Critical Face Pressure of a Tunnel Driven by a Shield Machine Considering Seismic Forces and Tunnel Shape Influence

Evaluating critical face pressure with high accuracy is an important topic for shield tunneling. The existing research focuses more on the influence of complex geological conditions or environmental factors, and there are few reports on the influence of tunnel shape on critical face pressure. In reality, the tunnel shape has a significant impact on the deformation zone in front of the tunnel face, which may lead to non-negligible differences in shield pressure. To fill this gap, an efficient analytical approach is proposed to estimate the critical face pressure considering different tunnel shapes in the framework of limit analysis. As earthquakes are potential threats to the tunnel face stability in seismically active regions, the seismic effect is also taken into account with the help of the pseudo-static method. Several cases with the same area but different tunnel shapes are investigated using the limit analysis method. A comparison with static analysis is given to highlight the influence of seismic forces on the tunnel face stability. The results show that the critical face pressures increase by 15.3% when the tunnel face shape changes from rectangular to circular, and by 23.5% when the horizontal seismic coefficient varies from 0 to 0.1. A further validation with a 3D finite difference method is performed with respect to four typical tunnel shapes considered in this study. Lastly, several stability charts are provided for a quick estimation of the critical tunnel face pressure subjected to seismic forces. It is concluded that the proposed method can be applied to a tunnel stability assessment of various cross-sections and is highly efficient compared with numerical simulations.