Numerical modelling of the propagation of fast landslides using the finite element method

This paper proposes a two-dimensional (2D) model for the analysis of the propagation of fast landslides involving a fluidized material such as debris and mud flows, flowslides and avalanching flows. The model is based on the Navier–Stokes depth-integrated equations. To incorporate the effect of steep slopes and centrifugal forces due to the high velocities characterizing the flowslides and the bed curvature, a curvilinear system of reference is used. The corresponding equations of motion are complemented by depth-averaged constitutive equations and bed friction laws. The resulting set of differential equations are solved using the two-step Taylor–Galerkin algorithm. This algorithm has been used by the authors to solve hydraulic and dam-break problems using the finite element method. Owing to the importance of the source term compared to the advection component, the proposed algorithm follows a splitting scheme using a fourth-order Runge–Kutta method for integrating the friction and slope components. The performance of the overall approach has been checked in a number of examples. The analysis of the results provides insights into the key elements of the model and shows the adequacy of the method to solve real problems where merging and splitting of the flow occur