Response of semicircular canyons and movable cylindrical cavities to SH
waves in anisotropic half-space geology
Abstract
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, the surface motion and
cavity edge motion have been topics of concern in ground vibration
problems. In this paper, wave scattering problems in elastic half-space
anisotropic media containing semicircular canyons and underground
movable cylindrical cavities are studied by using theoretical methods,
wave function expansion method, complex function method and mirror image
method to solve the control equations in the form of Helmholtz equations
satisfying zero stress boundary conditions, and the corresponding
displacement functions are solved. The origin singularity problem in the
scattered wave problem in anisotropic half-space medium using the mirror
method is improved. Then the unknown coefficients in the set of
equations to be solved by free boundary conditions combined with the
Fourier expansion method. The displacement field is a superposition of
appropriate wave fields. Finally, the effects of the relevant parameters
on the surface motion| w 1|(
w), the dynamic stress concentration factor (DSCF) and the
displacement amplitude| w 2|
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.