Benchmark solution
----------------------


Calculation method
~~~~~~~~~~~~~~~~~~~~~~~

The reference solution comes from the test case of the American software `Plaxis2D` [:ref:`1 <ref-1-v603006>`]
which calculates the stability factor using the SRM method (also available in
CALC_STAB_PENTE, cf. [:ref:`V6.03.507 <V6.03.507>`] and [:ref:`U4.84.47 <U4.84.47>`]).

The `Plaxis2D` test case itself refers to the result provided by Verruijt via
Bishop's method simplified [:ref:`2 <ref-2-v603006>`].


Benchmark result
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The result of `Plaxis2D` is shown in :numref:`fig2-Plaxis`. In method SRM,
the FS is incremented up to the discrepancy of the nonlinear finite element calculation.
Approaching the true FS value, the absolute displacement at the peak of the slope
tends towards infinity, which implies the emergence of a plasticized zone forming the
breaking surface that crosses the entire slope. The FS result is equal to 1.54 with
the error tolerance 0.001.

.. figure:: images/10000000000005B5000002D7EB9DBE788446A121.jpg
 :name: FIG2-plaxis
    :width: 70%

    **Plaxis2D result - FS plot as a function of absolute displacement at the peak of the slope**

.. _RefImage_10000000000005B5000002D7EB9DBE788446A121.jpg:


The :numref:`fig3-Verruijt` shows the result from the simplified Bishop method. We define in advance
a grid of the possible centers of the sliding circles in order to find the one
that minimizes FS. The FS obtained is equal to 1.534.

.. figure:: images/100000000000039A000002F28EF80BCF2D29DBEC.jpg
 :name: FIG3-lock
    :width: 40%

    **Verruijt - FS result and the critical area**

.. _refImage_100000000000039a000002f28 EF80BCF2D29DBEC .jpg: