Creep, Anisotropy and DestructurationDestructuration

Dr Minna Karstunenwith thanks to Prof. Pieter

Vermeer & Dr Martino Leoni

Acknowledgements• Co-workers:

– Dr Mike Kenny (USTRAT)– Dr Zhenyu Yin (previously USTRAT, now Nantes, soon )– Dr Martino Leoni (previously USTUTT, Wechselwirkung Studio Italiano)– Dr Mohammad Rezania (USTRAT)– Ms Daniela Kamrat-Pietraszewska (USTRAT/KELLER)– Mr Nallathamby Sivasithamparam (USTRAT/PLAXIS)– Mr Nallathamby Sivasithamparam (USTRAT/PLAXIS)– Mr Igor Mataic (HUT)– Prof. Pieter Vermeer (USTUTT)– Dr Gustav Grimstad (NGI)– Dr Ronald Brinkgreve (Plaxis bv/TUD)

• Sponsors:– GEO-INSTALL “Modelling Installation Effects in Geotechnical

Engineering” IAPP project funded by the EC 2009-2014– Experimental work has been funded by the Academy of Finland

(Grants 210744,128459)

GEO-INSTALL IAPPMarie Curie IAPP

GEO-INSTALL

PIAG-GA-2009-230638

Industry-Academia Partnerships and Pathways project funded by the EC/FP7 under programme ‘People’

•Total value €1.28M (2009-2013) for:

• Secondments• Post-doc appointments (Marie Curie

Fellowship) • Workshops, training courses and other

knowledge-exchange activities

Outline

• 1D Creep model• Experimental data

• 1D Creep model

• Influence of temperature

• Soft Soil Creep model• Soft Soil Creep model• 3D Soft Soil Creep model

• SSC parameters

• Modelling of natural clays• Anisotropy & destructuration

• S-CLAY1S and EVP-SCLAY1S

• Application: Murro test embankment

Creep modelling

with thanks to Prof. Pieter Vermeer, Dr Martino Leoni &

Load-controlled test: footing (3 x 3 m2) on dense sand

Set

tlem

ent (

mm

) 24 hours

Load (MN)S

ettle

men

t (m

m)

Briaud and Gibbens (1994)

Displacement-controlled load tests on floating micropiles

Load (kN)

Set

tlem

ent

(cm

)

20 40 60 80 100

1

s& = constant

Set

tlem

ent

(cm

)

Considering such a rate-type effect, it is important to do research on creep and stress relaxation.

= 10-4 a

= a= 10 a

CSV micropilesLength: 8mDiameter: 17 cm

2

3

4

s&s&

s&

rate of penetration

Alluvium

Kie

s

Beckenton

Time [days]

Se

ttle

me

nt

[m

m]

01 10 100 103 104

Measured time – settlement curve near Friedrichshafen

Classical soil Mechanics assumed an S-curve with a clear transition between consolidation and creep.

Sand

Fels

Fein NC-

Schluff

Se

ttle

me

nt

[m

m]

-450

mm600s =∞

time [years]

se

ttle

me

nt

[cm

]

Settlement curves of buildings in Drammen do not show S-shape (Bjerrum ,1967)

wP = 28% w = 51.5% wL = 28.2%

PLASTIC CLAY

SAND

OCReoc ����

1.2

SKOGER SPAREBANK

OCReoc ���� 1.1SCHEITLIES GATE 1

OCReoc =+ ∆

po

o

σ

σ' σs

ett

lem

en

t [c

m]

wP = 28% w = 51.5% wL = 28.2%

wP = 21.4% w = 34.6% wL = 35.5%

LEAN CLAY

Thickness varies with location

Thickness varies with location

Often OCR varies with depth. The indicated OCR values refer to the bottom of the clay layer.

OCReoc ���� 1.05KONNERUD GATE 16

OCReoc ����

0.9

TURNHALLEN

1D-consolidation and 1D-creep in single load step

Voi

d ra

tio e

σ

t

t

0

∆σ

Load step time

Cα = secondary compression indexor

creep index

teoclog t

1eeoc

Voi

d ra

tio e

eeoc = void ratio at end of consolidation teoc = time at end of consolidation

αeoc

eoc

te e - logC

t=Bjerrum (1967):

Data from 24-hours-load-stepping test on a NC-peat

total time of test (days) load step time (logscale)

den Haan (1994)

Cαααα

1

Load is daily doubled. First 3 load steps do not show S-curves. Except step 1, all slopes show Cαααα.

1 day

Typical 24 hours load stepping

1 day

CC = compression index CS = swelling index Cα = creep index

Each day: constant σ σ∆ = ⋅

Increase of preconsolidation stress due to creep after Bjerrum (1967)

e

NC-Line

State of overconsolidation can be reached both by creep and unloading

Cs

1

creep

oσ ′

σ′log

pσ = preconsolidation stress

Data can be modelled by relating the creep rate to OCR

NCL

e

e ≡&de

dt

OCR = 1

OCR = 1.3

OCR = 1.7

log σ’

Den Haan (1994)

ncee && =

1000/ee nc&& ≈

1000/1000/ee nc&& ≈

after Hanzawa (1989)

MSL24 = usual 24 h Multi – Stage Loading

CRS = Constant Rate of Strain test

τ = reference time

1 τ

Classical creep rate concepts:

α

−β =

c sC C

C

1D creep model

τ⋅−= α 1

10lnC

enc&β

=OCR

ee nc&&

Norton (1929):

