Stability Analysis of 3D Tunnel Face of Shallow Rectangular Shield Tunnel

In recent years, an increasing number of rectangular excavation sections have appeared in pipe-jacking shield tunnel projects. In previous studies, calculating the stability of a tunnel face in a noncircular shield tunnel usually required a circular section. It is carried out according to the principle of equivalent areas. Although this method makes it easy to calculate the stability, deviation still occurs. To solve this issue, the rectangular shield tunnel is used as the research object. Spatial discretization technology is used to extend the rotational failure mechanism of 3D rigid blocks to the tunnel face of rectangular tunnels. Moreover, it is accomplished under the theoretical background of the upper bound method. The MATLAB calculation results were compared with FLAC3D, and the process proved to have sufficient accuracy and a high efficiency. Then, the influences of the failure modes and limit support pressure by dimensionless parameters are studied. The results show that the parameters that have a great impact on the failure region and stability of the tunnel face are H/D, C/D, and the internal friction angle φ, and the parameters that have little influence on them are σs/c and γD/c. Finally, a dimensionless parameter design chart that has a limit support pressure with a rectangular tunnel and a single homogeneous frictional soil layer is drawn and fitted using a ternary quadratic polynomial. Furthermore, it can be used for preliminary design.