# Numerical Investigation of Water Inflow Characteristics in a Deep-Buried Tunnel Crossing Two Overlapped Intersecting Faults

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Investigations

#### 2.1. Numerical Calculation Model

^{−16}m

^{2}, the maximum permeability value of the fault core zone is 10

^{−11}m

^{2}, and the variation in permeability in damage zones obeys the Gaussian function. The rock permeability in the fault intersection area follows the principle of superposition. As displayed in Figure 1, zone A is the surrounding host rock zone, zone B is the fault damage zone as a transition zone, zone C is the fault core zone, and zone D is the overlapped damage zone of the faults. The absolute widths of the core zone C, the damage zone B, and overlapped damage zone D are 3 m, 20 m, and 20 m, respectively. The porosity value of the fault core zone and the fault damage zone is 0.5. Based on the simulation model of these intersecting faults, we explored the influence of the vertical relative positions and distance between the tunnel axis and the fault’s intersecting center on the seepage characteristics of groundwater and water inflow into the tunnel. In this study, we set the tunnel excavation face and the fault’s intersection center on the XY plane. Specifically, the calculation conditions are that while the tunnel excavation face enters the center of the model, the center of the fault intersection is located 40 m and 20 m directly above the tunnel excavation face (Y = 40 and Y = 20), coinciding with the tunnel axis (Y = 0), and 20 m and 40 m directly below the tunnel excavation face (Y = -20 and Y = -40), as shown in Table 1.

#### 2.2. Numerical Simulations

_{w}is groundwater density, Q

_{m}is flow rate, k is permeability, p is the pore pressure (PP), μ

_{w}is the dynamic viscosity of groundwater, H is groundwater head height.

_{r}= 1 × 10

^{−16}m

^{2}, and the permeability coefficients of the core zone and damage zone are calculated according to the water compression test. According to the results of the water compression test, the influence relationship between permeability k and distance x from the fault center was studied, and the relationship between x-k was fitted by Gaussian function. Where I is the unit matrix, ε

_{p}is a void ratio, F is the volume force, and k is the permeability of the fault surrounding rock which can be expressed as Equation (5).

_{f}is the constant permeability value in the core zone of the fault, k

_{r}is the constant permeability value of the host rock zone, d

_{1}and d

_{2}are the absolute width of the core zone and the damage zone, respectively, and x is the distance from the fault center.

## 3. Numerical Simulations When Tunnel Crosses Two Intersecting Faults

#### 3.1. Tunnel Is 40 m Beneath the Center of the Two Intersecting Faults

_{Y = 40}, XY

_{Z = 0}, YZ

_{X = 0}) while the tunnel is excavated to 40 m beneath these two intersecting faults (Y = 40).

_{Y = 0}, PP contours are distributed elliptically symmetrically along the x-axis, and the ellipse’s major axis is parallel to the z-axis. In the vertical downward direction, the PP value gradually increases with the burial depth of the tunnel in a circular or semicircular distribution nearby the tunnel face, as can be seen in the cross-section of YZ

_{X = 0}. The FV contours reveal that the groundwater flow direction is from the fault intersection zone and the damage zone to the tunnel excavation face, and the FV value is small with a maximum of 2.95 × 10

^{−3}m/s. The FV contours are symmetrically distributed with respect to the x-axis on the cross section of XZY = 40 and the y-axis on the cross section of YZ

_{X = 0}. While the tunnel excavation face arrived at 40 m directly below the overlapped intersection center, the PP near the excavation face and the tunnel wall about 1 m behind dissipated, forming a low-pressure zone. Therefore, groundwater is more likely to seep into the vicinity of the tunnel face. The permeability of the fault core zone and fault damage zone is much bigger than that of the host rock zone on either side, so the direction of the groundwater seepage is from the fault intersection zone and damage zone to the tunnel.

^{−8}m/s and 4.01 × 10

^{−8}m/s each. On sections of Y = 1.95 m, 0, −1.95 m, FV declines quickly and slowly within 3 m ahead of the excavation face. The maximum value of FV is 1.52 × 10

^{−7}m/s, 9.91 × 10

^{−8}m/s, and 2.50 × 10

^{−7}m/s, respectively. The velocity magnitude order near the tunnel face is U

_{Y = −1.95}> U

_{Y = 1.95}> U

_{Y = 0}. Overall, the FV peak occurs at the lower part of the excavation face. The value of FV is higher over a small distance in front of the excavation face but then falls off rapidly, after which it changes smoothly in the host rock. FV near the excavation face is apparently higher than that outside away from the excavation face, and it increases with increasing Y.

