3. Modeling A#

3.1. 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 fig4-modeleA.

_images/10000000000002E80000014375F37B521F4DCBED.png

3.2. Tested sizes and results#

The safety factor is tested at the last refinement of the mesh. The results are shown in Tableau 1.

Table 1: FS reference values (Modeling A)

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.

3.3. 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.