Scattering of SH-wave by a shallow U-shaped tunnel

Summary form only given. In general, analytical solution for the scattering problem of SH plane wave by a cavity in half-space primarily focused on the circular structure case. However, the case for U-shaped cavities, which are similar to the cross-section of the tunnels, was seldom mentioned in former references. The analytical solution for U-shaped cavity in elastic half space is gained by the multi-polar coordinate system and conformal mapping method. A scattering wave function satisfying zero-stress condition on horizontal surface is constructed in the complex plane, the problem can be inverted into a set of algebraic equations to solve coefficients of the scattering wave by least square method. The numerical examples of the dynamic stress concentration around U-shaped cavities and ground motion on subsurface U-shaped cavity impacted by SH-wave are given. The influences of the incident wave number, angle and depth are discussed. The research indicates that the shallow U-shaped tunnel has significant impact on wave propagation, and interaction between the U-shaped tunnel and the horizontal surface will complicate characteristics of ground motion, and will bring about great increase on dynamic stress around cavity. In this situation, enough attention should be paid on the interaction between the subsurface cavity and the horizontal surface in the seismic design of ground and underground structures.