# Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods of Analytical, Experimental, and Modeling Investigations

#### 2.1. Dupuit and Dupuit–Thiem Formulae

#### 2.2. Laboratory Experiments

#### 2.2.1. Seepage Sand-Tank and Boundary Conditions

#### 2.2.2. Ascending Relief Well (ARW) Design

#### 2.2.3. Laboratory Testing Protocol

#### Loading the Sand-Tank

^{3}), and 16 piezometers were installed between each two layers–in all 96 piezometers.

#### Sand Saturation

#### 2.3. Numerical Simulations

## 3. Results of Laboratory Sand-Tank Tests

_{x}is the radial distance, H is the outer boundary water level, p is the piezometric head, l

_{w}is the ARW penetrating length into the aquifer, s is the drawdown, and h is the height above the aquifer bottom. Here, l

_{nor}is also the ARW degree of penetration into the aquifer. The well radius r

_{w}was normalized as ${r}_{\mathrm{nor}}=\frac{{r}_{\mathrm{w}}}{{r}_{1}}$, using r

_{1}= 1 cm for the lab experiment, and 1 m for numerical modeling. The seepage fluxes Q

_{r1}for the fully penetrating well of radius r

_{1}= 1 cm (for lab experiment) and 1 m (numerical modeling), which were calculated for the case of complete drawdown, were used to determine the dimensionless seepage fluxes given by ${Q}_{\mathrm{nor}}=\frac{Q}{{Q}_{\mathrm{r}1}}$. The results are given below using dimensionless parameters.

#### 3.1. Piezometric Head Distribution

_{nor}= 19.5 and l

_{nor}= 1. For large values of the well radius and length, the piezometric heads were zero at different heights above the ARW center with a maximum seepage flux. The seepage characteristics in the vicinity and at the ARW are practically the same as those in the case of a fully penetrating pumping well. Figure 5 shows the piezometric head distribution vs. distance from a partially penetrating ARW with a small degree of penetration of l

_{nor}= 1/30 and a radius of r

_{nor}= 4.5. The figure shows the zero piezometric head inside and at the top of the ARW, and the piezometric heads above the well top being greater than zero, indicating the downward flow. Figure 6 depicts the piezometric head distribution along the height of the sand-tank at the well center R

_{nor}= 0 and at the radial distance R

_{nor}= 1/6. In particular, the piezometric heads at the heights of h

_{nor}= 1/6 and h

_{nor}= 1/3 above the ARW center were nearly the same.

_{nor}= 4.5) for different values of the ARW degree of penetration. The experimental results show that the piezometric head inside the ARW was zero, and a piezometric head dropped in the vicinity of the partially penetrating ARW. The water table is determined at the elevation where the piezometric heads is zero. Figure 5 and Figure 6 show that the piezometric heads in the vicinity and above the partially penetrating ARW were greater in the middle and smaller at the top and bottom of the well. With the increase of the radial distance from the ARW, this effect gradually disappeared, and the piezometric heads at different depths increased with depth (see Figure 4 and Figure 5).

_{nor}≥ 1/2, the piezometric head above the well is zero. For l

_{nor}≤ 1/3, the piezometric head above the well is greater than zero. Because experiments were conducted for only six values of ARW length for r

_{nor}= 4.5, it can be deduced that the critical length of the ARW penetration l

_{nor}ranges from 1/3 to 1/2.

#### 3.2. Seepage Flux

_{nor}) increases asymptotically with the increase of the degree of penetration l

_{nor}, which can be described by an exponential relationship (with R

^{2}> 0.96) given by:

_{0}and B

_{0}, ${Q}_{\mathrm{nor}}^{1}$, A

_{1}and B

_{1}are fitting parameters, and ${\zeta}_{\mathrm{c}}$ is the critical degree of penetration.

_{nor}= 14.5, ${\zeta}_{\mathrm{c}}=0.15$ for r

_{nor}= 9.5, and ${\zeta}_{\mathrm{c}}=0.35$ for r

_{nor}= 4.5. (The dependence of the critical degree of penetration ${\zeta}_{\mathrm{c}}$ on the well radius and the boundary head, based on the results of numerical simulations, is described below in Section “Numerical simulation results”). Figure 9 demonstrates a relationship between the seepage flux Q

_{nor}and the well radius r

_{nor}given by

^{2}> 0.96 and B

_{2}< 1, where ${Q}_{\mathrm{nor}}^{2}$, A

_{2}and B

_{2}are fitting parameters, r

_{nor}is the well radius.

## 4. Numerical Simulation Results

#### 4.1. Relationships between Seepage Flux, Well Length and Radius

^{2}> 0.99. The seepage flux increases with the increase in the well radius according to a power law relationship given by Equation (2) with R

^{2}= 1. The results of numerical simulations correspond to those from the laboratory experiments. Figure 10 and Figure 11 also show that the seepage flux increases with the increase in the degree of penetration, and asymptotically reaches the maximum value for ${l}_{\mathrm{nor}}\le {\zeta}_{\mathrm{c}}$. When the degree of penetration is greater than the critical value of ${\zeta}_{\mathrm{c}}$, the seepage flux reaches the maximum value and remains practically constant as the degree of penetration continues to increase. The critical degree of penetration ${\zeta}_{\mathrm{c}}$ decreases with the increase in the well radius, and increases with the increase of the boundary head.

#### 4.2. Seepage Characteristics

_{nor}distributions above the well for the case H

_{nor}= 1 and r

_{nor}= 1.0 in an unconfined aquifer are shown in Figure 12. For the partially penetrating ARW (for l

_{nor}from 1/60 to ½), shown in the subfigures (1)–(7) of Figure 12, the lines of the piezometric head of zero (i.e., indicating the water level) are located above the well screen (at x = 0), which correspond to the degree of penetration being less than the critical value of ${\zeta}_{\mathrm{c}}$. For the partially penetrating wells (for l

_{nor}= 2/3 and 5/6), shown in subfigures (8) and (9) and a fully penetrating well, shown in subfigure (10) of Figure 12, the lines of the zero piezometric head are below the top of the well, which correspond to conditions exceeding the critical value of ${\zeta}_{\mathrm{c}}$.

_{c}, the seepage flux of a partially penetrating ARW is the same as that of a fully penetrating well generating a maximum seepage flux. A similar pattern of the seepage flux was determined for a descending partially penetrating pumping well [57]. The piezometric head distribution characteristics determined using numerical modeling are consistent with the experimental results in the sand-tank described above in Section “Results of Laboratory Sand-Tank Tests.”

_{nor}= 1 and r

_{nor}= 1.0. The flow net indicates that the equipotential lines above the ARW are concaved in the vicinity above the ARW. The curvature of the arched shape equipotential lines gradually increases with the well length increase, and when the equipotential line intersects the water table line, the equipotential line bifurcates into two lines, symmetrically distributed around the ARW. When the ARW’s degree of penetration of exceeds the critical value of ${\zeta}_{\mathrm{c}}$, the equipotential lines are symmetrically distributed around the ARW. The streamlines shown in Figure 13 indicate that a single ARW can drain the entire aquifer regardless of the degree of penetration, and even for the degree of the penetration less than ${\zeta}_{\mathrm{c}}$, groundwater flow from the entire aquifer thickness is directed into the ARW.

#### 4.3. ARW’s Critical Degree of Penetration

_{nor}for different r

_{nor}, according to the relationship given by:

_{nor}is the ARW normalized well radius, H

_{nor}= H/M for the case of a confined aquifer, and H

_{nor}= H/H = 1 for an unconfined aquifer.

_{nor}and a small well radius, for example, when H

_{nor}> 2.0 and r

_{nor}< 0.2, even for a fully penetrating well, the piezometric head above the well still exceeds zero, and the maximum seepage flux is not reached, as shown in Figure 14. Figure 15 presents a contour map of ${\zeta}_{\mathrm{c}}$ for different H

_{nor}and r

_{nor}based on the results of numerical simulations. These results can be used for designing optimal ARWs to gain maximum seepage flux with minimum drilling lengths.

