3. Modeling A

3.1. Characteristics of modeling

This is a D_ PLAN_HM modeling using quadratic HM- XFEM elements. The bar on which the modeling is performed is divided into 5 QUAD8. The interface is unmeshed and cuts off the central element. So we have 3 HM- XFEM elements and 2 classical HM elements. As indicated in the Figure, the 3 elements XFEM are subdivided into sub-triangles (to perform the Gauss-Legendre integration on either side of the lips of the interface, but these triangular sub-elements are not mesh elements).

Figure 3.1-a : Characteristics of modelling

3.2. Characteristics of the mesh

The mesh consists of 5 quadratic quadratic quadratic cells (QUAD8).

3.3. Tested sizes and results

The results (resolution with STAT_NON_LINE) are summarised in the table below. To test all the nodes of the bar at the same time, we calculate MIN and MAX.

Quantities tested	Reference type	Reference value	Tolerance (%)
PRE1 (Y=4mand y=6m) MIN	“ANALYTIQUE”	8 MPa	0.001
PRE1 (Y=4mand y=6m) MAX	“ANALYTIQUE”	8 MPa	0.001
LAG_FLI (below) MIN	“ANALYTIQUE”	4.07748 kg.m²/s	0.01
LAG_FLS (above) MAX	“ANALYTIQUE”	4.07748 kg.m²/s	0.01

We can see (from the Figure) a clear discontinuity of the first derivative of the pore pressure field in the central element at the level of the cohesive interface. This suggests the good consideration of enrichment in the approximation of the pore pressure field by the Heaviside function. Moreover, the fluid pressure in the interface \({p}_{f}\) is indeed « transmitted » to the porous matrix, on both sides of the cohesive interface.

Figure 3.3-a : Field of pore pressure at t=10s