Understanding and modelling the whole instability mechanisms of a slope is a fundamental issue from a\ud scientific and technical viewpoint. To date, small strain Lagrangian approaches are mostly used in solid\ud mechanics for modelling the failure stage while Eulerian approaches are common in fluid mechanics for\ud propagation analysis. Consequently, a combination of both approaches allows analysing the stability, the\ud failure and the propagation stages in a unique mathematical framework. To this aim, the paper adopts a finite\ud element method with Lagrangian integration points (FEMLIP) which is currently implemented in the\ud ELLIPSIS code and it has been formerly used for applications in geophysics and civil engineering. This\ud method combines the robustness of an Eulerian mesh with the flexibility of a set of Lagrangian particles which\ud allows accounting for the history of the material. In this paper, FEMLIP is firstly validated referring to\ud benchmarks with analytical solutions and it is then tested for the large deformation drained analysis of a\ud vertical cut in coarse-grained soils. The obtained results are compared with those provided by standard\ud engineering methods such as (1) limit equilibrium method (LEM), (2) standard stress–strain elasto-plastic\ud FEM analysis. As a whole, the comparison underlines that FEMLIP is a reliable method to analyse both the\ud stability and the instability of a vertical cut, so highlighting that it can be confidently used to analyse more\ud complex problems related to natural slopes

A granular soil REV located on the upstream side of the erosion pipe front is modelled numerically, at the grain scale, by coupling the Discrete Element Method (DEM) with the Lattice Boltzmann Method (LBM) for the representation of the solid and fluid phases, respectively. The implementation of DEM follows a standard molecular dynamics approach and the interactions between grains are regulated by unilateral contacts and breakable bonds. A synopsis of the LBM scheme is provided, with focus on the implementation of non-slip conditions for moving boundaries and use of the Multiple Relaxation Time approach for improved numerical stability. The coupling scheme is described along with the criteria for setting the numerical parameters of the two methods. After a "dry" preparation procedure, the numerical REV is tested under fully saturated conditions and increasing pressure difference. Backward erosion is observed and a micromechanical inspection of the granular phase suggests that arching through force chains and the breakage of tensile bonds are prominent resistance and degradation mechanisms, respectively.