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


Geometry
---------

An axisymmetric rock mass is considered. It is separated into two parts by a vertical discontinuity :math:`[\mathrm{EF}]`.


.. image:: images/10000000000003620000034B4AF2642C88736111.jpg
    :width: 3.5311in
    :height: 3.4374in


.. _RefImage_10000000000003620000034B4AF2642C88736111.jpg:

Point coordinates (in meters):


.. csv-table::

    "", ":math:`x` "," :math:`y` ", "", ":math:`x` "," :math:`y`"
    ":math:`A` ", "0", "0"," 0", ":math:`D` ", "0", "1"
    ":math:`B` ", "1", "0"," 0", ":math:`E` "," ", "0.35", "0"
    ":math:`C` ", "1", "1"," :math:`F` "," ", "0.35", "1"



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


* Properties of intersticial fluid (liquid water):


.. csv-table::

    "Density", ":math:`1000{\mathrm{kg.m}}^{-3}`"
    "Viscosity", ":math:`{1.10}^{-3}\mathrm{Pa.s}`"
    "Compressibility", ":math:`{3.10}^{9}\mathrm{Pa}`"



* Properties of the massif:

The massif is elastic and has the following properties:


.. csv-table::

    "Young's module", ":math:`200\mathrm{MPa}`"
    "Poisson's Ratio", ":math:`\mathrm{0,25}`"
    "Porosity", ":math:`\mathrm{0,4055}`"
    "Intrinsic permeability", ":math:`\mathrm{1,688}{.10}^{-17}{m}^{2}`"



* Properties of the discontinuity:

The mechanical behavior of the discontinuity is given by Bandis's law. Its expression is detailed in the reference material [:ref:`R7.02.15 <R7.02.15>`].

The material parameters used are:


.. csv-table::

    "Initial normal stiffness :math:`{K}_{\text{ni}}` "," :math:`{1.10}^{9}{\mathrm{Pa.m}}^{-1}`"
    "Asymptotic opening :math:`{U}_{\mathrm{max}}` "," :math:`\mathrm{5,0}\mathrm{mm}`"
    "Coefficient :math:`\gamma` "," :math:`2`"
    "Tangential stiffness :math:`{K}_{\text{t}}` "," :math:`{1.10}^{12}{\mathrm{Pa.m}}^{-1}`"



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

The initial conditions are as follows:


* initial opening of the joint :math:`{\varepsilon }_{0}`: :math:`\mathrm{1,95}{.10}^{-5}m`


* initial hydraulic pressure in the massif: :math:`\mathrm{0,0}\mathrm{MPa}`


* initial radial and orthoradial compression stress: :math:`\mathrm{12,3}\mathrm{MPa}`


Boundary conditions
----------------------

The mechanical and hydraulic boundary conditions are as follows:


* On :math:`[\mathrm{AB}]`: imposed hydraulic pressure of :math:`\mathrm{1,0}\mathrm{MPa}`


* On :math:`[\mathrm{BC}]`: imposed mechanical pressure of :math:`\mathrm{12,3}\mathrm{MPa}` and zero hydraulic flow


* On :math:`[\mathrm{CD}]`: movements blocked in :math:`y` and zero hydraulic flow


* On :math:`[\mathrm{DA}]`: movements blocked in :math:`x` and zero hydraulic flow