Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits

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

Linghui Liu 1 , Mingfeng Lei 1,2,* , Chengyong Cao 1,* and Chenghua Shi 1 1 School of Civil Engineering, Central South University, Changsha 410075, China; [email protected] (L.L.); [email protected] (C.S.) 2 Key Laboratory of Engineering Structure of Heavy Haul Railway, Central South University, Changsha 410075, China * Correspondence: [email protected] (M.L.); [email protected] (C.C.); Tel.: +86-13787232438 (M.L.); +86-13908489486 (C.C.) Received: 2 September 2019; Accepted: 17 October 2019; Published: 19 October 2019

Abstract: The dewatering of deep foundation pits excavated in highly permeable geology usually requires waterproofing technologies to relieve groundwater flow. However, no effective prediction formula is yet available for determining water inflow in the presence of partial penetrating curtains. In this study, a dewatering project with partial penetrating curtains is analyzed via a finite difference method to show evident three-dimensional (3D) seepage characteristics. The standard curve and distortion functions are established under the assumption of an equivalent well by quantifying the blocking effects; thus, the empirical inflow prediction formulas for steady flow are further developed. Moreover, a dewatering design method based on the prediction formulas is proposed and applied to the field dewatering project in sand and gravel strata. Measured results show that dewatering efficiency is considerably enhanced by 3D flow, forming appropriate pressure distributions for dewatering construction. The uplift pressure below the pit bottom is controlled within a 25% safety margin to verify the reliability of the design method.

Keywords: sand and gravel strata; groundwater ﬂow; partial penetrating curtain; inﬂow prediction; dewatering scheme design

1. Introduction Social problems caused by the accelerated urbanization process, such as ground space congestion and rapid population growth, have persistently afflicted urban development. To solve these issues, numerous underground infrastructures (e.g., metro tunnels, stations) have been built using deep foundation pit technology [1]. Most excavation depths in urban areas have reached more than 20 m at present [2,3]. In the eastern coastal areas of China (e.g., Shanghai, Tianjin, and Hangzhou), considerable amounts of Quaternary marine and estuarine sediments have been alternately deposited, forming an alternating multi-aquifer system (MAS) composed of low-permeability clay, silt, saturated sand, and gravel layers [4–7]. Besides, these deposits frequently have high water tables as approaching the coast [8,9]. Thus, the excavation surface is commonly below the groundwater surface in such areas. For excavation stability, a dry construction environment is necessary, so groundwater control measures are supposed to be adopted during construction. However, the stratigraphic distribution of several MAS regions (such as Fuzhou City) is heterogeneous and discontinuous [10,11]. The voids or deficiencies of aquitards form hydraulic connections among aquifers and provide strong recharge capacity; in such cases, maintaining dry excavation conditions may be extremely difficult. Furthermore, the high water pressure may cause engineering disasters; for example, when overlying layers are

