Calculation and analysis of limit support force of shield tunnel excavation face under facing-slope conditions

Stability of excavation face is a key problem to shield tunnel construction technology. According to the present situation that the calculation of the limit support force of shield tunnel excavation face is rarely reported, based on the silo theory, a calculation model of the limit support force due to facing-slope construction is put forward by use of the limit equilibrium analysis method, and the track gradient is introduced. The corresponding formulas are obtained by theoretical derivation, and an engineering project is analyzed as an example. The results indicate that this method is reliable and can be applied to the design and construction in similar projects. Furthermore, the limit support forces to different track gradients are calculated for discussing their influences. Conclusions are drawn as follows: the limit support force of excavation face increases largely and linearly with the increase of the track gradient; but the rupture angle of soil before the excavation face decreases linearly with it, and the sum of them is approximately a constant. It can be seen that the existence of the track gradient has significant effect on the limit support force, and it should be fully taken into account during the design and construction process.