Response of Semicircular Canyons and Movable Cylindrical Cavities to SH Waves in Anisotropic Half-space Geology

Abstract

The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, we investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wave field in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space medium. Then, combining the free boundary conditions with a Fourier series expansion method we solve for the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency and time domain analysis, we investigate the effects of the relevant parameters on the surface motion| w1|( w), the dynamic stress concentration factor (DSCF) and the displacement amplitude| w2|. The results show that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but can also provide a basis for seismic design of underground structures.