1. 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 www.GeoMod.ch Implementation of a user- defined constitutive law for shales in Z_Soil

2. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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

3. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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 programs structure

4. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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: Elastic Plastic a : inverse of shear modulus b: inverse of plastic shear modulus m1 : inverse of coupling shear modulus m2 : inverse of plastic coupling modulus

5. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Short description of the constitutive law Anisotropic elasticity (transverse isotropic) Elastic (tangential) stiffnesses Elastic shear modulus (initial) Bulk modulus Elastic coupling modulus (initial) Isotropic elasticity

6. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Short description of the constitutive law Plastic deformation Shear and volumetric strains Plastic deformation (shear strain): No plastic coupling Induced volumetric plastic strain:

7. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Short description of the constitutive law Plastic deformation Yield surface or Failure surface q p Yield surface Cut-off surface

8. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Short description of the constitutive law Consolidation Pore-pressure dissipation (time dependent) Creep Volumetric scaling: volumetric strain rate Deviatoric scaling: shear strain rate Normality rule:

9. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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)

10. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Implementation in Z_Soil 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

11. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Implementation in Z_Soil User interface

12. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Implementation in Z_Soil 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

13. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland State variables (actual) Implementation in Z_Soil 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) constitutive law

14. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Applications - Simulation of triaxial tests Specimens geometry and numerical model Lab. specimen Z_Soil model (1/8)

15. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Applications - Simulation of triaxial tests Drained pure shear compression-extension test compression extension

16. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Applications - Simulation of triaxial tests Drained pure shear compression-extension test 'co (kPa) 1300 a, %0.5 m1, %0.3 Cbe, %0.75 b, %0.5 m2, % -0.4

17. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Isotropic unloading Applications - Simulation of triaxial tests

18. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Isotropic unloading 'co (kPa) 1100 a, %0.35 m1, %0.18 Cbe, %1.0633 b, %0.38 m2, %-0.3 Applications - Simulation of triaxial tests

19. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Drained shear compression test Applications - Simulation of triaxial tests

20. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Drained shear compression test 'co (kPa) 800 a, %0.35 m1, %0.66 Cbe, %3.03 b, %0.38 m2, %-0.35 Applications - Simulation of triaxial tests

21. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Consolidation test Applications - Simulation of triaxial tests

22. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Consolidation test Applications - Simulation of triaxial tests

23. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Shear to failure test Applications - Simulation of triaxial tests

24. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Shear to failure test 'co (kPa) 800 a, %0.35 m1, %0.66 Cbe, %3.03 b, %0.38 m2, % -0.35 Applications - Simulation of triaxial tests c (kPa) 800 27°

25. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Applications - Simulation of a deep excavation Simulation of a deep excavation

26. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Stress path Applications - Simulation of a deep excavation

27. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Variation of effective stresses with time Applications - Simulation of a deep excavation

28. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Mises stress distribution Applications - Simulation of a deep excavation

29. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Pore pressure change Applications - Simulation of a deep excavation

30. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Evolution of pore pressure change Pore pressures evaluated at r = 5.45 m Applications - Simulation of a deep excavation

31. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Displacements Displacements evaluated at r = 5 m Applications - Simulation of a deep excavation

32. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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

33. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland 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

34. A. Mellal & Ph. Bellwald www.GeoMod.ch Implementation of a constitutive law in Z_Soil Z_Soil Day, 27 August 2007, Lausanne, Switzerland Thank you !