The lining length is much larger than the diameter, so the dynamic response of a shallow buried lining subjected to incident plane P waves (Primary waves) and SV waves (Vertical Secondary waves) can be simplified as a two-dimensional plane problem, and the ground surface is approximated as a convex. The potential functions of incident P or SV waves, reflected P and SV waves by the ground surface, scattered waves by the outer side of the circular lining and the convex, and refracted waves in the lining are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion theory of wave functions. The single scattering problem of a circular lining shallow buried in a half space is taken as a multiple scattering problem by the lining and convex based on Graf’s addition theorem. The stresses and displacements at the interface of the lining and adjacent media are considered as continuous and the surfaces of half space and the inner side of the lining are free, and then the theoretical solutions of the complex coefficients of the potential functions are obtained. A circular concrete lining shallow buried in granite half-space is taken as an example, the influence of incident frequency of P or SV waves and the thickness of the lining on DSCF (dynamic stress concentration factors) of the inner side of the lining are studied, and DSCF of the granites are compared when there are lining or not.

Keywords: Dynamic responses; circular lining, incident plane waves, dynamic stress concentration factor

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