Response of Cylindrical Cavity under Semicircular Canyon Subjected to Antiplane Transverse Waves

For engineering the development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and canyon pipeline projects, surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, the wave scattering problem in an elastic half-space medium containing semicircular depressions and subsurface cylindrical cavity is investigated by using the theoretical method, the wave function expansion method, the complex function method and the mirror image method to solve the control equations in the form of Helmholtz equations satisfying the zero stress boundary conditions and to solve the corresponding displacement functions. Then the unknown coefficients in the set of equations to be solved by the free boundary conditions, combined with the Fourier expansion method. The displacement field is a superposition of the appropriate wave fields. Finally, the effects of the relevant parameters on the surface motion |w1|(w), the dynamic stress concentration factor (DSCF) of the cylindrical cavity and the displacement amplitude of the cylindrical cavity edge |w2| are investigated by frequency and time domain analysis. This study not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but also can provide a basis for seismic design of underground structures.