Ground motion of right-angle domain with a semi-circular cylindrical hill subjected to plane SH waves

Steady state responses in a right-angle domain with a semi-circular cylindrical hill to plane SH waves are analyzed, and the ground motion caused by hill scattering is discussed by using the Green function method and the integral equation method. The right-angle domain with a semi-circular hill is divided into two domains: Domain Ⅰ is right-angle space and Domain Ⅱ is semi-circular space. Green functions for the two domains are established, respectively: the image method is employed in Domain Ⅰ, and the Graf addition formula and wave function expansion method are employed in Domain Ⅱ. The conjunction condition is introduced between Domain Ⅰ and Domain Ⅱ. Distributed forces along conjunctive interface are adopted to formulate displacement and stress fields in the two domains which are continuous on the interface, and an integral equation for unknown forces is presented. Distribution of stress on the conjunctive interface and displacement amplitude on the horizontal surface are numerically solved to present the effects of incident wave number, angle and distance between hill and vertical bound of the right-angle domain on SH wave scattering of hill.