Modeling A
--------------

.. _Toc93483755:

Characteristics of modeling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The slope is modelled in D_ PLAN.
The slope mesh with foundation is shown in :numref:`fig4-modeleA`.

The mesh composed of quadratic triangular elements is refined
around the intersection between the slope and the foundation and also on the inclined side.

.. figure:: images/100002010000041D0000016AF3417D87D77DD0AB.png
 :name: FIG4-ModelA
    :width: 70%

    **Slope mesh with foundation**

.. _RefImage_100002010000041D0000016AF3417D87D77DD0AB.png:



We use the macro command CALC_STAB_PENTE with METHODE_STAB = 'SRM'
to analyze the stability of the slope at the 3 values of :math:`\lambda`
representing the two rupture mechanisms and the transition state.
The exponential increment refinement method is used
to estimate the safety factor to within 0.01.


.. _Toc93483756:


Tested sizes and results
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


We test the safety factor corresponding to the 3 values of :math:`\lambda`
selected. The reference values are shown in :ref:`Tableau 2<table2_v603507>`.

.. _table2_v603507 :

**Table 2**: FS reference values (Modeling A)

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

    "**Identification**", "**Aster Result**", "**Reference Value**", "**Error**"
    "FS (:math:`\lambda =\mathrm{1,0}`)", "1.46", "1.448", "0.8%"
    "FS (:math:`\lambda =\mathrm{1,5}`)", "2.03", "2.032"," 0.1%"
    "FS (:math:`\lambda =\mathrm{4,0}`)", "2.05", "2.032"," 0.9%"


Summary of results
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The result of the safety factors from the macro command CALC_STAB_PENTE
gives the maximum difference of 0.9% with respect to the reference solution.
This proves the relevance of the result and the applicability of method SRM
implemented in code_aster to the 2D model composed of an inhomogeneous material field.