The Ground Motion Of Orthotropic Isosceles Trapezoidal Convex Terrain Subjected To SH-waves

Earthquake is a natural disaster that endangers people's lives and causes property damage.As a kind of seismic wave,SH wave has made a lot of achievements in the scattering problem of its propagation in the ground.Up to now,the research on the propagation of SH waves in half-spaces with different terrains has still attracted widespread attention from scholars at home and abroad.Rocks and soil layers in nature often have anisotropic mechanical properties.Therefore,it is necessary to study the ground motion caused by SH waves in anisotropic convex terrain.In this paper,an isosceles trapezoidal protrusion close to the actual terrain such as a flat-topped mountain is used as a model,and the displacement response of a medium-waist trapezoidal protrusion in anisotropic medium under the action of SH waves is studied.Utilizing partitioning and fitting ideas,the region is divided into three parts by constructing two semicircular auxiliary boundaries.By using the continuity conditions of displacement and stress at the auxiliary boundary,the expressions of the wave fields such as incident wave,reflected wave,scattered wave and standing wave in each zone are deduced.At the same time,the idea of coordinate mapping is used to develop a wave field solution in anisotropic media.The continuous conditions at the auxiliary boundary will be used to obtain the infinite algebraic equations.The unknown coefficients will be solved by the series expansion and truncation of the finite terms.Expressions for displacement amplitudes of the horizontal surface in the half space and the surface of the isosceles trapezoidal protrusion are also given.Finally,Matlab was used to perform programming calculations to solve the unknown coefficients,and then the displacement response of each point was solved,and the results were analyzed and discussed.The numerical results show that the magnitude of the surface displacement depends on the following parameters: anisotropic medium parameters,slope and height of the trapezoidal mountain,the wave number of the SH wave,and the angle of incidence of the SH wave.The research in this paper also provides a certain theoretical basis for the ground motion problems in actual corresponding engineering.