# Impact of the Depth of Diaphragm Wall on the Groundwater Drawdown during Foundation Dewatering Considering Anisotropic Permeability of Aquifer

^{1}

^{2}

^{*}

## Abstract

**:**

_{W}) and the ratio of horizontal and vertical hydraulic conductivity of dewatering aquifer (R

_{C}) are varied. The relationship between approximate hydraulic gradient (Δi) and R

_{W}(or R

_{C}) can be fitted by Boltzmann curve (or logarithmic curve). Effective, suggested and control values of R

_{W}(or R

_{C}) are proposed, of which the suggested value is recommended in practical engineering. The effective, suggested and control value of R

_{W}can be calculated by logarithmical equation considering the value of R

_{C}.

## 1. Introduction

## 2. Project Description

#### 2.1. Engineering Overview

_{E}) of Zone-I is 17.44 m and that of Zone-II is 19.50 m. A diaphragm wall with a thickness of 0.8 m is constructed as the waterproof curtain. The buried depth of the diaphragm wall (D

_{W}) in Zone-I is 30.8 m, and 34.2m in Zone-II. Four pumping wells inside the pit and two observation wells outside the pit are arranged, which is shown in Figure 1.

#### 2.2. Engineering Geology and Hydrogeology

_{1}), sandy silt (2

_{3–1}), mucky clay (4), silty clay (5

_{1}), silt (5

_{2}), silty clay (6), mealy sand (7

_{1}), fine sand (7

_{2}), silty clay with mealy sand (8

_{1}) and silty clay (8

_{2}). The soil profile and properties of soil layers are presented in Figure 2.

_{1}and 2

_{3-1}and it is affected by rainfall, spring tides and surface water. The water inflow rate of a single well is 0.48–30 m

^{3}/d, and the hydraulic conductivity is 0.01–0.85 m/d;

_{1}and 5

_{2}. The water inflow rate of a single well is 5–15 m

^{3}/d, and the hydraulic conductivity is 0.26–0.78 m/d;

_{1}and 7

_{2}. The water inflow rate of a single well is 36–48 m

^{3}/d, and the hydraulic conductivity is 0.18–4.1 m/d [43].

#### 2.3. Pumping Test

_{s}is the overburden pressure between the bottom surface of the foundation pit and the top surface of the underlying confined aquifer (kPa); P

_{w}is the uplift force of artesian water in the initial state (kPa); h

_{i}is the thickness of each layer of soil between the bottom surface of foundation pit and top surface of the underlying confined aquifer (m); h

_{p}is the difference between the groundwater level and top surface of the confined aquifer (m); γ

_{si}is the unit weight of each soil layer between the bottom surface of the foundation pit and the top surface of the underlying confined aquifer (kN/m

^{3}); γ

_{w}is the unit weight of water (kN/m

^{3}); and F

_{s}is the safety coefficient, which is considered as 1.10 in this study [44].

## 3. Numerical Analysis

#### 3.1. Numerical Theory

_{ij}= hydraulic conductivity of different direction, i, j = axes of x, y, z in Cartesian coordinate system, H = hydraulic head of groundwater, q = external source/sink flux, t = time, and S

_{s}= specific storage, S

_{s}≈ γ

_{w}m

_{v}, γ

_{w}= unit weight of water, m

_{v}= soil coefficient of volume compressibility. Based on Terzaghi’s 1D consolidation theory, if the total vertical pressure is constant during the withdrawal or recharge of groundwater from an aquifer, the following equation could be applied:

#### 3.2. Model Setup

#### 3.3. Soil Parameters

#### 3.4. Model Verification

#### 3.5. Simulation Results

_{C}) are varied. The thickness of the dewatering confined aquifer (T

_{a}) is set as 10.8 m in this case. D ranges from 0 to 10.8 m with an increment of 1.2 m, and R

_{C}changes from 1 to 10 with an increment of 1.

_{C}equals 2. Groundwater drawdown outside the pit is obviously smaller than that inside the pit. The groundwater drawdown and ground settlement after dewatering of point G12, which is 5 m away outside the diaphragm wall is shown in Figure 8b. With the increasing of D, groundwater drawdown at point G12 decreases from 5.03 m (D = 0 m) to 3.53 m (D = 9.6 m). Ground settlement at point G12 decreases from 19.5 mm (D = 0 m) to 13.70 mm (D = 9.6 m). Both groundwater drawdown and ground settlement decrease gently initially and then change quickly.

