Lecture 3 - Drained and Undrained Behavior

 

Lecture 3 Drained Drain ed and and Undrained Undr Analysis and ained Analysis Consolidation Considerations Harry Tan Siew Ann Centre for Soft Ground Engineering National University of Singapore Some of the used material was originally created by: Prof. Helmut Schweiger, Technical University of Graz, Austria

Contents • Defini Definitio tion n drain drained ed / u undr ndrain ained  ed  • Draine Drained d / undr undrai ained ned soil soil behav behaviou iour  r  • Typical Typical resu results lts from from drained drained and undr undrained ained ttriaxi riaxial al tests tests • Skempt Skempton‘ on‘ss pa param ramete eters rs A and B

• Modell Modelling ing undra undraine ined d behavio behaviour ur with with Plaxis Plaxis • In terms terms of effecti effective ve stres stresses ses wit with h draine drained d strength strength param parameter eterss • In terms of effectiv effectivee stres stresses ses with undrain undrained ed strength strength paramete parameters rs • In term termss of tot total al sstr tress esses es

• Influence Influence of consti constitutiv tutivee model model and param parameter eterss • In Infl flue uenc ncee of di dila lata tanc ncy y • Undrained Undrained behav behaviour iour with Mohr Mohr-Coul -Coulomb omb Model Model • Undrained Undrained behav behaviour iour with Hard Hardening ening Soil Model

• Exca Excava vati tion on Exa Examp mple le • Summary

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Drained / undrained  • Dra Draine ined d an analy alysis sis appr appropri opriate ate when • Perm Permea eabi bili lity ty is is high high

• Rate Rate of of load loadin ing g is lo low w • Short term behavi behaviour our is not of of interest interest for for problem problem considered 

• Und Undra rain ined ed aana naly lysi siss ap appro propri priat atee wh when en • Permeabi Permeability lity is is low and and rate rate of loading loading is high high • Short term behaviour behaviour has has to be assess assessed  ed 

Drained / undrained  Suggestion by Vermeer & Meier (1998) for deep d eep excavations: T < 0.10 (U < 10 10% %) T > 0.40 (U > 70%) 0%)

T=

k E oed γw

D2

t

use use und undrained condi nditions use drained conditions

k = Eoed  = γw = D = t = T = U =

Permeability Oedometer modulus Unit weight of water  Dr Drai aina nage ge len eng gth Construction time Di Dime mens nsio ionl nles esss ti time me fa fact ctor  or  Degree of consolidation

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Undrai Und rained ned behavi behaviour  our  Implications of undrained soil behaviour: • Excess Excess pore pore pressur pressures es are are gener generated  ated  • No volum volumee ch chan ange ge In fact small volumetric strains develop because a finite (but high) bulk modulus of water is introduced in the finite element formulation

• Predicte Predicted d undrained undrained shear shear strength strength depends depends on soil soil model used • Assumption Assumption of dilata dilatancy ncy angle angle has serious serious effect effectss on results

Undrai Und rained ned behavi behaviour  our  Results from undrained triaxial tests using the Mohr-Coulomb and Hardening Soil Model

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Triaxi Tri axial al tes testt (N (NC) C) – drained / undrained  Typical results from drained (left) and undrained (right) triaxial tests on normally consolidated soils (from Atkinson & Bransby, 1978)

Triaxi Tri axial al tes testt (O (OC) C) – drained / undrained  Typical results from drained (left) and undrained (right) triaxial tests on overconsolidated soils

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Undr Un drai aine ned d tr tria iaxi xial al te test st– – NC / OC OC Typical results from undrained triaxial tests on (a) normally consolidated and (b) overconsolidated clay (from Ortigao, 1995)

Skempton’s Skemp ton’s parameters parameters A an and dB pw  B

Skempton 1954:

3

 A

σ3 ]

1

saturated soil of pore water  -- No Fully inflow / outflow - Bulk modulus modulus of soi soill grains is considered to be very high - Isotropic linear elastic elastic material behaviour (H (Hooke´s ooke´s law)

 

ε vol , pore water

vol , skeleton

vol , skeleton

=

vol , pore water

=

∆p' K ' n ∆p w

K '

E´ 3 1

2ν´

K w

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Skempton’s Skemp ton’s parameters parameters A an and dB ∆σ 

Assuming triaxial compression:

;  ∆σ    =

1

pw

=

1

2

 

3 pw

3

3K ' pw =

leading to

pw

with

B

3

B=

1 

⋅

1 

  A  1 nK '

2

∆σ  3

K w n

1 nK '

⎡ ⎢⎣

1 3

3

 

1

⎤ σ3 ⎥ ⎦

K w

σ3 ]

1

A =

1 3

K w

Skempton’s Skemp ton’s parameters parameters A an and dB • No Note tess on pa para rame mete ters rs A an and d B: • For Kw  large compared to K´, parameter B ~ 1.0 (corresponds to ∆ pw = ∆ p > ∆ p´ = 0) • Small Small amount amount of drapped drapped air air reduces reduces parame parameter ter B significantly (see next figure) figure) • Paramete Parameterr A depends on stress stress pa path, th, even for for elastic elastic material behaviour  • Paramete Parameterr A cannot be determ determined ined a priori priori for comple complex x elastic-plastic elastic-pl astic constitutive models but is a result of the model behaviour for the stress path followed

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Skempton’s Skemp ton’s parameters parameters A an and dB Dependence of pore pressure parameter B on degree of saturation

Undrai Und rained ned behavi behaviour our wit with h PLA PLAXIS XIS PLAXIS automatically adds stiffness of water when undrained material type is chosen using the following approximation:

K total

K total

K '

=

31

K w n

3 1

E'  1

νu

2

1

u

Eu

ν'

2ν u

=

2G 1 31

νu 2ν u

assuming νu = 0.495

 Notes: • This pro procedur ceduree gives reasonabl reasonablee B-values B-values only for ν´ < 0 0.3 .35 5! 6 • Real Real valu valuee of K w/n ~ 1.10 kPa (for n = 0.5) • In Versi Version on 8 B-value can be entere entered d explici explicitely tely for undrained materials materials

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Undrai Und rained ned behavi behaviour our wit with h PLA PLAXIS XIS Example 1:

E´ = 3 000 kPa kPa,,   ν´ = 0.3, 0.3,   νu = 0.495 Ktotal   = 115 000 kPa → K´ = 2 500 kPa, with

 B =

1 nK ' 1+ K w

→ K w/n = 112 500 kPa

= 0.978 > reasonable value for saturated soil

Example 2:

E´ = 3 00 000 0 kPa kPa,,   ν´ = 0. 0.45 45,,   νu = 0.495   = 103 103 kPa → K w/n = 93 103 kPa → K´ = 10 000 kPa, Ktotal B = 0.903 > poor value for saturated soil

Undrai Und rained ned behavi behaviour our wit with h PLA PLAXIS XIS Method A (analysis in terms of effective stresses): type of material behaviour: undrained  effective effective strength stiffness parameters parameters c´, E50ϕ ´,´,νψ ´´ Method B (analysis in terms of effective stresses): type of material behaviour: undrained  undrained strength parameters c = cu, ϕ = 0, ψ = 0 effective stiffness parameters E50´, ν´ Method C (analysis in terms of total stresses): type of material behaviour: drained  total strength parameters c = cu, ϕ = 0, ψ = 0 undrained stiffness parameters Eu, νu = 0.495

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Undrai Und rained ned behavi behaviour our wit with h PLA PLAXIS XIS  Notes on different methods: methods: • Method A: • Reco Recomm mmen ende ded  d  • Soil behaviour behaviour is always gove governed rned by effective stresses • Increase of shear strength during co consolidation nsolidation included  • Essential for exploiti exploiting ng features of advanced models models such as the Hardening Soil model, the Soft Soil model and the Soft Soil Creep model • Method B: • Only when no inform information ation on ef effective fective st strength rength param parameters eters is avilable • Cannot be used used with tthe he Soft Soi Soill model and the Soft Soft Soil Creep model • Method C: • NOT NOT recom recomme mend nded  ed  • No information information on excess pore pressure dist distribution ribution (total (total stress analysis) analysis)

Undrained Undra ined strength strength from from Mohr Mohr circ circle le Consider fully undrained isotropic elastic behaviour (Mohr Coulomb in elastic range) ∆ pw = ∆ p > ∆ p´ = 0

→ centre of Mohr Circle remains at the same point cu

1 2

 