Prandtl (1928):

Soderberg (1936):

o

α1ε (σ σ )

τ= −&

o

1ε sinh (ασ ασ )

τ= ⋅ −&

o

1ε ( exp (ασ ασ ) 1)

τ= ⋅ − −&

for σ > σο

for σ > σο

τ = temperature dependent

The reference time τ depends on the definition of the NC-line. When NCL is based on the usual one-day load stepping test, we have τ = 1 day. This is a default in PLAXIS.

e c s α

β

C Cσ 1 1e e e

ln10 σ ln10 τ OCR

′− −= + = +

′

&& & &

Typical soil data: 10/CC ≈ and / 30 27c sC CC C β

−≈ ⇒ = ≈

σ σ

Summation of elastic rate and creep rate

1D creep model

Typical soil data: 10/CC cs ≈ and / 30 27c sc

C CC C β

Cαα

−≈ ⇒ = ≈

This implies that the creep rate is negligibly small for OCR well beyond unity.

σ’p = function of void ratio and temperature

Tremendous influence of overconsolidation ratio

Example : Cc = 0.15 Cs = 0.015 Cα = 0.005

e

β 27⇒ =

1D creep model

27ncc

OCR

ee

&& =

1.7

1.3

1.0

OCR

e

NCL

σ′log

nce&

3nc 10e −⋅&

ce&

6nc 10e −⋅&

e

σσσσpo

e

Cαααα

1 day 8 days

∆σ

NC soils show S-shaped settlement curve; OC soils do not.

1D creep model

Step AStep A

log σσσσ’ log t = log ( teoc + t ‘ )

Cαααα

Treporti Silt data after Simonini et al. (2006); Berengo (2006)( wP = 25% w = 32% wL = 38%)

Step BStep B

Influence of temperature

Preconsolidation pressure from oedometer tests at various temperatures

Leroueil (2006):

−

∆⋅−⋅⋅σ=σ ∆α−

CsCce10ln

expexpc

Tpop

Cper01,0 °=α

α+

−σ−=σ Te

CsCc10ln c

pp&&&

after Eriksson (1989)

Soft Soil Creep model

1. 3D Soft Soil Creep model

2. SSC parameters

3. Options of SSC

Martino Leoni

3. Options of SSC

4. Application of SSC: Leaning tower of Pisa

5. Anisotropic creep model

q

3D Soft Soil Creep model

Modified compression index:

*

**

µ

κλβ

−=

10ln

* cC=λ

2C

β

τ

µκεεε

+=+=

'

'

'

' **

p

eqp

v

e

vvp

p

p

p&&&&

q

p´eqp′pp'

NCS

Isotropic preconsolidation pressure

Modified swelling index:

Modified creep index:

10ln

2* sC≈κ

10ln

* αµC

=

−=

**exp''

κλ

ε p

vp pp

&

Ellipses of Modified Cam Clay are taken as contours of volumetric strain rate

q

ce = a&

ce a& <<Current

3D Soft Soil Creep model

ac

v =ε&

ac

v <<ε&

2 2 2

1 2 2 3 3 1

1q (σ ' σ ' ) (σ ' σ ' ) (σ ' σ ' )

2= − + − + −

pp′ p´

eq pNCS: p p′ ′=

e a& <<

eqp′

1 2 3

1p ' (σ ' σ ' σ ' )

3= + +

Current stress

av <<ε

'''

*

2

pM

qpp eq +=

Comparison with Modified Cam Clay

Both models have summation:

Both models have hardening:

Both models have flow rule: eqp Λ

′∂=

∂

cε

σ

&

σ σ

(Isothermal case is considered)

3D Soft Soil Creep model

p

v

e

vv εεε &&& +=

−=

**exp''

κλ

ε p

vp pp

&

2eq eq eq

1 2 3 2 2

1 2 3

p p p qε ε ε ε 1 d

σ σ σ M pvolumetric

′ ′ ′∂ ∂ ∂ = + + = Λ ⋅ + + = Λ ⋅ − = Λ ⋅

′∂ ∂ ∂ & & & &

Modified Cam Clay: increase of density by primary loading NCS is yield locus

Creep model: increase of density by creep NCS is iso-creep rate locus

pcedddd εεεε ++=

'1 σε dDd

e −= Elastic strains according to Hooke’s law

3D model: Division of strains:

dgc

c

Soft Soil Creep model

'1

σλε

d

dgdd

cc = Creep strains (viscoplastic, time-dependent)

'2 σ

λεd

dgdd

fp= Plastic strains according to MC (at failure)

Typical performance of model for drained triaxial tests on NC-soil

q

NCS-slow

31 σσ −

fast test

3D Soft Soil Creep model

p'

0pp slow-ppfast-pp•

•

•

•

NCS-fast

1ε

fast test

slow test

• •

Performance of IC Model for undrained triaxial tests on NC-soils

q/2

FAST SHEARING• •

1 3σ σ−

••

3D Soft Soil Creep model

p´1ε

••

SLOWCu FAST

Cu SLOW

u

u

C1.00 0.10 log ε

C (ε 1%/h)= += += += +

====&&&&

&&&&

1.01.0

1.51.5

SSC Model

3D Soft Soil Creep model

Kulhawy & Mayne (1990): Manual on Estimating Soil Properties for Foundation Design

1010--33 1010--22 1010--11 101000 101011 101022 101033 101044 101055

0.50.5

26 CLAYS

ε (% /h )&&&&

10/** λ≈κ

30/** λ≈µ

10ln)e1(C

e1 0

c

0

*

+=

+

λ=λModified compression index:

Modified swelling index:

Modified creep index:

SSC parameters

FROM PLAXIS MANUAL, NOT SUITABLE FOR STRUCTURED CLAYS

0.15 0.25′ = ÷ν

Critical state friction angle:

Poisson’s ratio:

Initial conditions: POP or OCR

NC0K 1 sin′ ′→ ≈ −cs csϕ ϕ (Jaky)

σ ’ (logarithmic) time (logarithmic)

p’ (ln-scale)

εvλ*

κ*

time (ln-scale)

εv

µ*

consolidation

creep

Parameters of the SSC model

σ1’ (logarithmic)

e Cc

Cs

time (logarithmic)

e

Cα

consolidation

creep

Soft Soil Creep modelRelationships with other compression indices:

Cam-Clay -

Dutch literature

e+=

1

* λλ

e+=

1

* κκ

* 1=λ * 2

≈κ1* ≈µDutch literature

Den Haan

International lit.

'

pC=λ

.)(ontlpC≈κ

sC '3.2

* ≈µ

BA +=*λ A2* ≈κ C=*µ

)1(3.2

*

e

Cc

+=λ

e

Cs

+≈

1

*κ)1(3.2

*

e

C

+= αµ

Effective cohesion and steep cap

Options of SSC model

q

M*M MC

1

1

Failure MC

cap

Value of M* can be selected such that K0nc = 1 – sin ϕ´

The above picture would suggest the possibility of tensile stresses, but these can be omitted by using a „tension cut-off“

c´cot ϕ´'e

ppp´

'sin3

'sin6

cv

cvMφ

φ

−=

Usually assume

c’= 0 kPa

Options of SSC model

Initial stress state for overconsolidated soils

0pPOP σ′−σ=

input of POP

0σ′ pσ

input of OCRx

y

0σ′ pσ

nc0K

ν

1-ν1

σp

POP

yσ′

0yσ′

xσ′0xσ′

This procedure for estimating the initial horizontal stress gives results that are in good agreement with the correlation:

0 0nc

K K OCR≈ ⋅

SSC model The role of OCR in self-weight loading and creep:

-0.10

-0.05

0.00 Settlement [m]

OCR0=1.4

OCR0=2.0 Settlementof 10mthick layer

λ* 0.10

0 200 400 600 800 1000 -0.35

-0.30

-0.25

-0.20

-0.15

Time [day]

OCR0=1.0

OCR0=1.1

OCR0=1.4 λ* 0.10

κ* 0.02

µ* 0.005

νur 0.15

c’ 0.0 kPa

ϕ’ 25°

ψ 0°

K0nc 0.677

(1-sin ϕ’)

References

Creep in soft soils

Briaud and Gibbens (1994): Test and Prediction Results for Five Large Spread Footings on Sand, Proc. Spread Footing Prediction Symposium (Fed. High. Adm.) Eds J.L. Briaud, M.Gibbens, pp.92-128

Bjerrum, L. 1967. Engineering geology of norwegian normally-consolidated marine clays as related to settlements of buildings. Géotechnique, 17: 81-118.

Boudali, M. 1995. Comportement tridimensionnel et visqueux des argiles naturelles. PhD Thesis, Université Laval, Québec.

Buisman (1936): Results of long duration settlement tests, Proc. 1st Int. Conf. Soil Mech. and Found. Eng., Vol. 1, pp. 103-107.

Claesson, P. 2006. Creep around the preconsolidation pressure – a laboratory and field study. In CREBS Workshop. Edited by N.G.I. Oslo.

Den Haan (1994): Stress-independent parameter for primary and secondary compression, Proc. 13th Int. Conf. Soil Mech. and Found. Eng., New Delhi, Vol 1, pp 65-70.

Den Haan, E.J. 1996. A compression model for non-brittle soft clays and peat. Géotechnique, 46: 1-16.

Garlanger, J.E. 1972. The consolidation of soils exhibiting creep under constant effective stress. Géotechnique, 22: 71-78.Garlanger, J.E. 1972. The consolidation of soils exhibiting creep under constant effective stress. Géotechnique, 22: 71-78.

Janbu, N. 1969. The resistance concept applied to deformations of soils. In 7th ICSMFE. Mexico City, Vol.1.

Leroueil, S. 1987. Tenth Canadian Geotechnical Colloquium: Recent developments in consolidation of natural clays. Canadian Geotechnical Journal, 25: 85-107.

Leroueil, S. 2006. The isotache approach. Where are we 50 years after its development by Professor Šukljie?

Malvern, L.E. 1951. The propagation of longitudinal waves of plastic deformation in a bar of metal exhibiting a strain rate effect. Journal of Applied Mechanics, 18: 203-208.

Mesri (2006), Primary and secondary compression, In CREBS Workshop. Edited by N.G.I. Oslo.

Mesri & Godlewski (1977): Time and stress compressibility interrelationship, J. Geot. Eng. Div., ASCE 103, GT5, pp.417-430.

Odqvist, F.K.J: Mathematical Theory of Creep and Creep Rupture, Clarendon Press, Oxford, 1966

Perzyna P.: Fundamental Problems in Viscoplasticity, Advan. Appl. Mech., 9, 243-377, 1966

Šukljie, L. 1957. The analysis of the consolidation process by the isotaches method. In 4th ICSMFE, Vol.1, pp. 200-206.

