Scattering Of SH-Wave By A Semi-Cylindrical Hill Above A Subsurface Inclusion And Crack

Researching the influence of local irregular topography on ground motion is one of the most important problems in earthquake engineering. Based on the idea of domain division, the complex function and moving coordinate are used to study the scattering of steady-state SH wave by a semi-cylindrical hill above a subsurface inclusion or a crack, and a semi-cylindrical hill adjoins a semi-cylindrical canyon or a semi-cylindrical alluvial valley, as well as the ground motion of the hill. According to idiographic model, the whole solution domain is divided into several parts during the press of solving. One of them is a circle domain, which includes the boundary of the hill and the junction interface. First, the displacement solutions satisfying the boundary conditions are constructed in every domain by complex function and wave function expansion. Second, the method of moving coordinate is used to make the displacement solutions conjoin at the common boundary and satisfiy other boundary conditions. Then the solutions of the problem are reduced to solve several series of infinite linear algebraic equations. The work of this paper can be detailed as follows:1. Scattering of SH wave by a semi-cylindrical hill above a subsurface elastic inclusion or a removable rigid inclusion is determined. According to the domain division idea, the solution domain is divided into two parts. A standing wave function is constructed in part I , which satisfies the condition that traction free at the hill edge and arbitrary at the other part. In domain II, including the junction interface and the subsurface inclusion in half-pace, the scattered wave function satisfying the condition of traction free at the horizontal surface is constructed. Then emploied to the method of moving coordinate, the two solutions are matched up on the junction interface, and satisfying the boundary conditions at the inclusion edge. Then the problem can be reduced to solve a series of infinite linear algebraic equations. The computational results of surface displacement are presented together with the discussion. 2. This paper presents the models and solutions for the scattering of SH wave by a semi-cylindrical hill adjoins a semi-cylindrical canyon or a semi-cylindrical alluvial valley. The idea of domain division is also the key step during the press of solving. At first, the displacement field of the semi-cylindrical hill including a semi-cylindrical canyon under SH wave is provided. Then the scattering of SH wave by a semi-cylindrical hill adjoins a semi-cylindrical alluvial valley is solved based on the idea of domain division. The calculating results are provided respectively, and the variation of surface displacement amplitudes with wave numbers, angle of incidence and the ratio of canyon are discussed.3. A suitable Green function is constructed employed to the idea of domain division. That is the fundermental solution of displacement field for an elastic half space with a semi-cylindrical hill under an out-plane harmonic line source loading at an arbitrary point in matrix.4. The Green function is employed to discuss the influence of subsurface crack on the motion of semi-cylindrical hill under SH wave. Based on the problem of scattering of SH wave by a semi-cylindrical hill, the Green function is used to make a subsurface crack, and then the model of a semi-cylindrical hill above a subsurface crack can be built. The displacement field of semi-cylindrical hill including a subsurface crack under SH wave is given. Finally, the calculating results of the hill motion are plotted to show the effect of wave numbers, angle of incidence and the other parameters on the surface displacement amplitudes.