Upper bound solution of collapse pressure and permanent displacement of 3D tunnel faces using the pseudo-dynamic method and the kinematic approach

This work presents seismic stability analysis of tunnel faces under three-dimensional (3D) conditions. To consider the temporal and spatial features of seismic force, the pseudo-dynamic approach was employed and incorporated into the 'horn-like' mechanism. According to the limit analysis method and the Hoek-Brown strength criterion, analytical solution of collapse pressure on tunnel faces was derived. The permanent displacement of tunnel face was then calculated by virtue of the Newmark method. The effects of the parameters of seismic force and Hoek-Brown strength criterion on collapse pressure and failure range of tunnel faces were analyzed. The relationship between the Hoek-Brown strength criterion parameters, the supporting force, and the yield acceleration was discussed. Moreover, the permanent displacements at the top, center, and bottom of tunnel faces under seismic effect were examined. This paper proposes a new idea for seismic stability analysis of tunnel faces.