A Nonstationary Probablilistic Model for Pore Pressure Development and Site Response Due to Seismic Excitation

A complete probabilistic analysis for pore pressure development in layered horizontal soil deposits based upon nonstationary random vibration theory is developed in this study. This analysis includes: (1) Modeling the earthquake ground motions; (2) performing a response analysis; and (3) application of a probabilistic pore pressure generation model. By means of this complete analysis, a set of seismic fragility curves can be constructed such that the probability of liquefaction at any depth within a given soil profile can be expressed as a function of the Root Mean Square{RMS) of acceleration and duration of the earthquake excitation. The random vibration method developed herein provides an alternative approach to conventional deterministic equivalent uniform cycle methods for evaluating liquefaction potential.

In modeling the earthquake ground motions, a frequency independent amplitude-modulating function is introduced to describe the nonstationarity in intensity content. The amplitude-modulating function is a simple two-parameter trigonometric function developed in a normalized form for both duration and intensity. Frequency content of the earthquake ground motion is characterized through the normalized Tajimi-Kanai power spectral density function{PSD), which is fully described by a damping parameter and a frequency parameter. Statistics on the parameters describing the amplitude-modulating and PSD functions are evaluated from past earthquake records.

Response analysis is performed assuming the seismic excitation to consist of one dimensional vertically propagating shear waves. Incorporating random vibration theory, the response analysis produces time-dependent power spectral