# Finite-Difference Numerical Simulation of Dewatering System in a Large Deep Foundation Pit at Taunsa Barrage, Pakistan

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## Abstract

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^{2}. Two methods, constant head permeability test and Kozeny–Carman equation, were used to determine the hydraulic conductivity of riverbed strata, and numerical simulations using the three-dimensional finite-difference method were carried out. The simulations first used hydraulic conductivity parameters obtained by laboratory tests, which were revised during model calibration. Subsequently, the calibrated model was simulated by different aquifer hydraulic conductivity values to analyze its impact on the dewatering system. The hydraulic barrier function of an underground diaphragm wall was evaluated at five different depths: 0, 3, 6, 9, and 18 m below the riverbed level. The model results indicated that the aquifer drawdown decreases with the increase in depth of the underground diaphragm wall. An optimal design depth for the design of the dewatering system may be attained when it increases to 9 m below the riverbed level.

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Governing Equation

#### 2.1.1. Initial Condition

#### 2.1.2. Boundary Condition

_{xx}, K

_{yy}, K

_{zz}are the hydraulic conductivity parameters along the x, y, and z axis, respectively, and are assumed to be parallel to the traditional x-y coordinate system (LT

^{−1}); h is the piezometric head at (x, y, z) (L); W is the volumetric influx and/or efflux per unit volume of water (T

^{−1}); t is the time (T); S

_{s}denotes the specific storage (L

^{−1}); Ω represents the computational domain; Γ

_{1}, Γ

_{2}, and Γ

_{3}are the first, second, and phreatic surface boundaries, respectively; H

_{0}(x, y, z, t

_{0}) represents the initial head at points (x, y, z); H

_{1}(x, y, z, t) is the known water head at the boundary; q(x, y, z, t) represents the recharge capacity per unit area for the second type boundary condition; and n

_{x}, n

_{y}, and n

_{z}are the components of the unit normal vector on boundary Γ

_{2}along the x, y, and z directions, respectively.

#### 2.2. Finite-Difference Solution of the Groundwater Flow Model

_{i}is the total net inflow into the cell (L

^{3}T

^{−1}); S

_{s}denotes the aquifer specific storage; ΔV denotes the cell volume (L

^{3}); and Δh represents the piezometric head change over time Δt (T).

_{si,j,k}is the net flow into cell i, j, k from all external sources/stresses (L

^{3}T

^{−1}); h

_{i,j,k}is the piezometric head at node i, j, k; P

_{i,j,k}is the coefficient of the head from the external stresses (L

^{2}T

^{−1}); and Q

_{i,j,k}is the flow directly injected into the cell (L

^{3}T

^{−1}).

_{i,j−1/2,k}represents the volumetric flow between nodes i, j, k and i, j−1, k (L

^{3}T

^{−1}); Δr

_{j}, Δc

_{i}, and Δv

_{k}are the cell dimensions along the row, column, and vertical directions (L), respectively; and ∆h

_{i,j,k}/∆t is a finite-difference approximation for the piezometric head derivation, with respect to time (LT

^{−1}), which may be expressed by the finite-difference form, as shown below:

^{m}and t

^{m−1}are times at time levels m and m − 1 (T).

^{2}T

^{−1}), which may be defined as the ratio between the product of flow cross-sectional area and the coefficient of hydraulic conductivity to the length of the flow. The subscript “1/2” denotes the hydraulic conductivity between the nodes; for example, CR

_{i,j−1/2,k}describes the hydraulic conductivity between nodes i, j, k and i, j − 1, k.

^{m}, the seven heads are unknown, as they are part of the head distribution that is to be predicted. Such an equation cannot be solved independently as it represents a single equation with seven unknowns. However, this kind of equation can be written for each active cell in the mesh. A system of “n” equations with “n” unknowns is formed, as only one unknown head exists for each cell. Such a system may be solved simultaneously.

## 3. Case Study

#### Aquifer Hydrogeological Conditions

^{2}), ϕ is the porosity, d

_{e}is the effective particle diameter equal to d

_{10}size (on passing basis) in particle gradation curve, K represents the hydraulic conductivity (L/T), and µ is dynamic viscosity (for water µ = 0.01 g/cm-s).

_{A}, K

_{B}, and K

_{C}, are listed in Table 1.

