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


Geometry
---------


.. image:: images/10000000000002800000028D9DF5DADE3F7AC98C.png
    :width: 3.5425in
    :height: 2.9835in


.. _RefImage_10000000000002800000028D9DF5DADE3F7AC98C.png:

height: :math:`h=1m`

width: :math:`l=1m`

thickness: :math:`e=1m`

Point coordinates (in meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," :math:`D`"
    ":math:`x` ", "0. ", "0. ", "0.5", "1."
    ":math:`y` ", "0. ", "1. ", "0.5", "1."
    ":math:`z` ", "0. ", "0. ", "0.5", "0."



Property of materials
----------------------

elastic properties under the keyword ELAS:

:math:`E\mathrm{=}5000.0` in :math:`\mathrm{MPa}`

:math:`\nu \mathrm{=}0.12`

:math:`\alpha \mathrm{=}0.0`

viscoplastic properties under the key VISC_DRUC_PRAG:

:math:`{P}_{\mathit{ref}}\mathrm{=}0.1` in :math:`\mathrm{MPa}`

:math:`A\mathrm{=}1.5\mathrm{.}{10}^{\mathrm{-}12}` in :math:`{s}^{\mathrm{-}1}`

:math:`n\mathrm{=}4.5`

:math:`{p}_{\mathit{pic}}\mathrm{=}0.015`

:math:`{p}_{\mathit{ult}}\mathrm{=}0.028`

:math:`{\alpha }_{0}\mathrm{=}0.065`

:math:`{\alpha }_{\mathit{pic}}\mathrm{=}0.26`

:math:`{\alpha }_{\mathit{ult}}\mathrm{=}0.091`

:math:`{R}_{0}\mathrm{=}1.3021` in :math:`\mathrm{MPa}`

:math:`{R}_{\mathit{pic}}\mathrm{=}6.24808` in :math:`\mathrm{MPa}`

:math:`{R}_{\mathit{ult}}\mathrm{=}1.30808` in :math:`\mathrm{MPa}`

:math:`{\beta }_{0}\mathrm{=}\mathrm{-}0.15`

:math:`{\beta }_{\mathit{pic}}\mathrm{=}0.`

:math:`{\beta }_{\mathit{ult}}\mathrm{=}0.13`


Initial conditions, boundary conditions, and loading
-----------------------------

**Phase 1:**

The sample is brought to a homogeneous state of effective stresses: :math:`{\sigma }_{\mathrm{xx}}^{0}={\sigma }_{\mathrm{yy}}^{0}={\sigma }_{\mathrm{zz}}^{0}`, by imposing the corresponding total pressure on the front, right and upper faces and by imposing zero water pressures everywhere. The movements are blocked on the back (:math:`{u}_{x}=0`), left side (:math:`{u}_{y}=0`) and bottom (:math:`{u}_{z}=0`) faces.

**Phase 2:**

The movements are kept blocked on the rear (:math:`{u}_{x}=0`), left lateral (:math:`{u}_{y}=0`) and lower (:math:`{u}_{z}=0`) faces. On all sides, hydraulic flows are zero.

An imposed displacement is applied on the upper face in order to obtain a deformation :math:`{\varepsilon }_{\mathit{zz}}\mathrm{=}\mathrm{-}\mathrm{0,06}` (counted from the start of phase 2). On the front and right lateral faces, limit conditions under total stress are imposed:

:math:`\sigma \mathrm{.}n={\sigma }_{0}(=8\mathrm{MPa})`