Evaluating damping schemes for the discontinuum seismic analysis of masonry cross-vaults

Simulating the seismic behavior of unreinforced masonry (URM) structures is challenging due to their susceptibility to large deformations and significant damage. Capturing this highly nonlinear response requires advanced numerical modeling strategies to represent complex interactions such as block separation, debonding, friction, collision, etc. Discontinuum-based modeling strategies, such as the Distinct Element Method (DEM), are increasingly used in this context, given their explicit representation of bond failure and damage progression from minor cracks up to collapse. DEM relies on the explicit time integration scheme of motion equations; hence, the choice of the damping scheme becomes critical to ensuring accurate predictions in time-domain analysis. Typically, mass-proportional Rayleigh damping is used in dynamic analysis, often without its stiffness-proportional component, which reduces the critical timestep, ensuring numerical stability during the analysis. However, using only mass-proportional damping can skew results by overdamping low-frequency responses and underdamping high frequencies. This study implements and validates an alternative damping approach known as Maxwell damping, where multiple spring-dashpot elements are introduced at unit-mortar interfaces within a simplified micro-modeling framework. This work introduces an optimization algorithm to balance the Maxwell elements without heuristic approaches, ensuring uniform damping responses over the frequency range. The effectiveness of Maxwell damping is evaluated by comparing simulation results with experimental shake-table tests on a full-scale cross-vault URM specimen. The outcome of displacements, accelerations, damage evolution, and computational efficiency is compared with mass-proportional Rayleigh and zero-viscous damping models. This study is the first to establish Maxwell damping as an alternative damping relaxation scheme for seismic analysis of complex masonry systems using DEM.