Analytical solution for ground motion of a half space with a semi-cylindrical canyon and a beeline crack

In earthquake engineering and strong motion seismology, an important issue is to describe and analyse the displacement amplitudes and the relative phases of motions of infrastructures on or nearby the ground surface. In this paper, the influence of a beeline crack on the ground motion of a half space with a semi-cylindrical canyon under anti-plane loading is studied. A novel method combining Green's function and complex functions that can consider very irregular topography is developed for deriving the function of ground motion of the half space. Analytical expressions for the displacement and stress in the half space are obtained. Our results show that the positions and dimensions of the canyon and the beeline crack have a big influence on the ground motion. The crack can amplify the amplitudes of the motion significantly, and its influence cannot be neglected until the distance between the crack and the ground reaches up to 100 times more than the dimension of the crack.