A semi-analytical method for frictional contact analysis between rock mass and concrete linings

Abstract

The rock–lining interface typically exhibits a complex frictional contact behavior. Thus far, there has been no analytic method to analyze the frictional contact problems of arbitrary-shaped tunnels with concrete linings. In this work, we propose a novel analytic method to perform the frictional contact analysis of multiple lined tunnels based on the generalized complex variable method. Using two special composite analytic functions, the mechanical field in a multiply-connected domain can be accurately expressed, and the solution to the contact problem can thus be obtained in a closed mathematical form. In the present theoretical framework, the general contact condition is considered, where the contact mode is described using two complementary functions. The basic linear equations are obtained by satisfying the stress and contact boundary conditions at a finite number of discrete points. Since the contact analysis is a highly nonlinear problem, we propose an iterative scheme to determine the contact states at different positions on the rock–lining interface. Finally, a verification example and parametric investigation are performed to demonstrate the effectiveness and practicability of the proposed method.