###### Abstract  
Existing methods for calculating the ultimate support pressure of tunnel faces do not consider the control of seepage flow. Therefore, a model for calculating the ultimate support pressure under seepage conditions was established based on a two-dimensional water head distribution model and the upper bound theorem of limit analysis. The reliability of this method was verified through comparisons with other studies. Subsequently, the influence of water level and tunnel face water pressure coefficient on stability was analyzed. The results indicate that the ultimate support pressure is linearly positively correlated with the water level and tunnel face water pressure coefficient; as the water level increases and the water pressure coefficient decreases, the failure area extends and enlarges. Finally, an existing seepage flow calculation formula was introduced, and a method for calculating the ultimate support pressure based on seepage control was proposed. The appropriate tunnel face water pressure coefficient is determined through the seepage flow calculation formula, and the corresponding ultimate support pressure is then calculated. The results demonstrate that this method can provide better theoretical guidance for seepage control in tunnel faces in practical engineering.  
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Footnote †: journal: Applied sciences  
0000-0001-9999-2000-0000-0000-0000-0000-0000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-000000-0  
methods combining numerical results [25; 26]. Based on these methods, the stability of the tunnel face under seepage conditions has been widely studied, seemingly solving the problem perfectly. However, existing studies often assume the water pressure at the tunnel face to be zero, while DI's research indicates that the water pressure is usually not zero and has a significant impact on the stability of the tunnel face [27; 28]. DI's research highlighted common issues in existing studies and provided insights for future research but unfortunately did not provide a method for determining the water pressure at the tunnel face.  
In fact, after the tunnel face is exposed, the water pressure on the tunnel face directly affects the nearby seepage field, resulting in changes in seepage flow at the tunnel face. Therefore, to control the seepage flow at the tunnel face, it is necessary to apply the required earth and water pressure through the shield. From the parameter selections in existing studies, it is evident that the assumption of zero water pressure at the tunnel face is mainly applied to low-permeability strata. In such strata, the seepage flow is minimal, and not setting water pressure at the tunnel face does not lead to water inflow incidents [29; 30]. However, in highly permeable strata, failing to determine reasonable water pressure at the tunnel face can easily cause water inflow and even lead to engineering accidents.  
Therefore, this paper first establishes the relationship between water pressure and seepage flow at the tunnel face by calculating the seepage flow at the tunnel face, obtaining a reasonable water pressure at the tunnel face based on seepage flow control. Furthermore, a method for calculating the distribution of pore water pressure in front of the tunnel face is derived based on the analytical methods of the three-dimensional seepage field. By introducing the seepage flow calculation equation, a method for calculating the pore water pressure distribution based on seepage flow control is proposed. On this basis, an ultimate support pressure calculation model for the tunnel face in water-saturated strata is constructed using the upper bound theorem of limit analysis, and the stability of the tunnel face under seepage conditions is analyzed. Finally, by combining seepage flow control with earth stability control, a method for determining the ultimate support pressure of the shield tunnel face in water-saturated strata based on seepage flow control is proposed.