For the foundation

slope and backfill supported by retaining wall

which consist of the over-consolidation clay

dense sand or non-associated plasticity material

the appearance of strain localization during the gradual process of the failure and instability of these geotechnical structures will lead to the change of the type of governing partial differential equation. Furthermore

this change results in non-unique and the mesh-dependence of solutions obtained by standard finite element method (FEM). In order to overcome these difficulties

on the basis of the strong discontinuity analysis (SDA)

the embedded discontinuity finite element model is employed to investigate the failure processes of foundation

slope and backfill. Numerical examples show that this model can effectively simulate the post-failure processes of geotechnical structures and improve the objectivity of response with respect to the mesh size. The results also show that

this method can be taken as a beneficial supplement to traditional limit equilibrium method in stability analysis of slope and foundation.