Scattering And Seismic Ground Motion Of A Semi-Circular Hill And A Circular Inclusion Subjected By SH Wave In A Right-angle Domain

Earthquake is one of the biggest natural disasters for the human.China is located in the Pacific seismic belt and Eurasian seismic belt,which determines the basic national conditions of our country with frequent and severe earthquake.A mass of energy of Earthquake is accumulated through the plate motion of the interior earth,then the energy is released by seismic waves from the source to the earth surface,which causes severe earthquake disaster.The surface of the earth can be seen as a free surface,seismic wave will be reflected in the earth surface due to the constraint condition of the free surface,which leads to the double stress near the surface.Based on the surface complex landform and the underground space engineering structure,the constraint condition is added additionally,which causes the scattering under the action of seismic wave that results in the dynamic stress concentration with the significant site seismic response.The earth surface can be simplified as elastic solid,and seismic wave can be simplified as elastic wave.According to the relationship between the vibration vector and propagation vector,seismic wave can be divided into P wave and S wave.According to the relationship of the polarization direction and the observation plane,S wave can be divided into SH wave and SV wave.The earth surface is constructed by the rock and soil mainly.There is a significant difference for the tensile strength and compressive strength of the rock,but the shear performance is poor.However,seismic shear component plays an important role in earthquake disaster.To sum up,in this paper,one of the shear component of the seismic wave is simplified into SH wave,and a part of earth surface is simplified into a rectangular angle domain,and a complex landform of the surface is simplified to semi-circular hill,and the underground space engineering structure is simplified into a cylindrical inclusion.The engineering problem of seismic wave field is abstracted as a scientific question of a steady-state SH wave scattering caused by elastic rectangular domain with hill and inclusion.This paper can be divided into three parts:The first part investigates the steady-state SH plane wave scattering and ground motion in an elastic rectangular domain semi-circular hill.By means of the partition conjunction method,the rectangular domain with a semi-circular hill is divided into a rectangular domain and semi-circular domain,and the corresponding Green functions are constructed respectively.By the means of the partition conjunction,the definite integral equation is obtained,and the analytic solution corresponding the mathematical physics definite solution is solved numerically.According to the method of the dimensional analysis,the scaling law and dimensionless numbers are discussed,and the corresponding dimensionless number,dimensionless displacement and dynamic stress concentration factor are obtained.The correctness and precision of the solutions are analyzed by the numerical results,and the convergence and error are evaluated.At last,the influences of wave number,incident angle and the vertical boundary are discussed.The second part studies the steady-state SH plane wave scattering and ground motion in an elastic rectangular domain semi-circular hill and a circular hole.By means of the partition conjunction method,the rectangular domain with a semi-circular hill and circular hole is divided into a rectangular domain with a circular hole and a semi-circular domain,and the corresponding Green functions are constructed respectively.The steady-state scattering of SH waves by the angle elastic domain with the circular hole is solved.With the condition of partition conjunction,the definite integral equation is obtained,and the series solution to the problem is solved numerically.According to the method of dimensional analysis,the scaling law and dimensionless numbers are discussed.The correctness and precision of the solutions are analyzed by the numerical results,and the convergence and error are evaluated.At last,the influence of the size and location of the holes and dynamic stress concentration around the holes are discussed.The third part considers the steady-state SH plane wave scattering and ground motion in an elastic rectangular domain semi-circular hill and a circular inclusion.By means of the partition conjunction method,the rectangular domain with a semi-circular hill and circular inclusion is divided into a rectangular domain with a circular inclusion and a semi-circular domain,and the corresponding Green functions are constructed respectively.The steady-state scattering of SH waves by the angle elastic domain with the circular inclusion is solved.With the condition of partition conjunction,the definite integral equation is obtained,and the series solution to the problem is solved numerically.According to the method of dimensional analysis,the scaling law and dimensionless numbers are discussed.The correctness and precision of the solutions are analyzed by the numerical results,and the convergence and error are evaluated.At last,the influence of the shear modulus ratio and the quality density ratio of the inclusion and dynamic stress concentration around the inclusion are discussed.