Applications of Maxwell Damping for Time Domain Seismic Analyses

Abstract

Rayleigh damping is widely used in time-domain seismic site response and soil-structure interaction analyses. The stiffness-proportional part in Rayleigh damping is important to reduce high-frequency noises physically and numerically. The main drawback of Rayleigh damping is that the allowable numerical time step is drastically reduced in time-domain analyses, leading to a significantly higher calculation cost. For example, the calculation time using stiffness-proportional Rayleigh damping can be up to several weeks or even longer and can thus be less practical for routine applications to large models with many elements and/or with materials in high contrast of moduli. Maxwell damping is an alternative scheme that employs multiple Maxwell components in parallel to the constitutive model. With a proper choice of parameters for the Maxwell components, the damping ratio can be made approximately constant over a target frequency range. Maxwell damping is a promising tool for overcoming the two essential shortcomings of Rayleigh damping, namely, numerical inefficiency for large models and over-damping out of the frequency range but under-damping in the range. General guidelines on the application of Maxwell damping in geotechnical earthquake engineering, including parameter calibration, are presented in this paper. Several application examples of Maxwell damping in time domain, including seismic site response and soil-structure interaction analyses are illustrated. Numerical efficiency by Maxwell damping is discussed and compared with that by Rayleigh damping.