Effect of Longitudinal Gradient on 3D Face Stability of Circular Tunnel in Undrained Clay

The longitudinal gradient existed in shield-driven tunnel crossing river or channel has a longitudinal gradient, which is often ignored in most stability analyses of the tunnel face. Considering the influence of the longitudinal gradient into A(a) continuous velocity field, the present paper, conducting a limit analysis of the tunnel face in undrained clay, adopted to yield the upper-bound solutions of the limit pressure supporting on a three-dimensional tunnel face. The least upper bounds of the collapse and blow-out pressures can be obtained by conducting an optimization procedure. These upper-bound solutions are given in the design charts, which provide a simple way to assess the range of the limit pressure in practice. The influence of the longitudinal gradient becomes more significant with the increase of γD/su and C/D. The blow-out pressure for tunneling in a downward movement could be overestimated and the collapse pressure for tunneling in an upward movement could be conversely underestimated, with ignoring the influence of the longitudinal gradient.