# Analysis of the Limit Support Pressure of a Shallow Shield Tunnel in Sandy Soil Considering the Influence of Seepage

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Three-Dimensional Analytical Solution for Pore Water Pressure Distribution

^{3D}software, considering the symmetry of the tunnel. Here, the diameter of the tunnel $D$ is 6 m, the thickness of the covering soil $C$ is 12 m, the top surface is free and the hydraulic head pressure is fixed at 1 m, the bottom surface and the side wall of the tunnel are fixed and impermeable, the surrounding normal direction is fixed and impermeable, the tunnel face is fixed in the normal direction, the hydraulic head difference between the tunnel face and the ground surface is fixed at 0.5, 1.0 or 2.0 $D$, and the friction angle of the soil $\phi $ is 37°, 31° or 25°. Then, the distribution of pore water pressure is obtained by three-dimensional seepage calculation.

## 3. Limit Support Pressure of the Tunnel Face Considering the Influence of Seepage

#### 3.1. Establishment of the Failure Model

#### 3.2. Calculation of the Limit Support Pressure of the Tunnel Face

## 4. Comparative Analysis of the Limit Effective Support Pressure of the Tunnel Face Obtained by Different Methods

^{3}; the friction angle of the soil $\phi $ is 37°; the cohesion of the soil $c$ is 0; the additional pressure on the ground surface $q$ is 0.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Cloud image of the pore water pressure distribution. (

**a**) The friction angle of the soil $\phi $ = 37°; the hydraulic head difference between the tunnel face and the ground surface $\mathsf{\Delta}$ = 0.5 $D$; (

**b**) $\phi $ = 37°; $\mathsf{\Delta}$ = 1.0 $D$; (

**c**) $\phi $ = 37°; $\mathsf{\Delta}$ = 2.0 $D$; (

**d**) $\phi $ = 31°; $\mathsf{\Delta}$ = 2.0 $D$; (

**e**) $\phi $ = 25°; $\mathsf{\Delta}$ = 2.0 $D$ (unit: Pa).

**Figure 5.**Test model of excavation-seepage instability of the shield tunnel [3].

**Figure 6.**The ground collapse range of the vertical symmetry plane in the center of the tunnel and the plane in front of the tunnel face [3].

**Figure 11.**Comparison of the limit effective support pressure of the tunnel face under seepage conditions obtained by different methods.

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**MDPI and ACS Style**

Mi, B.; Xiang, Y.
Analysis of the Limit Support Pressure of a Shallow Shield Tunnel in Sandy Soil Considering the Influence of Seepage. *Symmetry* **2020**, *12*, 1023.
https://doi.org/10.3390/sym12061023

**AMA Style**

Mi B, Xiang Y.
Analysis of the Limit Support Pressure of a Shallow Shield Tunnel in Sandy Soil Considering the Influence of Seepage. *Symmetry*. 2020; 12(6):1023.
https://doi.org/10.3390/sym12061023

**Chicago/Turabian Style**

Mi, Bo, and Yanyong Xiang.
2020. "Analysis of the Limit Support Pressure of a Shallow Shield Tunnel in Sandy Soil Considering the Influence of Seepage" *Symmetry* 12, no. 6: 1023.
https://doi.org/10.3390/sym12061023