#### 4.4. Model Validation

## 5. Modified Dupuit and Dupuit–Thiem Formulae for a Single ARW

#### 5.1. Unconfined Aquifer

_{n}) and calculations using the Dupuit formula (Q

_{s}) for a single partially penetrating ARW in an unconfined aquifer, shown in Figure 1a, for r

_{nor}= 1.0 and the boundary head H

_{nor}= 1. One can see that the seepage flux calculated using the Dupuit equation is smaller than that determined from numerical simulations. For l

_{w}< l

_{c}, the effective water level drawdown above the ARW can be determined as the value s

_{eff}= s+l

_{w}, and a modified version of the Dupuit equation for the seepage flux Q

_{r}can be given by:

_{w}≥ l

_{c}, the ARW seepage flux can be calculated from the Dupuit equation, as for a fully penetrating pumping well.

#### 5.2. Confined Aquifer

_{eff}= s+l

_{w}is the effective piezometric head drawdown.

_{nor}= 1.0 and the boundary head H

_{nor}= 2 for different values of the well penetration are summarized in Table A4 and Figure 17b. Table A4 includes the seepage flux ${Q}_{\mathrm{nor}}^{\mathrm{n}}$ from numerical simulations, ${Q}_{\mathrm{nor}}^{\mathrm{s}}$ calculated using the Dupuit–Thiem formula, and ${Q}_{\mathrm{nor}}^{\mathrm{r}}$ from Equation (5). Table A4 also shows that the relative error of calculations ${Q}_{\mathrm{nor}}^{\mathrm{r}}$ using Equation (5) compared to the ${Q}_{\mathrm{nor}}^{\mathrm{n}}$ is from −24.88% to 1.1%, while the relative error of using the Dupuit–Thiem formula is from −33.17% to −51.87%.

#### 5.3. Confined-Unconfined Aquifer

_{nor}= 1.0 and the boundary head H

_{nor}= 7/6, are summarized in Table A5 and shown in Figure 17c. The relative error of calculations of Q

_{r}based on Equation (6), compared to numerical simulations, ranges from 2.37% to 8.87%.

#### 5.4. Comparison of Modified Dupuit–Thiem Formulae with Results of Laboratory Sand-Tank Experiments

## 6. Concluding Remarks

_{eff}= s+l

_{w}. It is shown that for the ARWs in an unconfined aquifer with the degree of penetration exceeding a critical value, the seepage flux can be calculated based on the original Dupuit formula, and for confined or unconfined-confined aquifers—based on the Dupuit–Thiem formulae for a fully penetrating well.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Results of calculations of the errors of the seepage flux Q

_{nor}(for l

_{nor}= 1 and r

_{nor}= 4.5, 9.5, 14.5 and 19.5) from numerical simulations and Dupuit formula in comparison to the laboratory sand-tank experiments.

Well Radius/r_{nor} | Seepage Flux Q_{nor} | Errors (%) | |||
---|---|---|---|---|---|

Lab Experiments | Dupuit Formula | Numerical Simulations | |||

${\mathit{Q}}_{\mathbf{nor}}^{\mathit{L}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{n}}$ | $\mathbf{Errors}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{n}}$ | $\mathbf{Errors}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | |

4.5 | 1.294 | 1.16 | 1.195 | −7.65 | 3.02 |

9.5 | 1.517 | 1.425 | 1.467 | −3.30 | 2.95 |

14.5 | 1.636 | 1.636 | 1.696 | 3.67 | 3.67 |

19.5 | 1.792 | 1.826 | 1.908 | 6.47 | 4.49 |

H_{nor} | 1 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | |
---|---|---|---|---|---|---|---|---|

r_{nor} | ||||||||

0.1 | 0.65 | 0.96 | ||||||

0.2 | 0.63 | 0.93 | ||||||

0.5 | 0.58 | 0.91 | ||||||

1 | 0.55 | 0.84 | 0.97 | 0.98 | ||||

2 | 0.49 | 0.76 | 0.93 | 0.97 | 0.98 | |||

4 | 0.42 | 0.66 | 0.85 | 0.94 | 0.96 | 0.98 | 0.99 | |

6 | 0.35 | 0.57 | 0.78 | 0.90 | 0.93 | 0.96 | 0.98 | |

10 | 0.29 | 0.48 | 0.67 | 0.80 | 0.9 | 0.93 | 0.95 |

**Table A3.**Seepage flux Q

_{nor}calculations for an unconfined aquifer with r

_{nor}= 1.0 and H

_{nor}= 1.

