Analytical Solutions for the Mechanical Responses of Shallow Double‐Arched Tunnel Subjected to Symmetric Loads

Abstract

Double-arched tunnel is a special kind of tunnel structure which is widely adopted for shallow rock tunnels. The internal forces within a double-arched tunnel are difficult to be determined due to its special geometry and complex interactions with surrounding rock masses. This paper presents a set of analytical solutions for determining the internal forces within the lining structure of shallow double-arched tunnel subjected to symmetric external loads. The double-arched tunnel is decomposed into three main parts, i.e., the arch rings, the side walls, and the middle wall. The force method and the elastic foundation beam model are employed for the arch rings and the side walls, respectively, while the middle wall is treated as a cantilever beam fixed at the bottom. Analytical solutions for the internal forces of the three parts are derived separately, which are continuous at the conjunctions of different parts. The derived analytical solutions are verified by comparing with the FEM simulation results. Finally, parametric studies are performed to investigate the influences of burial depth, elastic resistance coefficient, opening angle, and tunnel span on the internal forces based on which some recommendations are provided for the construction and design of the double-arched tunnels. The derived analytical solutions provide fast estimations for the internal forces and deformation of the double-arched lining structures, which will be a useful tool for design optimization.

Research on Construction Sequences and Construction Methods of the Small Clear-Distance, Double-Arch Tunnel under an Asymmetrical Load

“…Li et al [6] studied the effect of different distances as well as the surface slope on the surrounding rock pressure of an asymmetrical load on a small clear-distance tunnel. Yang et al [7] proposed an analytical solution to determine the internal forces of a shallow-buried, double-continuous arch tunnel support structure under symmetric loading. Combining the force method with the unbalanced force transformation method, Hu et al [8] proposed an internal force calculation method for Double-O-tube lining.…”

Numerical Simulation of Ultra-Shallow Buried Large-Span Double-Arch Tunnel Excavated under an Expressway

“…Hu et al [18] combined the unbalanced force transfer method with the force method to give an analytical solution for the internal force of a segmental prefabricated double-arch tunnel lining. Yang et al [19] proposed a set of analytical solutions to determine the internal forces of shallow buried double-arch tunnel lining structures under symmetric external loads. Lyu et al [20,21] proposed a new analytical method based on limit equilibrium analysis to calculate the tunnel pressure caused by the surrounding rock of layered double tunnels, and applied it to the pressure analysis of the metro twin-tunnels in Chongqing and Fuzhou, China.…”