Damping formulations for finite difference linear dynamic analyses: Performance and practical recommendations

An in-depth study is presented on some numerical formulations used to reproduce damping of motion in solid continua. The focus is addressed in particular to those formulations that in the finite difference geotechnical code FLAC can be exploited to perform linear analyses. The numerical investigations are performed through a simple 1D model of a homogeneous soil deposit interested by a shear wave motion coming from the bedrock, and a gravity dam model subjected to seismic excitations in presence of dam-water-foundation interaction. The Rayleigh damping method is tested in particular to find an appropriate choice of the control frequency in order to minimize the problems of high-frequency overdamping. The analyses also investigate two other formulations (the local damping and its variant, the combined damping) that present the major advantages in providing a frequency independent action and in needing not significant computational resources. Limits and principal drawbacks of their possible use are highlighted.