Ground Motion Synthesis On Local Topography Site By FK-SEM

The source,path and local site conditions are the three main factors affecting ground motion.Among them,the influence of site conditions on ground motion is quite complex.The analysis of observation data shows that the soil conditions of the site and the local sharp undulating terrain such as solitary hill,basin and river valley will significantly affect the characteristics of surface ground motion,which has been widely concerned and studied in earthquake engineering.Since the 1970 s,a large number of numerical methods such as finite element,finite difference,boundary element,boundary integral and discrete wave number method have been used to calculate the seismic response of complex sites on uniform half space.In the1980 s,a two-step method was formed to estimate the ground motion on the surface of buried crystalline basement and then use it as the input of seismic response analysis of shallow structures,which is still used today.Almost at the same time,the method of synthesizing seismic field by establishing the integrated model of source propagation path site conditions has attracted extensive attention.In order to express the influence of local site conditions on ground motion in detail,most of the analysis is based on threedimensional or two-dimensional numerical calculation,using finite element,finite difference or spectral element method(SEM),and the calculation model is extremely large.The size of discrete grid determines the reliability of numerical calculation in high frequency band.In order to ensure the accuracy of synthetic ground motion in high frequency band,the grid should be as small as tens or tens of meters.The detailed discrete grid leads to the contradiction between huge amount of computing and computing resources,which makes it difficult for the computing resources of general research and design units to complete integrated computing.According to the current understanding of regional crustal structure,the accuracy of deep part is lower than that of the shallow part.Therefore,with the surface of the buried crystalline substrate as the boundary,the broadband three-component ground motion field is used as the input for the numerical calculation of the shallow model.The calculation in two steps,deep and shallow,is a solution to the above problem.The main work of this paper is as follows:(1)On the basis of elaborating the basic principles of the method based on Green’s function in frequency-wavenumber domain(FK method)and the spectral element method(SEM),by setting absorption boundaries on the surface of the buried crystalline substrate,the connection between the two models of the deep part and the shallow part is realized.For the deep crustal structure,a large-scale overall model including the source,propagation path and simplified site conditions is established,and the FK method is used for modeling and calculation.For shallow structures including local protruding topography,a small-scale fine model is established,and SEM modeling is used for calculation.The framework of FK-SEM two-step method is initially established.(2)Taking the 2013 Lushan earthquake as an example,the observation records of four strong-motion stations in the study area(102.63°E-103.15°E,30.08°N-30.53°N)were compared with the ground motions synthesized by FK-SEM,which demonstrates the feasibility of the method.The research results show that the strong seismic segment of the synthetic ground motion in this paper lasts about 10 seconds,and the PGV is relatively large.The response spectrum of the synthetic ground motion in the effective frequency band is close to the strong earthquake record.The distribution trend of the Fourier spectrum of the synthetic ground motion is basically the same as that of the strong earthquake.The recorded Fourier spectra are consistent,and the spectral amplitudes are relatively close.It can express the difference in amplitude and waveform between the FN component and the FP component.The stability of this method(FK-SEM)is verified by comparing the results of this paper with those of FK method and the combination of FK method and finite element method(FK-FEM).The results show that the calculation process of this method is stable,and there is no low-frequency drift instability and highfrequency oscillation instability.The response spectrum of the synthesis result of the FK method is relatively close to the synthesis result in this paper,and the amplitude of the FK-FEM is slightly larger.The distribution trends of strong seismic recording and FK method of Fourier amplitude spectrum are basically consistent with the synthesis results of this paper.The spectral amplitude is relatively close,and the method in this paper is closer to strong earthquake records in the part below 2.0 Hz.The duration of the strong earthquake segment of the other two methods is larger.(3)A three-dimensional topographic model of the study area was established,and the FK-SEM was used to synthesize two orthogonal horizontal component ground motions,which verified its ability to express local prominent topography.Comparing the synthetic results with strong earthquake records,the waveforms of the velocity time history and PGV of the two are similar,and the duration of strong earthquake section is slightly shorter.At more than 1.0 second,the amplitude of response spectrum is relatively close,and individual stations are overestimated due to the influence of terrain and elevation.The comparison of the synthesis results between the method in this paper and the FK method and the FK-FEM shows that the PGV of the FK method is close to that of this method,and the PGV of the FK-FEM is slightly larger.The duration of the strong earthquake segment by the FK method is comparable to the synthetic results in this paper.The amplitude of the response spectrum is relatively close in the short-period section,and the amplitude of the response spectrum in the long-period section above 1.0 second is closer to the method in this paper.And the amplitude of the FK-FEM is slightly larger.The results in this paper are similar to the distribution of the energy of the strong earthquake records and the FK method in the frequency domain.The response spectrum amplitudes of the results above 1.0 s are in better agreement with the actual records,and the results of the FK-FEM are slightly larger than those of this paper.Comparing the results of the FK-SEM and the horizontal ground model considering the local protruding terrain site,the synthetic result considering the local protruding terrain in the period of more than 0.5 second is better than that of the horizontal ground.The local protruding terrain mainly affects the spectral value in the 0.5 second period,which is consistent with the law that the terrain effect mainly affects the middle and high frequency bands.In the frequency band below 1.0 Hz,the results in this paper are closer to strong earthquake records.