l_{nor} | s_{nor} | s_{nor}+l_{nor} | Seepage Flux Q_{nor} | Errors (%) | |||
---|---|---|---|---|---|---|---|

${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{n}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | |||

1/2 | 0.362 | 0.862 | 0.937 | 0.936 | 0.657 | −0.10 | −29.88 |

1/3 | 0.282 | 0.615 | 0.846 | 0.860 | 0.563 | 1.60 | −33.41 |

1/6 | 0.186 | 0.353 | 0.635 | 0.647 | 0.427 | 1.93 | −32.73 |

1/10 | 0.143 | 0.243 | 0.497 | 0.511 | 0.356 | 2.82 | −28.45 |

1/15 | 0.111 | 0.178 | 0.409 | 0.414 | 0.299 | 1.22 | −27.04 |

1/30 | 0.080 | 0.113 | 0.302 | 0.303 | 0.237 | 0.39 | −21.37 |

1/60 | 0.061 | 0.078 | 0.235 | 0.233 | 0.197 | −0.79 | −16.04 |

**Table A4.**Parameters used for calculations of the seepage flux for a confined aquifer with r

_{nor}= 1.0 and H

_{nor}= 2.

l_{nor} | s_{nor} | s_{nor}+l_{nor} | Q_{nor} | Errors (%) | |||
---|---|---|---|---|---|---|---|

${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{n}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | |||

1 | 0.652 | 1.652 | 1.050 | 1.153 | 0.523 | 9.83 | −50.18 |

5/6 | 0.628 | 1.461 | 1.031 | 1.042 | 0.507 | 1.10 | −50.81 |

2/3 | 0.575 | 1.242 | 0.972 | 0.913 | 0.472 | −6.10 | −51.46 |

1/2 | 0.499 | 0.999 | 0.874 | 0.767 | 0.421 | −12.20 | −51.87 |

1/3 | 0.402 | 0.736 | 0.723 | 0.605 | 0.354 | −16.35 | −51.11 |

1/6 | 0.269 | 0.436 | 0.504 | 0.390 | 0.257 | −22.72 | −49.02 |

1/10 | 0.203 | 0.303 | 0.384 | 0.289 | 0.206 | −24.75 | −46.30 |

1/15 | 0.170 | 0.237 | 0.312 | 0.241 | 0.181 | −22.87 | −42.19 |

1/30 | 0.120 | 0.153 | 0.227 | 0.172 | 0.139 | −24.47 | −38.88 |

1/60 | 0.096 | 0.112 | 0.176 | 0.132 | 0.118 | −24.88 | −33.17 |

**Table A5.**Parameters used for calculations of the seepage flux for a confined-unconfined aquifer with r

_{nor}= 1.0 and H

_{nor}= 7/6.

l_{nor} | s_{nor} | ${\mathit{h}}_{\mathbf{nor}}^{\mathbf{w}}$ | s_{nor}+l_{nor} | Q_{nor} | Errors (%) | |||
---|---|---|---|---|---|---|---|---|

${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{n}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | $\mathbf{Error}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | ||||

1 | 0.391 | 0.000 | 0.779 | 0.965 | 1.000 | 1.219 | 3.64 | 26.28 |

5/6 | 0.411 | 0.000 | 0.789 | 0.977 | 1.000 | 1.207 | 2.37 | 23.50 |

2/3 | 0.405 | 0.095 | 0.786 | 0.977 | 1.007 | 1.202 | 3.16 | 23.09 |

1/2 | 0.350 | 0.317 | 0.758 | 0.928 | 0.976 | 1.153 | 5.16 | 24.25 |

1/3 | 0.279 | 0.555 | 0.723 | 0.805 | 0.860 | 1.006 | 6.84 | 24.88 |

1/6 | 0.192 | 0.808 | 0.679 | 0.581 | 0.633 | 0.725 | 8.87 | 24.73 |

1/10 | 0.147 | 0.920 | 0.657 | 0.451 | 0.490 | 0.554 | 8.82 | 22.90 |

**Table A6.**Comparison of seepage flux calculations using data from the laboratory experiments, original and modified Dupuit formulae. Errors of original and modified Dupuit formulae are calculated in comparison to the results of laboratory sand-tank experiments.

