Abstract:Adopting the method of wave function expansion, the potential functions of incident, scattering and infracting SH waves are expanded to the form of series of Fourier - Bessel functions, and the expressions of potential functions in each local cylindrical coordinate are obtained with help of the Graf＇s addition theorem. The theoretical solutions of multiple scattering of SH waves by two separated tunnel linings are also obtained, according to the conditions that the stresses and displacements are continuous at the boundary of the linings and their adjacent rocks, and the inner sides of the linings are free. The digital calculation result indicats that the incident frequencies, the distances between the linings, the ratio of linings＇moduli to adjacent rocks, and the linings＇thicknesses are important factors which influence distributions of the normalized displacements and dynamic stress concentration factors on the inner sides of the two linings. The results provide some theoretical basis for earthquake evaluation of two or more linings
