# Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description

_{s}< M

_{u}) is selected for dewatering projects in deep aquifers [24]. With a fixed Q

_{w}and increasing elapsed time t, the hydraulic head dramatically decreases from its initial position until it finally reaches a stable value [35]. This study aims to explore steady seepage characteristics under partial penetrating curtains in the 4th dewatering model and to establish formalized Q

_{w}prediction formulas for a dewatering design. Furthermore, the corresponding dewatering design method shall be presented on the basis of these formulas.

## 3. Numerical Simulation

#### 3.1. Governing Equation

_{ij}is the permeability coefficient, and i, j, = 1, 2, 3; h is the hydraulic head; Q is the external source–sink flux; S

_{s}is the specific storage; t is the elapsed time; h

_{0}(x, y, z) is the initial head at point (x, y, z); h

_{1}(x, y, z, t) is the constant head on boundary Γ

_{1}; n

_{x}, n

_{y}, and n

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

_{2}along the x, y, and z directions, respectively; q(x, y, z, t) is the lateral recharge per unit area on boundary Γ

_{2}; Γ

_{1}is the boundary condition of the water table; and Γ

_{2}is the flux boundary condition.

_{h}is the horizontal permeability coefficient, and k

_{v}is the vertical permeability coefficient.

^{2}T

^{−1}); P

_{i}

_{, j, k}is the sum of the head coefficients between the source and the sink (L

^{2}/T); and Q

_{i}

_{, j, k}is the sum of the constants of the source and the sink (L

^{3}/T). When Q

_{i}

_{, j, k}< 0, groundwater is exiting the system (e.g., pumping); when Q

_{i}

_{, j, k}> 0, groundwater is entering the system (e.g., injection). S

_{i}

_{, j, k}is the cell’s specific storage. ∆r

_{j}, ∆c

_{j}, and ∆v

_{j}are the 3D dimensions of the cube cell (i, j, k). t

^{m}is the time in time step m (T). To represent the hydraulic gradient between nodes rather than the hydraulic gradient between cells, the subscript symbol “1/2” is adopted. For the steady flow that governs Equation (2), the storage term at the right side of the difference equation, i.e., Equation (4), is set to 0 to establish the corresponding difference equation.

#### 3.2. Simplification of Model Parameters

_{u}= 18 m) with a short screen length of 8 m. Notably, the aforementioned parameters can be changed individually in accordance with the requirement.

#### 3.3. Initial/Boundary Conditions

_{w}is the drawdown of the pumping well, and k is the aquifer’s permeability coefficient.

_{w}is approximately 8 m and the maximum permeability coefficient of a confined aquifer k is 36 m/d based on field conditions. The influence radius R is calculated as 480 m using Equation (5). The model range is supposed to extend to more than 480 m from the pit center. Then, a 1000-m-long, 1000-m-wide, and 60-m-deep FDM mesh is obtained. As shown in Figure 4, the horizontal direction has 129 rows and 141 columns. A fine mesh is found around the excavation area and gradually becomes a coarse mesh from the excavation center outward. In the vertical direction, the model of the three strata is divided into 22 layers and the confined aquifer is calculated in 18 layers.

^{−5}m/d) in the model. The location of the pumping wells and the observation points are shown in Figure 4b,c. The pressure heads of the aquifer top are measured for seepage field observation, and four pumping wells are located at the pit center as flux boundaries.

#### 3.4. Seepage Characteristics

_{w}until s

_{w}reaches 8 m and by changing the dewatering parameters individually within a reasonable range, as shown in Figure 5. The seepage field distribution is reflected by the measured drawdowns, and the improved dewatering efficiency is defined by a less q

_{w}((m

^{3}/d)/(m

^{2}∙m)), as follows:

_{w}increases linearly. In addition, this coefficient satisfies the linear relationship between k and q

_{w}in Darcy’s law. The result indicates that k affects dewatering efficiency only by changing flow velocities instead of the seepage field distribution.