_{C}when D is 4.8 m. Groundwater drawdown at point G12 is 4.71 m when R

_{C}is 2 and 4.25 m when R

_{C}is 10. Due to the decrease of vertical hydraulic conductivity, water supply from the boundary is more difficult which results in the decrease of groundwater drawdown and reduction of ground settlement outside the pit. The ground settlement at point G12 is 18.6 mm when R

_{C}is 1 and 15.7 mm when R

_{C}is 10. Moreover, comparing the change of groundwater drawdown and ground settlement outside the pit under different value of D and R

_{C}, the influence of D on the groundwater drawdown outside the pit is much larger than that of R

_{C}.

## 4. Discussion

#### 4.1. Groundwater Drawdown at Two Sides of Diaphragm Wall

_{C}is 10 with different R

_{W}, which is defined as the ratio of D to T

_{a}.

_{W}, the seepage path lengthens and the blocking effect is more. Therefore, the supply volume from outside to inside the pit decreases, which results in decreased drawdown outside the pit obviously. Due to the drawdown inside the pit being required to stay the same, the drawdown inside the pit (G11 and G21) varies slightly. For example, the drawdown of G11 ranges from 9.52 m (R

_{W}= 88.9%) to 8.73 m (R

_{W}= 0), and the variation is 0.79 m. Drawdown of G12 ranges from 4.91 m (R

_{W}= 88.9%) to 7.80 m (R

_{W}= 0), and the variation is 2.89 m. Moreover, the effect of dewatering is dissymmetry in the rectangle foundation pit. The ground drawdown outside the pit along the short side (e.g., G12) is larger than that along the long side (e.g., G22) [46,47].

#### 4.2. Penetrating Depth of Diaphragm Wall

_{W}when R

_{C}changes from 1 to 10. All the curves can be fitted by the Boltzmann curve, which is widely used in the simulation of different fields [48,49] and can be divided into three parts: initial gradual part (Part-I), middle sharp part (Part-II) and final gentle part (Part-III). With the increasing of R

_{W}, Δi increases gradually, due to the blocking effect of the diaphragm wall on the groundwater seepage being stronger. When D is larger than the filter length of pumping well, drawdown inside the pit changes little while drawdown outside decreases sharply, and this results in the sharp increase of Δi in Part-II. When R

_{W}keeps increasing, since the difference of drawdown at two sides of diaphragm wall keeps constant while the seepage distance is much longer, Δi increases gently at the Part-III.

_{C}ranges from 4 to 10 with R

_{C}ranges from 1 to 3. Part-III is not so specific when R

_{C}ranges from 1 to 3, since the permeability anisotropy is not obvious enough. Vertical hydraulic conductivity is close to the horizontal conductivity and the water supply from outside is relatively easy, which shortens the seepage distance relatively. When R

_{C}ranges from 4 to 10, Part-III can be distinguished obviously, due to the difficulty of vertical seepage.

_{W}when R

_{C}is 10 on section I-I and II-II, which is fitted by the Boltzmann curve. The x-coordinate of the maximum and minimum value of the second derivative of the curve is defined as the effective and control value of R

_{W}, which are the demarcation points of the three parts. With the increase of R

_{W}, Δi also increases due to the blocking effect of the diaphragm wall. Since D

_{W}is above the bottom of the pumping wells filter, the increase of Δi is gradual. When D

_{W}is over the effective value, Δi increases quickly, and the x-coordinate of the largest acceleration point (the contra-flexure point) is defined as the suggested value. If R

_{W}is over the control value, drawdown at G11 increases and that at G12 decreases, while the seepage distance also increases and this results in the little increment of Δi.

_{W}is 36.2%, 48.0% and 59.9% for section I-I, and 35.9%, 50.6% and 65.4% for section II-II, respectively. By a comprehensive consideration of Δi on two sections, the effective, suggested and control value of R

_{W}is 37%, 51% and 66% when R

_{C}is 10.

