Three-dimensional limit analysis of blow-out failure modes of shallow shield tunnels

Blow-out failure of shallow tunnels may occur during shield construction process. To study failure rules, based on the upper bound limit analysis of rigid blocks, three-dimensional expressions for the critical blow-out face pressures are derived using the existing failure modes, and the results are optimized by means of the nonlinear programming model. The relations between the critical blow-out face pressures and influence factors such as formation parameters and buried depth are studied. Meanwhile, the failure modes under different conditions are also explored by use of the program. The results show that both the buried depth and the internal friction angle have great effects on the critical pressures and failure modes. The failure regions mainly range from the surroundings to the surface above the face within blow-out failure. Finally, face stability of a shallow tunnel of Changsha Metro Line 2 (from Changsha Road to Sports Park) is discussed by using the upper bound method and the finite difference method. The results obtained by the two methods are in agreement, but the upper bound method is actually more convenient.