# Numerical Simulation of Tunnel Face Support Pressure in Layered Soft Ground
## 1 Introduction
[PERSON] [15] conducted a series of centrifugal tests to investigate the failure evolution mechanism and ultimate support pressure of excavation faces. [PERSON] [18] carried out a series of centrifugal tests to study sandy soil under different diameters and different soil diameter ratios. They found that the ratio of soil diameter had little effect on the support pressure when the working face was damaged, and the limiting support pressure had a linear relationship with the roadway diameter. [PERSON] [19] studied the evolution mechanism of roadway face instability under different foundation conditions, and they defined three failure modes: front extrusion, front caving, and back caving. [PERSON] [20] conducted a series of transparent clay model tests on the active stability of the shield face adjacent to the existing tunnel, based on the excavation process, failure mode, influence range, and support force. It was found that the failure mode of the shield tunnel working surface was the whole failure mode, which was approximately wedge-shaped and ladder-shaped along the longitudinal and transverse sections, respectively. However, due to its high cost and complex operation compared with other methods, the model test method is generally not employed for stability analysis of excavation faces. The third method of analysis is numerical analysis, which is a viable and effective approach for simulating complex shield construction. [PERSON] et al. [21] conducted a series of three-dimensional finite element simulations to assess tunnel surface stability under drainage conditions, taking into consideration factors such as friction angle and cohesion force. They derived a design equation for determining the limiting support pressure. [PERSON] et al. [22] utilized the three-dimensional finite element method to investigate the stability of undrained tunnel excavation faces when soil shear strength increases linearly with depth. Their study examined the influence of the cover diameter ratio, cover stress factor, and linear strength gradient ratio on undrained tunnel excavation surface stability, proposing a new design equation to calculate safety factors for homogeneous clay excavation surfaces in undrained tunnels where the shear strength increases linearly with depth. [PERSON] et al. [23] proposed a series of three-dimensional FDM models to analyze surface stability in shallow circular tunnels constructed in frictional/viscous frictional soils. They also introduced a simple approach for determining failure zone boundaries by considering different soil diameter ratios and shear strength parameters. [PERSON] et al. [24] used MIDAS for numerical simulation to study the influence of different soil strength parameters, covering diameter ratios, and tunnel diameters on tunnel excavation under uniform foundation conditions. At the same time, the collapse pressure required by the tunnel face during tunnel excavation in layered soil was preliminarily investigated. [PERSON] [25] used the FLAC-3D numerical simulation method to simulate the characteristics of a coal wall in a large mining face at different mining heights. [PERSON] [26] used a combination of numerical simulation and theoretical analysis to study the ultimate support pressure and failure area, analyze the influence of various factors on the stability of the roadway face, and reveal the mechanism of the roadway face collapse. [PERSON] [27] carried out numerical simulation to study the velocity distribution characteristics of the tunnel working face and above the vault. [PERSON] [28], based on the 3D head distribution model and the upper bound theorem of limit analysis, established the calculation model of limit support pressure of the shield tunnel working face. The influence of water level, internal friction angle, buried depth, and water pressure on the stability of the roadway working face was analyzed.