# Numerical Simulation and Analysis of the Influencing Factors of Foundation Pit Dewatering under a Coupled Radial Well and Curtain

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Conceptual Model

^{2}. Based on the groundwater flow field in the study area, the eastern and western boundaries of the simulation area were parallel to the groundwater flow lines and could be considered as zero-flux boundaries. Meanwhile, the southern and northern boundaries were perpendicular to the groundwater flow lines and could be considered as constant-head boundaries (Figure 2). The bottom and upper boundaries of the simulation domain were considered as impermeable and phreatic surface boundaries, respectively. The unconfined aquifer in the study area could be considered homogeneous and anisotropic, while ignoring infiltration recharge and evaporation in the study area. The vertical permeability coefficient was estimated to be one-tenth of the horizontal permeability value based on the hydrogeological investigation data, which corresponded to 20 and 2 m·d

^{−1}for horizontal and vertical permeabilities, respectively. The aquifer in the study area consists of alluvial sand and cobble layer, thus, the specific yield was established at 0.3 without considering the elastic release of the aquifer.

#### 2.3. Mathematical Model

_{xx}, K

_{yy}, and K

_{zz}are the hydraulic conductivity (m·d

^{−1}); μ is the specific yield; x, y, and z are the coordinate variables (m); t is the time variable (d); Ω is the range of the study area; A

_{1}and A

_{3}are the constant-head boundaries; A

_{2}and A

_{4}are the zero-flux boundaries; A

_{5}is the impermeable boundary; A

_{6}is the phreatic surface boundary;

**n**is the direction of the outer normal of each boundary, and H

_{0}is the initial head at the north and south boundaries (m).

^{3}·d

^{−1}); $d$ is the diameter of the radial pipes (m); $g$ is the acceleration of gravity (m·s

^{−2}); $\u2206H$ is the head loss (m); $v$ is the average flow rate in the pipes (m·d

^{−1}); $l$ is the length of the radial pipes (m); $\vartheta $ is the kinematic viscosity of water (m

^{2}·s

^{−1}), and $e$ is the coarseness degree of the inner wall of the pipes.

^{3}·d

^{−1}); $C$ is the conductance of pipes (m

^{2}·d

^{−1}), and ${H}_{p}$ is the head of pipe flow (m).

^{−1}); ${M}_{p}$ is the thickness of the pipe filter (m); $D$ is the wet perimeter of the pipe (m), and $l$ is the length of the pipe (m).

#### 2.4. Numerical Model

#### 2.5. Scheme Design

#### 2.6. Principles of Scheme Preference

## 3. Results and Discussion

#### 3.1. Pumping Well

^{−1}resulted in a reduction in pumping time from 87.5 to 21.5 days and a decrease in total pumping volume from 31.5 × 10

^{5}to 11.61 × 10

^{5}m³. As shown in Figure 7, correspondingly, the disturbed area of the flow field decreased from 33.45 × 10

^{5}to 9.04 × 10

^{5}m

^{2}, indicating that a smaller total pumping volume resulted in less disturbance to the flow field.

^{−1}. When the number of pumping wells was 36 and the total pumping rate was 8.87 × 10

^{5}m

^{3}, Figure 7 shows that the disturbed area of the flow field was 6.74 × 10

^{5}m

^{2}. It can be seen that, when 36 wells were deployed and the pumping capacity of a single well was 1700 m³·d

^{−1}, the time to reach the target water level was relatively quick; there was a lower total amount of pumping, and there was less disturbance to the groundwater flow field. Continuing to increase the number of wells would increase the construction cost, and there would be no significant improvement in dewatering efficiency. Thus, the solution of 36 wells with a single-well pumping capacity of 1700 m³·d

^{−1}was considered to be the preferred scheme. The disturbance of the seepage field in and near the foundation pit was analyzed using this scenario (Figure 8). Using pumping wells (Figure 8a,c), the water level in the pit was rapidly decreased to below the bottom depth of the pit, owing to the radius of influence of each pumping well being superimposed on the others around the pit, while the head distribution in the pit was relatively uniform. After the dewatering, the drawdown was highest in the vicinity of the pumping well, followed by that observed in the foundation pit, while the cone of depression was centered in the pit and decreased uniformly outwards in a sub-circular shape. Within a 100 m radius of the foundation pit, the water table dropped to a depth of more than 4 m. In addition, this scenario disturbed the seepage field to a greater extent.

#### 3.2. Radial Well

#### 3.2.1. Diameter of the Radial Pipes

#### 3.2.2. Conductance of the Radial Pipes

^{−1}). The area of disturbance in the seepage field caused by the dewatering decreased due to the reduction in total volume of water pumped (Figure 10). The results showed an increase in the efficiency of the radial pipes and the spatial influence of dewatering as a result of the increased conductance of the radial pipes. Moreover, the water level in the foundation pit changed rapidly, resulting in a decrease in the water level to the target value in a relatively short time. Indeed, the efficiency of the radial pipes can be improved significantly when the conductance is equal to the aquifer hydraulic conductivity (20 m·d

^{−1}). In other words, the inflow of the radial pipes could be close to the amount of water flow in the aquifer. Therefore, increasing the conductance of the radial pipes may not significantly enhance the efficiency of the dewatering.

