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


Geometry
---------

A cube with a side of :math:`1m`.


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

*Elastic properties:*

:math:`E+150.{10}^{6}\mathrm{Pa}`

:math:`\nu =0.3`

*Model specific settings**Infelas: *


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


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

*Hydraulic properties*:


.. csv-table::

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


Bibliographical references
---------------------------


1. Gérard, P., Charlier R., Barnichon, J.D., Su, J.D., Su, K. Shao, Su, K. Shao, J-F, Duveau, G., Giot, R., Chavant, C. Collin, F. "Numerical modeling of coupled mechanics and gas transfer" Journal of Coupled Mechanics and Gas Transfer" Journal of Theoretical and Applied Mechanics, Journal of Theoretical and Applied Mechanics, Journal of Theoretical and Applied Mechanics, Sofia, 2008, vol. 38, No. 1, pp. 101-120.