## 4. Numerical Model

#### 4.1. Spatial Discretization and Boundary Conditions

^{2}including 106 rows and 115 columns with a denser grid size of 4 × 4 m (Figure 2). Three sides of the foundation pit (upstream, left, and downstream sides) were surrounded by the river water storage throughout the construction period, and these sides were treated as constant head boundaries as the variation in the river water level was less than 1 m during the construction period. Therefore, an average river water level of 129.84 m was selected for the simulation.

^{−10}m/s [39,40,41], and inserted down to the level of 117 m (layers 1–3). The hydraulic conductivity parameters of all the strata in the calculation range are listed in Table 1.

#### 4.2. Model Identification and Calibration

#### 4.3. Error Analysis

## 5. Dewatering System Optimization

#### 5.1. Selection of Diaphragm Wall Depth

#### 5.1.1. Scheme-I

#### 5.1.2. Scheme-II

#### 5.1.3. Scheme-III

#### 5.1.4. Scheme-IV

#### 5.1.5. Scheme-V

#### 5.2. Hydraulic Conductivity Variation

#### 5.2.1. Scenario-I

#### 5.2.2. Scenario-II

#### 5.2.3. Scenario-III

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gulick, L.H. Irrigation Systems of the Former Sind Province, West Pakistan. Geogr. Rev.
**1963**, 53, 79. [Google Scholar] [CrossRef] - Zaidi, S.M.A.; Amin, M.; Ahmadani, M.A. Performance evaluation of Taunsa barrage emergency rehabilitation and modernization project. In Proceedings of the 71st Annual Session Proceedings Pakistan Engineering Congress, Karachi, Pakistan, 26–30 July 2011; pp. 650–682. [Google Scholar]
- Basharat, M.; Rizvi, S.A. Groundwater extraction and waste water disposal regulation—Is lahore aquifer at stake with as usual approach. In Proceedings of the Pakistan Engineering Congress, Karachi, Pakistan, 26–30 July 2011; pp. 135–152. [Google Scholar]
- Basharat, M. Spatial and temporal appraisal of groundwater depth and quality in LBDC Command-Issues and Options. Pak. J. Engg. Appl. Sci
**2012**, 11, 14–29. [Google Scholar] - Hsi, J.P.; Carter, J.P.; Small, J.C. Surface subsidence and drawdown of the water table due to pumping. Development
**1994**, 44, 381–396. [Google Scholar] [CrossRef] - Luo, Z.; Zhang, Y.; Wu, Y. Finite element numerical simulation of three-dimensional seepage control for deep foundation pit dewatering. J. Hydrodyn. Ser. B
**2008**, 20, 596–602. [Google Scholar] [CrossRef] - Wang, J.; Feng, B.; Liu, Y.; Wu, L.; Zhu, Y.; Zhang, X.; Tang, Y.; Yang, P. Controlling subsidence caused by de-watering in a deep foundation pit. Bull. Eng. Geol. Environ.
**2012**, 71, 545–555. [Google Scholar] [CrossRef] - Younger, P.L.; Robins, N.S. Challenges in the characterization and prediction of the hydrogeology and geochemistry of mined ground. Geol. Soc. Lond. Spec. Publ.
**2002**, 198, 1–16. [Google Scholar] [CrossRef][Green Version] - Jiang, S.; Kong, X.; Ye, H.; Zhou, N. Groundwater dewatering optimization in the Shengli no. 1 open-pit coalmine, Inner Mongolia, China. Environ. Earth Sci.
**2013**, 69, 187–196. [Google Scholar] [CrossRef] - Wang, J.; Hu, L.; Wu, L.; Tang, Y.; Zhu, Y.; Yang, P. Hydraulic barrier function of the underground continuous concrete wall in the pit of subway station and its optimization. Environ. Geol.
**2009**, 57, 447–453. [Google Scholar] [CrossRef] - Xu, Y.S.; Shen, S.L.; Ma, L.; Sun, W.J.; Yin, Z.Y. Evaluation of the blocking effect of retaining walls on groundwater seepage in aquifers with different insertion depths. Eng. Geol.
