Semi‐empirical model for site effects on acceleration time histories at soft‐soil sites. Part 1: formulation and development

A criterion is developed for the simulation of realistic artificial ground motion histories at soft‐soil sites, corresponding to a detailed ground motion record at a reference firm‐ground site. A complex transfer function is defined as the Fourier transform of the ground acceleration time history at the soft‐soil site divided by the Fourier transform of the acceleration record at the firm‐ground site. Working with both the real and the imaginary components of the transfer function, and not only with its modulus, serves to keep the statistical information about the wave phases (and, therefore, about the time variation of amplitudes and frequencies) in the algorithm used to generate the artificial records. Samples of these transfer functions, associated with a given pair of soft‐soil and firm‐ground sites, are empirically determined from the corresponding pairs of simultaneous records. Each function included in a sample is represented as the superposition of the transfer functions of the responses of a number of oscillators. This formulation is intended to account for the contributions of trains of waves following different patterns in the vicinity of both sites. The properties of the oscillators play the role of parameters of the transfer functions. They vary from one seismic event to another. Part of the variation is systematic, and can be explained in terms of the influence of ground motion intensity on the effective values of stiffness and damping of the artificial oscillators. Another part has random nature; it reflects the random characteristics of the wave propagation patterns associated with the different events. The semi‐empirical model proposed recognizes both types of variation. The influence of intensity is estimated by means of a conventional one‐dimensional shear wave propagation model. This model is used to derive an intensity‐dependent modification of the values of the empirically determined model parameters in those cases when the firm‐ground earthquake intensity used to determine these parameters differs from that corresponding to the seismic event for which the simulated records are to be obtained. Copyright © 2004 John Wiley & Sons, Ltd.