r_{nor}(l_{nor}). | s_{nor} | Q_{nor} | Errors (%) | |||
---|---|---|---|---|---|---|

Lab Experiments | Modified Dupuit Formula | Dupuit Formula | ||||

${\mathit{Q}}_{\mathbf{nor}}^{\mathit{L}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | ${\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | $\mathbf{Errors}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{r}}$ | $\mathbf{Errors}\mathbf{of}{\mathit{Q}}_{\mathbf{nor}}^{\mathbf{s}}$ | ||

4.5(1/30) | 0.20 | 0.988 | 0.853 | 0.801 | −13.66 | −18.93 |

4.5(1/12) | 0.23 | 1.061 | 1.011 | 0.875 | −4.71 | −17.53 |

4.5(1/6) | 0.33 | 1.217 | 1.264 | 1.066 | 3.86 | −12.41 |

9.5(1/30) | 0.37 | 1.313 | 1.267 | 1.220 | −3.50 | −7.08 |

9.5(1/12) | 0.40 | 1.411 | 1.366 | 1.267 | −3.19 | −10.21 |

**Figure A2.**Photographs of seepage well screens (

**a**) and well covers (

**b**) used in the sand-tank experiments.

**Figure A4.**3-D numerical discretization of the flow domains for simulations of: (

**a**) the sand-tank experiments, and (

**b**) the confined aquifer.

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**Figure 1.**Schematic diagrams of a partially penetrating ascending relief well Ascending Relief Wells (ARW) in (

**a**) an unconfined aquifer, (

**b**) a confined aquifer, and (

**c**) a confined-unconfined aquifer. On the figures, s is the drawdown of water table, h

_{w}is the height of the water table above the well, l

_{w}is well screen length, r

_{w}is well radius, H is the initial piezometric head, M is the aquifer thickness, and K is hydraulic conductivity.

**Figure 2.**Schematic depicting initial and boundary conditions of the radial flow to a partially penetrating well in the sand-tank tests.

**Figure 3.**Schematic design diagram (

**a**) and a photograph (

**b**) of the seepage sand-tank used for laboratory experiments.

**Figure 4.**Piezometric head p

_{nor}distribution for the case of r

_{nor}= 19.5 and l

_{nor}= 1, i.e., a fully penetrating well in the laboratory sand-tank experiments.

**Figure 5.**Piezometric head p

_{nor}distributions for the case of r

_{nor}= 4.5 and l

_{nor}= 1/30 in the laboratory sand-tank experiments.

**Figure 6.**Piezometric head p

_{nor}distribution at radial distances R

_{nor}of 0 and 1/6 for the case of r

_{nor}= 4.5 and l

_{nor}= 1/30 in the laboratory experiment.

**Figure 7.**Piezometric head p

_{nor}distribution for the case of r

_{nor}= 4.5 for different penetrating lengths l

_{nor}. For partially penetrating wells: (

**a**) l

_{nor}= 1/30, (

**b**) l

_{nor}= 1/12, (

**c**) l

_{nor}= 1/6, (

**d**) l

_{nor}= 1/3, (

**e**) l

_{nor}= 1/2, and for a fully penetrating well: (

**f**) l

_{nor}= 1. The dashed red lines indicate the length of the well screened interval.

**Figure 8.**Relationship between the seepage flux Q

_{nor}and the degree of penetration l

_{nor}for different well radii.

**Figure 9.**Relationship between seepage flux Q

_{nor}and well radius r

_{nor}for different degree of penetration l

_{nor}, based on the results of the sand-tank experiments.

**Figure 10.**Relationships between the seepage flux Q

_{nor}and the degree of well penetration l

_{nor}for different boundary conditions: (

**a**) H

_{nor}= 1, (

**b**) H

_{nor}= 2, (

**c**) H

_{nor}= 3, and (

**d**) H

_{nor}= 4.

