Damping considerations for rocking block dynamics using the discrete element method

It is well established that unreinforced masonry (URM) buildings develop damage-forming collapse mechanisms during high-intensity earthquakes, with these mechanisms exhibiting large rocking displacements before collapsing. The Discrete Element Method (DEM) of analysis can realistically capture phenomena that involve large movements of elements, resulting in the technique being ideal for simulating the collapse of URM building elements. Consequently, extensive research using DEM to analyse the seismic response of URM buildings and building components has recently been published. However, the variety of reported damping approaches that have apparently led to DEM results that successfully replicate physical observations underscores the need for consistent guidance related to the assignment of damping factors. The Rayleigh damping distribution model implemented in the DEM software 3DEC was used to study the differences between mass proportional (MP) and stiffness proportional (SP) damping configurations. After reviewing phenomena that need to be damped and previous works where damping was implemented, the capabilities and drawbacks of the time-efficient MP damping configuration were studied and the results compared to simulations with SP damping. When considering numerical simulations that incorporated MP damping and led to results that were seemingly well-matched to experimental tests, it was found that the apparent robustness of decisions pertaining to the adopted input parameters was deceptive in most cases. Consequently, SP damping was recommended for all DEM rocking simulations, even though MP damping could be used with satisfactory accuracy in certain situations discussed herein. A pragmatic relationship between both damping strategies was proposed.