Abstract To reveal the surrounding rock displacement distribution of shield tunnels under different displacement boundary conditions, it simplified it as the second basic problem of elastic semi-infinite plane with a circular hole, and the expression of two complex variable functions [φ(z)] and [ψ(z)] as well as an analytical general formula of the displacement component (u, v) at any point on a rock mass were deduced by combining the elastic complex function theory and five different displacement convergence modes around a tunnel. The displacement distribution rules of surrounding rock under different buried depths and displacement boundary conditions were discussed. Based on the theoretical formula, surface settlement of a certain project was predicted and a comparison between the predicted data and measured data was made. The results show that: when the tunnel radius r0 is 4.0 m, the Poisso ratio μ is 0.3, and the tunnel depth h is 2r0 to 6r0, then the maximum relative surface settlement Δvmax ranges from 0.33 to 1.94, and the influence area induced by surface settlement ranges from 28.7 m to 124.1 m; the buried depth has little influence on the maximum relative horizontal displacement Δumax, which is located near the central horizontal line of a tunnel; in five different modes of displacement convergences, the solution results of two displacement boundary conditions are consistent with the measured surface settlements, and therefore these two theoretical solutions can be used as a foundation of tunnel design and construction.
Abstract：
To reveal the surrounding rock displacement distribution of shield tunnels under different displacement boundary conditions, it simplified it as the second basic problem of elastic semi-infinite plane with a circular hole, and the expression of two complex variable functions [φ(z)] and [ψ(z)] as well as an analytical general formula of the displacement component (u, v) at any point on a rock mass were deduced by combining the elastic complex function theory and five different displacement convergence modes around a tunnel. The displacement distribution rules of surrounding rock under different buried depths and displacement boundary conditions were discussed. Based on the theoretical formula, surface settlement of a certain project was predicted and a comparison between the predicted data and measured data was made. The results show that: when the tunnel radius r0 is 4.0 m, the Poisso ratio μ is 0.3, and the tunnel depth h is 2r0 to 6r0, then the maximum relative surface settlement Δvmax ranges from 0.33 to 1.94, and the influence area induced by surface settlement ranges from 28.7 m to 124.1 m; the buried depth has little influence on the maximum relative horizontal displacement Δumax, which is located near the central horizontal line of a tunnel; in five different modes of displacement convergences, the solution results of two displacement boundary conditions are consistent with the measured surface settlements, and therefore these two theoretical solutions can be used as a foundation of tunnel design and construction.
2016, Vol. 53 