An upper-bound analytical model of blow-out for a shallow tunnel in sand considering the partial failure within the face

Abstract

This paper proposes a three-dimensional analytical model of blow-out for a shallow tunnel in sand. Upper bound theorem is adopted to deduce the analytical solutions of limit support pressure, and a dimensionless parameter called partial failure ratio is defined to describe the range of partial failure within the tunnel face. A series of numerical simulations are carried out to analyse the limit support pressure and failure zone on the limit conditions. Finally, the analytical solutions including the partial failure ratio and limit support pressure obtained by the proposed model are compared with those obtained by the numerical simulation and the existing global failure model approaches. Results show that the proposed model in this paper can not only analyze the partial failure with better accuracy, but can also consider the global failure. The proposed model has more extensive applicability in analyzing the face stability of blow-out for a shallow shield tunnel.