total stresses

cu

CU tests

How to determine strength parameters c and ’1 = 3 + ( d)f - uf 

Mohr – Coulomb failure envelo e in terms of   effective stresses

 ,   s   e   r    t   s   r   e    h    S

Mohr – Coulomb a ure enve ope n terms of total stresses

’ =

uf 

3-u

Effective stresses at failure

’ cu

u

CU tests reng

parame ers c an

Shear strength parameters in terms of total stresses are ccu and cu

o

a ne

rom

es

parameters in terms of effective stresses are c’ and ’

c’ = c and

CU tests Failure envelopes or san an

ay, ccu an c =

Mohr – Coulomb failure enve ope n erms o effective stresses

 ,   s   s   e   r    t   s   r   a   e

Mohr – Coulomb failure envelope in terms of total stresses

   S 3a

’

cu

Some practical applications of CU analys 1. Embankment constructed rapidly over a soft clay deposit

Soft clay

= in situ und shear stre

Some practical applications of CU analys 2. Rapid drawdown behind an earth dam

Core

= Undrained sh

Some practical applications of CU analys 3. Rapid construction of an embankment on a natural slope

= In situ undrained shear strength Note: Total stress arameters from CU test c

and

can be

Unconsolidated- Undrained test (UU Test)

Initial specimen condition C=

No

Specimen conditio during shearing

3

=

3+

No

Initial volume of the sample = A 0 × H0 Volume of the sample during shearing = A × H Since the test is conducted under undrained condition, =

 A

Unconsolidated- Undrained test (UU Test) 0

Step 2: After application of hydrostatic cell pressure ’3 = = C

No

3

=

’3

c

c

3-

uc 3

3 Increase of cell

Unconsolidated- Undrained test (UU Test) Step 3: During application of axial load ’1 =

+ drainage

3

=

’3 =

+ uc ±

d

3-

ud

ud = AB Increase of pwp due to increase of deviator stress

3+

d Increase stress

of

Unconsolidated- Undrained test (UU Test) Combining steps 2 and 3,

uc = B

ud = AB

3

d

Total pore water pressure increment at any stage, u

u = uc + ud u=B [

3+

A

d]

Unconsolidated- Undrained test (UU Test) ,

, ’ ’V0 = ur 

Step 1: Immediately after sampling

0

’h0 = ur 

-ur 

0

’VC No drainage

r

-

C

-ur  C

uc = -ur 

c

’h = ur 

(Sr  = 100% ; B = 1)

Step 3: During application of axial load

No drainage

C

’V =

C+

+u

C C

-ur 

c

± u

’h =

C+

Unconsolidated- Undrained test (UU Test) , Step 3: At failure

’Vf  =

+ drainage

, ’

C

-ur 

c

± uf 

C

+

f  +

ur -

c

’hf  = C + u = ’3f 

Mohr circle in terms of effective stresses do not depend on pressure. Therefore, we get only one Mohr circle in terms of effective s different cell pressures

Unconsolidated- Undrained test (UU Test) , Step 3: At failure

’Vf  =

+ drainage

, ’

C

-ur 

c

± uf 

C

+

f  +

ur -

’hf  = C + u = ’3f 

Mohr circles in terms of total stresses Failure envelope,

c

c

Unconsolidated- Undrained test (UU Test) Effect of degree of saturation on failure envelope

S < 100%

3c

3b

S > 100%

c

3a

b

a

Some practical applications of UU analys 1. Embankment constructed rapidly over a soft clay deposit

Soft clay

= in situ und shear stre

Some practical applications of UU analys 2. Large earth dam constructed rapidly with no change in water content of soft clay

Core

= Undrained sh

Some practical applications of UU analys 3. Footing placed rapidly on clay deposit

= In situ undrained shear strength

Unconfined Compression Test (UC Test) 1=

VC

+

=0

Unconfined Compression Test (UC Test) 1=

VC

+

3=

f 

 ,   s   e   r    t   s   r   a    h    S

0 qu

Normal s

Various correlations for shear strength For NC clays, the undrained shear strength (c u) increases w effective overburden pressure,  ’0

cu

 '

 0.11  0.0037( PI )

Skempton (1957)

Plasticity Index as a % For OC clays, the following relationship is approximately true

 (OCR)            Overconsolidated      Normally Consolidat ed  u ' 0

u ' 0

0.8

Ladd (

Shear strength of partially saturated soils In the previous sections, we were discussing the shear str saturated soils. However, in most of the cases, we will e

Water 

Pore water pressure, u

Air 

press

ore press Effective stress, ’

Effec stres

Shear strength of partially saturated soils Bishop (1959) proposed shear strength equation for unsaturated soils as follows

  f 

 c'( n  ua ) 

(ua

 u w )tan  '

Where, n  –

ua

u –u

= Net normal stress = Matric suction

= a parameter depending on the degree of saturation ( = 1 for fully saturated soils and 0 for dry soils)

Fredlund et al (1978) modified the above relationship as follows

  f 

 c'( n  ua ) tan  '(ua  u w ) tan  

b

, tan

b=

Rate of increase of shear strength with matric suction

Shear strength of partially saturated soils

  f 

 c'( n  ua ) tan  '(ua  u w ) tan  

Same as saturated soils

b

 Apparent cohesion

Therefore, strength of unsaturated soils is much higher than the strength

’

- ua

How

 f 

it

'

become

n



a

Same as saturated soils

possible

'

a



b

w

 Apparent cohesion due to matric suction

’ Apparent cohesion

- ua