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Prediction of the state of roof collapse is a big challenge in tunnel engineering, while the limit analysis theory makes it possible to derive the analytical solutions of the collapse mechanisms. In this work, an exact solution of collapsing shape in shallow underwater tunnel is obtained by using the variation principle and the upper bound theorem based on nonlinear failure criterion. Numerical results under the effect of river water and supporting pressure are derived and discussed. The maximum water depth above the river bottom surface is determined under a given buried depth of shallow cavities and the critical depth of roof collapse is obtained under a constant river depth. In comparison with the previous results, the present solution shows a good agreement with the practical results.
Prediction of the state of roof collapse is a big challenge in tunnel engineering, while the limit analysis theory makes it possible to derive the analytical solutions of the collapse mechanisms. In this work, an exact solution of collapsing shape in shallow underwater tunnel is obtained by using the variation principle and the upper bound theorem based on nonlinear failure criterion. The maximum water depth above the river bottom surface is determined under a given buried depth of shallow cavities and the critical depth of roof collapse is obtained under a constant river depth. In comparison with the previous results, the present solution shows a good agreement with the practical results.