Upper bound solution of passive instability on the face of longitudinal inclined shallow buried shield tunnel based on rotation–translation mechanism

Abstract

To better evaluate the passive failure mode of shallow shield tunnel faces in sandy soil strata, tunnel faces passive failure mode was investigated considering the longitudinal inclination in this study. A three-dimensional rotation–translation mechanism that simultaneously considers the longitudinal inclination of the tunnel and partial failure of the tunnel face based on the upper bound limit analysis method was presented. The mechanism comprised two rigid translation blocks and one rigid rotation block. Subsequently, the reliability of the proposed mechanism was verified using the horizontal rigid translation mechanism and numerical simulation considering the longitudinal inclination. Finally, the effects of tunnel longitudinal inclination (δ), cover depth ratio (C/D), soil internal friction angle (ϕ), and the possible presence of uniform surface surcharge (σS) on the limit support pressure of the tunnel face and the partial failure range was assessed. The results indicated that the partial failure range of the tunnel face gradually increased with δ When C/D<1. Conversely, global failure of the tunnel face occurred at different longitudinal inclinations when C/D≥1. The rotation angle (θ) of the rotational failure zone was sensitive to the longitudinal inclination (δ) and decreased with δ at the same coverage depth ratio.