Synthesis Of Spatially Varying Earthquake Ground Motions And Its Application In Seismic Response Analysis Of Subway Tunnel

Urban rail traffic system is one of the most important infrastructures in China,and a lot of seismic damage investigations indicate that underground structures(e.g.subway tunnel)would subject to severe damage under strong earthquake.Thus,the studies on the seismic characteristics of subway tunnel are the demand of national strategy and of the safe operation and hazard mitigation of lifeline engineering.Subway tunnel is one kind of largescale structures,on which the spatially varying earthquake ground motions(SVEGMs)have a significant influence.The numerical seismic analysis of subway tunnel entails raw and artificial accelerograms and the numerical model of subway tunnel is typically large and contains numerous nodes on its boundary.Therefore,the seismic analysis of large-scale subway tunnel needs a great deal of real and artificial accelerograms with spatial variation,which can be generated by conditional and unconditional simulation,respectively.However,the current simulation methods exhibit low efficiency.Thus,focusing on the improvement of the simulation efficiency,a series of studies were conducted as follow(1)In the aspect of unconditional simulation of SVEGMs,an efficient method was developed based on the singular value decomposition(SVD)of power spectral density(PSD)matrix.Using a numerical example,it was found that compared with Cholesky and eigendecomposition,the values contained in the derived matrices from SVD and root decomposition are more rational.Then,the decomposition efficiency of SVD and that of root decomposition was compared.Results showed that the efficiency of SVD is remarkably higher than that of root decomposition,especially when the simulation points are numerous.By using an example of application,the validness of the SVD-based method for simulating SVEGMs is verified.(2)A novel and efficient method named Hilbert spectral representation method(HSRM)was presented for conditional simulation of spatially correlated earthquake ground motions(SCEGMs),based on the Hilbert-Huang transform(HHT).A known record can be decomposed into a series of intrinsic mode functions(IMFs)and a residual function using HHT.Introducing a set of random phase angles into the IMFs yields the underlying random process.Targeting on each IMF,simulated IMFs for every field point can be derived through a spatial correlation model.Only the correlation at the predominant frequency of each target IMF was considered such that the frequency dependence of the spatial correlation structure was simplified.SCEGMs can then be obtained by superposition of simulated IMFs and the original residual function.The ensemble averages of mean,variance and Hilbert spectra of the simulated motions are equal to the targets.The validness of the proposed method was proven through examples.(3)To assess the error of HSRM and find the optimal type of this method,statistic errors from six types of HSRM were analyzed and compared,considering the fundamental types of HSRM and matrix decomposition methods.Two kinds of errors and the unity formulas for random phase-and random amplitude-based HSRM were introduced.The closed-form solutions of errors of temporal mean,variance and cross-covariance were derived,which was verified by comparing the estimated values with the closed-form ones.The optimal type of HSRM was then found by comparing the closed-form solutions of covariance of the HSRMs.(4)In terms of the proposed conditional and unconditional simulation methods as well as the Suai shield tunnel project,the intersegment opening width responses of shield tunnel under multiple support excitation(MSE)and identical support excitation(ISE)were compared.The generalized response displacement method(GRDM)and a large-scale refined FEM model were then utilized to proceed with the study.Numerous accelerograms on bedrock,including horizontal and vertical components,were generated using the proposed conditional and unconditional methods to realize MSE.Results showed that the MSE can lead to a higher opening width of tunnel in general.The distribution of longitudinal opening width is highly related to the site conditions,earthquake input types and intensities.