#### 4.3. Ratio of Horizontal and Vertical Hydraulic Conductivity

_{C}when R

_{W}changes from 0 to 88.89% is shown in Figure 13. Δi increases with the increase of R

_{C}at all curves, because the permeability in vertical direction reduces and water supply from outside to inside is less. Therefore, the difference value of drawdown on the two sides of the diaphragm wall increases. When R

_{W}is less than 33.33%, the increment of Δi is slight and the acceleration is slow. Since the buried depth of the diaphragm wall is above the filter of the pumping wells, the blocking effect is not obvious and drawdown at the two sides of the diaphragm wall varies little. When R

_{W}is larger than 33.33%, the blocking effect of the diaphragm wall is obvious and the variation of Δi increases obviously.

_{C}when R

_{W}is 77.78%, of which all the relationship can be fitted by logarithmic curve. Groundwater supply from outside to inside requires flow from the bottom of the diaphragm wall, which means vertical permeability is important for the seepage process. Because of the large value of R

_{C}and low vertical hydraulic conductivity, groundwater supply becomes difficult and Δi increases. The acceleration of Δi decreases, and due to the decrease of vertical hydraulic conductivity is limited.

_{C}is smaller than the effective value, Δi is small. The groundwater drawdown outside the pit is large and the environmental effect due to foundation dewatering is adverse. When R

_{C}is over the control value, water supply is difficult and the environment effect is good. If R

_{C}of the dewatering aquifer in the engineering field is small, some measurements can be adopted to increase R

_{C}to control the environment effect. By comprehensive consideration of economy and construction technology, the suggested value should be recommended. The suggested value is defined as the x-coordinate of midpoint of effective and control value. The effective, suggested and control value of R

_{C}is 3.4, 4.8 and 5.2 for section I-I, and those values are 4.0, 5.4 and 6.8 for section II-II when R

_{W}is 77.78%.

#### 4.4. Relationship Between R_{W} and R_{C}

_{W}and R

_{C}, all cases are conducted and the relationship is shown in Figure 15. The control and suggested value of R

_{W}decreases with the increase of R

_{C}, while the effective value of R

_{W}increases with the increase of R

_{C}. All the relationships between R

_{W}and R

_{C}can be fitted by the logarithmic function, of which the characteristic is that the curve changes quickly firstly and the acceleration decreases. By the fitted equation, it is convenient to calculate the control, suggested and effective value of R

_{W}according to different values of R

_{C}.

_{C}is 1.5, the control, suggested and effective value of R

_{W}for section I-I is 80.1%, 55.8% and 31.6% respectively. Those values are 93.9%, 63.9% and 34.2% for section II-II. Therefore, R

_{W}is recommended to be approximately 64% when R

_{C}is 1.5. As per the dissymmetry effect of the foundation pit mentioned above, control and suggested value of R

_{W}on section II-II is larger than that on section I-I, since the drawdown outside the diaphragm wall on section II-II is larger and drawdown inside the diaphragm wall is close.

## 5. Conclusions

_{W}), the ratio of horizontal and vertical hydraulic conductivity in dewatering confined aquifer (R

_{C}) are analyzed by numerical simulation based on an engineering case in Shanghai. The following conclusions can be obtained from this study:

_{W}, due to the increased blocking effect of the diaphragm wall. The relationship between Δi and R

_{W}can be fitted by the Boltzmann curve, which can be divided into three parts: initial gradual part, middle sharp part and final gentle part. The suggested value of R

_{W}is defined as the x-coordinate of the contra-flexure point of the curve. By comprehensive considering of Δi on two sections along the long and short sides of the foundation pit, the suggested value of R

_{W}is 51% when R

_{C}is 10.

_{C}, because the smaller vertical permeability makes the supply of groundwater from outside to inside the pit more difficult. The relationship between Δi and R

_{C}can be fitted by the logarithmic function, which also can be divided into three parts: poor effect part, general effect part and good effect part. X-coordinate of demarcation points of three parts are defined as the effective and control value of R

_{C}. The suggested value of R

_{C}is defined as the midpoint of effective and control value.

_{C}is small, measurements should be adopted to increase R

_{C}to the suggested value. By a comprehensive considering of Δi on two sections along the long and short sides of the foundation pit, suggested value of R

_{C}is 5.4 when R

_{W}is 77.78%.