**2014**, 183, 254–264. [Google Scholar] [CrossRef] - Wu, Y.-X.; Shen, S.-L.; Wu, H.-N.; Xu, Y.-S.; Yin, Z.-Y.; Sun, W.-J. Environmental protection using dewatering technology in a deep confined aquifer beneath a shallow aquifer. Eng. Geol.
**2015**, 196, 59–70. [Google Scholar] [CrossRef] - Mahmoud, H.; Elghany, A.; Ahmed, A. Optimization for number of vertical drainage wells in highly heterogenious aquifers. Int. J. Multidiscip. Res. Rev.
**2015**, 2, 569–582. [Google Scholar] - Wang, J.; Huang, T.; Sui, D. A case study on stratified settlement and rebound characteristics due to dewatering in shanghai subway station. Sci. World J.
**2013**, 2013. [Google Scholar] [CrossRef] - Xu, B.; Yan, C.; Sun, Q.; Liu, Y.; Hou, J.; Liu, S.; Che, C. Field pumping experiments and numerical simulations of shield tunnel dewatering under the Yangtze River. Environ. Earth Sci.
**2016**, 75, 715. [Google Scholar] [CrossRef] - Alonso, C.; Ferrer, A.; Soria, V. Finite element simulation of construction site dewatering. In Proceedings of the International Conference on Engineering and Mathematics ENMA 2008, Bilbao, Spain, 7–9 July 2008. [Google Scholar]
- Chen, G.X.; Lei, W. Application 3D numerical simulation on foundation pit dewatering design of nanchang international financial center. Adv. Mater. Res.
**2010**, 108, 1482–1485. [Google Scholar] [CrossRef] - Demirbaş, K.; Altan-Sakarya, A.B.; Önder, H. Optimal dewatering of an excavation site. In Proceedings of the Institution of Civil Engineers-Water Management; Thomas Telford Ltd.: London, UK, 2012; Volume 165, pp. 327–337. [Google Scholar]
- Roy, D.; Robinson, K.E. Surface settlements at a soft soil site due to bedrock dewatering. Eng. Geol.
**2009**, 107, 109–117. [Google Scholar] [CrossRef] - Tokgoz, M.; Yilmaz, K.K.; Yazicigil, H. Optimal aquifer dewatering schemes for excavation of collector line. J. Water Resour. Plan. Manag.
**2002**, 128, 248–261. [Google Scholar] [CrossRef] - Zhou, N.; Vermeer, P.A.; Lou, R.; Tang, Y.; Jiang, S. Numerical simulation of deep foundation pit dewatering and optimization of controlling land subsidence. Eng. Geol.
**2010**, 114, 251–260. [Google Scholar] [CrossRef] - Ye, X.W.; Ran, L.; Yi, T.H.; Dong, X.B. Intelligent risk assessment for dewatering of metro-tunnel deep excavations. Math. Probl. Eng.
**2012**, 2012, 618979. [Google Scholar] [CrossRef] - Wang, J.; Feng, B.; Yu, H.; Guo, T.; Yang, G.; Tang, J. Numerical study of dewatering in a large deep foundation pit. Environ. Earth Sci.
**2013**, 69, 863–872. [Google Scholar] [CrossRef] - Geravandi, E.; Kamanbedast, A.A.; Masjedi, A.R.; Heidarnejad, M.; Bordbar, A. Laboratory Investigation of The Impact of Armor Dike Simple and L-Shaped in Upstream and Downstream Intake of the Hydraulic Flow of the Kheirabad River to Help Physical Model. Fresenius Environ. Bull.
