A method for generating fully non-stationary and spectrum-compatible ground motion vector processes

Abstract

ABSTRACT:Earthquake ground motion spatial variability can influence significantly the response of certain structures. In order to accurately evaluate probabilistic characteristics of the seismic response of structures, the Monte Carlo simulation technique is still the only universal method of analysis when strong nonlinearities and input uncertainties are involved. Consequently, realizations of ground motion time histories taking into account both time and spatial variability need to be generated.Furthermore, for some design applications, the generated time histories must also satisfy the provision imposed by certain seismic codes stating that they have to be also response-spectrumcompatible. For these purposes, a spectral-representation-based methodology for generating fully non-stationary and spectrum-compatible ground motion vector processes at a number of locations on the ground surface is proposed in this paper. The simulated time histories do not require any iterations on the individual generated sample functions so that Gaussianity and prescribed coherence are suitably preserved. The methodology has also the advantage of providing the fully non-stationary and spectrum-compatible cross-spectral density matrix of the ground motion timehistories that can be used for reliability studies in an analytic stochastic fashion.2

Anti-symmetric mode excitation and seismic response of base-isolated bridges under asynchronous input motion

“…The latter strongly depends on the coherency model used [66]; however, such an examination goes beyond the scope of the present study. Similarly to Saxena, Deodatis, and Shinozuka [45] twenty sample functions of input motion sets were generated for each combination using the method of Cacciola & Deodatis [28], which is based on the spectral representation technique. The effects of asynchronous excitation were investigated with the use of a foundation element model which accounts for soil-structure-interaction by introducing appropriate dynamic impedances for each soil and excitation pair.…”

“…The method proposed by Cacciola & Deodatis [28] is used herein for the generation of m-variate, fully non-stationary, spectrum-compatible ground motion vector processes. This method considers the simulated ground motion vector process ( ) as the superposition of two other processes ( ) = ( ) + ( ) : (a) a fully non-stationary process ( ), with known crossspectral density matrix S L (ω,t) that represents the desired geological and seismological conditions, and (b) a quasi-stationary corrective process ( ) , the cross-spectral density of which S C (ω) has to be determined so as the simulated motions to be spectrum-compatible.…”

“…It is also noted that the use of the particular, and in fact of any other model from the literature, is quite subjective given that the seismotectonic environment of the Lissos bridge does not necessarily match that of the sites wherein the empirical or semi-empirical models were developed [66]. As a result, the use of the above coherency model is solely made for the purposes of comparison with the work of Cacciola & Deodatis [28].…”

“…To overcome these weaknesses, Shields [26] recently presented a method that updates the evolutionary PSD through random functional perturbations. In addition, the method of Cacciola [27] for the simulation of fully non-stationary, spectrum-compatible earthquake motions at a single point, was extended for the purposes of multi-variate simulation by Cacciola & Deodatis [28]. In this method, spectrum compatibility is satisfied through the superposition of an appropriate corrective quasi-stationary process to a "known" fully non-stationary process that represents the seismological properties of the region.…”

Simulation of spatially correlated earthquake ground motions for engineering purposes

“…Deodatis (1996a) proposed an iterative scheme to simulate spatially varying nonstationary, response spectrum compatible ground motions. Cacciola and Deodatis (2011) further gave an approach without iterations. These methods are both based on the spectral representation method of Cholesky decomposition, and can also be extended to be used by the root operation proposed in this study.…”