# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 1 Introduction  
Rectangular tunnels are widely used in the construction of urban underground projects such as subways, which have advantages such as high space utilization and little impacts on ground traffic, etc. As a trenchless technique, box jacking is often adopted in urban construction. The stability of the tunnel face is one of the most important factors in tunneling. It is necessary to ensure face stability during the excavation of a tunnel. The cross section of a rectangular tunnel tends to be large, and the support pressure is unevenly distributed, both of which greatly increase the risk of tunnel face instability. The methods to study the stability of a tunnel boring face mainly include theoretical analysis [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30], model testing, and numerical simulation [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. Theoretical analysis presents a clear force model, and the force analysis is scientific and accurate, which is ideal for engineering applications. Commonly used theoretical methods mainly include upper limit analysis and limit equilibrium analysis. Limit analysis methods [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15] construct a damage maneuver mechanism according to the plastic flow law for soil in the critical state and use an energy balance to derive the judgment criteria for the destabilization of the excavation surface. [PERSON] et al. [1] studied the active failure mode of shield tunneling in undrained clay soil under 2D plane strain conditions and proposed the calculation method of the ultimate support pressure and stability coefficient. [PERSON] [2] proposed a 3D cone model, constructed a translational maneuver field that satisfies the motion permission, and derived the upper limit solution of the limit support pressure. According to [PERSON] & [PERSON] [2], [PERSON] et al. [3] improved the cone model, and a 3D failure mechanism composed of a rigid cone and a logarithmic spiral shear body was proposed. [PERSON] et al. [4; 5; 6] focused on the elliptical failure area and the circle of the cone model and constructed the 3D logarithmicspiral failure mechanism for the first time using spatial discretization technology to achieve the full-section instability of the failure mechanism. Based on the spatial discretization technology, [PERSON] et al. [7; 8; 9] extended an advanced 3D failure mechanism into the face stability analysis in anisotropic and nonhomogeneous soils, achieved to generate a failure mechanism for a non-circular tunnel face to estimate the safety factor of a tunnel face. [PERSON] et al. [10] used both planar triangular blocks and spiral blocks to construct an active instability maneuvering model and studied the influence of the tunnel excavation step on the stability of the driving face. [PERSON] et al. [11] constructed the passive instability failure mechanism of a shallow tunnel driving face and considered the pore water, the influence of pressure, and an uneven overload on the stability of the driving face. [PERSON] et al. [12; 13] developed 2D and 3D kinematically admissible mechanisms, and the composite mechanism comprises rotational and translational blocks for analyzing the passive face stability during shield tunneling. [PERSON] et al. [14] considered rectangular cross-sectional shield tunneling and derived the upper-bound solution of support pressure applied to maintain the face stability. [PERSON] et al. [15] proposed an analytical model of face stability for a tunnel under anisotropic seepage based on the limit analysis upper-bound method. However, the maneuver model construction rule in limit analysis is influenced by the boundary conditions, and the construction model is complicated, which reduces the applications of limit analysis in engineering. In contrast, limit equilibrium analysis is more adaptable to the boundary conditions and easier to analyze by constructing a rigid-body limit equilibrium model. [PERSON] et al.