Semi-analytical Method for Dynamic Respones Calculation of Tunnel Buried in Foundation with Unsaturated Super-stratum

Abstract:

This paper presents an analytical method to calculate the dynamic response of tunnel embedded in saturated foundation with an unsaturated super-stratum. The vibration characteristics of foundation soil and tunnel lining were simulated by unsaturated wave equation and shell vibration equation respectively. Based on the method of separating variables and Helmholtz vector decomposition theorem， the expression of total wave field can be obtained， which includes cylindrical wave and plane wave. The system dynamic response was solved by the wave function transformation method， based on the boundary assumptions of foundation surface， soil interface and tunnel soil interface. The proposed method was verified by comparing with the existing models. Finally， based on the proposed method， the dynamic response of system was analyzed by a cases study. The results show that the displacement response of the ground is affected by the overlying unsaturated soil layer. The critical velocity is less affected by the saturation of overlying soil and mainly affected by the characteristics of soil that tunnel located.