4. B modeling

4.1. Characteristics of modeling

B modeling is*bidimensional* and*quasistatic*. We use modeling with integration sub-integrated (MODELISATION = “D_ PLAN_HM_SI_DIL “). A second expansion gradient model is used. The constituent parameters of the second gradient model are determined so as not to change the basic solution of the macroscopic problem. In particular, we choose the penalty coefficient small: PENA_LAGR = 1,

The second gradient model makes it possible to treat the phenomena of material instability linked to the loss of ellipticity of the stress-strain tensor, and which result in the localization of the deformations. Here, we are not really trying to regularize the problem (given that there is no material instability), but to implement the second gradient model in a relatively representative test case,

This modeling is also used to test the possibility of carrying out a dynamic analysis under seismic stress with operator DYNA_NON_LINE. To do this, the blocking condition at the bottom of the column of the static step is replaced by the assignment of absorbent border elements. Then the same seismic stress is used in imposed acceleration as in tests WDNP101.

4.2. Characteristics of the mesh

For the D_ PLAN_HM_SI_DIL modeling, each soil layer is represented by a QUAD8 element, i.e. 11 elements in total.

4.3. Tested sizes and results

Unchanged compared to the A modeling for the static part. The maximum acceleration response over a short time interval is also tested in non-regression.

4.4. Comments

These results validate the ability of second expansion gradient modeling to be used for calculations with gravity loading, then with seismic loading.