References

Yin, J.-H. 1999. Nonlinear creep of soils in oedometer tests. Géotechnique, 49(2): 699-707.

Yin, J.-H., and Graham, J. 1999. Elastic viscoplastic modelling of the time dependent stress-strain behaviour of soils. Canadian Geotechnical Journal, 36: 736-745.

Isotropic (Soft Soil Creep model) creep model:

Stolle, D.F.E., Bonnier, P.G., and Vermeer, P.A. 1997. A soft soil model and experiences with two integration schemes. In NUMOG VI. Edited by

Pietruszczak S. and Pande G.N. Montreal. 2-4 July 1997. Balkema, Rotterdam.

Vermeer, P.A., and Neher, H.P. 1999. A soft soil model that accounts for creep. In Int.Symp. "Beyond 2000 in Computational Geotechnics". Edited by

R.B.J. Brinkgreve. Amsterdam. Balkema, Rotterdam, pp. 249-261.

Vermeer, P.A., Stolle, D.F.E., and Bonnier, P.G. 1998. From the classical theory of secondary compression to modern creep analysis. In Computer Methods and Advances in Geomechanics. Edited by Yuan. Balkema, Rotterdam.

Neher H.P., Wehnert M., Bonnier, P.G. (2001): An Evaluation of Soft Soil Models Based on Trial Embankments. Proc. 10°Int. Conf. on Computer Methods and Advances in Geomechanics (Eds Desai et al.), Vol.1, pp. 373-378, Balkema, Rotterdam.

Neher H.P., Vogler U., Vermeer P.A., Viggiani C. (2003): 3D Creep Analysis of the Leaning Tower of Pisa. Proc. Int. Workshop on Geotechnics of Soft Soils (Eds Vermeer et al.), pp. 607-612. Noordwijkerhout, The NetherlandsSoils (Eds Vermeer et al.), pp. 607-612. Noordwijkerhout, The Netherlands

Anisotropic (creep) modelling:

Anandarajah, A., Kuganenthira, N., and Zhao, D. 1996. Variation of Fabric Anisotropy of Kaolinite in Triaxial Loading. Journal of Geotechnical Engineering, 122(8): 633-640.

Leoni, M., Karstunen M. and Vermeer P.A. 2007. Anisotropic creep model for soft soils. Submitted for publication

Näätänen, A., Wheeler, S.J., Karstunen, M., and Lojander, M. 1999. Experimental investigation of an anisotropic hardening model for soft clays. In 2nd International Symposium on Pre-failure Deformation characteristics of Geomaterials. Edited by M. Jamiolkowski, R. Lancellotta, and D. Lo Presti. Torino, Italy, pp. 541-548.

Vermeer, P.A., Leoni, M., Karstunen, M., and Neher, H.P. 2006. Modelling and numerical simulation of creep in soft soils. In ICMSSE Conference, Vancouver, p. 57-71

Wheeler, S.J., Näätänen, A., Karstunen, M., and Lojander, M. 2003. An anisotropic elastoplastic model for soft clays. Canadian Geotechnical Journal, 40: 403-418.

Anisotropy and Destructuration- Modelling of natural clays- Modelling of natural clays

Dr Minna Karstunen

With thanks to Mirva Koskinen, Zhenyu Yin, Martino Leoni & many others

Outline

• Introduction: some key features of natural clays

• Constitutive modelling of soft natural soils• Constitutive modelling of soft natural soils– Large strain anisotropy → S-CLAY1– Bonding and destructuration → S-CLAY1S– Viscosity and time-dependence → ACM & EVP-

SCLAY1S & AniCreep

Structure of Natural Clays• Soil structure consists of:

– fabric (anisotropy)– interparticle bonding

(sensitivity)

Reconstituted Naturalλλλλ

For a constant ηηηη stress path:

ln p'

v

Reconstituted

soil

Natural

soil

λλλλi

1

1

Due to plastic straininggradual degradation of bonding (destructuration) and changes in fabric

Structure of Natural Clays

• Fabric of clay:

e.g. Craig (1974): (a) dispersed; (b) flocculated; (c) bookhouse; (d) turbostratic(e) natural clay with silt particles

Leroueil & Vaughan (1990)

1D Compression

2

2.4σ'pi = 6 kPa σ'p = 45 kPa

3.2

4

Intact

Remoulded

Vanttila clay

σ'pi = 0.37 kPa σ'p = 29 kPa

0.8

1.2

1.6

1 10 100 1000

σσσσ'v (kPa)

e

Intact

Remoulded

(a)

Murro clay

0.8

1.6

2.4

0.1 1 10 100 1000 10000

σσσσ 'v (kPa)

e

(d)

1D Compression

0.03

0.04Intact

Remoulded

Murro clay

0.06

0.08

0.1Intact

Remoulded

Vanttila clay

0

0.01

0.02

1 10 100 1000

σσσσ'v (kPa)

Cαα αα

e

(b)

0

0.02

0.04

0.06

1 10 100 1000 10000

σσσσ 'v (kPa)

Cαα αα

e

(e)

After Leroueil & Vaughan (1990)

After Leroueil & Vaughan (1990)

Mexico City Clay (Mesri et al. 1975) The Grande Baleine clay (Locat & Lefebre 1982)