**2018**, 27, 263–276. [Google Scholar] - Yihdego, Y.; Danis, C.; Paffard, A.; Yihdego, Y.; Danis, C.; Paffard, A. Groundwater Engineering in an Environmentally Sensitive Urban Area: Assessment, Landuse Change/Infrastructure Impacts and Mitigation Measures. Hydrology
**2017**, 4, 37. [Google Scholar] [CrossRef] - Gao, D.; Liu, Y.; Wang, T.; Wang, D.; Gao, D.; Liu, Y.; Wang, T.; Wang, D. Experimental Investigation of the Impact of Coal Fines Migration on Coal Core Water Flooding. Sustainability
**2018**, 10, 4102. [Google Scholar] [CrossRef] - Ma, X.; Fan, Y.; Dong, X.; Chen, R.; Li, H.; Sun, D.; Yao, S.; Ma, X.; Fan, Y.; Dong, X.; et al. Impact of Clay Minerals on the Dewatering of Coal Slurry: An Experimental and Molecular-Simulation Study. Minerals
**2018**, 8, 400. [Google Scholar] [CrossRef] - Vukelić, Ž.; Dervarič, E.; Šporin, J.; Vižintin, G.; Vukelić, Ž.; Dervarič, E.; Šporin, J.; Vižintin, G. The Development of Dewatering Predictions of the Velenje Coalmine. Energies
**2016**, 9, 702. [Google Scholar] [CrossRef] - Guo, X.; Sun, X.; Ma, J. Numerical Simulation of Three-dimensional Soil Water Content Distribution in Water Storage Pit Irrigation. Fresenius Environ. Bull.
**2018**, 27, 7390–7400. [Google Scholar] - Sege, J.; Wang, C.; Li, Y.; Chang, C.-F.; Chen, J.; Chen, Z.; Osorio-Murillo, C.A.; Zhu, H.; Rubin, Y.; Li, X. Modeling water table drawdown and recovery during tunnel excavation in fractured rock. In AGU Fall Meeting Abstracts; American Geophysical Union: San Francisco, CA, USA, 2015. [Google Scholar]
- You, Y.; Yan, C.; Xu, B.; Liu, S.; Che, C. Optimization of dewatering schemes for a deep foundation pit near the Yangtze River, China. J. Rock Mech. Geotechnol. Eng.
**2018**, 10, 555–566. [Google Scholar] [CrossRef] - Wu, J.; Xue, Y. Groundwater Dynamics; China Water and Power Press: Beijing, China, 2009.
- McDonald, M.G.; Harbaugh, A.W. A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model; US Geological Survey: Reston, VA, USA, 1988.
- Harbaugh, A.W.; Banta, E.R.; Hill, M.C.; Mcdonald, M.G.; Groat, C.G. MODFLOW-2000, The U.S. Geological Survey Modular Groundwater Model User Guide to Modularization Concepts and the Groundwater Flow Process; U.S. Geological Survey, Open-File Report 00-92; U.S. Department of the Interior: Washington, DC, USA, 2000.
- Head, K.H.; Epps, R. Manual of Soil Laboratory Testing; Pentech Press London: London, UK, 1986; Volume 3. [Google Scholar]
- Carman, P.C. Fluid flow through granular beds. Trans. Chem. Eng.
**1937**, 15, 150–166. [Google Scholar] [CrossRef] - Mohan, S.; Sreejith, P.K.; Pramada, S.K. Optimization of open-pit mine depressurization system using simulated annealing technique. J. Hydraul. Eng.
**2007**, 133, 825–830. [Google Scholar] [CrossRef] - Zaidel, J.; Markham, B.; Bleiker, D. Simulating seepage into mine shafts and tunnels with MODFLOW. Ground Water
**2010**, 48, 390–400. [Google Scholar] [CrossRef] - Shoji, Y.; Kumeda, M.; Tomita, Y. Experiments on Seepage through Interlocking Joints of Sheet Pile, Report of the Port and Harbour Institute; Nagase: Yokosuka, Japan, 1982; Volume 21. [Google Scholar]
- Fell, R.; MacGregor, P.; Stapledon, D. Geotechnical Engineering of Embankment Dams; Balkema: Park City, UT, USA, 1992; ISBN 9054101288. [Google Scholar]
- Sellmeijer, J.B.; Cools, J.; Decker, J.; Post, W.J. Hydraulic resistance of steel sheet pile joints. J. Geotechnol. Eng.
**1995**, 121, 105–110. [Google Scholar] [CrossRef] - Omer, J.R. Integrating finite element and load-transfer analyses in modelling the effects of dewatering on pile settlement behaviour. Can. Geotechnol. J.
**2012**, 49, 512–521. [Google Scholar] [CrossRef] - Wang, J.; Feng, B.; Guo, T.; Wu, L.; Lou, R.; Zhou, Z. Using partial penetrating wells and curtains to lower the water level of confined aquifer of gravel. Eng. Geol.
**2013**, 161, 16–25. [Google Scholar] [CrossRef]