_{v}/k

_{h}): The sedimentary process forms a thin sticky layer that prevents vertical flow, and seepage velocity varies in different directions [41]; thus, seepage pressure distribution and vertical velocity change. The increasing anisotropy causes q

_{w}to decline nonlinearly with rising water table due to an increase in vertical hydraulic gradient and the inevitable detour flow. Consequently, dewatering efficiency is enhanced.

_{u}/M ratio remains fixed (0.5), while q

_{w}also increases. A large hydraulic recharge area and a long flow path are obtained when the 3D seepage field is stretched vertically, enhancing hydraulic recharge and raising the groundwater head to the aquifer top.

_{u}): The penetration of curtains generates the blocking effects (i.e., flow direction transfer, flow path lengthening, and seepage area reduction). Water table rises, and q

_{w}is reduced gradually when M

_{u}increases. The superposition of the wall–well effect has been proved to affect the distribution of seepage field in simulations; that is, upper-part flows slow down and turn downward, whereas flow velocities below the wall increase [42]. Besides, numerical results in Figure 5d show the minor dewatering effort requirement with the squeezing deformation of wall-bottom seepage field. The phenomena in simulations indicate that the squeezed seepage field produces additional vertical flows and results in substantial energy consumption and enhanced dewatering efficiency. However, flow velocity increases may also bring about erosive phenomena [42].

_{s}): The design value of l

_{s}relies on field conditions, such that a small l

_{s}will produce a small q

_{w}with the water table maintained outside. Thus, minimal influence is exerted on the seepage field distribution outside with various l

_{s}values, but a long flow path is produced inside.

_{u}, l

_{s}) changes separately or both factors are influenced (k

_{v}/k

_{h}); thus, dewatering efficiency is significantly affected.

## 4. Quantification of Blocking Effects

_{w}in advance. The formalized inflow prediction formulas are established on the basis of seepage characteristic analysis by quantifying the link between dewatering parameters with Q

_{w}.

#### 4.1. Equivalent Pumping Well Inflow

_{T}is proposed under the hypothesis of parallel flow, in which the pit is regarded as a full penetrating pumping well in the absence of 3D flow, as shown in Figure 6.

_{T}value of the equivalent pumping well:

_{h}; s is the drawdown inside the equivalent well and is substituted by the average drawdown on the confined aquifer’s top inside the pit, as shown in Figure 6b; r is the inner radius of the equivalent well that can be determined using the formula L × B = 2πr

^{2}, as shown in Figure 6a; and T is the transmissivity of the aquifer.

#### 4.2. 3D Seepage Field Distortion Function

_{c}–s curve are obtained under various conditions by adjusting inflow in the numerical model. The inflow modification factor Q

_{d}of the equivalent well with barriers can be calculated under a particular drawdown s as follows:

#### 4.2.1. Normalized Form

_{d}(M

_{u}/M), non-standard thickness coefficient M

_{d}(36/M), permeability anisotropy coefficient k

_{d}(k

_{d}/k

_{h}), and well screen insertion ratio l

_{d}(l

_{s}/M

_{u}). In the standard state, the normalized parameters are set as k

_{d}= 1, l

_{d}= 1, and M

_{d}= 1 (M = 36 m).

#### 4.2.2. Standard Curve

_{c}–s) with different b

_{d}and Thiem results (Q

_{T}–s) can be obtained by specifying an inflow set, as shown in Figure 7a. The resulting curves show the linear distribution but with different slopes. All the slopes of the numerical result curves are greater than that of the Thiem result curve. An increase in b

_{d}gradually increases the curve slope of the numerical results. Such increase shows that a large b

_{d}will enhance sensitivity between inflow and drawdowns. The Q

_{d}–b

_{d}curves can be calculated using Equation (8) by setting different s values, and all the curves under different s values converge to a single curve, as shown in Figure 7b. Such convergence indicates that the inflow reduction caused by the 3D flow is uniform under different drawdowns in a particular state. By regarding this converged curve as the standard curve and writing Q

_{d}as Q

_{s}in this state, a separate nonlinear function of the standard curve can be expressed by artificially defining the line type boundary (b

_{d}= 0.75) as follows:

_{d}, k

_{d}, and l

_{d}). Thus, additional distortion functions are required.

