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


Geometry
---------

     Geometry is a square [:ref:`1mx1m <1mx1m>`]


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

Elastic properties:

:math:`E\mathrm{=}150{10}^{6}\mathit{Pa}`

:math:`\nu \mathrm{=}0.3`

Parameters specific to the GonfElas model:

:math:`{\beta }_{m}\mathrm{=}0.1142`

Reference pressure :math:`A\mathrm{=}1.\mathit{Mpa}`

Hydraulic properties:


.. csv-table::

    "Liquid water", "Density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`)
    Heat at constant pressure (:math:`{\mathit{J.K}}^{\mathrm{-}1}`)
    coefficient of thermal expansion of liquid (:math:`{K}^{\mathrm{-}1}`)
    Compressibility (:math:`\mathit{Pa}\mathrm{-}1`)
    Viscosity (:math:`\mathit{Pa.s}`)", "1.103
    4180
    10-4
    5.10-10
    10-3"
    "Gas", "Molar mass (:math:`\mathit{kg.}{\mathit{Mol}}^{\mathrm{-}1}`)
    Heat at constant pressure (:math:`{\mathit{J.K}}^{\mathrm{-}1}`)
    Viscosity (:math:`\mathit{Pa.s}`)", "0.002
    1000
    9. 10-6"
    "Skeleton", "Heat capacity at constant stress (:math:`{\mathit{J.K}}^{\mathrm{-}1}`)", "1000"
    "Constants", "Ideal gas constant", "8,315"
    "Homogenized coefficients", "Homogenized density (:math:`{\mathit{kg.m}}^{\mathrm{-}3}`)
    Biot coefficient
    Parameters of the Van-Genuchten model
    :math:`N`
    :math:`\mathit{Pr}(\mathit{Mpa})`
    :math:`\mathit{Sr}` ", "2000
    1
    1.61
    16.106
    0"
    "Reference state", "Porosity
    Temperature (:math:`K`)
    Capillary pressure (:math:`\mathit{Pa}`)
    Gas pressure (:math:`\mathit{Pa}`)", "0.366
    303
    0.
    10"



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

At :math:`t=0`:


* :math:`\mathit{Pgaz}=1\mathit{atm}`


* :math:`S=\mathrm{0,5}` (i.e. :math:`\mathit{Pc}=\mathrm{44,7}\mathit{Mpa}` and :math:`{p}_{w}=-44.6\mathit{Mpa}`)


* Total compressive stress equal to -1 atm.


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

All trips are blocked at the edge (:math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0`).

The flows are zero.

The initial saturation is :math:`\text{50 \%}`: we increase the saturation and we follow the evolution of the total stress. By definition, swelling pressure is the stress obtained upon complete restoration.

To do this, a loading of capillary pressure decreasing linearly in :math:`\mathrm{1s}` between :math:`\mathrm{44,7}\mathit{Mpa}` and :math:`\mathrm{-}10\mathit{Mpa}` is imposed on the entire domain.