'o x

  sin

'o y

'

c' cos ϕ'

Mohr Circle for evaluating undrained shear strength (plane strain)

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Influence of constitutive model Parameter sets for Hardening Soil mod el  el  ref 

ref 

nc

E 50  

E ur   

Eoed  

ref 



 

c

ur 

p  

m

K0  

R f  

kN/m 2 

kN/m 2 

kN/m 2

°

°

kN/m 2

-

kN/m 2

-

-

-

HS_1

30 000

9 0 000

30 0 00 35 0 / 1 0

0 .0

0 .2

100

0.75 0.42 6 0. 0.9

HS_2

5 0 0 0 0 1 5 0 0 00 5 0 0 0 0 3 5

0

0 .0

0 .2

100

0 . 7 5 0 .4 2 6 0 . 9

HS_3

15 000

4 5 000

15 15 0 00 35

0

0 .0

0 .2

100

0 . 7 5 0 .4 2 6 0 . 9

HS_4

30 000

9 0 000

40 40 0 00 35

0

0 .0

0 .2

100

0 . 7 5 0 .4 2 6 0 . 9

HS_5

30 000

9 0 000

15 15 0 00 35

0

0 .0

0 .2

100

0 . 7 5 0 .4 2 6 0 . 9

HS_6

5 0 0 0 0 1 5 0 0 00 3 0 0 0 0 3 5

0

0 .0

0 .2

100

0 . 7 5 0 .4 2 6 0 . 9

Model Number

ref 

Parameters for MC Model 2

E = 30 000 kN/m   =

0.2

 =

35°  35° 

 =

0° and 10°  10°  

see also Schweiger (2002)

Comparison MC-HS (influence ψ) Simulation Simulatio n of undrained triaxial triaxial compression compression test – MC / HS model - q vs ε1 300 275 250 225 200    ] 175   m    /    N 150    k    [   q 125

   2

100 75

MC non dil MC dil HS_1 non dil HS_1 dil

50 25 0 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

ε1  [%]

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Comparison MC-HS (influence ψ) Simulation Simulatio n of undrained triaxial triaxial compression compression test – MC / HS model - q vs p´ 300 MC non dil MC dil HS_1 non dil HS_1 dil total stress path

275 250 225 200    ] 175   m    /    N 150    k    [   q 125

   2

100 75 50 25 0 0. 00

25. 00

50.00

75.00

100.00 125.00 150.00 175.00 200.00 225.00 250.00 2

p' [kN/m ]

Comparison MC-HS (influence ψ) Simulation Simulati on of undrained triaxial compr compression ession test – MC / HS model -  ∆ pw vs ε1 100 90    ]    2

  m    /    N    k    [   e   r   u   s   s   e   r   p   e   r   o   p   s   s   e   c   x   e

MC non dil MC dil HS_1 non dil HS_1 dil

80 70 60 50 40 30 20 10 0 -10 -20 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

ε1  [%]

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Comparison MC-HS (influence ψ) Simulation Simulati on of undrained tria triaxial xial compres compression sion test – MC / HS model - A vs ε1 1.0 0.9 MC dil non dil MC HS_1 non dil HS_1 dil

0.8 0.7 0.6 0.5    A   r   e    t   e   m   a   r   a   p

0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

ε1  [%]

Parameter Param eter variati variation on – Hard Hardening ening S Soil oil Simulation Simulati on of undrained tria triaxial xial compres compression sion test – HS model - q vs p´ 150

125

100    ]

HS_1 HS_2 HS_3 HS_4 HS_5 HS_6 total stress path

   2

  m    /    N 75    k    [   q

50

25

0 0. 00

25.00

50.00

75. 00

100.00

125.00

150.00

2

p' [kN/m ]

12

 

Parameter Param eter variati variation on – Hard Hardening ening S Soil oil Simulation Simulati on of undrained tria triaxial xial compres compression sion test – HS model - q vs ε1 150

125

100    ]

   2

  m    /    N 75    k    [   q

50

HS_1 HS_2 HS_3 HS_4 HS_5 HS_6

25

0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

ε1  [%]

