Significance of Rayleigh damping in nonlinear numerical seismic analysis of tunnels

Abstract

There is no convincing approach to determine the soil viscous damping in the time-history dynamic analysis of tunnels due to the forms and inherent limitations of viscous damping. The users determine viscous damping with a certain degree of arbitrariness that increases the uncertainties of numerical predictions, which has not previously been considered and quantified. Therefore, in this study, the commonly used Rayleigh formulation is considered and its impacts on the nonlinear seismic behavior of tunnels combined with the Mohr-Coulomb failure criterion are investigated through a two-dimensional finite difference code. Potential problems of the improper use of damping parameters are demonstrated through a simple case. After that, four approaches of modeling damping proposed in previous studies are compared to account for the input motions, the intensities, and the target damping ratios. Numerical results reveal that the target damping ratios and the damping determination approaches have an important influence on the tunnel response analyses. The additional Rayleigh damping leads to a reduction of the time step. It is shown that the difference caused by various damping determination approaches generally decreases with the target damping ratio (ξtar) decreases or the intensity of input motion (PGA) increases.