λλλλ

POKO clay 8.5-10.0 m

St=12

Vanttila clay 2.3-3.1 m

St>30

1.0

1.2

1.2

1.4

λλλλ

Triaxial Tests with Constant Stress Ratio

λλλλ

λλλλi

λλλλ

0.0

0.2

0.4

0.6

0.8

-1.0 -0.5 0.0 0.5 1.0

ηηηη1111

λλλλ 1111 , κ, κ, κ, κ

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.5 0.0 0.5 1.0

ηηηη1111

λλλλ 1111 , κ, κ, κ, κ

λλλλi

λλλλ

λλλλi

λλλλ

-0.25

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

p'/σv c', kPaq/

vc',

kPa

191 kPa 241 kPa

310 kPa 380 kPa

Winnipeg clay

M = 0.67

-20

0

20

40

60

80

0 20 40 60 80p', kPa

q, k

Pa

Marjamäki clayDepth 5.5-6.1 m

M = 0.84

-30

0

30

60

90

0 30 60 90p', kPa

q, k

Pa

Bothkennar clayDepth 5.3 - 6.3 m

M = 1.4

yield points from p'-εv

from q-εs

-30

0

30

60

90

0 30 60 90

p', kPa

q, k

Pa

yield points

undrainedfailure

Mexico City clay Depth 1.7 m

M=1.75

φ’ = 18-43 degrees

Wheeler et al. (2003)

On modelling anisotropy

• Elastic anisotropy (Ev, Eh…) easy to model but values for parameters very difficult to measuremeasure

• Plastic anisotropy relates to anisotropy associated with LARGE (irrecoverable) strains

Modelling Plastic Anisotropy1. Standard elasto-plastic framework (kinematic or

translational hardening laws) – Note: cannot use invariants

• Nova (1985), Banerjee & Yousif (1986), Dafalias (1986), Davies & Newson (1993), Whittle & Kavvadas (1994), Wheeler & al. (2003)

2. Micromechanical models2. Micromechanical models

i. Multilaminate framework• Zienkiewicz & Pande (1977), Pande & Sharma (1983),

Pietruszczak & Pande (1987), Karstunen (1998), Wiltafsky (2003), Neher et al. (2001, 2002), Mahin Roosta et al. (2004)

ii. Microplane models• Bazant (995), Chang & Liao (1990), Chang & Gao (1995),

Chang & Hicher (2005), Yin et al. (2009)

Modelling Destructuration

• Concept of an intrinsic yield surface proposed by Gens & Nova (1993)– Lagioia & Nova (1995), Rouainia & Muir Wood (2000),

Kavvadas & Amorosi (2000), Gajo & Muir Wood Kavvadas & Amorosi (2000), Gajo & Muir Wood (2001), Liu & Carter (2002), Karstunen et al. (2005)

q

p’ pm’ pmi’

M 1

M

1

α 1

CSL

CSL

Modelling Time-Dependence & Creep

– Creep models:• ACM (Leoni et al. 2008) and ACM-S (under development)• AniCreep (Yin et al., submitted for publication)• Time-resistance S-CLAY1S (Grimstad & al. in press)

– Overstress model:– Overstress model:• EVP-SCLAY1S (Karstunen & Yin, in press)

q

p’ pm’ pmi’

M 1

M

1

α 1

CSL

CSL

p’ σ’y

σ’x

σ’z

α

−σ

−σ

y

x

'p'

'p'

Deviatoric stress vector

−α

−α

y

x

1

1

Deviatoric fabric tensor (in vector form)

Definitions:

τ

τ

τ

−σ=σ

zx

yz

xy

z

y

d

2

2

2

'p'

3

''''p

zyx σ+σ+σ=

α

α

α

−α

−α

=α

zx

yz

xy

z

y

d

2

2

2

1

1

13

zyx=

α+α+α

S-CLAY1S Model(Karstunen et al. 2005)

p’

α 0

20

40

60

80

40

60

80

σ’y

{ } { }[ ] { } { } [ ] 0'p'p'p2

3M'p'p

2

3F md

T

d

2

dd

T

dd =−

α

αα−−α−σα−σ=43421

0

20

40

60

80

0

20

σ’z

σ’x

S-CLAY1S Model(Karstunen et al. 2005)

q

M 1

α 1

CSL

p’ σ’y

α Natural yield curve

“intrinsic” yield curve

p’ pm’ pmi’

M

1

CSL

σ’x

σ’z

mim 'p)x1('p +=Intrinsic yield surface

{ } { }[ ] { } { } [ ] 0'p'p'p2

3M'p'p

2

3F md

T

d

2

dd

T

dd =−

αα−−α−σα−σ=

Hardening Laws:

κ−λ

ε=

i

p

vmimi

d'vp'dp

1) Size of the intrinsic yield surface

2) Degradation of bonding2) Degradation of bonding

( )

ε+ε−= p

d

p

v dbdaxdx

3) Rotation of the yield surface

εα−

ηβ+⟩ε⟨α−

ηµ=α p

dd

p

vdd d)3

(d)4

3(d

'p

dσ=η

α

−α

−α

−α

=αxy

z

y

x

d2

1

1

1

α−α

α−α−

α−α

=α )(3

1

)(3

2

)(3

1

yx

yx

yx

d

−α

−α−

−α

=α )33(3

1

)33(3

2

)33(3

1

x

x

x

d

α−

α

α−

=α3

3

23

d

Fabric Tensor (Assuming Initial Cross Anisotropy)

