A semi-conservative depth-averaged material point method for fast flow-like landslides and mudflows

We present a two-dimensional semi-conservative variant of the depth-averaged material point method (DAMPM) for modeling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier–Stokes equations with the inclusion of an appropriate bed friction model and material rheology, namely Voellmy and the depth-integrated Bingham viscoplastic stress model, respectively. After assessing the accuracy and performance of the proposed numerical method by means of several idealized benchmarks, we test its behavior in a realistic scenario. •The method accurately reproduces realistic landslides and mudflow run-out.•The method can be effectively applied to real scenarios with complex bed topologies.•A well-balanced DAMPM formulation is presented and tested on different topographies.•The method ensures the conservation of mass and momenta between particles and nodes.