关键词: Laplace变换, 弹性衬砌, 动力响应, 集中荷载, 饱和土

Abstract:

Considering the interaction between soil and lining in a deeply embedded circular tunnel, the non-axisymmetrical dynamic response of a saturated soil-lining coupled system under step concentrated load was investigated. Based on the Biot’s theory and elasticity, using the Laplace transform and Fourier series, analytical expressions of displacements, stresses and pore water pressure of the saturated soil-lining system subject to step concentrated load were obtained in the Laplace transform domain under the boundary conditions of the lining and the continuity conditions on the interface between the saturated soil and lining. Numerical solutions of the dynamic responses of the saturated soil and lining system were obtained with a Crump method of the inverse Laplace transform. The influences of mechanical and geometric parameters of the soil and lining on the dynamic response of the system were analyzed. It was shown that dynamic response of the soil in a distance from the tunnel center more than 5 times of the radius was much less than that of the soil in the vicinity of tunnel. Influences of stiffness and thickness on displacements and stresses of the soil were significant, while the influences on pore water pressure were trivial. Furthermore, compressibility of pore water had stronger influence on the amplitude of the stress than that of the displacement of the soil.

Key words: elastic lining ,  concentrated load ,  dynamic response ,  Laplace transform, saturated soil