A Nodal Discontinuous Galerkin Method for Non-linear Soil Dynamics

We investigate the potential capabilities of the discontinuous Galerkin method (DG-FEM) for non-linear site response analysis. The method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and the capabilities for accurate simulations of strongly non-linear wave phenomena of the finite volume technique. It has been successfully applied to elastic, visco-elastic and anisotropic media. The natural next step is to extend the method to non-linear soil rheologies. We develop a discontinuous Galerkin method (nodal approach) for seismic waves in heterogeneous non-linear 1D media. The method is based on high-order Lagrangian interpolation within elements, upwind fluxes, and a fourth-order Runge-Kutta time scheme. The parallel Iwan model is used to account for the non-linear soil behavior with hysteresis loops based on extended Masing rules. Comparison with different numerical methods shows satisfactory results for some canonical cases, at least for strains lower than 1%. Validation with real kik-Net data is work in progress within the Prenolin benchmark project (see this volume).