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

Abstract

SUMMARYA criterion is developed for the simulation of realistic artiÿcial ground motion histories at soft-soil sites, corresponding to a detailed ground motion record at a reference ÿrm-ground site. A complex transfer function is deÿned 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 ÿrm-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 artiÿcial records. Samples of these transfer functions, associated with a given pair of soft-soil and ÿrm-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 di erent 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 in uence of ground motion intensity on the e ective values of sti ness and damping of the artiÿcial oscillators. Another part has random nature; it re ects the random characteristics of the wave propagation patterns associated with the di erent events. The semiempirical model proposed recognizes both types of variation. The in uence of intensity is estimated by means of a conventional one-dimensional shear wave propagation model. This model is used to derive an intensity-dependent modiÿcation of the values of the empirically determined model parameters in those cases when the ÿrm-ground earthquake intensity used to determine these parameters di ers from that corresponding to the seismic event for which the simulated records are to be obtained.

Semi‐empirical model for site effects on acceleration time histories at soft‐soil sites. Part 2: calibration

“…As expected, the response of a group of oscillators vibrating with those values of damping ratio would be very long. As mentioned in Reference [1], the values obtained for ÿ do not seem to be consistent with those that would be expected for the internal damping in the soil layers or losses due to wave dispersion at the soil-foundation interface; however, the low values that were identiÿed are realistic in terms of the large ampliÿcations observed in the ETFs (although not shown here, the ETF for event 4 at the SCT site shows very pronounced peaks with amplitudes larger than 250, and an identiÿed value of ÿ equal to 0.28%).…”

“…In spite of the short duration of the excitation (Figures 13 and 14), the time and frequency characteristics of the simulated acceleration time histories are realistic representations of their recorded counterparts. Independently of the seismic ampliÿcation phenomenon experienced in the valley, those characteristics are attained here due to the low damping ratio values of the ÿtted oscillators, to the much faster decay of the response of the oscillators with high natural frequency than of those with low natural frequency, and to the identiÿcation of oscillators with similar frequencies and with dynamic participation factors of the same order [1].…”

“…In the ÿrst case, the model parameters used ignore the intensity of the earthquake of interest. In the second case, the model parameters are adjusted in accordance with that intensity, following the procedure proposed in Reference [1].…”

“…This article addresses the assessment of the capability of the Semi-empirical Model for Ground Motion Ampliÿcation (SMGMA) developed in Reference [1] to simulate realistic ground motion time histories that account for site e ects. For this purpose, 'predictions' are made of acceleration time histories recorded at several soft-soil sites in the Valley of Mexico, during a number of earthquakes.…”

Influence of dynamic soil–structure interaction on the nonlinear response and seismic reliability of multistorey systems

“…The algorithms applied to the generation of simulated ground acceleration time histories on soft soil for given values of M w and R are presented in References [2,8,9]. These algorithms have been shown to generate artificial acceleration records with realistic amplitude and frequency evolutionary properties, consistent with the intensity-dependent nonlinear behaviour of the local soil layers [8,9]. The selected soft soil sites are those designated as SCT, CAO and D84.…”