## 5 Conclusions  
The novelty of this study lies in proposing an effective method for assessing the stability of 3D tunnel faces in unsaturated soils. The study investigated the differences in the stability of 3D tunnel faces when using linear and nonlinear strength models through the application of the kinematically limited analysis (KLA) and strength reduction method (SRM). This investigation encompassed diverse tunnel geometric factors, distinct soil kinds, and varying nonlinear strength models and groundwater sutions. The impact of matric suction on soil strength was modeled through the extended M-C failure criterion. By incorporating the horned failure mechanism, the external work rate and internal dissipation work rate were computed, and an implicit solution for the \(FS\) was derived using the SRM. Subsequently, a comparison with the numerical results and a parameter analysis were performed. Based on the aforementioned findings and discussions, the following conclusions can be drawn:  
1. In the case of a linearly increasing matric suction distribution, the suction stress distribution initially increases linearly with the distance from the groundwater level and then gradually becomes less steep, transitioning to a nonlinear pattern. The suction stress curve derived from the nonlinear estimation equation for extremely fine-grained soil will degrade into a linear form. The suction stress distribution in fine-grained soil is more complex than in other soils, exhibiting a decreasing trend in suction stress when the distance from the groundwater level is sufficiently large.
2. Considering the influence of suction stress is advantageous for enhancing the stability of tunnel faces. This impact varies across different soils, with the least effect on sandy soil, followed by fine-grained soil (silt), and the greatest impact on extremely fine-grained soil. When matric suction reaches a sufficiently high level, the increase in suction stress may slow down or even decrease, as observed in fine-grained soils, leading to the stabilization of or a reduction in the stability of tunnel faces. For extremely fine-grained soil, the contribution of suction stress to the stability of tunnel faces is nearly a linear function of \(\varphi^{b}=\varphi^{\prime}\).
3. Compared to the uniform matric suction distribution condition, the stability of tunnel faces under the condition of linearly increasing matric suction distribution is more influenced by the burial depth ratio C/D. For sandy and fine-grained soils, the stability of tunnel faces is less affected by C/D, and the difference is not significant under saturated conditions. For extremely fine-grained soil and clay, the factor of safety increases linearly with C/D until it stabilizes. The stability of the tunnel faces is significantly improved compared with that under saturated conditions. These two types of soil can significantly reduce the economic costs of practical tunnel construction.  
Methodology, Y.Y.; Resources, H.L.; Data curation, Y.Y.; Writing--original draft, Y.Y.; Writing--review and editing, H.L.; Supervision, J.Z. All authors have read and agreed to the published version of the manuscript.  
The Changzhou Science and Technology Support Programme: Study on Key Technologies for the Prevention and Control of Surface Deformation Induced by the Construction and Operation of the Changzhou Metro Tunnel (CE20235048) funded this study.  
Not applicable.  
The analysis data are available from the corresponding author on reasonable request.