Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

Abstract

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A₁/A₂, σ_ci1/σ_ci2 and σ_tm1/σ_tm2 and an increase in B₁/B₂, γ₁/γ₂. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σ;_s. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

Keywords

shallow tunnels / three-dimensional collapse / double-layer rock mass / Hoek-Brown failure criterion / variation analysis / upper bound limit analysis

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