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Visco Modified CamClay model: Triaxial Driver versus Semi-Analytical Solution

Problem description

This example uses the Triaxial Driver to simulate a visco-elasto-plastic oedometric compression test of a Visco Modified CamClay solid. Oedometric condition with zero lateral strain together with loading/unloading axial strain periods are imposed. Semi-analytical results for the mean and shear stress variations \Delta p and \Delta q can be established, considering the Perzyna approach, for the imposed oedometric boundary conditions as (Runesson et al. 1999) :

\Delta p = K(\Delta\varepsilon_{V} - \Delta\lambda \frac{\partial G}{\partial p})

\Delta q = 2\mu(\Delta\varepsilon_{V} - \Delta\lambda \frac{3}{2}\frac{\partial G}{\partial q})

where K and \mu are elastic bulk and shear moduli, G is the plastic potential and \Delta\lambda is the visco-plastic multiplier that can be approximated by:

\Delta\lambda = \frac{\Delta t}{t_*} \frac{F}{3\mu\frac{\partial F}{\partial q}\frac{\partial G}{\partial q} + K\frac{\partial F}{\partial p}\frac{\partial G}{\partial p} + h}

in which \Delta t is the time increment, t_* is the relaxation time, F is the stress function defining the visco-plastic yield surface and h is the hardening rate defined by:

h = -\frac{\partial F}{\partial \lambda}

These solutions are implemented in a Python script associated to this example for verifying GEOS results.

Input files

This validation example uses two GEOS xml files that are located at:

inputFiles/triaxialDriver/triaxialDriver_base.xml

and

inputFiles/triaxialDriver/triaxialDriver_ViscoModifiedCamClay.xml

It also uses a set of table files located at:

inputFiles/triaxialDriver/tables/

A Python script for the semi-analytical solutions presented above as well as for post-processing the GEOS results is provided at:

src/docs/sphinx/advancedExamples/validationStudies/viscoplasticity/ViscoModifiedCamClay/TriaxialDriver_vs_SemiAnalytic_ViscoModifiedCamClay.py

For this example, we focus on the Task and the Constitutive tags.

Task

The imposed axial strain loading/unloading periods, the lateral zero strain, and the initial stress are defined in the Task block as:

.. literalinclude:: ../../../../../../../inputFiles/triaxialDriver/triaxialDriver_ViscoModifiedCamClay.xml
    :language: xml
    :start-after: <!-- SPHINX_TASK -->
    :end-before: <!-- SPHINX_TASK_END -->

Constitutive laws

The elasto-visco-plastic parameters are defined as:

.. literalinclude:: ../../../../../../../inputFiles/triaxialDriver/triaxialDriver_base.xml
    :language: xml
    :start-after: <!-- SPHINX_MATERIAL_VISCO_MODIFIED_CAMCLAY -->
    :end-before: <!-- SPHINX_MATERIAL_VISCO_MODIFIED_CAMCLAY_END -->

All constitutive parameters such as density, viscosity, and the bulk and shear moduli are specified in the International System of Units.

A comparison between GEOS results and semi-analytical results

The simulation results are saved in a text file, named ViscoModifiedCamClayResults.txt. A comparison between the results given by the TriaxialDriver solver in GEOS and the semi-analytical results presented above is shown below. The discrepancy between these results may due to the difference between the Duvaut-Lions approach and the Perzyna approach for time dependant behavior when applying for the Modified CamClay model as discussed by Runesson et al. (1999).

.. plot:: docs/sphinx/advancedExamples/validationStudies/viscoplasticity/ViscoModifiedCamClay/TriaxialDriver_vs_SemiAnalytic_ViscoModifiedCamClay.py

To go further

Feedback on this example

For any feedback on this example, please submit a GitHub issue on the project's GitHub page.