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

.. _Toc93483755:

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




According to the preliminary study, the extremities of the surface are determined
break and configure ``X1_ MINI = X1_ = X1_ MAXI = 3.0`` and ``X2_ MINI = X2_ MAXI =13.4``
in order to speed up the calculation. Finding the optimal radius with the terminals of
the search space automatically determined by the macro command.

We take advantage of the CALC_STAB_PENTE mesh adaptation feature
to improve the accuracy of the FS. Refinement stops until "NB_RAFF_MAXI = 4"
since beyond the 4th refinement the FS does not change significantly.

At the exit of CALC_STAB_PENTE, we obtained the fracture surface shown in :numref:`fig4-modeleA`.


.. figure:: images/10000000000002E80000014375F37B521F4DCBED.png
 :name: FIG4-ModelA
    :width: 70%

    **Break surface from CALC_STAB_PENTE**

.. _RefImage_10000000000002E80000014375F37B521F4DCBED.png:



.. _Toc93483756:


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

The safety factor is tested at the last refinement of the mesh.
The results are shown in :ref:`Tableau 1<table1_v603006>`.

.. _table1_v603006 :

**Table 1**: FS reference values (Modeling A)

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

    "**NUME_RAFF**", "**Identification**", "**Aster Result**", "**Reference Value**", "**Error**"
    "4", "FS", "1.5469235715723666", "1.534", "0.84%"


The error of CALC_STAB_PENTE is of the same order of magnitude as that of `Plaxis2D` (0.4%)
compared to the result of the literature. This error is explained by:


* The different discretizations of the space of geometric variables
    of the fracture surface.
* The various hypotheses on the shape of the base of the slices.
    In CALC_STAB_PENTE the base is circular. The angle of inclination is measured by
    the derivative of the equation of the circle at the center of the base.
* Numerical error produced when calculating the self-weights of the slices.


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

The FS result from macro command CALC_STAB_PENTE gives the difference of 0.84%
compared to the reference solution. This proves the relevance of the result of
the Bishop method and the associated optimization algorithm in CALC_STAB_PENTE.