Interaction Between Trapezoidal Convex Terrain And Shallow Buried Inclusion Under SH-wave

The problem of scattering of elastic waves is a key issue in earthquake engineering research.Different topographic features will have different effects on the distribution of surface displacement amplitude under the action of seismic waves,and the existence of underground structures will also affect the propagation of SH waves.Therefore,the theoretical methods to study the effects of local terrain and subsurface structures on ground motion have been widely concerned by scholars at home and abroad.The problem of the influence of local topography and subsurface structures on elastic wave propagation is addressed to provide a theoretical basis for the response of subsurface structures near dams to seismic waves and the influence of surface displacement amplitudes in actual projects.Based on the wave function expansion method and the complex variable function method,this paper investigates the interaction between the trapezoidal raised terrain and the shallow buried inclusions under the action of SH waves by using the region-matching techniques.Firstly,the problem model is divided into four regions.Among them,region 1 is an elastic half-space containing cylindrical holes and semicircular canyon,region 2 is a sector domain containing two circular arcs,region 3 is a semicircular domain with the diameter of the upper base of the trapezoidal bulge,and region 4 is a cylindrical inclusions.The scattered wave expressions satisfying the stress freedom at the surface of the half-space and the semicircular canyon are constructed in region 1 by using the wave function expansion method with the complex variable function method,while the standing wave field expressions satisfying the stress freedom at the upper bottom edge of the trapezoidal projection and the two waists are constructed in regions 2and 3,and the analytical expressions of the stress components corresponding to the wave fields are obtained based on the intrinsic relations of the medium.Then the coordinates are shifted and unified in the complex plane,and the boundary conditions such as displacement continuity and stress continuity at each boundary are used to establish an infinite algebraic system of equations by means of Fourier expansion in the complex domain,and the unknown coefficients in the scattered and standing waves are solved by truncating the finite term solution equations through programming with sufficient accuracy and convergence.The correctness of the method is demonstrated by degenerating and comparing with existing studies.Finally,specific arithmetic examples are given,and the effects of geometric and physical parameters such as the radius and burial depth of cylindrical inclusions,the slope and height of trapezoidal convex terrain,the wave number,angle of incidence,and the wave number ratio inside and outside the inclusions on ground shaking are discussed through numerical analysis.The results show that the increase of the slope and the decrease of the height of the convex terrain will amplify the surface displacement amplitude,the variation of the radius of the inclusion and its wave number ratio of inside to outside around a specific value will lead to a tendency that the caused surface displacement amplitude will first fall and then rise or rise and then fall,and other parameters will also have some influence on the ground vibration.