^{3}/h at the excavation face and the total groundwater inflow rate of 0.015 m

^{3}/h by integrating the FV over the area.

#### 3.2. Tunnel Is 20 m Beneath the Center of Cross Faults

_{Y = 20}, XY

_{Z = 0}, YZ

_{X = 0}) are shown in Figure 4.

_{Y = 20}section, the PP contours are symmetrically circular along with the x-axis. The pore pressure distributes semi-circularly near the excavation face on the vertical section and gradually increases with the increase in the tunnel burial depth. From the FV contours, we find that water flows to the tunnel from the intersection zone and the damage zone of faults above the tunnel. As the fault intersection center is closer to the tunnel, the water flow velocity increases, with a maximum of 1.25 × 10

^{−3}m/s. On the XZ

_{Y = 20}section, the FV contour appears approximately symmetrically distributed for the x-axis. Water flows along the fault into the tunnel excavation face. On the YZ

_{X = 0}section, the FV contour is symmetrically distributed for the y-axis. The value of FV above the tunnel vault is expressively more significant than below the tunnel floor.

^{−4}m/s and 6.60 × 10

^{−4}m/s, respectively. Flow velocities gradually decrease within 1 < D ≤ 9 m range of the excavation face until reaching zero as D > 9 m. When Y = 0, the maximum value of FV occurs at the excavation face, which is 2.12 × 10

^{−4}m/s. Flow velocity is gradually reduced within 0 < D ≤ 9 m range of the excavation face until zero at D > 9 m. When Y = −3.9 m and −1.95 m, the velocities are low and overall change little.

^{3}/h at the excavation face and the total water inflow rate of 35.67 m

^{3}/h by integrating the FV over the area.

#### 3.3. Tunnel Is at the Center of the Fault Intersection

_{Y = 0}, XY

_{Z = 0}, YZ

_{X = 0}) while the tunnel excavation face is in the center of the two intersecting faults (Y = 0).

_{Y = 0}section, PP contour appears elliptical symmetrically for the x-axis, with the ellipse’s major axis along with the z-axis. On the vertical profile, the PP contour distributes in a funnel shape. The FV contours in Figure 2b,d,f show that groundwater flows mainly from the overlapped intersection zone and the damage zone of faults to the tunnel. The FV value is increased with a maximum magnitude of 0.0205 m/s. On the XZ

_{Y = 0}section, the FV contour is symmetrically distributed along the x-axis. Groundwater flows from both sides of the tunnel to the inside along the fault intersection.

_{Y = 1.95}= U

_{Y = −1.95}> U

_{Y = 0}> U

_{Y = 3.9}= U

_{Y = −3.9}.

^{3}/h at the excavation face and the total water inflow rate of 1813.16 m

^{3}/h by integrating the FV over the area.

#### 3.4. Tunnel Is 20 m above the Center of the Two Intersecting Faults

_{Y = −20}, XY

_{Z = 0}, YZ

_{X = 0}) while the tunnel is excavated to 20 m above the two intersecting faults (Y = −20).

_{Y = 0}, the PP contours are distributed elliptically symmetrically along the x-axis, and the ellipse’s major axis is parallel to the z-axis. On the vertical downward section, pore pressure gradually increases with the burial depth and is displayed in a funnel-shape near the excavation face. As shown in the FV contours, groundwater mainly flows from the overlapped intersection zone and the damage zone of the faults to the tunnel, with a maximum value of 1.26 × 10

^{−3}m/s. The FV contour appears symmetrically with respect to the x-axis on the section of XZY = 0 and the y-axis on the section of YZ

_{X = 0}. The value of FV underneath the tunnel floor is expressively bigger than that above the tunnel vault.

^{−5}m/s, 1.85 × 10

^{−4}m/s, 6.62 × 10

^{−4}m/s, and 2.60 × 10

^{−4}m/s, respectively. Flow velocities are gradually reduced within a 9 m range of the excavation face until reaching zero. In the range of 0~5 m of the host rock zone, the flow velocities below the tunnel floor are bigger than that at the tunnel vault and above, and the flow velocities at the tunnel vault or floor are bigger than that at the tunnel face and the surrounding areas. The magnitude order of the velocities is U

_{Y = −1.95}> U

_{Y = −3.9}> U

_{Y = 0}> U

_{Y = 1.95}> U

_{Y = 3.9}.

^{3}/h at the excavation face and the total water inflow rate of 34.51 m

^{3}/h by integrating the FV over the area.

#### 3.5. Tunnel Is 40 m above the Center of the Two Intersecting Faults

_{Y = −40}, XY

_{Z = 0}, YZ

_{X = 0}) while the tunnel is excavated to 40 m above these two intersecting faults (Y = −40).

_{Y = −40}section, the PP contours are symmetrically elliptical with respect to the x-axis, and the central axis is parallel to the z-axis. On the YZ

_{X = 0}section, pore pressure increases with the burial depth and is presented in a funnel shape near the excavation face. The FV contours reveal that groundwater mainly flows from the overlapped intersection zone and the damage zone of faults to the tunnel with a small FV and the maximum value is just about 2.03 × 10

^{−5}m/s. Five measuring lines were placed 50 m in front of the excavation face to monitor and explore the variation law of PP and FV as listed in Table 2 and Figure 11.

^{−8}m/s and 3.64 × 10

^{−8}m/s. On the section of Y = 0, FV decreases slowly from the maximum value of 9.88 × 10

^{−8}m/s until it approaches 0. Within 9 m in front of the excavation face, FV decreases gradually first and then slowly until it approaches zero. In 0~3 m of the host rock zone, FV at and below the tunnel floor is much higher than that at the tunnel vault and above, and FV at the tunnel vault or floor is bigger than that at the tunnel face and the surrounding areas. Their magnitudes are in the order of U

_{Y = −1.95}> U

_{Y = 1.95}> U

_{Y = 0}> U

_{Y = −3.9}> U

_{Y = 3.9}.

^{3}/h at the excavation face and the total inflow rate of 0.016 m

^{3}/h by integrating the FV over the area.

## 4. Discussion

_{Y = 20}= P

_{Y = −20}> P

_{Y = 40}= P

_{Y = −40}> P

_{Y = 0}. In summary, when the fault intersection is in Y = ±40 and Y = ±20, the surrounding rock near the tunnel face has low permeability, which has little effect on the water pressure around the excavation face. Due to the stress release during the tunnel excavation progress, a low-pressure region is formed near the excavation face, which has a more significant influence on the distribution of pore pressure in the tunnel-surrounding rock than the influence of the two overlapped intersecting faults.

_{Y = 0}> U

_{Y = 20}= U

_{Y = −20}> U

_{Y = 40}= U

_{Y = −40}. When the tunnel approaches the fault intersection, the flow velocity increases by orders of magnitude, reflecting that the distance to the fault intersection significantly impacts the fluid flow velocity in the tunnel-surrounding rock. The water inflow rate around the excavation face and the total water inflow rate into the tunnel are shown in Table 3 and Figure 14. It has been found that when the fault intersection center position is at Y = 0, the inflow rate value is the largest, and when the fault intersection center position is at Y = ±40 m and Y = ±20 m, the water inflow rates are the same. It shows that the relative vertical location of the intersecting faults has little effect on the flow field.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Li, S.; Liu, B.; Nie, L.; Liu, Z.; Tian, M.; Wang, S.; Su, M.; Guo, Q. Detecting and monitoring of water inrush in tunnels and coal mines using direct current resistivity method: A review. J. Rock Mech. Geotech. Eng.
**2015**, 7, 469–478. [Google Scholar] [CrossRef] - Xu, Z.; Lin, P.; Xing, H.; Pan, D.; Huang, X. Hydro-mechanical Coupling Response Behaviors in Tunnel Subjected to a Water-Filled Karst Cave. Rock Mech. Rock Eng.
**2021**, 54, 3737–3756. [Google Scholar] [CrossRef] - Li, S.C.; Wang, X.T.; Xu, Z.H.; Mao, D.Q.; Pan, D.D. Numerical investigation of hydraulic tomography for mapping karst conduits and its connectivity. Eng. Geol.
**2021**, 281, 105967. [Google Scholar] [CrossRef] - Wang, X.; Kong, X.Z.; Hu, L.; Xu, Z. Mapping conduits in two-dimensional heterogeneous karst aquifers using hydraulic tomography. J. Hydrol.
**2023**, 617b, 129018. [Google Scholar] [CrossRef] - Wang, X.T.; Li, S.C.; Xu, Z.H.; Mao, D.; Pan, D. An interval risk assessment method and management of water inflow and inrush in course of karst tunnel excavation. Tunn. Undergr. Space Technol.
**2019**, 92, 103033. [Google Scholar] [CrossRef] - Xu, Z.H.; Wang, W.Y.; Lin, P.; Nie, L.C.; Wu, J.; Li, Z.M. Hard-rock TBM jamming subject to adverse geological conditions: Influencing factor, hazard mode and a case study of Gaoligongshan Tunnel. Tunn. Undergr. Space Technol.
**2021**, 108, 103683. [Google Scholar] [CrossRef] - Xu, Z.H.; Yu, T.F.; Lin, P.; Wang, W.Y.; Shao, R.Q. Integrated geochemical, mineralogical, and microstructural identification of faults in tunnels and its application to TBM jamming analysis. Tunn. Undergr. Space Technol.
**2022**, 128, 104650. [Google Scholar] [CrossRef] - Xue, Y.; Kong, F.; Li, S.; Zhang, Q.; Qiu, D.; Su, M.; Li, Z. China starts the world’s hardest “Sky-High Road” project: Challenges and countermeasures for Sichuan-Tibet railway. Innovation
**2021**, 2, 100105. [Google Scholar] [CrossRef] - Li, X.; Zhang, P.; He, Z.; Huang, Z.; Cheng, M.; Guo, L. Identification of geological structure which induced heavy water and mud inrush in tunnel excavation: A case study on Lingjiao tunnel. Tunn. Undergr. Space Technol.
**2017**, 69, 203–208. [Google Scholar] [CrossRef] - Wang, X.T.; Li, S.C.; Xu, Z.H.; Hu, J.; Pan, D.; Xue, Y. Risk assessment of water inrush in karst tunnels excavation based on normal cloud model. Bull. Eng. Geol. Environ.
**2019**, 78, 3783–3798. [Google Scholar] [CrossRef] - Wang, Y.; Yang, W.; Li, M.; Liu, X. Risk assessment of floor water inrush in coal mines based on secondary fuzzy comprehensive evaluation. Int. J. Rock Mech. Min. Sci.
**2012**, 52, 50–55. [Google Scholar] [CrossRef] - Sun, W.; Zhou, W.; Jiao, J. Hydrogeological classification and water inrush accidents in China’s coal mines. Mine Water Environ.
**2016**, 35, 214–220. [Google Scholar] [CrossRef] - Xu, Z.H.; Bu, Z.H.; Pan, D.D.; Li, D.Y.; Zhang, Y.C. A novel numerical method for grouting simulation in flowing water considering uneven spatial and temporal distribution of slurry: Two-Fluid Tracking (TFT) method. Comput. Geotech.
**2022**, 147, 104756. [Google Scholar] [CrossRef] - Xue, Y.G.; Kong, F.M.; Li, S.C.; Qiu, D.; Su, M.; Li, Z.; Zhou, B. Water and mud inrush hazard in underground engineering: Genesis, evolution and prevention. Tunn. Undergr. Space Technol.
**2021**, 114, 103987. [Google Scholar] [CrossRef] - Wu, Q.; Xu, H.; Pang, W. GIS and ANN coupling model: An innovative approach to evaluate vulnerability of karst water inrush in coalmines of north China. Environ. Geol.
**2008**, 54, 937–943. [Google Scholar] [CrossRef] - Wang, X.T.; Li, S.C.; Xu, Z.H.; Lin, P.; Hu, J.; Wang, W. Analysis of Factors Influencing Floor Water Inrush in Coal Mines: A Nonlinear Fuzzy Interval Assessment Method. Mine Water Environ.
**2019**, 38, 81–92. [Google Scholar] [CrossRef] - Kun, M.; Onargan, T. Influence of the fault zone in shallow tunneling: A case study of Izmir Metro Tunnel. Tunn. Undergr. Space Technol.
**2013**, 33, 34–45. [Google Scholar] [CrossRef] - Abdollahi, M.S.; Najafi, M.; Bafghi, A.Y.; Marji, M.F. A 3D numerical model to determine suitable reinforcement strategies for passing TBM through a fault zone, a case study: Safaroud water transmission tunnel, Iran. Tunn. Undergr. Space Technol.
**2019**, 88, 186–199. [Google Scholar] [CrossRef] - Wu, J.; Wang, X.; Wu, L.; Lu, Y.-N.; Han, Y.-H. Parametric Study of Water Inrush in a Tunnel Crossing a Fault Based on the “Three Zones” Fault Structure. KSCE J. Civ. Eng.
**2022**, 26, 3600–3619. [Google Scholar] [CrossRef] - Jeon, S.; Kim, J.; Seo, Y.; Hong, C. Effect of a fault and weak plane on the stability of a tunnel in rock-a scaled model test and numerical analysis. Int. J. Rock Mech. Min. Sci.
**2004**, 41, 486–491. [Google Scholar] [CrossRef] - Zheng, Z.; Liu, R.; Zhang, Q. Numerical Simulation and Risk Assessment of Water Inrush in a Fault Zone that Contains a Soft Infill. Mine Water Environ.
**2019**, 38, 667–675. [Google Scholar] [CrossRef] - Wu, J.; Wu, L.; Sun, M.; Lu, Y.-N.; Han, Y.-H. Analysis and Research on Blasting Network Delay of Deep-Buried Diversion Tunnel Crossing Fault Zone Based on EP-CEEMDAN-INHT. Geotech. Geol. Eng.
**2022**, 40, 1363–1372. [Google Scholar] [CrossRef]

