# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 1 Introduction
[16] established a 3D wedge model based on the limit equilibrium method using the silo theory and proposed a calculation method for the limit support pressure. [PERSON] [17] extended the calculation model to layered soil conditions and analyzed the earth pressure and mud-water balance shield construction limit support pressure. [PERSON] [18] studied the influence of the soil arching effect on the stability of the tunnel excavation surface, optimized the calculation model, and put forward the expression of support pressure. [PERSON] et al. [19] considered the face stability of rectangular pipe jacking under the condition of gravel formation and used the trapezoidal wedge model to derive the expression of the active failure limit support pressure of the excavation face. [PERSON] et al. [20] assumed that the failure area is an arc-shaped wedge and derived the active limit support force calculation formula for the lower excavation face under dry sand conditions based on the silo theory. [PERSON] et al. [21], based on the limit equilibrium method, proposed a logarithmic spiral prism model considering the unsupported length to analyze the stability of the shallow tunnel driving face in sand. [PERSON] et al. [22] extended the calculation model to stratified soil conditions and derived the ultimate support pressure for the earth pressure and mud-water balance shield construction. [PERSON] et al. [23; 24] modified the 3D wedge model by assuming the sliding block shape to be a trapezoidal wedge when the excavation surface is destabilized and obtained better calculation results for the support force. [PERSON] et al. [25; 26; 27] investigated the analytical solutions for the responses of tunnels excavated in rock masses and verified the proposed solutions by numerical simulations. The existing theoretical studies mainly focus on the stability of tunnel boring faces in circular cross-sections, and there is less research on rectangular cross-sections, and there are especially few theoretical studies on the uneven distribution of support pressure in the boring face. [PERSON] et al. [28] focused on the situation in which the working face chamber is exposed to free air due to obstruction removal. In this situation, the support pressure distribution on the working face is characterized by zero in the middle. At this point, the soil in the middle of the working face has a great risk of destabilization because, without support pressure, the soil is likely to have an insufficient shear strength to maintain stability. This paper investigates the stability of the box tunnel working face. An improved wedge-prism model is established for the uneven distribution of support pressure at the tunnel face due to the large cross-section and the characteristic behavior of the cutter head. In the proposed model, the wedge and prim blocks are each divided into three blocks according to the characteristics of the support pressure distribution. The support pressure distribution on the working face is characterized as concave. Therefore, the soil in the middle with a small support pressure has a downward sliding tendency relative to the soil on both sides because the support pressure is not sufficient to maintain stability, and even active damage may occur. Assuming that the support pressure on both sides of the tunnel face is known and taking into account the interactions between the blocks, the smaller support pressure in the middle can be calculated by force analysis. The rationality of the proposed model is investigated, and the results given by the proposed method are compared with those obtained by numerical simulation.