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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 516
    :height: 265


.. _RefImage_Object_1.svg:

Point coordinates (in meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C`"
    ":math:`x` ", "0. ", "0. ", "0.5"
    ":math:`y` ", "0. ", "1. ", "0.5"
    ":math:`z` ", "0. ", "0. ", "0.5"



Property of materials
----------------------

:math:`E\mathrm{=}\mathrm{22,4}{10}^{3}\mathit{kPa}`

:math:`\nu \mathrm{=}\mathrm{0,3}`

Biot coefficient :math:`b\mathrm{=}1`

Water is supposed to be incompressible: :math:`\text{UN\_SUR\_K}\mathrm{=}0`


.. csv-table::

    "Settings CJS1: :math:`\beta \mathrm{=}\mathrm{-}\mathrm{0,03}` "," :math:`\gamma \mathrm{=}\mathrm{0,82}` "," :math:`{R}_{m}\mathrm{=}\mathrm{0,289}` "," :math:`{P}_{a}\mathrm{=}\mathrm{-}100\mathit{kPa}`"



Initial conditions, boundary conditions, and loading
-----------------------------


Pure mechanical modeling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Phase 1:**

The sample is brought to a homogeneous state:

.. image:: images/Object_2.svg
    :width: 516
    :height: 265


.. _RefImage_Object_2.svg:

, by imposing the corresponding confinement pressure on the front, right lateral and upper faces. The movements are blocked on the back sides (

.. image:: images/Object_3.svg
    :width: 516
    :height: 265


.. _RefImage_Object_3.svg:

), left lateral (

.. image:: images/Object_4.svg
    :width: 516
    :height: 265


.. _RefImage_Object_4.svg:

) and lower (

.. image:: images/Object_5.svg
    :width: 516
    :height: 265


.. _RefImage_Object_5.svg:

).

**Phase 2:**

We keep the movements blocked on the rear faces (

.. image:: images/Object_6.svg
    :width: 516
    :height: 265


.. _RefImage_Object_6.svg:

), left lateral (

.. image:: images/Object_7.svg
    :width: 516
    :height: 265


.. _RefImage_Object_7.svg:

) and lower (

.. image:: images/Object_8.svg
    :width: 516
    :height: 265


.. _RefImage_Object_8.svg:

). An imposed displacement is applied on the upper face:

.. image:: images/Object_9.svg
    :width: 516
    :height: 265


.. _RefImage_Object_9.svg:

, so as to obtain a deformation

.. image:: images/Object_10.svg
    :width: 516
    :height: 265


.. _RefImage_Object_10.svg:

(counted from the start of phase 2). On the front and right lateral faces, the displacements are respectively imposed.

.. image:: images/Object_11.svg
    :width: 516
    :height: 265


.. _RefImage_Object_11.svg:

and

.. image:: images/Object_12.svg
    :width: 516
    :height: 265


.. _RefImage_Object_12.svg:

, so as to have zero volume deformation for the sample, that is to say finally that we impose

.. image:: images/Object_13.svg
    :width: 516
    :height: 265


.. _RefImage_Object_13.svg:

. This is the way to reproduce the behavior of the solid phase during an undrained triaxial test.


Modeling coupled with hydraulics
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Phase 1:**

The sample is brought to a homogeneous state of effective constraints:

.. image:: images/Object_14.svg
    :width: 516
    :height: 265


.. _RefImage_Object_14.svg:

, by imposing the corresponding total pressure on the front, right lateral and upper faces and by imposing zero water pressures everywhere. The movements are blocked on the back sides (

.. image:: images/Object_15.svg
    :width: 516
    :height: 265


.. _RefImage_Object_15.svg:

), left lateral (

.. image:: images/Object_16.svg
    :width: 516
    :height: 265


.. _RefImage_Object_16.svg:

) and lower (

.. image:: images/Object_17.svg
    :width: 516
    :height: 265


.. _RefImage_Object_17.svg:

).

**Phase 2:**

We keep the movements blocked on the rear faces (

.. image:: images/Object_18.svg
    :width: 516
    :height: 265


.. _RefImage_Object_18.svg:

), left lateral (

.. image:: images/Object_19.svg
    :width: 516
    :height: 265


.. _RefImage_Object_19.svg:

) and lower (

.. image:: images/Object_20.svg
    :width: 516
    :height: 265


.. _RefImage_Object_20.svg:

).

On all sides, hydraulic flows are zero.

An imposed displacement is applied to the upper face in order to obtain a deformation.

.. image:: images/Object_21.svg
    :width: 516
    :height: 265


.. _RefImage_Object_21.svg:

(counted from the start of phase 2). On the front and right lateral faces, limit conditions under total stress are imposed:


.. image:: images/Object_22.svg
    :width: 516
    :height: 265


.. _RefImage_Object_22.svg: