A versatile, nonstationary stochastic ground-motion model accounting for the time variation of both intensity and frequency content typical of real earthquake ground motions is formulated and validated. An extension of the Thomson's spectrum estimation method is used to adaptively estimate the evolutionary power spectral density (PSD) function of the target ground acceleration record. The parameters of this continuous-time, analytical, stochastic earthquake model are determined by least-square fitting the analytical evolutionary PSD function of the model to the target evolutionary PSD function estimated. As application examples, the proposed model is applied to two actual earthquake records. In each case, model validation is obtained by comparing the second-order statistics of several traditional ground-motion parameters and the probabilistic linear-elastic response spectra simulated using the earthquake model with their deterministic counterparts characterizing the target record.

Fully nonstationary analytical earthquake ground-motion model

https://web.hku.hk/~junyang/pdf/Yang_Li_Lin_SDEE.pdf

A simple approach to integration of acceleration data for dynamic soil–structure interaction analysis

Accurate and highly efficient algorithms for structural stationary/non-stationary random responses

Seismic spatial effects for long-span bridges, using the pseudo excitation method

Structural responses to arbitrarily coherent stationary random excitations

This paper develops a theory to compute the statistical properties for the response of a surface-mounted pipeline to seismic excitations. Making the assumptions that the pipeline behaves like an infinitely long Euler-Bernoulli beam on evenly spaced supports, that the seismic motion is statistically stationary in time but nonhomogeneous in space, and that the seismic inputs are fed into the pipeline system through the supports, solutions are obtained for the spectral densities of the structural response. The theory developed is aplicable to any spectral distributions.

Multiply Supported Pipeline under Seismic Wave Excitations

A model for earthquake ground motion is developed using principles of geophysics and stochastics in a sequence of two papers. In the first paper, the earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is modeled as a concentrated seismic moment located within one of the layers. The partial differential equations for the seismic motion in each layer are solved using a Fourier finite-Hankel transformation approach, and solutions in terms of state vectors of displacements and forces are converted to wave vectors composed of up-going and down-going waves. Transmission and reflection matrices are obtained for each layer, for each layer-to-layer interface, and for the free ground-surface boundary to characterize their roles in transmitting and reflecting a wave motion. The use of these matrices allows the numerical calculation to be channeled in the directions of wave propagation, resulting in better numerical accuracy. An example is included for illustration.

Earthquake Ground Motion Modeling. I: Deterministic Point Source

The pulse shape function obtained in a companion paper is incorporated in the development of a stochastic earthquake model. It is assumed that seismic ground motion is caused by shear dislocation that propagates along a line. This line source is further discretized into point sources at equal intervals. The times at which seismic signals are activated are assumed to be Poisson events with a time‐varying average occurrence rate λ(t) per unit time. This is equivalent to assuming an average speed λ(t) for the propagation of shear dislocation. The strengths of seismic signals emitted from discretized point sources are assumed to be independent and identically distributed random variables. A generalized version of the random‐pulse‐train theory is used to compute the mean and auto‐correlation functions of the ground motion at one site, and the cross‐correlation function at two sites. The auto‐correlation and cross‐correlation functions can then be converted to the evolutionary spectral density and evolutionary ...

Earthquake Ground Motion Modeling. II: Stochastic Line Source

An earthquake model is developed, in which the earth is idealized as horizontally stratified layers and the seismic source as propagating dislocation along a line. The line source is further discretized into point sources at equal intervals, and the times at which seismic signals are emitted from the source points are assumed to be Poisson events. The strengths of individual sources are assumed to be independent and identically distributed random variables. A generalized version of the random-pulse-train theory is then used to compute the mean and covariance functions of the ground motion at one site, and the cross-covariance function at two sites. The covariance and cross-covariance functions are converted to the evolutionary spectral density and cross-evolutionary density of the ground motion, which are useful in the computation of the statistics of structural response to earthquake excitations.. Numerical examples are given for illustration.

Y. K. Lin

Papers

Multiply Supported Pipeline under Seismic Wave Excitations

Earthquake Ground Motion Modeling. I: Deterministic Point Source

Earthquake Ground Motion Modeling. II: Stochastic Line Source

Stochastic Earthquake Modeling with Discretized Line Source