13

zyx=

α+α+α

zx α=α

0zxyzxy =α=α=α { } { }d

T

d2

32 αα=α

α

α

zx

yz

xy

2

2

2

0

0

03

0

0

03

0

0

03

By following the standard procedure

]D['

F

'

Q]D[

1]D[]D[ e

Teeep

σ∂

∂

σ∂

∂

β−=

σ∂

∂

σ∂

∂+=β

'

Q]D[

'

FH

eT

Elasto-Plastic Matrix

σ∂

∂

σ∂

∂

ε∂

∂+

∂

∂

ε∂

∂

∂

∂+

σ∂

∂

σ∂

∂

ε∂

α∂+

∂

∂

ε∂

α∂

α∂

∂+

∂

∂

ε∂

∂

∂

∂−=

d

T

d

p

d

p

vd

T

d

p

d

d

p

v

d

T

d

p

v

mi

mi '

Q

'

Qx

3

2

'p

Qx

x

F

'

Q

'

Q

3

2

'p

QF

'p

Q'p

'p

FH

For S-CLAY1S:

S-CLAY1S has been implemented in SAGE Crisp (by Zentar at GU) and PLAXIS 2D v8.2 (by Wiltafsky at GU) and PLAXIS 2D Version 9, using NR (by Sivasithamparam at USTRAT/PLAXIS) in 2010.

S-CLAY1 and MCC• By setting x to zero and using an

oedometric value (1D) for compressibility λcompressibility λ

S-CLAY1 model (anisotropy only)

• By setting, in addition, α and µ to zero

MCC model (isotropy only)

Additional State Variables and Soil Constants

Symbol Definition Method

α0Initial inclination of the yield curve

Estimated via φ’

β Proportion constant Estimated via φ’

S-CLAY1

β

µ Rate of rotation ≈ (10…20)/λK0

x0Initial amount of bonding ≈ St -1

λiSlope of intrinsic compression line

Oedometer test on reconstituted soil

b Proportion constant For most clays 0.2-0.3

a Rate of destructuration Typically 8-11

S-CLAY1S

Tests on Reconstituted Claysa) Murro clay

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70

p' (kPa)

q (

kP

a)

Yield pointsM=1.6α=0.46

max

p'm=35.5 kPa

Max. stress during η0

loading

b) POKO clay

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70

p' (kPa)

q (

kP

a)

Yield points

M=1.2α=0.43

max

p'm=42.0 kPa

Max. stress during η0

loading

-30 -30

c) Otaniemi clay

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70

p' (kPa)

q (

kP

a)

Yield pointsM=1.3α=0.42

max

p'm=26.0 kPa

Max. stress during η0

loading

d) Vanttila clay

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70p' (kPa)

q (

kP

a)

Yield points

M=1.35

α=0.40

max

p'm=26.0 kPa

Max. stress during η0

loading

-0.05

0.05

0.15

-50 0 50 100 150

q (kPa)

εεεε d

0.0

0.1

0.2

1.5 2.5 3.5 4.5 5.5ln p'

εεεε v

Simulations with S-CLAY1

0.25

-0.05

0.05

0.15

0.25

0.0 0.1 0.2 0.3

εεεε v

εεεε d

CAE 3216R

S-CLAY1

MCC

CAD 3216R

Reconstituted Murro clay

6.9-7.6 m

ηηηη0=0.98, ηηηη1=-0.62, ηηηη2=0.60

0.3

Karstunen & Koskinen (2004)For full validation, see Karstunen & Koskinen (2008), Can. Geotech. J.

a) Murro clay

-10

0

10

20

30

40

50

0 10 20 30 40 50 60 70

q (

kP

a)

M=1.6

α=0.63p'm=34.5 kPa

b) POKO clay

-10

0

10

20

30

40

50

0 10 20 30 40 50 60 70

q (

kP

a)

M=1.2

α=0.46p'm=49 kPa

Tests on Natural Clay Samples

-20

p' (kPa)

-20

p' (kPa)

c) Otaniemi clay

-10

0

10

20

0 10 20 30

p' (kPa)

q (

kP

a)

M=1.3

α=0.50p'm=19.5 kPa

d) Vanttila clay

-10

0

10

20

0 10 20 30

p' (kPa)

q (

kP

a)

M=1.35

α=0.52p'm=18.5 kPa

Viscosity of Natural Clays

1

2C

ae (

%)

Murro clay

0

1

10 100 1000σ'v (kPa)

Cae

(%

)

Mc

1

qe vp

ij ij ijε ε ε= +& & & ( )vp d

ij

ij

fFε µ φ

σ

∂=

∂&

d

ij

f

σ

∂

∂

Principle of EVP-SCLAY1S

B

Me

1

p’

p’mdp’m

sp’mis

Intrinsic yield surface

Static yield surface

Dynamic loading surface

A

B

( ) exp 1 1d

m

s

m

pF N

pµ φ µ

= ⋅ − −

Model Parameters• Anisotropy parameters

– 1 additional state variable (of tensorial form) describing anisotropy– 2 additional soil constants– All can be estimated based on standard oedometer and triaxial tests for soil with previous K0

history

• Destructuration parameters• Destructuration parameters– 1 additional state variable describing the amount of bonding– 2 additional soil constants– Ideally need oedometer tests on reconstituted sample, but can be estimate based on

standard oedometer test at high stresses

• Viscosity parameters– 2 additional soil constants that need to be optimised– Optimization requires either:

• Oedometer/triaxial tests with two different strain rates or• Long term oedometer/triaxial tests or• Pressometer tests with different strain rates etc.

