# Stability Analysis of Box Tunnel Working Face under Non-Uniform Support Pressure
## 1 Introduction  
Rectangular tunnels are frequently used in the construction of urban underground space initiatives such as metros, due to their benefits, such as better space utilization and less interference with surface traffic. Most urban construction employs non-excavation methods, with rectangular boring machines used for excavation. Large rectangular tunnel sections with an uneven pressure distributions and large pressure differences can easily lead to ground instability. In exceptional situations, such as when clearing openings, the local support pressure may be zero, significantly raising the risk of ground instability. Regarding the stability of tunnel working faces, many studies have employed limit equilibrium, limit analysis [1; 2; 3; 4; 5; 6; 7; 8; 9], numerical analysis [10; 11; 12; 13], laboratory experiments [14; 15; 16; 17; 18], and other methods. The limit equilibrium method has been extensively applied due to its straightforward concept and physical meaning. Most analyses of limit equilibrium have been based on the silo-wedge model and determined by force equilibrium. [PERSON] [19] first proposed the wedge calculation model based on [PERSON]'s [20] silo theory, and this model has been continuously enhanced by subsequent research. Overlying soil is an important part of the research of the silo-wedge model. [PERSON] et al. [21] considered the arching effect of overlying soil. [PERSON] et al. [22] utilized the silo-wedge model to investigate the impact of overlying soil on passive and active surface failure and to determine the critical covering depth for shield tunnels. [PERSON] et al. [23] established the concept of the multi-arch; identified the bearing arch at the upper end of the arch area, the friction area in the middle, and the stability area; and consequently proposed a three-dimensional multi-arch model. In addition, [PERSON] et al. [24; 25] used a theoretical model to examine the stability of the excavation surface of mud water-type and earth pressure-balanced-type shield machines, considering the effect of mud-water injection on the excavation surfaceand groundwater seepage force. [PERSON] et al. [26] adapted the computational model to unevenly stratified soil conditions to determine the ultimate supporting pressure of soil pressure and mud-water balanced shield construction. [PERSON] [27; 28] modified the model into a trapezoidal wedge shape and optimized the ultimate supporting force calculation results. [PERSON] et al. [29] analyzed the stability of a shield tunnel excavation face under inclined conditions and calculated the ultimate supporting force. [PERSON] et al. [30] adapted the trapezoidal wedge model to rectangular pipe jacking to investigate the stability of a rectangular pipe jacking excavation face in a sand gravel stratum. [PERSON] et al. [31] assumed that the sliding block in the failure zone had the shape of a curved wedge and determined the active limit supporting force of the excavation face under dry sand conditions. [PERSON] et al. [32] analyzed the critical failure mode of a tunnel face under various parameters in the limit equilibrium state and calculated the safety factor using the horizontal strip method [33] and the strength reduction method. [PERSON] [34] investigated the stability of a tunnel face using the numerical method, and the automatic calculation of the safety factor was performed with Plaxis 3D, using the strength reduction technique. Existing theories concentrate mainly on the uniform support force, while studies of local support have been limited. However, there will be situations of no local support in practical engineering, such as opening the warehouse to clear obstacles. This paper investigates the stability of a rectangular tunnel face. In consideration of the uneven pressure distribution of the face support, i.e., the characteristics of local support, the concept of strength reduction is introduced into the limit equilibrium analysis, and force analysis is conducted using the silo-wedge model and horizontal bar division method.