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


Presentation
------------

In this test case, we study the thermo-hydro-mechanical behavior of a saturated porous medium constituted by a single fluid: water in its liquid phase. In *Code_Aster*, this is a THM model. The associated law of fluid behavior is of type LIQU_SATU.


Geometry
---------

We consider a cube with a side of 1 m centered on the center of the :math:`(-\mathrm{0,5}\le x\le \mathrm{0,5};-\mathrm{0,5}\le y\le \mathrm{0,5};-\mathrm{0,5}\le z\le \mathrm{0,5};)` axis.


.. image:: images/10010F2C00001C0000001C3388288620E469299A.svg
    :width: 277
    :height: 290


.. _RefImage_10010F2C00001C0000001C3388288620E469299A.svg:


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

.. csv-table::

    "solid", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Drained Young's module :math:`E(\mathrm{Pa})`
    Poisson's ratio
    Coefficient of thermal expansion of solid :math:`({K}^{-1})` "," :math:`2.\times {10}^{3}`
    :math:`225.\times {10}^{6}`
    :math:`0.`
    :math:`8.\times {10}^{-6}`"
    "Fluid", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Heat at constant pressure :math:`({\mathrm{J.K}}^{-1})`
    Coefficient of thermal expansion of liquid :math:`({K}^{-1})`
    Derivative of the conductivity of the fluid with respect to temperature", ":math:`{10}^{3}`
    :math:`2.85\times {10}^{6}`
    :math:`{10}^{-4}`
    :math:`0.`"
    "Thermal", "Homogenized conductivity :math:`({\mathrm{W.K}}^{-1}{m}^{-1})`
    Derivative of conductivity homogenized with respect to temperature", ":math:`1.7`
    :math:`0.`"
    "Homogenization coefficients", "Coefficient of :math:`\mathrm{Biot}`
    Porosity", ":math:`{10}^{-12}`
    :math:`0.4`"
    "Homogenized coefficients", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Constant stress heat :math:`({\mathrm{J.K}}^{-1})` "," :math:`1.6\times {10}^{3}`
    :math:`2.85\times {10}^{6}`"



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


* Full item:

fluid pressure :math:`\mathrm{PRE1}=500.0\mathrm{Pa}` (no flow or variation in the mass of water)


* Underside:

trips :math:`{u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0\mathrm{m.}`


* Upper side:

Displacement :math:`{u}_{z}={10}^{-3}m`


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

The displacement fields, pressure, temperature are initially all zero, the reference temperature is set to :math:`{T}_{0}\mathrm{=}273°K`.