0

5

10

15

εε εεv (

%)

Exp. 1.43x10-5 s-1

Exp. 2.13x10-6 s-1

Exp. 1.07x10-7 s-1

EVP model

110

120

130

(kP

a)

ExperimentEVP model with α & χEVP model without α & χ

Without destructuration With

destructuration

CSR oedometer test (Batiscan Clay)

60 80 100 120 140 160 180 200 220 240

20

25

σσσσ'v (kPa)

(a) α=0 & χ=0

50 100 150 200 250 300

0

5

10

15

20

25

σσσσ'v (kPa)

εε εεv (

%)

Exp. 1.43x10-5 s-1

Exp. 2.13x10-6 s-1

Exp. 1.07x10-7 s-1

EVP model

(d) Anisotropy &destructuration

10-9

10-8

10-7

10-6

10-5

10-4

70

80

90

100

dεεεεv/dt

σσ σσ' p

(kP

a)

Destructuration can improve predictions on CSR oedometer test on structured clays

With destructuration

Without destructuration

0

50

100

150

200

250

q (

kP

a)

Exp. C150EVP model α=0,χ=0

0

50

100

150

200

250

q (

kP

a)

Exp. C150EVP model α=0,χ=0EVP model χ=0EVP model with α&χ

-25

0

25

50

75

100

δδ δδu

(kP

a)

Exp. C150EVP model α=0,χ=0

CSR triaxial test (Hong Kong Marine Deposit)Compression

EVP-SCLAY1

EVP-SCLAY1SEVP-MCC

Destructuration effect

0 5 10 15 20-50

εεεεa (%)

EVP model α=0,χ=0EVP model χ=0EVP model with α&χ(a)

0 50 100 150 200 250-50

p' (kPa)

(b)

0 5 10 15 20-50

εεεεa (%)

EVP model α=0,χ=0EVP model χ=0EVP model with α&χ(c)

0 50 100 150 200 250-150

-100

-50

0

50

100

150

p' (kPa)

q (

kP

a)

Exp. E150EVP model α=0,χ=0EVP model χ=0EVP model with α&χ

(b)

-20 -15 -10 -5 0-100

-50

0

50

100

εεεεa (%)

δδ δδu

(kP

a)

Exp. E150EVP model α=0,χ=0EVP model χ=0EVP model with α&χ

(c)

-20 -15 -10 -5 0-150

-100

-50

0

50

100

150

εεεεa (%)

q (

kP

a)

Exp. E150EVP model α=0,χ=0EVP model χ=0EVP model with α&χ

(a)

Extension

Anisotropy effect

Long-term oedometer test (Batiscan clay)

0

5

10

15

(%

)

σ'v=78 kPa

σ'v=90 kPa

σ'v=98 kPa

σ'v=109 kPa

0.2

0.3

0.4

e

ExperimentPrediction with χPrediction without χ

Without destructurationWith

destructuration

101

103

105

107

109

20

25

30

35

time (s)

εε εεv (

%)

ExperimentPrediction with χPrediction without χ

σ'v=121 kPa

σ'v0

=65 kPa

50 75 100 125 1500

0.1

0.2

σσσσ'v (kPa)

Cαα αα

e

With destructuration

Without destructuration

destructuration

Destructuration is very important to predicting the long-term behaviour of oedometer tests on structured clays

2

3

4

εa (

%)

CAUCR1 q=14.4 kPaCAUCR2 q=17.3 kPaCAUCR3 q=20.0 kPaEVP-SCLAY1SEVP-SCLAY1EVP-MCC

(a)

(a)

Undrained triaxial creep test (Vanttila clay)

EVP-SCLAY1S

EVP-MCC

10-6

10-4

10-2

εa/d

t (%

/s)

Secondary creep

Tertiary creep (c)

EVP-SCLAY1

101

102

103

104

105

106

0

1

Time (s)

- Inclusion of anisotropy improves predictions of undrained creep test on natural clay

- Inclusion of destructuration can reproduce three creep stages (including creep rupture)

EVP-SCLAY1S

101

102

103

104

105

106

10-8

Time (s)d

ε

CAUCR1 q=14.4 kPaCAUCR2 q=17.3 kPaCAUCR3 q=20.0 kPaEVP-SCLAY1SEVP-SCLAY1 (c)

Primary creep

Application: Murro Test Embankment

• Geometry2 m

1

2

10 m

S2 (S5, S7) S3 S4S1S6

I1 I2

U1

U2U3

U4

U5U6

U7

E

Cross Section

S: settlement plates

I: Inclinometers

U: Pore pressure probes

E: Extensometers

• Site InvestigationU8

• Site Investigation

0

5

10

15

20

25

0 50 100

Su (kPa)

Dep

th (

m)

0 25 50

Content (%)

OrganicClay

0 60 120

w (%)

w

wL

wP

0 10 20

St

12 15 18

γ (kN/m3)

1 2 3

e0

2D FE Analysis

• FE Mesh (PLAXIS v.8)

Embankment fillGroundwater level

Dry crust OCR=7

Soft clay OCR=1

Plane strain

1456 elements

15-noded triangles

11861 stress points (EVP-SCLAY1S)

(EVP-SCLAY1S)

