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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 341
    :height: 283


.. _RefImage_Object_1.svg:

height: :math:`h=\mathrm{1m}`

width: :math:`l=1m`

.. code-block:: text

    thickness: :math:`e=1m`

    For C and D models, a 2D geometry will also be distinguished from :math:`\mathrm{1m}\mathrm{\times }\mathrm{1m}`.


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


* 3D general case (transverse isotropy)

Settings specific to ELAS_ISTR:

:math:`{\%}_{L}=9\mathit{GPa}` :math:`{\%}_{N}=18\mathit{GPa}` :math:`{N}_{L}=0.24` :math:`{N}_{L}=0.48` :math:`{G}_{L}=8.88\mathrm{GPa}`

The transverse anisotropy coordinate system is defined by the nautical angles :math:`\alpha =30°` and :math:`\beta =-60°`.


* 2D general case (orthotropy)

Settings specific to ELAS_ORTH:

For the C and D models, which are D_ PLAN, a variant will be made by considering that the 2D plane corresponds to the anisotropy plane. In this case:

:math:`{\%}_{L}=9\mathit{GPa}` :math:`{\%}_{T}=18\mathit{GPa}` and :math:`{\%}_{N}=9\mathit{GPa}`

:math:`{N}_{L}=0.48` :math:`{N}_{L}=0.24` :math:`{{\rm N}}_{\%}=0.48` :math:`{G}_{L}=8.88\mathrm{GPa}`

The transverse anisotropy coordinate system is defined by the nautical angle :math:`\alpha =40°`.


* Parameters related to THM (here without impact since the pressure is kept zero):

:math:`\text{PORO}=0.14`, the Biot coefficients :math:`{B}_{L}=0.3` and :math:`{B}_{N}=0.6`.


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

On the edge :math:`x=\mathrm{1m}`: application of lockdown :math:`P=\mathrm{25MPa}`

On the edge plane :math:`z=\mathrm{1m}`: application of confinement :math:`P=\mathrm{29MPa}` (3D case)

On the plane edge :math:`y=\mathrm{1m}`: application of a movement of :math:`\mathrm{0,01}m` following a ramp of :math:`\mathrm{1s}`.

Symmetry conditions are applied to the other edges and the pressure is maintained at zero everywhere (total drainage).


Initial conditions
--------------------

The initial constraints are anisotropic (in the global plane), i.e.:

:math:`{\sigma }_{\mathrm{xx}}=-\mathrm{25MPa}`; :math:`{\sigma }_{\mathrm{yy}}=-\mathrm{22MPa}`; :math:`{\sigma }_{\mathrm{zz}}=-\mathrm{29MPa}`