A. Mellal & Ph. Bellwald Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007,...

A. Mellal & Ph. Bellwald

www.GeoMod.ch

Implementation of a constitutive law in Z_Soil

Z_Soil Day, 27 August 2007, Lausanne, Switzerland

Aïssa Mellal, GeoMod Consulting Engineers, Lausanne

Philippe Bellwald, Consulting Engineer, Aigle

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Implementation of a user-defined constitutive law for

shales in Z_Soil


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Outline

Introduction Short description of the constitutive law

Anisotropic elasticity Yield / failure surface Consolidation Creep

Implementation in Z_Soil User interface Algorithm

Applications Simulation of triaxial tests Simulation of a deep excavation

Issues, remarks and conclusion


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Introduction

Deformation due to stress relief following excavations Immediate effects: undrained deformation Time dependent effects

Specific law for swelling shales (clayey shales) Elasto-plastic behaviour Consolidation/swelling (pore pressure dissipation) Drained creep (evolving deviatoric/volumetric strains)

Implementation in Z_Soil User interface (input data) User defined routine (algorithm)

• Conformity with Z_Soil program’s structure


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Short description of the constitutive law

Background Laboratory tests on shales by Ph. Bellwald (PhD, MIT, 1990) Lab. testing and modelling of shale behaviour by G. Aristorenas

(PhD, MIT, 1992) / Prof. Herbert Einstein

Elasto-plastic constitutive law Hyperbolic relationship of strain vs. deviatoric stress:

22 qb

qa

coco

2221 q

mq

m

cocovol

Elastic Plastic

ppvol b

m 2

baq

co

a : “inverse” of shear modulus

b: “inverse” of plastic shear modulus

m1 : “inverse” of coupling shear modulusm2 : “inverse” of plastic coupling modulus


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Anisotropic elasticity (transverse isotropic) Elastic (tangential) stiffnesses

01 m

eevol a

m 1

aG co

i

1mH co

i

B

co

CK

3026.2

Elastic shear modulus (initial)

Bulk modulus

Elastic coupling modulus (initial)

Isotropic elasticity

eCB 1

3026.2


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Plastic deformation Shear and volumetric strains

ppvol b

m 2

Plastic deformation (shear strain):

No plastic coupling

22 qb

co

ep

222 q

m

co

evolvol

pvol

Induced volumetric plastic strain:

02 m


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Plastic deformation

Yield surface

cmqbF octy 234

cIm

JbFy 12

2 33

2or

Failure surface

kIJFf 12

)'sin3(3

'sin2

)'sin3(3

'cos'6

ck

q

p

Failure surface

Yield surface

Cut-off surface


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Consolidation Pore-pressure dissipation (time dependent)

Creep Volumetric scaling: volumetric strain rate

Deviatoric scaling: shear strain rate

tmc

vol 3026.2

t

mc

3026.2

bm

mm 2

Normality rule:


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Implementation in Z_Soil

Documentation “How to implement user supplied model within Z_SOIL system”,

2003• Creating script files for user interface

• Organization of compilation environment

• Programming user supplied model

• Sample data

Template file “usr1.for” (example)

Software Z_SOIL 3D, V6.97 Fortran compiler (Visual Studio)


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Creating user interface Modify script file “zsoil.usm” to add the new constitutive law to

the list of materials

File location: C:\Program Files\Z_Soil\Z_Soil 3D 6.97\CFG

“Elastic” parameters

“Non-linear” parameters


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User interface


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Activate “shale” model Modify file “SuppliedModels.for” to add a link (call) to the new

constitutive law

File location: C:\Program Files\Z_Soil\Z_Soil 3D 6.97\UserModels\Calc\UserModles


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State variables (actual)


“shale” model Initialization of state variables:

• Current , C (size of Y.S.)• Plasticity, failure flags

Computation of a new stress state

Update of state variables

,

State variables (new)

actual

oct

new

constitutive law


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Applications - Simulation of triaxial tests

Specimen’s geometry and numerical model

1

32

Lab. specimen Z_Soil model (1/8)

1

32

32 32


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Drained pure shear compression-extension test

2

32

31

31

q

p

compression

extension


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Drained pure shear compression-extension test

