Seismic simulation of inelastic soils via frequency-dependent moduli and damping

Although soils are known to exhibit nonlinear behavior even at small strains, evaluations of the response of sedimentary basins to strong seismic motions are almost always based on linear, elastic solutions incorporating frequency-independent damping. The principal reasons for this relate to the robustness of the linear algorithm and the ease with which the required parameters can be determined experimentally in engineering practice. Most often, but not always, attempts are made in these analyses to compensate for the inelastic behavior by adjusting the material parameters for the representative levels of strain by means of an iterative method. However, both the standard iterative method and the direct linear solution without iterations suffer from two important shortcomings. First, they do not account for the effect of high confining pressures on inelastic behavior. However, it is known from experiments with sands subjected to cyclic shearing strains under confining pressures of up to 5 Mpa, that in highly confined samples, the material remains nearly elastic for a larger range of strains than do those samples subjected to a lesser pressure. Second, the amplification analyses disregard the fact that small-amplitude, high-frequency components of deformation involve hysteresis loops with little modulus degradation or damping (i.e., nearly elastic secondary loops). Thus, motions computed at the surface of the basin with the standard method usually exhibit unrealistically low amplitudes at high frequencies. This article presents the results obtained with a series of "true" nonlinear numerical analyses with inelastic (Masing-type) soils and layered profiles subjected to broadband earthquake motions, taking into account the effect of the confining pressure. These show that it is possible to simulate closely the actual inelastic behavior of rate-independent soils by means of linear analyses in which the soil moduli and damping change with frequency. It is emphasized that the variation in the linear model of the material parameters with frequency arises solely because the strains have broad frequency content, and not because the materials exhibit any rate dependence when tested cyclically. The proposed new model is successfully applied to a 1-km-deep model for the Mississippi embayment near Memphis, Tenn. The seismograms computed at the surface not only satisfy causality (which cannot be taken for granted when using frequency-dependent parameters), but their spectra contain the full band of frequencies expected.