Reference problem
=====================

Geometry
---------

.. figure:: images/Object_1.svg
 :align: center
 :width: 480
 :height: 360

 Height: :math:`h=1` m, width: :math:`l=1` m, thickness: :math:`e=1` m.

 .. _RefImage_Object_1.svg:


Material properties
----------------------

Model CAM_CLAY
^^^^^^^^^^^^^^^^

The parameters specific to model CAM_CLAY [:ref:`r7.01.14 <R7.01.14>`] _, as far as modeling A is concerned, are:

* :math:`\mu =276923` Pa, :math:`e_0=2`, :math:`\lambda =0.2`, :math:`\kappa =0.05`, :math:`M=1.02`,, :math:`{P}_{cr}^0=5` kPa, :math:`K_{cam}=0` Pa, :math:`{P}_{trac}=0` Pa.

 **Note:**

 The initial void index :math:`e_0` is associated with the initial porosity by the relationship :math:`e_0=PORO/(1-PORO)`.


Model MCC
^^^^^^^^^^
The parameters specific to the model MCC [:ref:`r7.01.48 <R7.01.48>`] _ are given in the following table concerning the C modeling.

.. list-table::

 *-**Effect**
   - **Appellation**
   - **Definition**
   - **Symbol**
   - **Value**
 * - Isotropic nonlinear elasticity
   - | *BulkModulus*
     | *ShearModulus*
     | *SwellingIndex*
   - | Compressibility module
     | Shear module
     | Elastic nonlinearity index
   - |:math: `K`
     |:math: `\ mu`
     |:math: `\ kappa`
   - | 160 MPa
     | 100 MPa
     | 50
 * - Initial elasticity domain
   - | *initCritPress*
     | *critstateSlope*
     | *TensileYieldStress*
   - | Initial critical pressure
     | Critical state slope
     | Isotropic tensile strength
   - |:math: `p_ {c0} `
     |:math: `M`
     |:math: `\ sigma_0`
   - | 1 MPa
     | 1
     | 10 kPa
 * - Kinematic-isotropic work hardening
   - | *IncoplastIndex*
   - | Plastic incompressibility index
   - |:math: `\ beta`
   - | 50


Boundary conditions and loads
-------------------------------------

An oedometric test consists in imposing on the specimen a variation in vertical load while maintaining zero lateral deformations. It can be drained (the interstitial fluid pressure does not change during the test) or non-drained (the fluid pore pressure changes in the sample). Here we are interested in the drained case. The variation in the effective mean pressure, noted :math:`p'`, is therefore equal to that of the total pressure :math:`p`.

In modeling A, the oedometric test is performed with a stress state initiated at :math:`\boldsymbol{\sigma}=-P_{conso}^0\boldsymbol{I}` with :math:`{P}_{conso}^0=2P_{cr}^{0}-P_{trac}` preconsolidation. The vertical load is controlled with a displacement varying from :math:`{U}_{z}=0` to :math:`{U}_{z}=-0.1` m (which corresponds to a maximum axial compression deformation equal to :math:`10\%`) on the upper face of the cubic sample.

In modeling C, the oedometric test is carried out with an initially zero stress state. The vertical load is controlled by increasing the pressing force :math:`-\sigma_{zz}` to :math:`10` MPa before discharging up to :math:`10` kPa.


 **Note:**

 In modeling A, the operator CREA_CHAMP defines the initial non-zero stress state :math:`\boldsymbol{\sigma}=-P_{conso}^0\boldsymbol{I}` across the entire element at Gauss points.