Understanding of granular materials under rapid motion is of importance to many phenomena in nature and industrial applications. During landslides and avalanches as well as in mixing and storing processes as in silos granular materials undergo phase transitions from solid to fluid state of matter. At rest, the material is characterised by dilatant elasto-plastic behaviour that is rate independent. For low densities and high shear-rates fluid properties dominate. A continuum mechanical approach for dense granular flow including both aspects is presented. Therefore, frictional stresses, representing the rateindependent aspects, extend the viscous stresses using the generalised visco-plastic constitutive model with Coulomb friction as proposed by Chen and Ling [
]. The differentiation between solid and fluid state of matter results from a comparison between current shear stress and plastic yield criterion. The model is able to represent many experimental results for moderately fast granular flows introducing an artificial viscosity that includes internal friction and depends on the current strain rate. To simulate the flow of granular material that travels large distances the material is described by the Navier-Stokes-equations. This requires the formulation of all balance equations for momentum and mass and the constitutive equations using velocity variables.
The space-time finite element method is applied to discretise the weak form of balance and constitutive equations. This allows the monolithic coupling between the flowing material and any possible surrounding structure [
]. The method is extended by the level set technique [
] to model the motion of the free surface between granular material and air in order to represent landslides and the complete discharge of silos.