Implementation of a userdefined constitutive law for shales

Outline Ø Introduction Ø Short description of the constitutive law Ä Anisotropic elasticity Ä

Introduction Ø Deformation due to stress relief following excavations Ä Immediate effects: undrained deformation

Short description of the constitutive law Ø Background Ä Laboratory tests on shales by

Short description of the constitutive law Ø Anisotropic elasticity (transverse isotropic) Ä Elastic (tangential)

Short description of the constitutive law Ø Plastic deformation Ä Shear and volumetric strains

Short description of the constitutive law Ø Plastic deformation Ä Failure surface Ä Yield

Short description of the constitutive law Ø Consolidation Ä Pore-pressure dissipation (time dependent) Ø

Implementation in Z_Soil Ø Documentation Ä “How to implement user supplied model within Z_SOIL

Implementation in Z_Soil Ø Creating user interface Ä Modify script file “zsoil. usm” to

Implementation in Z_Soil ØUser interface Implementation of a constitutive law in Z_Soil A. Mellal

Implementation in Z_Soil Ø Activate “shale” model Ä Modify file “Supplied. Models. for” to

Implementation in Z_Soil Ø “shale” model Ä Initialization of state variables: • Current ,

Applications - Simulation of triaxial tests Ø Specimen’s geometry and numerical model Z_Soil model

Applications - Simulation of triaxial tests Ø Drained pure shear compression-extension test compression extension

Applications - Simulation of triaxial tests Ø Drained pure shear compression-extension test s'co (k.

Applications - Simulation of triaxial tests Ø Isotropic unloading Implementation of a constitutive law

Applications - Simulation of triaxial tests Ø Isotropic unloading s'co (k. Pa) 1100 a,

Applications - Simulation of triaxial tests Ø Drained shear compression test Implementation of a

Applications - Simulation of triaxial tests Ø Drained shear compression test s'co (k. Pa)

Applications - Simulation of triaxial tests Ø Consolidation test Implementation of a constitutive law

Applications - Simulation of triaxial tests Ø Shear to failure test Implementation of a

Applications - Simulation of triaxial tests Ø Shear to failure test s'co (k. Pa)

Applications - Simulation of a deep excavation Ø Simulation of a deep excavation Implementation

Applications - Simulation of a deep excavation Ø Stress path Implementation of a constitutive

Applications - Simulation of a deep excavation Ø Variation of effective stresses with time

Applications - Simulation of a deep excavation Ø Mises stress distribution Implementation of a

Applications - Simulation of a deep excavation Ø Pore pressure change Implementation of a

Applications - Simulation of a deep excavation Ø Evolution of pore pressure change Pore

Applications - Simulation of a deep excavation Ø Displacements evaluated at r = 5

Issues, remarks Ø Lateral earth pressure coefficient (initial K 0 state) Ø Initial stresses

Conclusion Ø Constitutive law successfully implemented in Z_Soil Ø Triaxial laboratory tests simulated with

Thank you ! Implementation of a constitutive law in Z_Soil A. Mellal & Ph.

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Implementation of a userdefined constitutive law for shales in Z_Soil Aïssa Mellal, Geo. Mod Consulting Engineers, Lausanne Philippe Bellwald, Consulting Engineer, Aigle www. Geo. Mod. ch Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Outline Ø Introduction Ø Short description of the constitutive law Ä Anisotropic elasticity Ä Yield / failure surface Ä Consolidation Ä Creep Ø Implementation in Z_Soil Ä User interface Ä Algorithm Ø Applications Ä Simulation of triaxial tests Ä Simulation of a deep excavation Ø Issues, remarks and conclusion Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Introduction Ø Deformation due to stress relief following excavations Ä Immediate effects: undrained deformation Ä Time dependent effects Ø Specific law for swelling shales (clayey shales) Ä Elasto-plastic behaviour Ä Consolidation/swelling (pore pressure dissipation) Ä Drained creep (evolving deviatoric/volumetric strains) Ø Implementation in Z_Soil Ä User interface (input data) Ä User defined routine (algorithm) • Conformity with Z_Soil program’s structure Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Short description of the constitutive law Ø Background Ä Laboratory tests on shales by Ph. Bellwald (Ph. D, MIT, 1990) Ä Lab. testing and modelling of shale behaviour by G. Aristorenas (Ph. D, MIT, 1992) / Prof. Herbert Einstein Ø Elasto-plastic constitutive law Ä Hyperbolic relationship of strain vs. deviatoric stress: a : “inverse” of shear modulus b: “inverse” of plastic shear modulus m 1 : “inverse” of coupling shear modulus m 2 : “inverse” of plastic coupling modulus Elastic Plastic Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

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

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

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

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

Implementation in Z_Soil Ø Documentation Ä “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 Ä Template file “usr 1. for” (example) Ø Software Ä Z_SOIL 3 D, V 6. 97 Ä Fortran compiler (Visual Studio) Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Implementation in Z_Soil Ø Creating user interface Ä Modify script file “zsoil. usm” to add the new constitutive law to the list of materials File location: C: Program FilesZ_Soil 3 D 6. 97CFG “Elastic” parameters “Non-linear” parameters Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Implementation in Z_Soil ØUser interface Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Implementation in Z_Soil Ø Activate “shale” model Ä Modify file “Supplied. Models. for” to add a link (call) to the new constitutive law File location: C: Program FilesZ_Soil 3 D 6. 97User. ModelsCalcUser. Modles Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Implementation in Z_Soil Ø “shale” model Ä Initialization of state variables: • Current , C (size of Y. S. ) • Plasticity, failure flags Ä Computation of a new stress state , State variables (actual) constitutive law Ä Update of state variables Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch State variables (new)

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

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

Applications - Simulation of triaxial tests Ø Drained pure shear compression-extension test s'co (k. Pa) a, % 0. 5 m 1, % 0. 3 Cbe, % 0. 75 b, % m 2, % Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch 1300 0. 5 -0. 4

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

Applications - Simulation of triaxial tests Ø Isotropic unloading s'co (k. Pa) 1100 a, % 0. 35 m 1, % 0. 18 Cbe, % Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch 1. 0633 b, % 0. 38 m 2, % -0. 3

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

Applications - Simulation of triaxial tests Ø Drained shear compression test s'co (k. Pa) 800 a, % 0. 35 m 1, % 0. 66 Cbe, % 3. 03 b, % 0. 38 m 2, % Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch -0. 35

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

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

Applications - Simulation of triaxial tests Ø Shear to failure test s'co (k. Pa) 800 a, % 0. 35 m 1, % 0. 66 Cbe, % 3. 03 b, % 0. 38 m 2, % -0. 35 c’ (k. Pa) 800 f’ 27° Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

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

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

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

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

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

Applications - Simulation of a deep excavation Ø Evolution of pore pressure change Pore pressures evaluated at r = 5. 45 m Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

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

Issues, remarks Ø Lateral earth pressure coefficient (initial K 0 state) Ø Initial stresses from BC Initial s Ø Works only in 3 -D : need to simplify to 2 -D version for fast analyses Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

Conclusion Ø Constitutive law successfully implemented in Z_Soil Ø Triaxial laboratory tests simulated with good agreement with experiment Ø Simulation of a deep excavation with long-term consolidation Ø Next: improve certain details (initial stresses, 2 -D, Kh) Ø Next: test efficiency on a “real” full-scale problem Implementation of a constitutive law in Z_Soil A. Mellal & Ph. Bellwald Z_Soil Day, 27 August 2007, Lausanne, Switzerland www. Geo. Mod. ch

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