#### 3.2.3. Number of Radial Pipes

#### 3.2.4. Drawdown of the Shaft

^{−1}, the number of radial pipes reached 12, and the shaft drawdown reached 14 m, there was no apparent improvement in dewatering efficiency by continuing to change the parameters. Therefore, an optimal scheme was selected with a radial pipe conductance of 15 m·d

^{−1}, a pipe diameter of 0.14 m, a radial pipe number of 12, and a shaft drawdown of 14 m. The variation in the seepage field in this scheme was analyzed, as shown in the water level variation diagram (Figure 13a). The use of radial wells for dewatering created a sub-circular cone of depression that extended from the center of the foundation pit uniformly in all directions. However, the radial well scheme provided a more suitable level of water control than the pumping well scheme. The seepage field disturbance from dewatering was primarily concentrated at the bottom of the pit and near the radial pipe, decreasing with an increasing distance from the bottom. Alternatively, the curtain resulted in a significant drop depth of the shaft in a short time compared with that of the no-curtain scheme (Figure 12).

#### 3.3. Optimal Dewatering Scheme

^{3}·d

^{−1}) and the optimal radial well dewatering solution (radial pipe conductance of 15 m·d

^{−1}, pipe diameter of 0.14 m, number of radial pipes of 12, and drawdown of shaft of 14 m) were selected for comparison.

#### 3.4. Land Subsidence

## 4. Conclusions

^{−1}, pipe diameter of 0.14 m, number of radial pipes of 12, and drawdown of shaft of 14 m) was the most suitable scheme. The coupled radial well-curtain method was found to be an efficient dewatering method that effectively prevented the lowering of the groundwater level in the area outside the pit, thus reducing the risk of land subsidence in the surrounding area.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the study area and (

**b**) contour map of water table. Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. (Data from Shaanxi Hydrogeology Engineering Geology and Environment Geology Survey Center).

**Figure 4.**Scheme layout plan for dewatering. (

**a**) Scheme with only pumping wells; (

**b**) Scheme with only radial wells; (

**c**) Scheme of pumping wells and curtains; (

**d**) Scheme of radial wells and curtains.

**Figure 5.**Layouts of the different numbers of radial pipes. (

**a**) Layout scheme of 8 radial pipes; (

**b**) Layout scheme of 12 radial pipes; (

**c**) Layout scheme of 16 radial pipes; (

**d**) Layout scheme of 20 radial pipes.

**Figure 6.**Single well pumping rate versus drainage time. The different curves in the diagram represent different numbers of pumping wells. (

**a**) No curtain; (

**b**) Curtain.

**Figure 7.**Area of groundwater flow field disturbance by dewatering of the foundation pits (Area with a drawdown depth greater than 1 m).

**Figure 8.**Local water level variation: (

**a**) Plan view of pumping wells only; (

**b**) Plan view of curtain and pumping wells; (

**c**) Cross-sectional view of pumping wells only; (

**d**) Cross-sectional view of curtain and pumping wells. (The line segments A-A′ and B-B′ represent the positions of the profiles of the two schemes respectively).

**Figure 9.**Drainage effects of different pipe diameters: (

**a**) Effect of pipe diameter on total pumping rate; (

**b**) Effect of pipe diameter on the area of disturbance of the seepage field, selected as a reference for drawdown greater than 1 m.

**Figure 10.**Drainage effects with different pipe conductance: (

**a**) Effect of pipe conductance on total pumping rate; (

**b**) Effect of pipe conductance on the area of disturbance of the seepage field, selected as a reference for drawdown greater than 1 m.

**Figure 11.**Drainage effects with different numbers of pipes: (

**a**) Effect of the number of pipes on total pumping rate; (

**b**) Effect of the number of pipes on the area of disturbance of the seepage field, selected as a reference for drawdown greater than 1 m.

**Figure 12.**Drainage effects with different drawdowns of the shaft: (

**a**) Effect of drawdown of the shaft on total pumping rate; (

**b**) Effect of drawdown of the shaft on the area of disturbance of the seepage field, selected as a reference for drawdown greater than 1 m.

**Figure 13.**Local water level variation: (

**a**) Plan view of radial wells only; (

**b**) Plan view of curtain and radial wells; (

**c**) Cross-sectional view of radial wells only; (

**d**) Cross-sectional view of curtain and radial wells. (The line segments A-A′ and B-B′ represent the positions of the profiles of the two schemes respectively).

**Table 1.**Hydrogeological parameters of the study area. (Data from Shaanxi Hydrogeology Engineering Geology and Environment Geology Survey Center).

Landform Characteristics | Hydraulic Conductivity (m·d^{−1}) | Hydraulic Gradient | |
---|---|---|---|

Alluvial Plain | River Floodplain | 40–70 | 0.1–0.2% |

First Terrace | 17–60 | ||

Second Terrace | 13–47 | ||

Third Terrace | 4.7–16 | ||

Loess Tableland | 0.1–2.8 | 0.5–0.15% |

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## Share and Cite

**MDPI and ACS Style**

Du, S.; Liu, P.; Wang, W.; Shi, W.; Li, Q.; Li, J.; Li, J.
Numerical Simulation and Analysis of the Influencing Factors of Foundation Pit Dewatering under a Coupled Radial Well and Curtain. *Water* **2023**, *15*, 1839.
https://doi.org/10.3390/w15101839

**AMA Style**

Du S, Liu P, Wang W, Shi W, Li Q, Li J, Li J.
Numerical Simulation and Analysis of the Influencing Factors of Foundation Pit Dewatering under a Coupled Radial Well and Curtain. *Water*. 2023; 15(10):1839.
https://doi.org/10.3390/w15101839

**Chicago/Turabian Style**

Du, Shaoshao, Peng Liu, Wei Wang, Wei Shi, Qi Li, Jianhua Li, and Jiaqi Li.
2023. "Numerical Simulation and Analysis of the Influencing Factors of Foundation Pit Dewatering under a Coupled Radial Well and Curtain" *Water* 15, no. 10: 1839.
https://doi.org/10.3390/w15101839