This study examines the response of soil profiles with nonlinear properties to several hundred synthetic seismograms, generated to represent rock ground motions from magnitude 6.4 and 7.0 scenario earthquakes. Two shear-wave velocity models (developed to represent Class CD and D sites with water table at 3 m) are tested. The computed ratios of peak ground acceleration (PGA) between the surface of the soil profile and the bedrock decreases with increasing PGA values. The transition from amplification to deamplification occurs at about 0.2–0.3 g. The spectral acceleration (SA) ratios, defined as the ratios of SA between the surface of the soil profile and the input, vary with the natural period of the oscillators. At short periods less than 0.3 sec, the behavior of the SA ratios is similar to the PGA ratios: amplification for lower input SA and deamplification for higher input SA level. At longer periods, the influence of the input SA level on SA ratio decreases, and deamplification is seldom observed.

We define the mean trends of these calculations as rock motion modification curves (RMM curves). The use of these curves is as follows: a ground-motion relation on rock is multiplied by the RMM curve for that ground motion to obtain the expected ground-motion relation at the soil surface. This procedure is applied to six sets of empirical ground-motion relations. A majority of the empirical ground-motion relations are consistent with the RMM curves. In the best case, the comparisons indicate that the empirical soil site PGA and SA ground-motion relations are very close to the predicted curves at all epicentral distances. For both PGA and SA, the differences between the empirical and predicted curves are within one standard deviation of the empirical curves. It is quite encouraging that this physical model for soil behavior predicts the average characteristics of the surface motion, given the highly scattered nature of the data set.

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