#### 4.2.3. Distortion Function

_{d}–b

_{d}curves with different k values are presented in Figure 8a using the same analysis method as that for the standard curve. The results show that all the curves are consistent with those of the standard curve, indicating that k is a non-disturbing factor for the seepage field distribution. Modification is unnecessary because only flow velocity is changed.

_{d}): Similarly, the Q

_{d}–b

_{d}curves under different k

_{d}values are established and shown in Figure 8b. A decrease in k

_{d}increases the deviation between Q

_{d}and Q

_{s}, but linear deviations (the offset value <10%) occur as k

_{d}approaches 0.2 and below. By disregarding this linear deviation and modifying Q

_{s}to Q

_{d}under the corresponding k

_{d}, the distortion function of permeability anisotropy is constructed as follows:

_{d}): Figure 8c presents the Q

_{d}–b

_{d}curves under different M

_{d}values. The figure shows that the Q

_{d}–b

_{d}curves diverge as M

_{d}changes with a similar line type. When M

_{d}> 1, the curve moves upward; otherwise, it shifts downward. By quantifying the variation of the standard curve, the distortion function of aquifer thickness is given as:

_{d}): To utilize the wall–well effects, a short screen length is provided in the field to lengthen flow path. The Q

_{d}–b

_{d}curves at different l

_{d}values are shown in Figure 8d. The line type of the curves remains, but the curves move downward with decreasing l

_{d}values. The variation can be quantified using the following distortion function of screen length:

#### 4.2.4. Inflow Prediction with Partial Penetrating Curtains

_{s}can be approximately modified to Q

_{d}by multiplying it to the normalized distortion function as follows:

## 5. Field Application

#### 5.1. Design Method of the Dewatering Scheme

_{u}is determined through design precision and hydraulic conditions.

#### 5.2. Dewatering Design of the Shuibu Metro Station

#### 5.2.1. Hydrogeological Conditions of the Area

_{h}= 24.5 m/d and k

_{v}= 15 m/d.

#### 5.2.2. Depressurization Requirements

#### 5.2.3. Dewatering Scheme Design

_{u}(2 m), as set by construction organizations, various alternative schemes with different M

_{u}(integers) are presented in Figure 11. (b) The short well screen (l

_{s}= M

_{u}/3) is selected to enhance the wall–well effect. (c) R is set as 330 m (west) and 370 m (east) on the basis of the field pumping tests and Equation (5). (d) Q

_{T}is calculated using Equation (7) with a value of 4328 m

^{3}/d (west) and 5187 m

^{3}/d (east). (e) The distortion functions (normalized) and inflow of each scheme are presented in Table 3 and Figure 12, respectively.

#### 5.2.4. Comparison of Dewatering Control Schemes

_{w}of 2450 m

^{3}/d (west) and 2694 m

^{3}/d (east) is selected.

#### 5.2.5. Deviation Control Curves

_{u}, and 10% deviations are set in this study. (b) The partial failure of non-reinforced concrete curtains changes the blocking effects, and curtains with half-part failure (5 m) are assumed to be the limit state. Hence, deviation control curves are calculated using the inflow prediction formulas shown in Figure 13. On this basis, three levels of dewatering system states are presented: Wall-failure, layer-fluctuation, and normal states. The upper limits of the deviation control curves are presented in Figure 13. Cautious schemes are then adopted on the basis of the crossover points of the deviation control curves and safe drawdown lines. In this project, the corresponding control inflow is 3600, 3000, and 2400 m

^{3}/d under safe drawdowns.

#### 5.2.6. Location of Pumping Wells

^{3}/d) are located inside each section of the pit to ensure its construction safety under normal state (2400 m

^{3}/d). For the wall-failure state, two reserved pumping and observation wells (G: 600 m

^{3}/d) are added (total of 3600 m

^{3}/d). Given the high porosity and compressibility of the silty sand layer, observation wells (SW) outside the pit are installed to observe head changes in the silty sand layer with high external sensitivity.

