Conditional simulation of non-stationary spatially variable ground motions for long-span bridges across non-uniform site conditions

Abstract

Non-stationary spatially variable ground motions (SVGMs) are commonly modelled as multivariate oscillatory processes based on evolutionary power spectral density (EPSD) functions. The existing conditional simulation algorithms require the known EPSD functions. The EPSD functions are usually assumed to be identical for all locations, which is unreasonable for long-span bridges because variable soil conditions are practically observed at different bridge piers. This paper proposes a conditional simulation algorithm for non-stationary SVGMs in consideration of non-uniform site conditions. The spatial interpolation tool, termed inverse-distance-weighted (IDW) interpolation, is introduced to estimate the EPSD functions at sites without ground motion measurement. Subsequently, the covariance matrix of the random Fourier coefficients of the multivariate oscillatory processes can be calculated. The Kriging estimation is adopted to obtain the unknown random Fourier coefficients, from which the time histories of the non-stationary SVGMs can be conditionally simulated. The proposed conditional simulation algorithm is first validated through a numerical example, in which the EPSD functions of non-uniform sites are represented by a non-stationary Kanai-Tajimi spectrum with different soil parameters. Then, the algorithm is applied to the Jiuzhou Channel Bridge, a navigation channel bridge of the Hong Kong-Zhuhai-Macau Bridge (HZMB), with complex soil and water conditions. Based on the limited in-situ seismic measurement data, the site characteristics in the bridge area are analysed, and the ground motion time histories at all piers can be generated.