The lining lengths are much larger than the diameters, and so the dynamic responses of two shallow buried linings subjected to incident plane P and SV waves can be simplified as a two-dimensional plane problem. 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 linings and the convex, and refracted waves in the linings are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion theory of wave functions. The stresses and displacements at the interface of the linings and adjacent media are considered as continuous and ground surface and the inner side of the linings are free, and then the theoretical solutions are obtained about the complex coefficients of the potential functions. Two circular concrete linings shallow buried in granite half-space are taken as an example, and the influence of normalized incident frequencies of P or SV waves and center distance of the two linings on DSCF (dynamic stress concentration factors) of the inner side of the linings are studied.

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

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