中文摘要：

采用波函数展开法，将入射、散射和折射SH波的位移势函数展开成Fourier—Bessel函数的级数形式，根据Graf加法定理，得到了任一局部圆柱坐标系下的波场势函数的表达式。根据隧道衬砌与周围岩体都在界面处应力和位移连续及衬砌内边界完全自由的边界条件，得到了分离式双隧道衬砌对入射平面，SH波的多重散射问题的理论解。通过数值计算分析得出：入射频率、衬砌间距、衬砌与围岩的模量比及衬砌的厚度等是影响衬砌内侧的无量纲位移和动应力集中因子分布的重要因素，为双衬砌或多衬砌的地震评价提供了理论依据。

英文摘要：

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