Water 2019, 11, 2182; doi:10.3390/w11102182 www.mdpi.com/journal/water Water 2019, 11, 2182 2 of 19 excavated, the exposed pit bottom may suffer from groundwater uplift action, resulting in bottom uplift failure and even water inflowing towards the excavation [12,13]. Thus, groundwater pressure around a pit must be controlled by reasonable methods. The dewatering decompression method has been commonly applied to the groundwater pressure control so far [14]; however, drawdowns caused by excessive pumping may lead to the development of a depression cone around a pit that further induces pore compression of the aquitard and forms ground settlements [15–19]. Thus, waterproofing technology has been used to alleviate water flow during dewatering by utilizing low-permeability curtains, such as deep mixing piles [20,21], jet grouting piles [22,23], diaphragm walls [24], and other structures that can fully or partially block seepage. However, defects frequently occur at the full penetrating wall with a long penetrating length [25,26] and lead to partial leakage, causing ground collapse and endangering the safety of surrounding buildings. Thick aquifers limit the utilization of the full penetrating wall and other partial penetrating wall schemes are accepted in the field. The dewatering design of deep foundation pits with partial penetrating curtains has been widely researched in recent years. Many studies have focused on settlement control and blocking effects via numerical and field test methods [27–32]. Studies have shown that curtains in the seepage field change flow direction, path, and section and also increase the hydraulic gradient. The combination of partial penetrating wells and curtains can form a complex three-dimensional (3D) seepage field, and the coupled non-Darcy flow further consumes seepage energy [33,34]. The anisotropy of aquifer permeability can also enhance dewatering efficiency [35]. The coupled wall–well effect has been further studied with the maturity of experimental methods [36,37], and scale experiments have been performed to verify the coupled effect and explore optimal wall–well locations. These studies have gradually explored the seepage mechanism of partial penetrating curtains and provided scientific design recommendations. At present, the numerical method is commonly applied to dewatering designs of deep excavations with partial penetrating walls. However, this design method is not efficient due to its modeling complexity that requires considerable calculation effort. Formalized inflow prediction formulas are necessary to ensure the reliability of designs. However, no analytical solution is yet available because of the complex 3D seepage field caused by partial penetrating curtains. Thus, the current study aims to quantify the blocking effect and propose inflow prediction formulas for foundation pits with partial penetrating curtains. Furthermore, a corresponding design method is presented in this paper.

2. Problem Description This investigation is performed on typical layered strata in Fuzhou City. The geographical location of the study area is presented in Figure1. Figure2 shows the longitudinal sectional view of the strata distribution of the station. The confined and phreatic aquifers within regions with an overall thickness of 56 m are separated by the upper aquitard (III: silt). The phreatic layer is mostly composed of miscellaneous fill with blocked hydraulic connections to confined aquifers. A confined aquifer is composed of layered sand (V) and gravel (VII) layers. The gravel layer generates a hydraulic connection with the sand layer through the ‘connected area’ of the incompletely sealed lower aquitard (VI: silty clay). This area is intermittently distributed at the bottom of the sand layer, and it produces a strong hydraulic recharge that exerts considerable impact on excavations. All of the formation parameters in the field are listed in Table1. The metro station foundation pit is 169.6 m long and 19.7 m wide, with a pit bottom bury depth of 16.5 m. This foundation pit is long and narrow but equally divided into two sections by the middle wall. The pit bottom is located in the silty sand (IV) layer above the confined aquifers. The overlying soil pressure decreases with an increase in excavation depth, posing a risk of uplift failure below the excavation surface. Water 2019, 11, x FOR PEER REVIEW 3 of 19 Water 20192019,, 11,, 2182x FOR PEER REVIEW 33 of of 19 19

Minjiang River Minjiang River Shuibu station Shuibu station Shuibu station foundationShuibu pit station Fuzhou Wset section Eastfoundation section Gutian pit road Fuzhou Wset section East section Gutian road Nearby buildings Wulongjiang Nearby buildings RiverWulongjiang China East River Chinasea East sea

(a) (b) (a) (b)

FigureFigure 1. (a) Geographical 1. (a) Geographical location location of the study of the site. study (b) site.Plan (viewb) Plan of the view foundation of the foundation pit. pit. Figure 1. (a) Geographical location of the study site. (b) Plan view of the foundation pit. Elevation(m) 8Elevation(m) 8 I II I 0 I West zone II III I 0 East zone -8 West zone III East zone -8 Station area -16 IV Station area VI -16 IV -24 V VI -24 V VII -32 VII VI VI VII -32 VII VI -40 VI -40 VII -48 VIII I: Miscellaneous fill II: BlockVII stone III: Silt IV: Silt sand -48 VIII V: SandI: Miscellaneous fill VI: Silty clayII: Block stone VII: GravelIII: Silt VIII: GraniteIV: Silt sand Figure 2. Geological profile of the Shuibu Metro Station. VFigure: Sand 2. Geological proﬁleVI: of Silty the clay Shuibu Metro Station.VII: Gravel VIII: Granite Figure 2. Geological profile of the Shuibu Metro Station. (a) Table 1. Hydraulic parameters in geological exploration data.