#### 5.3. Field Verification

^{3}/d (four wells) to ensure the stability of the pit bottom. The dewatering system is within the range of the normal state curve and the (M

_{u}+ 10%) deviation control curve shown in Figure 13a. Hence, a 25% design safe margin is set for the west section dewatering design. For the head variations in the upper aquitard outside the pit, Figure 16b shows the measured data during pumping. Drawdowns are around 1 m and 0.5 m near the west and east sides, respectively. These findings satisfy the control value (2 m) required by construction safety. Moreover, several heads outside return to their initial states due to the powerful recharge of aquifers. The constant stability of the excavation surface in the entire construction process verifies the reliability of the design method.

## 6. Discussion

- A quantitative analysis is based on the assumption that aquifer permeability is uniformly distributed at each point in the influence domain. However, many deep structures (e.g., pile foundations and high-rise building basements) have dispersed clay and grouting structures around the pumping influence area; this condition reduces the regional permeability of aquifers [35]. When these obstructions are located in regions with dense flows (e.g., foundation pit scope and curtain bottom), dewatering efficiency is substantially improved due to flow blocking.
- Non-Darcy flow occurs with a fast flow velocity [34] that is evident at the wall bottom and near the pumping well. Moreover, the wall–well effects enhance the non-Darcy flow effect and further promote dewatering efficiency.
- The parameter coupling effect is not considered in formula establishment. For example, when k
_{d}decreases and the other parameters vary to extend the vertical flow path, groundwater control efficiency may be improved rather than the multiplication of distortion functions caused by the separate variation of parameters.

## 7. Conclusions

- FDM is adopted to analyze dewatering seepage characteristics with curtains. The results show that the seepage field with various parameters exhibits different distributions and flow velocities that affect steady inflow Q
_{w}. Among the parameters, k plays a key role in flow velocity. Meanwhile, the other parameters, such as k_{v}/k_{h}, M, M_{u}, and l_{s}, change the seepage field distribution. - Inflow prediction formulas for pits with partial penetrating curtains in high-permeability aquifers are proposed under the assumption of an equivalent well by establishing the function of the Q
_{d}–b_{d}curve and quantifying seepage deformation. - A design method for dewatering schemes is proposed and applied to the dewatering design of the Shuibu Metro Station. The scheme of a 31.5 m reinforced concrete diaphragm wall combined with a 10.5 m non-reinforced concrete wall is adopted. Considering the design deviation of the formation generalization and curtain leakage, four main pumping wells combined with two reserved pumping wells are located in each subsection of the excavation for groundwater control. This design scheme maintains a safe margin of 25%, and the external drawdown is controlled within 1 m in the field to ensure safety during inside and outside excavations.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Problem sketch: (

**a**) plan view of the rectangle excavation pit; (

**b**) cross-section view of barriers and aquifers. Note: Q

_{w}= pumping rate of wells; L = inner length of the retaining wall; B = inner width of the retaining wall; M = thickness of the confined aquifer; M

_{u}= insertion depth of the barrier; M

_{n}= distance from bottom of barrier to the lower aquitard; l

_{s}= screen length.

