Anti-planar response due to cylindrical cavity with linear crack under semicircular canyon

Surface depressions and subsurface defects have been a trendy topic in ground shaking problems. In the case of canyon tunnels and canyon pipeline projects, surface movement and cavity edge stress concentrations have been a concern in the design, and the effects of cracks need to be considered if the underground structure contains cracks. In this paper, the wave scattering problem in an elastic half-space medium containing semicircular depression(canyon), cylindrical cavity and crack is investigated by using theoretical methods, the wave function expansion method, the complex function method and the mirror image method to solve the control equation in the form of Helmholtz equation satisfying the zero-stress boundary condition, and the corresponding displace-ment function is solved. The Green function method and the crack "cutting" technique are used to construct cracks. The unknown coefficients in the system of equations to be determined are solved by free boundary conditions combined with Fourier expansion. The displacement field is a superposition of appropriate wave fields. Finally, the effects of the relevant parameters on ground motion |w| (w), dynamic stress intensity factor (DSIF) of the tip of crack and the dynamic stress concentration factor (DSCF)of the cylindrical cavity were investigated by frequency and time domain analysis. This study not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but also provides a basis for the seismic design of underground structures.