• Embankment fill (Mohr Coulomb)

11861 stress points

The embankment construction took 2 days

• Embankment construction

Thickness (m) E (kN/m2) υ' φ’ ψ’ c’(kN/m

2) γ (kN/m

3)

0.0-2.0 40 000 0.35 40° 0° 2 19.6

Foundation Soil

• From oedometer tests

• From triaxial tests

0

5

10

15

20

25

0 0.3 0.6

Dep

th (

m)

λλι

0

5

10

15

20

25

0 0.03 0.06

Dep

th (

m)

0

5

10

15

20

25

0 100 200

Dep

th (

m)

σ'vp

σ'v0

0

5

10

15

20

25

0.1 10 1000

Dep

th (

m)

kv

kh

λ, λιk σ'vp, σ'v0 (kPa) k (E-9 m/s)

0

50

100

150

0 50 100 150 200

q (

kP

a)

0.0-1.6 m: M=1.7

1.6-3.0 m: M=1.7

0

50

100

0 50 100 150

3.0-6.7 m: M=1.65

0

50

100

150

0 50 100 150 200

p' (kPa)

q (

kP

a)

6.7-10.0 m: M=1.5

10.0-15.0 m: M=1.45

0

50

100

150

0 50 100 150 200

p' (kPa)

15.0 -23.0 m: M=1.4

Viscosity from long-term oedometer tests:

N=10, µµµµ=1x10-10 s-1

-0.6

-0.4

-0.2

0

Set

tlem

ent

(m)

S2S5S1S3S4S6EVP model

-0.6

-0.4

-0.2

0

Set

tlem

ent

(m)

E2 -1,5m

E3 -2,5m

E4 -3,4m

E5 -4,4m

E6 -5,4m

E7 -6,4m

E8 -8,4m

EVP

Settlements

centreline

2 m off

5 m off

-0.8

0 1000 2000 3000 4000

Time (day)

-0.8

0 1000 2000 3000 4000

Time (day)

EVP

-0.8

-0.6

-0.4

-0.2

0

0.2

0 5 10 15 20 25 30 35

Distance from centreline (m)

Ver

tica

l d

isp

lace

men

t (m

)

EVP modelAfter construction210 days756 days1132 days1966 days3058 days

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

1 10 100 1000 10000 100000

Time (day)

Set

tlem

ent

(m)

S2S5S1S3S4S6EVP model

δu dissipation

74 years

274 years

Viscosity effect

5 m off

centreline

0

5

10

Dep

th (

m)

207 days

274 years after

construction

Horizontal Displacements

I20

5

10

Dep

th (

m)

274 years

I1

15

20

25

-50 0 50 100 150

Displacement (mm)

Dep

th (

m)

207 days

754 days

1137 days

2001 days

3201 days

EVP model

15

20

25

-50 0 50 100 150

Displacement (mm)

Dep

th (

m)

2 days207 days754 days1137 days2001 days3201 daysEVP model

Effect of υυυυ’ and kh /kv ? not well estimated, or soil non-homogeneity

Good performance for the early consolidation stage, but underestimated for later stage

Excess Pore Pressures

5

10

15

20

25

30

35

Ex

cess

pore

pre

ssu

re (

kP

a)

U2-2.0 m

U3-3.5 m

EVP-SCLAY1S

U2

U3

10

15

20

25

30

35

40

U4-5.5 m

U5-7.5 m

U5

U4

0

5

1 10 100 1000 10000 100000

(a)

0

5

1 10 100 1000 10000 100000

(b)

0

5

10

15

20

25

30

1 10 100 1000 10000 100000

Time (day)

Ex

cess

pore

pre

ssu

re (

kP

a)

U6-9.0 m

U7-12.0 m

U6

U7

(c)

0

5

10

15

20

25

30

35

40

1 10 100 1000 10000 100000

Time (day)

U1-15.0 m

U8-20.0 m

U1

U8

(d)

Good agreement achieved

Some Key References:

• M. Karstunen, C. Wiltafsky, H. Krenn, F. Scharinger & H.F. Schweiger (in press). Modelling the stress-strain behaviour of an embankment on soft clay with different constitutive models. International Journal of Numerical and Analytical Methods in Geomechanics.

• M. Karstunen & M. Koskinen (2008). Plastic anisotropy of soft reconstituted clays. Canadian Geotechnical Journal 45: 314-328

• M. Karstunen, H. Krenn, S.J. Wheeler, M. Koskinen & R. Zentar (2005). The effect of anisotropy and destructuration on the behaviour of Murro test embankment. ASCE International Journal of Geomechanics 5(2):87-97.ASCE International Journal of Geomechanics 5(2):87-97.

• M. Karstunen & M. Koskinen (2004). Anisotropy and destructuration of Murro clay. In: Advances in Geotechnical Engineering. The Skempton Conference, London 29-31 March 2004. Thomas Telford. Vol. 1 pp. 476-486.

• M. Leoni, M. Karstunen & P. Vermeer (2008). Anisotropic creep model for soft soils. Géotechnique 58 (3): 215-226

• S.J. Wheeler, A. Näätänen, M. Karstunen & M. Lojander (2003). An anisotropic elasto-plastic model for natural soft clays. Canadian Geotechnical Journal 40:403-418.

• M. Karstunen, & Z.-Y. Yin (in press- 2010). Modelling time-dependent behaviour of Murro test embankment. Accepted for publication in Géotechnique.