The Ground Motion Of Isosceles Trapezium Hill Under SH Wave

In earthquake engineering, one of the main concerns is to study the effects of surface topography on ground motions. The ground motion of a isosceles trapezium hill under SH wave is studied in this paper based on methods of wave function expanding, complex variable function, moving coordinate system and by employing idea of assistant function and conjunction.Firstly, the model can be divided into two domains, where domain I involves an isosceles trapezium hill with a arc top and a semi-circular bottom, domain II is a half space with a nearby semi-circular canyon. Secondly, a standing wave function is constructed in domain I, which satisfies the traction free condition at the trapezium edges. In domain II, a scattering wave function generated by the nearby semi-circular canyon which satisfies the condition of traction free at the horizontal surface is constructed. Therefore, this problem can be reduced another one, which satisfies the condition of displacement and stress continuity at the interfaces between the two boundaries. Thirdly, according to the surface free condition at the upper bottom of isosceles trapezium, a series of infinite algebraic equations, which are solved by Fourier transform after truncating finite items are established. Finally, numerical examples are plotted to show the ground motion. The influences of several physical parameters and geometrical parameters on isosceles trapezium hill and nearby horizontal ground are discussed.