Mixed strain-displacement finite elements for landslide and avalanche release prediction

Determination of the initial detaching volume is one of the major challenges in snow avalanche and debris flow forecast. Soil liquefaction due to loss of cohesion results in landslides, whereas quasi-brittle failure triggers the release of snow avalanches. Induced strain softening is the main cause of failure in both cases. In the recent decades, the finite element method has established as the preferred choice for stability analyses, thanks to the possibility of describing complex geometries, different materials and diversified boundary conditions. However, standard displacement-based formulations lack the necessary accuracy and/or stability in problems involving material nonlinearities and strain localization, yielding mesh biased and/or pressure locked solutions. Previous research, conducted by Cervera et al. (2009), showed that the use of the pressure/displacement mixed formulation, aimed to tackle incompressibility in elasticity and plasticity, alleviates many of those numerical issues. The objective of this contribution is to present a novel strain/displacement mixed finite element. In order to deal with equal order interpolations, Variational Multiscale Stabilization is introduced. Regarding the constitutive model, local plasticity models as Von Mises and Drucker-Prager with nonlinear softening are used. The formulation benefits from some crucial advantages. On the one hand, such mixed finite element formulation provides an enhanced rate of convergence in the strain (and stress) field with respect to displacement/pressure and standard irreducible FEM. On the other hand, the method succeeds in addressing both incompressible and compressible plasticity problems. Moreover, this method allows the prediction of strain concentration bands neither suffering from mesh dependence nor requiring the introduction of auxiliary tracking techniques. The performance of the proposed formulation is assessed in a set of 2D and 3D numerical benchmarks using low order finite elements (P1P1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms).