A 3-D analytical continuous upper bound limit analysis for face stability of shallow shield tunneling in undrained clays

For face stability of shallow shield tunneling in undrained clays, a 3-D analytical continuous upper bound limit analysis method is developed. A set of empirically based analytical expressions for tunneling induced ground displacement field is employed within the upper bound theorem, and a particle swarm optimization technique is applied to determine the least favorable collapse domain and the corresponding minimum required tunnel face support pressure and maximum permissible stability number. Verification is conducted by using a finite element limit analysis software and a finite element simulation software, and by comparing with previous theoretical upper bound schemes, and it is found that the method is reliable, less conservative than the finite element limit analysis software and previous theoretical upper bound schemes. Parametric analysis indicates that when the soil unit weight is sufficiently large and/or the soil cohesion sufficiently small, tunnel face support pressure is necessary, and the larger the tunnel cover, the larger the soil unit weight and/or the smaller the soil cohesion, the larger the minimum required support pressure.