The Study On Analytical Solutions Of Transient Responses Of Arc-shaped Canyon And Basin By Incident SH Waves

The topographical site of earthquake ground motion is an important issue in the fields of seismology and engineering,and is also a hot topic in scientific research nowadays.When the strong ground motion is brilliantly recorded in California during 1940,which is the first in the human history,works has been going on since.According to the actual observations and earthquake damage investigations,the arc-shaped canyon and the arc-shaped sedimentary basin are selected as the research objects,and the highly destructive SH waves are selected as the incident waves in this paper.At present,the analytical solutions to scattering of seismic waves are presented in the frequency domain and valid only in narrow frequency band,from which cannot be obtained the reliable transient solution.To solve this problem,the author derives the broad-band frequency-domain analytical solution to the scattering of SH waves by arc-shaped canyon.In the paper,the author obtains the broad-band frequency-response function for different spatial locations by this broad-band frequency-domain analytical solution used,and further,by Fourier transform,presents the analytical solution to the transient response of canyon topography incident by SH waves.Based on the above,in this paper,it is studied that the fundamental characteristics of transient response of canyon under the inputs of impulses and real ground motions,with the emphasis of probing into the amplifying effect of the canyon on ground motion.The effect is defined by the ratio between the parameters,such as the peak and the spectral acceleration,etc.,of seismic responses around the canyon,to those of seismic responses of free field,i.e.the elastic half space.It is demonstrated that,under the impulse input,the displacement of the canyon corner was amplified distinctly,which is related to the impulse duration and the incident angle.As to the input of real ground motion,the spectral acceleration at the corner on the wave-meeting side of canyon is significantly amplified,with the maximum spectral ratio being as high as 2.0,which is related to the canyon geometries and the incident angle.In addition,the numerical solution based on the four-node quadrilateral isoparametric element and the viscoelastic artificial boundary method are verified,and its accuracy is verified.Analytical solution to scattering problem of seismic waves is an important tool to study amplification effects induced by local site,topography,and basin,on ground motion.For the scattering of SH waves by arc-shaped sedimentary basin,most analytical solutions are presented in frequency domain,and cannot be applied directly to probe the amplification effects of such irregularities on the peaks and response spectra of ground motion.Based on the stationary broad-band analytical solution for the dynamic response of arc-shaped sedimentary basin by incident SH waves,it is presented in this paper that the transient analytical solution for the antiplane dynamic response of arc-shaped sedimentary basin by Fourier transform.From the transient solution,they are studied which include the amplification effects of sedimentary basin on peak ground acceleration,velocity,displacement,and spectral accelerations of different natural periods by incident EI Centro waves.The results reveal that the width,depth,and shear velocity of sediment layer significantly influence the amplification effects of basin on ground motion,and the maximum value of spectral ratio of ground-motion response spectrum exceeds 2.0.Furthermore,as to large basin with the width to 10 km,it imposes significant influence on long-period ground motion.Therefore,the aseismic design of longperiod structures located in large basins,such as high-rise building,large-scale fluid reservoir,and long-span bridge,should take into account of the effects of basin on the design ground motion parameters.Finally,in this paper the author summarizes the whole research,provides a way to study the amplification effect of arc-shaped canyon and sedimentary basin,gives some analysis results,and provides some practical value and basis for the quantitative evaluation of ground motion and the application of response spectrum method for seismic fortification.At the same time,the content to be further carried out in this paper is explained,and the possible development direction of the research on the effect of local topography on ground motion,including the canyon and basin of incident SH waves,is prospected.