Rak-50 3149 n. l14- Anisotropy Bonding and Creep
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Transcript of Rak-50 3149 n. l14- Anisotropy Bonding and Creep
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.