## 1 Introduction  
In recent years, the development of urban rail transit in China has been changing rapidly. Up to now, a total of 36 cities in mainland China have constructed and put into operation urban rail transit, with a total mileage of 5766.6 km. Among them, 4354.3 km of subway accounted for 75.6%. In urban rail transit construction, the shield method is often used for subway construction. Shield tunneling is a three-dimensional dynamic process. The magnitude of the supporting force of excavation surface during construction determines the impact degree of shield excavation on surrounding strata. With the increase or decrease in the supporting force, different displacement of surrounding strata will occur. When the supporting force of excavation face is less than limit minimum supporting force, the soil will lose its stability, and the corresponding instability accidents of excavation face have been reported frequently [1]. Therefore, the determination of the limit supporting pressure provides a basis for ensuring the normal construction of the shield and the selection of control pressure. At present, domestic and foreign scholars have conducted many studies on the stability of the excavation face. Theoretical methods include the excavation surface stability coefficient method [2], the plastic limit analysis method [3; 4; 5], the wedge-shaped limit equilibrium analysis method [6; 7], etc. In terms of experimental research, [PERSON] et al. [8] confirmed through a centrifugal model test of sand that when the excavation surface of sand tunnel is destroyed, the front is a wedge and the upper part is a prism. Due to the tedious calculation process of the limit analysis method based on the elastoplastic theory, it is difficult apply to practical engineering. However, the wedge-shaped calculation model has specific calculation assumptions and clear concepts, so it is widely used in the calculation of limit-supporting force for shield tunnels. [PERSON] [9] first proposed a three-dimensional limit equilibrium model for the stability analysis of tunnel excavation face. The model consists of a wedge in front of excavation face and its upper silo. Then, [PERSON] and [PERSON] [10] established a new limit equilibrium model of excavation face stability based on [PERSON] [9]. In this model, the front of the excavation face was a wedge and its upper part was a prism cuboid; [PERSON] [11], [PERSON] [12], [PERSON] [13], [PERSON] [14] and [PERSON] [15] improved the model and further derived the analytical solution. However, in the above studies, the destabilizing \"prisms\" all extend to the surface in the limit state. The height of the \"prism\" is roughly equal to the distance from the top of the tunnel to the surface, and it is not affected by the shielding depth ratio of the shield, which is obviously inconsistent with the actual project. Furthermore, previous studies on the stability of shield excavation surfaces only focused on isotropic soil. However, in fact, due to the natural deposition and the change of soil stress, the strength of soil is anisotropic. [PERSON] [16] verified the anisotropy equation of soil strength derived by [PERSON] [17] with experiments; [PERSON] et al. [18; 19] used laboratory tests to study the anisotropy of undrained shear strength of cohesive soil caused by principal stress rotation. The Casagrande anisotropy equation has been widely used in the study of slope stability [20], foundation pit anti-uplift stability [21] and foundation bearing capacity [22]. However, there is no relevant literature to discuss the limit equilibrium solution of the limit support force of shield excavation surface in anisotropic soil. The instability mode of excavation face and the anisotropy of soil strength will inevitably have a greater influence on the ultimate supporting force of shield tunnel excavation face.