**Figure 3.**Pore pressure and flow velocity within 30 m ahead of the tunnel face as a function of distance away from the tunnel face (Y = 40 m).

**Figure 5.**Pore pressure and flow velocity within 30 m ahead of the tunnel face as a function of distance away from the tunnel face (Y = 20 m).

**Figure 7.**Pore pressure and flow velocity within 30 m ahead of the tunnel face as a function of distance away from the tunnel face (Y = 0 m).

**Figure 9.**Pore pressure and flow velocity within 30 m ahead of the tunnel face as a function of distance away from the tunnel face (Y = −20 m).

**Figure 11.**Pore pressure and flow velocity within 30 m ahead of the tunnel face as a function of distance away from the tunnel face (Y = −40 m).

**Figure 14.**Bar chart of water inflow rates with different relative locations of the fault intersection (Y).

Factor | Classification | ||||
---|---|---|---|---|---|

The location of intersecting faults (m) | Y = 40 | Y = 20 | Y = 0 | Y = −20 | Y = −40 |

Number | Location of Measuring Line | Number of Points |
---|---|---|

1 | X = 0~50 m, Y = 3.90 m | 100 |

2 | X = 0~50 m, Y = 1.95 m | 100 |

3 | X = 0~50 m, Y = 0.00 m | 100 |

4 | X = 0~50 m, Y = −1.95 m | 100 |

5 | X = 0~50 m, Y = −3.90 m | 100 |

Location of the Fault Intersection | Y = 40 m | Y = 20 m | Y = 0 m | Y = −20 m | Y = −40 m |
---|---|---|---|---|---|

Flow rate at the excavation face (m^{3}/h) | 0.005 | 12.5 | 670.4 | 12.0 | 0.006 |

Flow rate at the tunnel perimeter (m^{3}/h) | 0.010 | 23.2 | 1142.8 | 22.5 | 0.010 |

Total flow rate (m^{3}/h) | 0.015 | 35.7 | 1813.2 | 34.5 | 0.016 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, J.; Lu, Y.; Wu, L.; Han, Y.; Sun, M.
Numerical Investigation of Water Inflow Characteristics in a Deep-Buried Tunnel Crossing Two Overlapped Intersecting Faults. *Water* **2023**, *15*, 479.
https://doi.org/10.3390/w15030479

**AMA Style**

Wu J, Lu Y, Wu L, Han Y, Sun M.
Numerical Investigation of Water Inflow Characteristics in a Deep-Buried Tunnel Crossing Two Overlapped Intersecting Faults. *Water*. 2023; 15(3):479.
https://doi.org/10.3390/w15030479

**Chicago/Turabian Style**

Wu, Jing, Yani Lu, Li Wu, Yanhua Han, and Miao Sun.
2023. "Numerical Investigation of Water Inflow Characteristics in a Deep-Buried Tunnel Crossing Two Overlapped Intersecting Faults" *Water* 15, no. 3: 479.
https://doi.org/10.3390/w15030479