Retaining wall ThicknessCross-section S r Layer Soil Layer(a) Type k (m/d) k (m/d) s e w (Barrier) (m) h v (1/m) (kN/m3) B Fill and PhreaticRetaining wall Cross-section I and II (Barrier) 4.0~6.0 8.64 8.64 - - 18.5 block stone aquifer Pumping well Pumping well Upper B III Silt 8.0~12.0 0.0055 0.0015 5 10-4 1.67 15.7 aquitard × Silt with Upper PumpingL well Pumping well IV 10.0~12.0 0.54 0.3 5 10-4 - 16.2 sand aquitard × Conﬁned L -4 V Sand 16.0~18.0Pumping well Q 24 (Isotropy) 2 10 1.50 19.0 (b) aquifer w × Silty clay AquitardPhreatic aquifer Retaining wall VI 0.0~6.0 0.003(Barrier) 0.002 5 10-4 0.71 19.5 (dispersive) (partial)(b) Pumping well Qw × ConﬁnedUpper aquitard VII Gravel Phreatic aquifer4.0~6.0 40Retaining 40 wall - - 17.0 aquifer (Barrier) IV Granite AquitardConfined Upperaquifer aquitard Bottom - - - - 21.0

To investigate seepageLower characteristics, aquitardConfined aquifer the pit section is simpliﬁed into a rectangular section.

Figure3 shows the problem sketch. In general, the 4th dewatering model ( ls < Mu) is selected for

dewatering projects in deep aquifersLower [ 24aquitard]. With a ﬁxed Qw and increasing elapsed time t, the hydraulic

Water 2019, 11, x FOR PEER REVIEW 3 of 19

Minjiang River Shuibu station Shuibu station foundation pit Fuzhou Wset section East section Gutian road

Nearby buildings Wulongjiang River China East sea

(a) (b)

Figure 1. (a) Geographical location of the study site. (b) Plan view of the foundation pit.

Elevation(m) 8 I II I 0 West zone III East zone -8 Station area -16 IV VI -24 V VII -32 VII VI VI Water 2019-40, 11, 2182 4 of 19 VII VIII head dramatically-48 decreases from its initial position until it ﬁnally reaches a stable value [35]. This study aims to explore steady seepageI: Miscellaneous characteristics fill underII: Block partial stone penetrating curtainsIII: Silt in the 4th dewateringIV: Silt sand model and to establishV formalized: Sand Qw predictionVI: formulasSilty clay for a dewateringVII: Gravel design. Furthermore,VIII: Granite the corresponding dewateringFigure design2. Geological method profile shall of bethe presentedShuibu Metro on Station. the basis of these formulas. (a)

Retaining wall Cross-section (Barrier)

Pumping well Pumping well

(b) Pumping well Qw Phreatic aquifer Retaining wall (Barrier)

Upper aquitard

Confined aquifer

Lower aquitard

Figure 3. Problem sketch: (a) plan view of the rectangle excavation pit; (b) cross-section view of barriers and aquifers. Note: Qw = pumping rate of wells; L = inner length of the retaining wall; B = inner width of the retaining wall; M = thickness of the conﬁned aquifer; Mu = insertion depth of the barrier; Mn = distance from bottom of barrier to the lower aquitard; ls = screen length.

3. Numerical Simulation

3.1. Governing Equation To obtain the conservative inflow design value, non-Darcy flow is disregarded, but the assumption of Darcy’s law and the continuity condition are adopted. The governing equation and boundary conditions of 3D groundwater seepage in the saturated media of confined aquifers are established as follows [38]: = ∂h governing equation : kij h Q SS ∂t ∇ ∇ − initial conditon : h(x, y, z, t) t=t0 = h0 (x, y, z) (1) boundary conditions : h(x, y, z, t) = h1(x, y, z, t) Γ1 kij h = q(x, y, z, t) ∇ Γ2 where is the Laplace operator; k is the permeability coefficient, and i, j, = 1, 2, 3; h is the hydraulic ∇ ij head; Q is the external source–sink flux; Ss is the specific storage; t is the elapsed time; h0(x, y, z) is the initial head at point (x, y, z); h1(x, y, z, t) is the constant head on boundary Γ1; nx, ny, and nz are the unit normal vector on boundary Γ2 along the x, y, and z directions, respectively; q(x, y, z, t) is the lateral recharge per unit area on boundary Γ2; Γ1 is the boundary condition of the water table; and Γ2 is the flux boundary condition. When the 3D seepage field approaches a steady state, the flow rate of boundary elements tends to be 0. The governing equation of Equation (1) can be written as follows:

