FEM-BEM Modeling of Dynamic Responses of a Fluid-Filled Lined Tunnel under a Water Hammer

Abstract

A frequency-domain finite element method and boundary element method (FEM-BEM) coupled numerical method is presented to investigate the dynamic responses of a fluid-filled lined tunnel buried in the ground. The fluid is modeled as an inviscid and compressible liquid, the lining is mimicked as an elastic hollow cylinder, and the ground is modeled as an elastic medium. Initially, based on the Laplace transform and Galerkin method, dynamic governing equations of fluid and those of lining are solved. Meanwhile, dynamic governing equations of ground are solved using methods of Laplace transform, and Helmholtz decomposition together with a reciprocal theorem. In the following stage, fluid, lining, and ground are coupled and solved successfully according to conditions of deformation compatibility and force balance on their interfaces. The solutions in the time domain are obtained with the aid of the inverse Laplace transform. Comparisons with previous studies have validated the proposed numerical method. The dynamic water pressure inside the tunnel and the dynamic radial displacement of the lining under the water hammer are obtained. It is concluded that ignoring the effect of ground may overestimate the magnitude of lining radial displacements and inaccurately evaluate the axial distribution of the displacement. When the stiffness ratio of ground to lining exceeds a certain critical level, the displacement dramatically reduces.