Layer | Depth (m) | K_{A} (m/d) ^{1} | K_{B} (m/d) ^{1} | K_{C} (m/d) ^{1} | |||
---|---|---|---|---|---|---|---|

C-H ^{2} | K-C ^{3} | C-H ^{2} | K-C ^{3} | C-H ^{2} | K-C ^{3} | ||

1 | 0–3 | 8.06 | 6.51 | 8.41 | 7.06 | 8.12 | 6.51 |

2 | 3–6 | 6.16 | 5.22 | 5.93 | 4.98 | 7.04 | 4.98 |

3 | 6–9 | 7.14 | 5.98 | 7.19 | 5.98 | 6.89 | 5.47 |

4 | 9–12 | 8.11 | 5.98 | 8.53 | 6.51 | 8.58 | 7.64 |

5 | 12–15 | 9.17 | 7.64 | 8.61 | 6.78 | 8.80 | 7.06 |

6 | 15–18 | 10.05 | 8.24 | 9.69 | 7.64 | 10.76 | 8.86 |

^{1}Hydraulic conductivity values at borehole locations BH-A, BH-B, BH-C.

^{2}Constant head permeability test.

^{3}Kozeny–Carman-equation-based hydraulic conductivity values.

Well Nos. | Capacity (m^{3}/d) | Well Nos. | Capacity (m^{3}/d) |
---|---|---|---|

1–26 | 1223 | 32–34 | 2085 |

27 | 2078 | 35–36 | 1467 |

28–30 | 1467 | 37–58 | 2078 |

31 | 2690 | 59–70 | 1223 |

Parameter | Layer 1 0–3 m | Layer 2 3–6 m | Layer 3 6–9 m | Layer 4 9–12 m | Layer 5 12–15 m | Layer 6 15–18 m | Layer 7 18–300 m |
---|---|---|---|---|---|---|---|

Kh (m/d) | 8 | 6 | 6.5 | 7.5 | 9 | 10 | 10 |

Kv (m/d) | 7 | 5.5 | 5.75 | 7 | 8 | 8.8 | 8.5 |

Time (day) | Calibrated | Scheme-I | Scheme-II | Scheme-III | Scheme-VI | Scheme-V |
---|---|---|---|---|---|---|

0 | 125.92 | 125.92 | 125.92 | 125.92 | 125.92 | 125.92 |

20 | 120.32 | 122.74 | 121.39 | 120.68 | 120.32 | 121.24 |

35 | 117.84 | 120.38 | 119.03 | 118.27 | 117.84 | 116.34 |

50 | 116.71 | 119.27 | 117.92 | 117.14 | 116.71 | 116.18 |

65 | 115.42 | 117.97 | 116.62 | 115.85 | 115.42 | 115.03 |

80 | 115.73 | 118.29 | 116.94 | 116.17 | 115.73 | 115.15 |

95 | 115.96 | 118.51 | 117.16 | 116.39 | 115.96 | 115.06 |

112 | 115.42 | 117.97 | 116.62 | 115.85 | 115.42 | 115.30 |

Average | 117.92 | 120.13 | 118.95 | 118.28 | 117.92 | 117.53 |

Time (day) | Calibrated | Scenario-I | Scenario-II | Scenario-III | |||
---|---|---|---|---|---|---|---|

0 | 125.92 | 125.92 | 125.92 | 125.92 | 125.92 | 125.92 | 125.92 |

20 | 120.32 | 120.67 | 119.68 | 121.11 | 119.15 | 121.55 | 118.60 |

35 | 117.84 | 118.53 | 116.97 | 119.27 | 116.30 | 120.13 | 115.30 |

50 | 116.71 | 117.45 | 115.80 | 118.21 | 115.25 | 119.11 | 114.28 |

65 | 115.42 | 116.12 | 114.57 | 116.86 | 114.14 | 117.91 | 113.22 |

80 | 115.73 | 116.48 | 114.82 | 117.30 | 114.29 | 118.47 | 113.36 |

95 | 115.96 | 116.73 | 115.01 | 117.56 | 114.41 | 118.70 | 113.39 |

112 | 115.42 | 116.14 | 114.49 | 116.95 | 113.93 | 118.21 | 112.98 |

Average | 117.92 | 118.50 | 117.16 | 119.15 | 116.67 | 120.00 | 115.88 |

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## Share and Cite

**MDPI and ACS Style**

Ahmad, I.; Tayyab, M.; Zaman, M.; Anjum, M.N.; Dong, X. Finite-Difference Numerical Simulation of Dewatering System in a Large Deep Foundation Pit at Taunsa Barrage, Pakistan. *Sustainability* **2019**, *11*, 694.
https://doi.org/10.3390/su11030694

**AMA Style**

Ahmad I, Tayyab M, Zaman M, Anjum MN, Dong X. Finite-Difference Numerical Simulation of Dewatering System in a Large Deep Foundation Pit at Taunsa Barrage, Pakistan. *Sustainability*. 2019; 11(3):694.
https://doi.org/10.3390/su11030694

**Chicago/Turabian Style**

Ahmad, Ijaz, Muhammad Tayyab, Muhammad Zaman, Muhammad Naveed Anjum, and Xiaohua Dong. 2019. "Finite-Difference Numerical Simulation of Dewatering System in a Large Deep Foundation Pit at Taunsa Barrage, Pakistan" *Sustainability* 11, no. 3: 694.
https://doi.org/10.3390/su11030694