LAUSR

Abstract The kinematic approach of limit analysis is explored in three-dimensional face stability of large-diameter tunnels in soils with linearly increasing undrained strength with depth. Due to the slurry density by a shield machine, the support pressure is not uniformly distributed on the face. Such a non-uniform distribution cannot be ignored, especially for the large-diameter shield tunnels. This paper includes it into the stability analysis of the tunnel face subjected to local and global failures. The failure mechanism with a spherical cap is adopted to obtain the least upper-bound solutions of local stability of the tunnel face. To evaluate its global stability, a continuous velocity field with a toric envelope is employed and yields the critical pressures on tunnel face against collapse and blow-out. The calculated results are compared with the solutions derived from other well-established methods for verification of the presented approach. An approximation formula based on the derived upper-bound solutions, is given to directly calculate the necessary collapse and blow-out pressures, which can be used for preliminary design in practice. An example is given to illustrate its convenient use.