_{W}with R

_{C}is fitted by logarithmic function, and these values of R

_{W}can be calculated by the values of R

_{C}. By comprehensive consideration of the two sections along the long and short sides of the foundation pit, the suggested value of R

_{W}ranges from 48% to 65% when R

_{C}ranges from 1 to 10.

_{W}and R

_{C}, which can be used in foundation pit dewatering engineering in layered soil to obtain well dewatering effects and reduce environmental effects. Certainly, the specific value of suggested R

_{W}and R

_{C}may change in different engineering projects considering the different geometrical characteristics and hydrogeological strata in different place.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Plan view of foundation pit and layout of pumping and observation wells (recreated based on [42]).

**Figure 7.**Comparison of measured and simulated groundwater level of observation wells in pumping test.

**Figure 8.**Groundwater drawdown and ground settlement with different value of D: (

**a**) Section I-I; (

**b**) Point G12.

**Figure 9.**Groundwater drawdown and ground settlement with different value of D: (

**a**) Section I-I; (

**b**) Point G12.

**Figure 11.**Relationship between Δi and R

_{W}when R

_{C}changes from 1 to 10: (

**a**) section I-I; (

**b**) section II-II.

**Figure 13.**Relationship between Δi and R

_{C}when R

_{W}changes from 0 to 88.89%: (

**a**) section I-I; (

**b**) section II-II.

**Figure 15.**Relationship between control, suggested and effective R

_{W}and R

_{C}: (

**a**) section I-I; (

**b**) section II-II.

Pumping Well | Observation Well | First-Step Dewatering | Second-Step Dewatering | ||
---|---|---|---|---|---|

Pumping Time (d) | Discharge Rate (m^{3}/d) | Pumping Time (d) | Discharge Rate (m^{3}/d) | ||

P1, P2 | OB1, OB2 | 0–3 | 169.1 | 12–15 | 223.5 |

3–11 | 42.3 | 15–27 | 61.3 | ||

P3, P4 | 0–3 | 96.3 | 12–15 | 229.7 | |

3–11 | 30.6 | 15–27 | 41.9 |

No. | Hydrogeological Strata | Thickness (m) | γ (kN/m^{3}) | e | K_{h} (m/d) | K_{v} (m/d) | S_{S} (m^{−1}) |
---|---|---|---|---|---|---|---|

1 | Aq01 | 8.8 | 19 | 0.80 | 4.00 × 10^{−3} | 2.00 × 10^{−3} | 3.50 × 10^{−3} |

2 | AdI | 4 | 17.4 | 1.25 | 2.32 × 10^{−3} | 9.05 × 10^{−5} | 8.51 × 10^{−5} |

3 | Aq02 | 13.2 | 18.9 | 0.84 | 5.80 × 10^{−2} | 6.70 × 10^{−3} | 1.15 × 10^{−3} |

4 | AdII | 4 | 19.4 | 0.94 | 8.80 × 10^{−5} | 1.20 × 10^{−5} | 1.67 × 10^{−4} |

5 | AqI | 10.8 | 18.9 | 0.77 | 4.91 | 2.45 | 3.14 × 10^{−3} |

6 | AdII | 25.9 | 18.3 | 0.92 | 2.32 × 10^{−3} | 9.90× 10^{−4} | 8.01 × 10^{−3} |

Diaphragm wall | 1.00 × 10^{−10} | 1.00 × 10^{−10} | 1.00 × 10^{−9} |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.-w.; Xu, Y.-s.
Impact of the Depth of Diaphragm Wall on the Groundwater Drawdown during Foundation Dewatering Considering Anisotropic Permeability of Aquifer. *Water* **2021**, *13*, 418.
https://doi.org/10.3390/w13040418

**AMA Style**

Wang X-w, Xu Y-s.
Impact of the Depth of Diaphragm Wall on the Groundwater Drawdown during Foundation Dewatering Considering Anisotropic Permeability of Aquifer. *Water*. 2021; 13(4):418.
https://doi.org/10.3390/w13040418

**Chicago/Turabian Style**

Wang, Xu-wei, and Ye-shuang Xu.
2021. "Impact of the Depth of Diaphragm Wall on the Groundwater Drawdown during Foundation Dewatering Considering Anisotropic Permeability of Aquifer" *Water* 13, no. 4: 418.
https://doi.org/10.3390/w13040418