**Figure 4.**Finite difference mesh: (

**a**) Three-dimensional (3D) view of the mesh; (

**b**) plan view of the mesh around the pit; (

**c**) central cross-section of the mesh.

**Figure 5.**Water table on the central cross-section with variation dewatering parameters: (

**a**) Permeability; (

**b**) permeability anisotropy; (

**c**) aquifer thickness; (

**d**) insertion depth of barriers; (

**e**) screen length of pumping well.

**Figure 7.**Variation results in the standard state: (

**a**) Q

_{w}–s curve with different b

_{d}; (

**b**) standard curve.

**Figure 8.**Variation curve of Q

_{d}–b

_{d}with varying dewatering parameters: (

**a**) Permeability coefficient; (

**b**) permeability anisotropy coefficient; (

**c**) non-standard thickness coefficient; (

**d**) well screen insertion ratio.

**Figure 10.**Hydrogeological conditions of the area: (

**a**) Hydrogeological map of Fuzhou basin and coastal plain; (

**b**) hydrogeological profile of the metro line.

**Figure 15.**Numerical simulation of the dewatering system: (

**a**) West section dewatering; (

**b**) overall pit dewatering.

**Figure 16.**Groundwater level variation during excavation: (

**a**) Aquifer top within the pit; (

**b**) upper aquitard outside the pit.

Layer | Soil Layer | Type | Thickness (m) | k_{h} (m/d) | k_{v} (m/d) | S_{s} (1/m) | e | r_{w} (kN/m^{3}) |
---|---|---|---|---|---|---|---|---|

I and II | Fill and block stone | Phreatic aquifer | 4.0~6.0 | 8.64 | 8.64 | - | - | 18.5 |

III | Silt | Upper aquitard | 8.0~12.0 | 0.0055 | 0.0015 | 5 × 10^{−4} | 1.67 | 15.7 |

IV | Silt with sand | Upper aquitard | 10.0~12.0 | 0.54 | 0.3 | 5 × 10^{−4} | - | 16.2 |

V | Sand | Confined aquifer | 16.0~18.0 | 24 (Isotropy) | 2 × 10^{−4} | 1.50 | 19.0 | |

VI | Silty clay (dispersive) | Aquitard (partial) | 0.0~6.0 | 0.003 | 0.002 | 5 × 10^{−4} | 0.71 | 19.5 |

VII | Gravel | Confined aquifer | 4.0~6.0 | 40 | 40 | - | - | 17.0 |

IV | Granite | Aquitard | Bottom | - | - | - | - | 21.0 |

No. | Soil Layer | M (m) | k_{h} (m/d) | k_{v} (m/d) | S_{s} (1/m) |
---|---|---|---|---|---|

1 | Phreatic aquifer | 6 | 8.64 | 8.64 | - |

2 | Aquitard | 18 | 0.005 | 0.001 | 5 × 10^{−4} |

3 | Confined aquifer | 36 | 24 | 24 | 2 × 10^{−4} |

Section | L_{p} | Q_{s} | α | β | η | Q_{d} | Section | L_{p} | Q_{s} | α | β | η | Q_{d} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

West | 0 | 0.634 | 0.76 | 1.60 | 1.18 | 0.916 | East | 0 | 0.601 | 0.76 | 1.52 | 1.02 | 0.711 |

2.5 | 0.575 | 0.76 | 1.60 | 0.99 | 0.699 | 2.5 | 0.549 | 0.76 | 1.52 | 0.94 | 0.598 | ||

4.5 | 0.529 | 0.76 | 1.60 | 0.94 | 0.604 | 4.5 | 0.507 | 0.76 | 1.52 | 0.90 | 0.533 | ||

6.5 | 0.482 | 0.76 | 1.60 | 0.90 | 0.531 | 6.5 | 0.466 | 0.76 | 1.52 | 0.88 | 0.478 | ||

8.5 | 0.435 | 0.76 | 1.60 | 0.88 | 0.468 | 8.5 | 0.424 | 0.76 | 1.52 | 0.87 | 0.427 | ||

10.5 | 0.372 | 0.76 | 1.60 | 0.87 | 0.393 | 10.5 | 0.363 | 0.76 | 1.52 | 0.86 | 0.361 | ||

12.5 | 0 | 0.76 | 1.60 | 0.86 | 0 | 12.5 | 0 | 0.76 | 1.52 | 0.85 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Liu, L.; Lei, M.; Cao, C.; Shi, C.
Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata. *Water* **2019**, *11*, 2182.
https://doi.org/10.3390/w11102182

**AMA Style**

Liu L, Lei M, Cao C, Shi C.
Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata. *Water*. 2019; 11(10):2182.
https://doi.org/10.3390/w11102182

**Chicago/Turabian Style**

Liu, Linghui, Mingfeng Lei, Chengyong Cao, and Chenghua Shi.
2019. "Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata" *Water* 11, no. 10: 2182.
https://doi.org/10.3390/w11102182