Surface Motion Of Slope And Half Space With Cavity By SH Wave

China is a country with frequent earthquakes.The investigation of seismic hazard shows that the special topography will be seriously damaged,the mechanism of earthquake has drawn great attention.However,the existing theoretical methods can not explain its seismic mechanism of some specific topography.Therefore,it is of great significance in the study of seismic wave propagation for theory and engineering application.The scattering of seismic waves by topography will amplify ground motion in some local areas,so that earthquake disasters will be highlighted in some specific areas.During the earthquake,the disturbance of wave field potential makes the scattering problem of seismic waves in specific topography more difficult.In the scattering of seismic waves by 3-sided wedge space,a slope and half space with a quadrangular cavity,it is difficult to obtain an analytical solution because of the irregularity of the boundary.In view of the above three problems,this article has carried on the research,the main content and the innovation are as follows:(1)According to the geometry model,a specific virtual arc is adopted to divide the 3-sided wedge to two subregions with corresponding local and global coordinate system.In the local coordinate system,the wave function expansion method is used to obtain the wave fields in each subdomain respectively: the solution of SH wave in the 2-sided wedge space is used as the free field.The outward scattered wave field generated by the virtual circular arc surface vibration and the free field together constitute the total displacement field of the outer region;the wave field in the inner region is the standing wave series with undetermined coefficients.Using the Graf addition theorem,the expression of the inner wave field is converted into the integral coordinate system,and the undetermined coefficients are solved by satisfying the displacement continuity and stress equilibrium conditions along the ficticious arc.Thus the analytic expressions of the wave fields within each subregion in the 3-sided wedge space are obtained,and the high and low frequency surface motion of the 3-sided wedge space with different geometries are analyzed.(2)In the investigation of the surface motion of slope by SH waves,the virtual arc and wave function expansion methods are used to obtain the series expression of displacement fields in each subregion.The undetermined coefficients in the solution function are obtained through continuous conditions along the virtual arc.The exact geometric relation between the local coordinate and the global coordinate system and the Fourier expansion are used to achieve the coordinate transformation.Such that the analytical solution are obtained and the surface motion of the slopes with different topographies are analyzed.(3)For the scattering of SH waves in a half space with a quadrangular cavity,the displacement fields of the three subdomains are solved via the virtual circle and the wave function expansion method.The undetermined coefficients in the series expression of the wave field are obtained through the displacement continuity and stress equilibrium conditions along the virtual circle.The coordinate transformation is achieved by exact geometric relation between the local coordinate and global coordinate system and the Fourier expansion.The undetermined coefficient equation group is solved by the least square method.Due to the flexibility of this model,quadrilateral voids can be transformed into rectangular holes and cracks in different directions by different parameters.Finally,the scattering of seismic waves by specific rectangular,vertical and inclined cracks are analyzed.