-2000

-1000

0

1000

2000

0 500 1000 1500 2000

p, kPa

q, k

Pa

-2000

-1000

0

1000

2000

-2 -1 0 1 2

vol, %

q, k

Pa

-2000

-1000

0

1000

2000

-2 -1 0 1 2

, %

q, k

Pa

-1.5

-1

-0.5

0

0.5

-2 -1 0 1 2

, %

vo

l, %

'co (kPa) 1300

a, % 0.5

m1, % 0.3

Cbe, % 0.75

b, % 0.5

m2, % -0.4


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Isotropic unloading



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Isotropic unloading

0

200

400

600

800

1000

0 500 1000 1500 2000

p, kPa

q, k

Pa

200

400

600

800

1000

1200

-0.5 0 0.5

, %

p, k

Pa

-1

-0.5

0

0.5

100 1000 10000

log(p), kPa

vo

l, %

'co (kPa) 1100

a, % 0.35

m1, % 0.18

Cbe, % 1.0633

b, % 0.38

m2, % -0.3



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Drained shear compression test



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Drained shear compression test

0

500

1000

1500

2000

-1 -0.5 0 0.5 1

vol, %

q, k

Pa

0

500

1000

1500

2000

0 500 1000 1500 2000

p, kPa

q, k

Pa

-1

-0.5

0

0.5

1

0 0.5 1 1.5 2

, %

vo

l, %

'co (kPa) 800

a, % 0.35

m1, % 0.66

Cbe, % 3.03

b, % 0.38

m2, % -0.35


0

500

1000

1500

2000

0 0.5 1 1.5 2

, %

q, k

Pa


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Consolidation test



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Consolidation test

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

Time (min)

vo

l (%

)

k = 8e-12 m/s k = 4.8e-12 m/s



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Shear to failure test



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0

1000

2000

3000

0 1000 2000 3000 4000 5000

p, kPa

q, k

Pa

Shear to failure test

0

1000

2000

3000

-4 -3 -2 -1 0 1 2 3 4

vol, %

q, k

Pa

-3

-2

-1

0

1

2

3

0 1 2 3 4 5 6

, %

vo

l, %

'co (kPa) 800

a, % 0.35

m1, % 0.66

Cbe, % 3.03

b, % 0.38

m2, % -0.35


c’ (kPa) 800’ 27°

0

1000

2000

3000

0 1 2 3 4 5 6

, %

q, k

Pa


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Applications - Simulation of a deep excavation

Simulation of a deep excavation


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Stress path

-3000

-2000

-1000

0

1000

2000

3000

0 1000 2000 3000 4000 5000

'oct, kPa

m s

qrt

(J2)

, kP

a

Springline Crow n/Invert

Failure Envelope (+) Failure Envelope (-)



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Crown/Invert

-5000

-4000

-3000

-2000

-1000

0

0.01 0.1 1 10 100 1000

Time (years)

Str

ess,

kP

a

Eff.Stress-YY EFF.STRESS-XX Eff.Stress-ZZ

Variation of effective stresses with time


Springline

-5000

-4000

-3000

-2000

-1000

0

0.01 0.1 1 10 100 1000

Time (years)

Str

ess,

kP

a

Eff.Stress-YY EFF.STRESS-XX Eff.Stress-ZZ


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Mises stress distribution



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Pore pressure change



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Evolution of pore pressure changeCrown/Invert

-1500

-1000

-500

0

0.01 0.1 1 10 100 1000

Time (years)

u

, kP

a

Springline

-1500

-1000

-500

0

0.01 0.1 1 10 100 1000

Time (years)

u, k

Pa

Pore pressures evaluated at r = 5.45 m



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Displacements Crown/Invert

0

0.01

0.02

0.03

0.04

0.05

0.01 0.1 1 10 100 1000

Time (years)

Dis

pla

cem

nt,

m

Springline

0

0.01

0.02

0.03

0.04

0.05

0.01 0.1 1 10 100 1000

Time (years)D

isp

lace

men

t, m

Displacements evaluated at r = 5 m



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Issues, remarks

Lateral earth pressure coefficient (initial K0 state) Initial stresses from BC

Works only in 3-D : need to simplify to 2-D version for fast analyses

Initial


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Conclusion

Constitutive law successfully implemented in Z_Soil Triaxial laboratory tests simulated with good agreement

with experiment Simulation of a deep excavation with long-term

consolidation Next: improve certain details (initial stresses, 2-D, Kh) Next: test efficiency on a “real” full-scale problem


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Thank you !

A. Mellal & Ph. Bellwald Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007,...

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