The task of this work is to study the scattering of SH waves by homogeneous lining structures in unbounded inhomogeneous medium. The shear modulus is assumed to be a function of coordinates (x,y). A two-dimensional scattering model is established. Based on the complex function theory, the expressions of wave field in the lining medium are derived. Meanwhile, a displacement auxiliary function and a pair of mapping functions are introduced to obtain the wave field expressions in inhomogeneous media. The unknown coefficients in the expression can be solved by boundary conditions on the lining structure. The stress concentration phenomenon on the lining structure is discussed in numerical examples. The distributions of dynamic stress concentration factor on the inner and outer boundary are analyzed under different influencing factors. Finally, it is found that the inhomogeneous parameters and reference wave numbers of the medium have an obvious influence on the distribution of dynamic stress concentration factor.

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.