Aïssa Mellal , GeoMod Consulting Engineers, Lausanne

1. Implementation of a user-defined constitutive law for shales in Z_Soil Aïssa Mellal, GeoMod Consulting Engineers, Lausanne Philippe Bellwald, Consulting Engineer, Aigle www.GeoMod.ch

2. 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. 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

4. 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: a : “inverse” of shear modulus b: “inverse” of plastic shear modulus m1 : “inverse” of coupling shear modulus m2 : “inverse” of plastic coupling modulus Elastic Plastic

5. 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. Short description of the constitutive law • Plastic deformation • Shear and volumetric strains Plastic deformation (shear strain): Induced volumetric plastic strain: No plastic coupling

7. Short description of the constitutive law • Plastic deformation • Yield surface • Failure surface or Yield surface q Failure surface p Cut-off surface

8. 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. 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. 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. Implementation in Z_Soil • User interface

12. 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. 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) State variables (actual) constitutive law

14. Applications - Simulation of triaxial tests • Specimen’s geometry and numerical model Z_Soil model (1/8) Lab. specimen

15. Applications - Simulation of triaxial tests • Drained pure shear compression-extension test compression extension

16. Applications - Simulation of triaxial tests • Drained pure shear compression-extension test

17. Applications - Simulation of triaxial tests • Isotropic unloading

18. Applications - Simulation of triaxial tests • Isotropic unloading

19. Applications - Simulation of triaxial tests • Drained shear compression test

20. Applications - Simulation of triaxial tests • Drained shear compression test

21. Applications - Simulation of triaxial tests • Consolidation test

22. Applications - Simulation of triaxial tests • Consolidation test

23. Applications - Simulation of triaxial tests • Shear to failure test

24. Applications - Simulation of triaxial tests • Shear to failure test c’ (kPa) 800 f’ 27°

25. Applications - Simulation of a deep excavation • Simulation of a deep excavation

26. Applications - Simulation of a deep excavation • Stress path

27. Applications - Simulation of a deep excavation • Variation of effective stresses with time

28. Applications - Simulation of a deep excavation • Mises stress distribution

29. Applications - Simulation of a deep excavation • Pore pressure change

30. Applications - Simulation of a deep excavation • Evolution of pore pressure change Pore pressures evaluated at r = 5.45 m

31. Applications - Simulation of a deep excavation • Displacements Displacements evaluated at r = 5 m

32. 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 s

33. 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. Thank you !