A Visco-Elastic Model with Loading History Dependent Modulus and Damping for Seismic Response Analyses of Soils

It is well established that soils exhibit non-linear behavior even at small strain levels. Yet, most evaluations of the seismic response of soil deposits utilize an equivalent linear methodology, i.e. elastic solutions incorporating constant damping. In such solutions the modulus and damping constants are adjusted by means of an iterative approach to correlate to the maximum strain. In doing so, the smaller amplitude, high-frequency component motions are forced to use the same modulus degradation and damping as that of the lower frequency motions. As a consequence, the computed motions at the surface of a deposit often exhibit unrealistic low amplitudes at high frequencies when the strong input motions are applied. This article presents a modified Kelvin model, in which the modulus and damping are treated as loading history dependent coefficients for each loading-unloading branch. This model works in the program FLAC in a time domain integration procedure. Based on the peak strain level experienced in the previous half cycle, the modulus degradation and viscosity are updated for the current branch. Numerical analyses for a soft soil site are presented and compared with those obtained using the equivalent linear method implemented in the program SHAKE for a recorded motion at Treasure Island. The site response analysis of another soft clay site for a higher design input motion shows that the computed PGA and response spectral could be higher than those obtained from a typical equivalent linear analysis.