A 3D torus-slice model for limit equilibrium analysis of shield tunnel face under soil arching effect

Abstract

This paper proposes a torus-slice model to estimate the tunnel face critical support pressure, (σcrit) from the shield machine under the influence of soil arching. The failure envelope of the tunnel face is created by a cluster of discrete points using a spatial discretization technique. The vertical earth pressure loaded on the failure soil mass in front of the face is determined by an arching mechanism based on the rotation trajectory of the major principal stress. The tunnel face support pressure distribution is derived from the stress interaction using a stepwise method between the horizontal slices divided from the torus. The comparisons between the centrifuge tests and analytical solutions demonstrate the accuracy of the proposed model. The pressure distribution is further validated by the results of a FLAC3D model and analytical solutions. The failure envelope is compared to the geometry of the shear band from the numerical model, indicating the rationality of the proposed method. With an improved geometry considered, the proposed torus-slice model demonstrates the advantages over the classical silo-wedge model. Finally, the effects of material and geometrical parameters on a required tunnel face pressure are discussed. The results show that the soil internal friction angle φ’, cohesion c’, the soil-shield interface friction angle δ, and the geometric shape factor Tm all have significant effects on the tunnel face stability.