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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 480
    :height: 360


.. _RefImage_Object_1.svg:

height: :math:`h\mathrm{=}\mathrm{10m}`

width: :math:`l\mathrm{=}1m`

.. code-block:: text

    thickness: :math:`e\mathrm{=}1m`


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

:math:`E\mathrm{=}39.5E+9\mathit{Pa}`

:math:`\nu \mathrm{=}\mathrm{0,245}`

:math:`\rho \mathrm{=}2370\mathit{kg}\mathrm{/}{m}^{3}`

:math:`\alpha \mathrm{=}1.E\mathrm{-}5`

For model ENDO_ISOT_BETON and under the BETON_ECRO_LINE keyword:

:math:`{\sigma }_{y}={6.10}^{6}\mathrm{Pa}`; :math:`{E}_{T}=-{6.10}^{5}\mathrm{Pa}`

For model MAZARS:

:math:`k\mathrm{=}0.7`; :math:`{\varepsilon }_{\mathit{d0}}\mathrm{=}1.5{10}^{\mathrm{-}4}`; :math:`{A}_{c}\mathrm{=}1.15`; :math:`{A}_{t}\mathrm{=}1.0`;; :math:`{B}_{c}\mathrm{=}1391.3`; :math:`{B}_{t}\mathrm{=}10000.`

Some characteristics related to the Thermo-Hydraulic problem are summarized in the following table:


+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
|Liquid water            |Density (                                                                                                                                                                             |1.103                                                                                                                   |
+                        + :math:`{\mathrm{kg.m}}^{-3}`                                                                                                                                                         +                                                                                                                        +
|                        |)                                                                                                                                                                                     | 4180 0.6619310-4                                                                                                       |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        | Calorific capacity (:math:`J{\mathrm{kg}}^{-1}{K}^{-1}`) Coefficient of thermal expansion of liquid (:math:`{K}^{-1}`)                                                               |                                                                                                                        |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
|Vapeur                  |Calorific capacity                                                                                                                                                                    |1870                                                                                                                    |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        | Molar mass (:math:`\mathrm{kg}{\mathrm{mole}}^{-1}`)                                                                                                                                 | 28.96 10-3                                                                                                             |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
|Initial state           |Porosity                                                                                                                                                                              |0.149                                                                                                                   |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        | Capillary Pressure (:math:`\mathrm{Pa}`) Gas Pressure (:math:`\mathrm{Pa}`) Initial Liquid Saturation                                                                                | 0. 1.013 E5 0.74                                                                                                       |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
|Constants               |Ideal gas constant                                                                                                                                                                    |8,315                                                                                                                   |
+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+
|Homogenized coefficients|Homogenized density                                                                                                                                                                   |2265                                                                                                                    |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        | Capillary curve Biot Coefficient                                                                                                                                                     |                                                                                                                        |
+                        +                                                                                                                                                                                      + .. image:: images/Object_8.svg                                                                                         +
|                        |                                                                                                                                                                                      |    :width: 480                                                                                                         |
+                        +                                                                                                                                                                                      +    :height: 360                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+                        +                                                                                                                                                                                      +                                                                                                                        +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+                        +                                                                                                                                                                                      + 1                                                                                                                      +
|                        |                                                                                                                                                                                      |                                                                                                                        |
+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+



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

The mechanical boundary conditions are such that displacements perpendicular to each of the facets are prevented. Wetting consists in the application of capillary pressure on the upper face of the structure, which decreases over time.