GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL

The Green’s function of an elastic half space including a semi-circular lining hill while a bearing out-of-plane harmonic line source load on a horizontal interface has been considered, using the method of complex functions. The solution of Green’s function is given by the idea of ‘conjunction’. Firstly, we divide the solution domain into two domains. The one is a cylindrical lining, and the second one is an elastic half space with the semi-circular canyon. Secondly, we construct the scattering wave of semi-circular canyon satisfying the stress free boundary condition on the horizontal interface and the standing wave of cylindrical lining satisfying the stress free boundary condition on the semi-circular hill. Finally, we conjoin the two domains to satisfy the continuous condition of displacement and stress around the common ‘conjunction’ boundary and the stress free boundary condition of a circular lining inside boundary, and a series of infinite algebraic equations can be obtained to settle this problem. In the end, the computing expressions of the ground motion in the horizontal surface near elastic lining are given and discussed.