Frequency- and pressure-dependent dynamic soil properties for seismic analysis of deep sites

Abstract

Most of the analytical techniques for evaluating the response of soil deposits to strong earthquake motions employ numerical methods, initially developed for the solution of linear elastic, small - strain problems. Various attempts have been made to modify these methods to handle nonlinear stress - strain behavior induced by moderate to strong earthquakes. However, questions arise regarding the applicability of commonly used standardized shear modulus degradation and damping curves versus shear strain amplitude. The most widely employed degradation and damping curves, are those originally proposed by Seed & Idriss, 1969. Laboratory experimental data (Laird & Stokoe, 1993) performed on sand samples, subjected to high confining pressures, show that for highly confined materials, both the shear modulus reduction factor [G /G[alpha] and the damping [zeta ] versus shear strain amplitude fall significantly outside the range used in standard practice, overestimating the capacity of soil to dissipate energy. The equivalent linear iterative algorithm also diverges when soil amplification is performed in deep soft soil profiles, due to the assumption of a linear hysteretic damping being independent of frequency. High frequencies associated with small amplitude cycles of vibration have substantially less damping than the predominant frequencies of the layer, but are artificially suppressed when all frequency components of the excitation are assigned the same value of hysteretic damping. This thesis presents a simple four - parameter constitutive soil model, derived from Pestana's (1994) generalized effective stress formulation, which is referred to as MIT-S1. When representing the shear modulus reduction factors and damping coefficients for a granular soil subjected to horizontal shear stresses imposed by vertically propagating shear [SH] waves, the results are found to be in very good agreement with available laboratory experimental data. Simulations for a series of " true" non-linear numerical analyses with inelastic (Masingtype) soils and layered profiles subjected to broadband earthquake motions, taking into account the effect of the confining pressure, are thereafter presented. The actual inelastic behavior is closely simulated by means of equivalent linear analyses, in which the soil moduli and damping are frequency dependent. Using a modified linear iterative analysis with frequency- and depth-dependent moduli and attenuation, a 1-km deep model for the Mississippi embayment near Memphis, Tennessee, is successfully analyzed. 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.