# Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure
## 4 Conclusions  
The large cross-section of the tunnel and the features of soil cutting and discharging caused by multiple cutter heads and screw conveyors tend to cause an uneven distribution of support pressure, which has the risk of instability. This study develops a theoretical model based on the limit equilibrium method for the stability analysis of a box tunnel face in non-cohesive soil. A parametric analysis for the proposed solution is performed. The proposed model is verified by the numerical model. The main conclusions can be summarized as follows:  
(1) The obtained support pressure distribution on the working face was uneven, with a large support pressure on both sides and small one in the middle. Accordingly, the failure  
Figure 16: Variations in \(s_{2}/\gamma D\) depending on \(\varphi^{\prime}\).  
mechanism was composed of a prism (upper part) and a wedge (lower part), which were both divided into three blocks. The relatively small support force acting on the middle block (II) led to its tendency to slide and the risk of destabilization. The interaction forces between the blocks were obtained by force analysis. Assuming that the tunnel face was in the active failure limit state, the support pressure acting on block I was obtained using the active earth pressure coefficient; then, the support pressure acting on block II could be calculated by limit equilibrium analysis;  
(2) The formula of the limit support pressure was obtained. The influences of the strength parameters and geometric parameters on the tunnel face stability were investigated in the parametric analysis. The limit support pressure rose with the increase in the partially supported ratio and the width-height ratio, and the pressure dropped greatly with the increasing internal friction angle;  
(3) The applicability of the proposed model was verified by comparing it with the numerical model built in OptumG3. The results of the proposed model have a similar pattern of variation with that of the numerical model, showing that the proposed model agrees well with the numerical model. For projects using similar tunnel machines, the theoretical solution presented in this paper can predict the collapse geometry and provide valuable guidance for risk control.  
Conceptualization, M.Y. and W.L.; methodology, M.Y. and W.L.; software, B.W.; validation, M.Y. and B.W.; investigation, P.G.; writing--original draft preparation, M.Y.; writing--review and editing, W.L. and J.Y.; supervision, W.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China under grant number 51978430, Powerchina Huadong Engineering Corporation Limited (KY2019-ZD-02), the Key R&D Program of Zhejiang Province (2019C03111).  
Not applicable.  
The data presented in this study are available upon request from the corresponding authors.  
The authors declare no conflict of interest.  
The following symbols are used in this paper:  
\(D\) height of tunnel  
\(L\) width of tunnel  
\(C\) cover depth  
\(B\) width of partially supported area  
\(c^{\prime}\) effective cohesion  
\(q^{\prime}\) effective angle of internal friction  
\(\gamma\) the total unit weight  
\(\sigma_{\rm s}\) ground surcharge  
\(S_{1}\) support force acting on block I  
\(S_{2}\) support force acting on block II  
\(\theta\) wedge angle between slanted failure plane and the horizontal  
\(K_{0}\) lateral stress coefficient  
\(K_{\rm a}\) active earth pressure coefficient  
\(R\) ratio of the volume of the prism to its side area  
\(N_{\gamma}\) coefficient related to \(\gamma\)  
\(N_{c}\) coefficient related to \(c^{\prime}\)  
\(\kappa\) dimensionless coefficient  
\(\varepsilon^{-}\) dimensionless coefficient  
\(\varepsilon^{+}\) dimensionless coefficient