Parameter Param eter variati variation on – Hard Hardening ening S Soil oil Simulation Simulati on of undrained triaxial compr compression ession test – HS model - ∆ pw vs ε1 80 70    ]    2

  m 60    /    N    k    [   e   r 50   u   s   s   e 40   r   p   e   r   o 30   p   s   s   e   c 20   x   e

HS_1 HS_2 HS_3 HS_4 HS_5 HS_6

10 0 0 .0 0

1.00

2 .0 0

3.00

4.00

5 .00

6.00

ε1   [%]

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Parameter Param eter variati variation on – Hard Hardening ening S Soil oil Simulation Simulati on of undr undrained ained tria triaxial xial compr compression ession tes testt – HS model - A vs ε1 0.8 0.7 0.6    A 0.5   r   e    t   e 0.4   m   a   r   a   p 0.3

HS_1 HS_2 HS_3 HS_4 HS_5 HS_6

0.2 0.1 0.0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

ε1  [%]

Summary • Undra Undraine ined d analys analysis is shoul should d be perfor performe med d in effective stresses and with effective stiffness and strength parameters • Undra Undraine ined d shea shearr str streng ength th is result of the constitutive model • Care must be be taken taken with choice choice of value value for dilatancy dilatancy angle angle • Note Note that that for for NC-s NC-soil oilss in genera general: l: • Factor Factor of sa safety fety again against st fa failur iluree is lower for short term (undrained) conditions for loading problems (e.g. embankment) • Factor Factor of sa safety fety again against st fa failur iluree is lower for long term (drained) conditions for unloading problems (e.g. excavations)

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Real Excavation Case in Stiff Residual Soils-What is likely Field Conditions?

T =

H = 15 m

cv *t  2

 H 

Cv=66 m2/day Cv=125 m2/day Cv=53 m2/day

What is West Coast Station Situation ??? Consolidation Considerations in Excavation Parameters Paramete rs for West Coast Station • Cv= 50 m2/day • H=15 m • t = 100 da days • T=50 T=50*10 *100/ 0/(1 (15*1 5*15) 5) = 22. 22.2 2 >>> >>> 0.4 0.4 • Situation Situation on on Passive Passive Side is likel likely y to be be DRAINED DRAINED Condition

15

 

Excess PP at Formation Level for k=1e-7 and 1e-8 m/s

Cases of k=1e-7 to 1e-9 m/s Displacements at Formation Level

16

 

Cases of k=1e-7 to 1e-9 m/s BMs at Formation Level

Wall Deflection Deflection at B (15/83.8 (15/83.85 5 – 1.65m abo above ve FL) Ux at B Ux at B [m] 0.2 DRN

UND 0.15

k=1e-7

k=1e-8

0.1

k=1e-9

0.05

0 0

50

100

150

200

250

Time [day]

17

 

Heave at C(0 C(0/78.7 /78.7 – 3.5m be below low FL FL)) Uy at C Heave at C [m] 0.035 DRN 0.03 UND 0.025

k=1e-7

0.02

k=1e-8

0.015

k=1e-9

0.01

5e-3

0

-5e-3 0

30

60

90

120

Time [day]

Seng Se ngka kang ng – Cant Cantil ilev ever er CBP CBP Wal Walll Type 3 Wall - 1000mm CBP 115

I4- 4 4// 02 02/ 03 03

I4- 8 8// 04 04/ 03 03

110

   ) 105    m    (    L    R    n    o    i    t    a   v    e    l    E100

Undrained Drained Consolidate 100 days

95

90 0

0.05

0.1

0.15

0.2

0.25

0.3

Wall Deflection (m)

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References  Atkinson, J.H., Bransby, Bransby, P.L. (1978) The Mechanics of Soils, An Introduction to Critical State Soil Mechanics. McGraw Hill Ortigao, J.A.R. (1995) Soil Mechanics in the Light of Critical State Theories – An Introduction. Balkema Schweiger, H.F. (2002) Some remarks on pore pressure parameters parameters A and B in undrained undrained analyses with the Hardening Soil Model. Plaxis Bulletin No.12 Skempton, A.W. (1954) The Pore-Pressure Coefficients A and B. Geotechnique, 4, 143-147 Vermeer, P.A., Meier, C.-P. (1998) Proceedings Int. Conf. on Soil-Structure Soil-Structure Inter Interaction action in Urban Civil Engineering, Engineering, Darmstadt, 177-191

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