Required Lining Pressure for the Stability of Twin Circular Tunnels in Soils

Abstract

In this study, the stability of twin circular tunnels in purely cohesive and cohesive-frictional soils was evaluated. It is assumed that the internal compressive normal pressure (σi) required to support the tunnels, by means of lining and the anchorage system, becomes uniform (isotropic) on the tunnels' periphery. The interference effect of twin tunnels on the magnitude of σi was examined by employing upper-bound limit analysis in conjunction with finite elements and linear optimization. The internal support pressure (σi) needed to maintain the stability of the tunnels is expressed in the form of a dimensionless parameter (σi/c), which becomes a function of the dimensionless variables S/D, H/D, γD/c, ϕ, and m, where c refers to soil cohesion, S is the clear spacing between the tunnels, H implies tunnel cover, D corresponds to diameter of each tunnel, ϕ is the internal friction angle of soil mass, and m accounts for the rate at which the cohesion increases linearly with depth. The effect of the changes in S/D on the magnitude of σi/c was examined for different combinations of H/D, γD/c, m, and ϕ. The results are presented in the form of nondimensional stability charts that can be readily employed by practicing engineers for the purpose of design.