Finite element modeling of snow-pack lying on a slope, considering snow as isotropic compressible viscoplastic media

Abstract

A simple extension of the von Mises plasticity is proposed in which the equivalent stress is defined as a function of deviatoric and hydrostatic stresses. Non-linearity is accounted by extending NortonHoff equation for incompressible material to snow, a porous material. For developing a multi-axial constitutive equation a complementary viscoplastic potential, expressed as a function of the equivalent stress tensor, is introduced. With this potential the strain-rate tensor is obtained. Coefficients of the constitutive equation were computed with the help of experimental data. This constitutive equation is utilized to investigate the stress and velocity distribution in a snow-pack with a weak layer on a uniform slope. This weak layer has a super weak zone, responsible for initiating avalanches. Self-weight of snow is the only external force being considered. The finite-element code, based upon a plane-strain idealization, is used. Linear constitutive equation is used to give an initial guess as Newton-Raphson method has been employed for solving the system of non-linear equations. For non-linear case convergence criterion is implemented for both unknown velocities and residual forces. The effects of super-weak zone, thickness of weak layer and length of snow slab on shear stresses and deformation rates have been studied.