**Figure 11.**Relationships between the seepage flux Q

_{nor}and the well radius r

_{nor}for different boundary conditions: (

**a**) H

_{nor}= 1, (

**b**) H

_{nor}= 2, (

**c**) H

_{nor}= 3, (

**d**) H

_{nor}= 4.

**Figure 12.**Results of simulations of the water piezometric head p

_{nor}distribution around the ARW in the unconfined aquifer for different well length l

_{nor}: (

**1**) l

_{nor}= 1/60, (

**2**) l

_{nor}= 1/30, (

**3**) l

_{nor}= 1/15, (

**4**) l

_{nor}= 1/10, (

**5**) l

_{nor}= 1/6, (

**6**) l

_{nor}= 1/3, (

**7**) l

_{nor}= 1/2, (

**8**) l

_{nor}= 2/3, (

**9**) l

_{nor}= 5/6, (

**10**) l

_{nor}= 1 (for the case of H

_{nor}= 1 and r

_{nor}= 1.0). The x-axis is the normalized radial distance from the well.

**Figure 13.**The flow net around the ARW in the unconfined aquifer for different well length l

_{nor}: (

**1**) l

_{nor}= 1/60, (

**2**) l

_{nor}= 1/30, (

**3**) l

_{nor}= 1/15, (

**4**) l

_{nor}= 1/10, (

**5**) l

_{nor}= 1/6, (

**6**) l

_{nor}= 1/3, (

**7**) l

_{nor}= 1/2, (

**8**) l

_{nor}= 2/3, (

**9**) l

_{nor}= 5/6, (

**10**) l

_{nor}= 1 (for the case H

_{nor}= 1 and r = 1.0). The x-axis is the radial distance from the well.

**Figure 16.**Comparison of the relationships between the seepage flux Q

_{nor}with l

_{nor}= 1 and r

_{nor}= 4.5, 9.5, 14.5 and 19.5 from numerical simulations, Dupuit formula and laboratory sand-tank experiments.

**Figure 17.**Seepage flux calculations using the results of numerical modeling (Q

_{n}), original Dupuit (Q

_{s}) and modified Dupuit formula (Q

_{r}) for the cases of: (

**a**) an unconfined aquifer, (

**b**) confined aquifer, and (

**c**) confined-unconfined aquifer.

**Figure 18.**Comparison of the results of calculations of the seepage flux from the laboratory sand-tank experiments, original and modified Dupuit formulae.

**Table 1.**Formulae for steady-state seepage flux in unconfined, confined, and confined-unconfined aquifers.

Types of Aquifers | Seepage Flux (Q) |
---|---|

Unconfined (Dupuit) | $Q=1.366\frac{K(2H-s)s}{\mathrm{lg}\frac{R}{{r}_{w}}}$ |

Confined (Dupuit–Thiem) | $Q=2.73\frac{KM{s}_{}}{\mathrm{lg}\frac{R}{{r}_{w}}}$ |

Confined-Unconfined (Dupuit–Thiem) | $Q=1.366\frac{K(2HM-{M}^{2}-{h}_{w}{}^{2})}{\mathrm{lg}\frac{R}{{r}_{w}}}$ |

_{w}is the well radius, M is the thickness of the aquifer, R is the radius of influence of the pumping well, h

_{w}is the water level in the pumping well.

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**MDPI and ACS Style**

Wang, W.; Faybishenko, B.; Jiang, T.; Dong, J.; Li, Y.
Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer. *Water* **2020**, *12*, 919.
https://doi.org/10.3390/w12030919

**AMA Style**

Wang W, Faybishenko B, Jiang T, Dong J, Li Y.
Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer. *Water*. 2020; 12(3):919.
https://doi.org/10.3390/w12030919

**Chicago/Turabian Style**

Wang, Wenxue, Boris Faybishenko, Tong Jiang, Jinyu Dong, and Yang Li.
2020. "Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer" *Water* 12, no. 3: 919.
https://doi.org/10.3390/w12030919