Reference problem
---------------------

.. _Toc93483749:

Geometry
~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: images/10000000000002EE0000015BE07BD7BCF17FD564.png
 :name: fig1-geom-ssnp007
    :width: 60%

    **Slope geometry with low layer**


.. _RefImage_10000000000002EE0000015BE07BD7BCF17FD564.png:


We are studying a slope built on the foundation at height :math:`H`,
in which there is a weak layer that develops in parallel with the
slope at the beginning and flattens around the foot just before exiting the slope.
Since the cohesion of the soil depends on the height of the slope, we choose :math:`H=3m`
without any influence on the score of the FS.
The geometry of the slope is shown in :numref:`fig1-geom-ssnp007`.



.. _Toc93483751:


Material properties
~~~~~~~~~~~~~~~~~~~~~~


Material properties are shown in :ref:`Tableau 1<table1_v603007>`.

.. _table1_v603007 :

**Table 1**: Properties of slope materials

.. csv-table::
 :name: tab-1
    :header-rows: 1
    :widths: auto
    :align: center

    "", "**Slope**", "**Low layer**"
    "Density :math:`\rho` (kg/m³)", "3000", ""
    "Cohesion force :math:`c` (kPa)", ":math:`0.25\rho \mathit{gH}` "," :math:`0.25\lambda \rho gH`"
    "Expansion angle :math:`\psi` (deg)", "0", ""
    "Friction angle :math:`\varphi` (deg)", "0", ""


Stability is analyzed with the Mohr-Coulomb failure criterion.


.. _Toc93483752:


Boundary conditions and loads
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Stability under the effect of gravity alone is analyzed.

The following mechanical loads are therefore applied to the model:

* Gravity with :math:`g=\mathrm{9,81}m/{s}^{2}`