Implementation and validation of the direct method for effective simulation of dynamic dam-foundation interaction

For the seismic analysis of dams, the spatial variation of the ground motion around the underlying canyon, generated by Dynamic Soil-Structure Interaction (DSSI), may introduce differential displacements, possibly detrimental for the stability of high dams. The Direct Method (DM) is the most general procedure to numerically simulate the local spatial variation of the ground motion, when performing both linear and nonlinear seismic DSSI analyses. This method relies on the availability of special Free-Field Boundaries (FFBs), which shall input the seismic wave train and simultaneously absorb outgoing waves at the artificial boundary of the adopted FEM model. However, FFBs are seldom implemented by default in most commercial FEM codes. An original implementation of the DM in Comsol Multiphysics is here presented and validated against available analytical solutions. The present work demonstrates that rigorous DSSI analyses can be correctly performed in the above-mentioned mechanical context, even by using standard FEM programs, once the FFBs are correctly implemented and handled.