# Stability Analysis of Box Tunnel Working Face under Non-Uniform Support Pressure
## 2 Materials and Methods
### Theoretical Model Construction  
As shown in Figure 2(a), the conventional silo-wedge model includes a lower wedge and an upper silo, with the lower wedge having a height of \(D\), a width of L, and a soil column of C. As shown in Figure 2(b), the silo-wedge model was established under open silo conditions, based on the characteristics of irregular support pressure distribution proposed in this paper. The safety factor was calculated using the horizontal fractionation method in this paper. In the case of layered soils, the most unfavorable soil layer was selected for the study,  
Figure 1: Characteristics of pressure distribution in soil bin of rectangular roadheader. I and III are pressure stabilisation zones. II is a pressure fluctuation zone. Figure 2: Location schematic diagram of man lock. and the resulting safety factor was the most conservative. This paper therefore assumes that the rectangular pipe jacking machine was used to tunnel in homogeneous soils under unfavorable conditions. The lower part of the model corresponds to the characteristics of the support pressure distribution at the working face and divides the soil body in front of the working face into three sections (I, II, and III), with block II not being subject to support pressure and having a width of B. The upper part of the model corresponds to the overlying soil of the three lower blocks, which are also divided into three portions (IV, V, and VI), thereby dividing the model into six blocks. The support forces s1 acting on blocks I and III are sufficient to maintain these two blocks in equilibrium. Block II is unsupported by the support force due to the open barn condition, which poses a destabilizing risk. Block V, which is located in the upper part of block II, is affected by the soil arch effect and tends to follow the sliding of block II. To examine the stability of block II under the influence of the remaining parts, block II is used as the object of study, and its stability safety factor is computed using strength discounting and limit equilibrium analysis. The damage mechanism discussed in this paper is that, in ultimate equilibrium, the overburden load is equal to the load carrying capacity of the wedge; when the load applied to the wedge (block II) by the overburden (block V) exceeds the force such that the wedge can no longer withstand it at the boundary of the wedge, the wedge will reach its ultimate state and break. The load applied by the overburden layer (\(V_{silo}\)) is calculated by the silo theory [33]; the load carrying capacity of the wedge is calculated by the horizontal strip method [33], where the relevant shear force is discounted [32] by Equation (1); and then the corresponding safety factor is obtained by the ultimate equilibrium analysis. In ultimate equilibrium, the overburden load is equal to the load-carrying capacity of the wedge; when the load applied to the wedge (block II) by the overburden (block V) exceeds the force that the wedge can withstand at its boundary, the wedge reaches its ultimate state and fails. The load applied by the overburden layer (\(V_{silo}\)) is computed using the silo theory [33]; the load carrying capacity of the wedge is computed using the horizontal strip method [33], where the relevant shear force is discounted [32] by Equation (1); and then the corresponding safety factor is obtained using the ultimate equilibrium analysis:  
\[f_{s}=\frac{\tau_{\max}}{\tau} \tag{1}\]  
where \(\tau_{\max}\) is the maximum shear strength of the soil, and \(\tau\) represents the actual exerted shear strength. Figure 3: Calculation model.