k 2h = 0 (2) ij∇ Water 2019, 11, 2182 5 of 19

Aquifers are commonly heterogeneous along the vertical direction and homogeneous along the horizontal direction. Therefore, Equation (2) is rewritten as: ! ! ∂2h ∂2h ∂2h kh + + kv = 0 (3) ∂x2 ∂y2 ∂z2 where kh is the horizontal permeability coefficient, and kv is the vertical permeability coefficient. At present, the preceding governing equations have no analytic solution yet because of the blocking effect. Hence, a finite difference method (FDM) can be applied. The seepage field is discretized into 3D cells, and then the difference equation is established at the cell (i, j, k) as follows [39]: CR hm hm + CR hm hm i,j 1/2,k i,j 1,k i,j,k i,j+1/2,k i,j+1,k i,j,k − × − − × − +CC hm hm + CC hm hm i 1/2,j,k i 1,j,k i,j,k i+1/2,j,k i+1,j,k i,j,k − × − − × − (4) m m m m +CVi,j,k 1/2 h h + CVi,j,k+1/2 h + h − × i,j,k 1 − i,j,k × i,j,k 1 − i,j,k − m m 1 h h − +P hm + Q = S r c v i,j,k− i,j,k i,j,k i,j,k i,j,k i,j,k ∆ j∆ i∆ k tm tm 1 − − hm i j k m where i, j, k is the head of the cell ( , , ) at the time step , (L); CR, CC, and CV are the hydraulic 2 1 conductivity between adjacent nodes (L T− ); Pi, j, k is the sum of the head coefficients between the 2 3 source and the sink (L /T); and Qi, j, k is the sum of the constants of the source and the sink (L /T). When Qi, j, k < 0, groundwater is exiting the system (e.g., pumping); when Qi, j, k > 0, groundwater is entering the system (e.g., injection). Si, j, k is the cell’s specific storage. ∆rj, ∆cj, and ∆vj are the 3D dimensions of the cube cell (i, j, k). tm 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. The calculation domain of seepage is discretized into a difference grid on the basis of Equation (4), and then the head of each element can be solved using an iterative algorithm [40].

3.2. Simplification of Model Parameters The numerical model is established on the basis of Equation (4). To investigate seepage characteristics, all of the field strata are summarized as three main layers in the model: The phreatic, aquitard, and confined aquifers. Table2 provides the simplified parameters in the calculation model on the basis of the Fuzhou strata. The typical size of a rectangle station pit section is adopted in the calculation: L = 60 m, B = 20 m, and the depth of the retaining wall is 42 m (Mu = 18 m) with a short screen length of 8 m. Notably, the aforementioned parameters can be changed individually in accordance with the requirement.

Table 2. Simpliﬁed parameters in the calculation model.

No. Soil Layer M (m) kh (m/d) kv (m/d) Ss (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 ×

3.3. Initial/Boundary Conditions To avoid the boundary effect, Siechardt’s empirical formula is applied to calculate the pumping influence radius, as follows [38]: R = 10sw √k (5) where sw is the drawdown of the pumping well, and k is the aquifer’s permeability coefficient. Water 2019, 11, x FOR PEER REVIEW 5 of 19

At present, the preceding governing equations have no analytic solution yet because of the blocking effect. Hence, a finite difference method (FDM) can be applied. The seepage field is discretized into 3D cells, and then the difference equation is established at the cell (i, j, k) as follows [39]:

mmmm CRhhCRhhi,1/2,,1,, jki jki j ,,1/2,,1,, ki jki jki , j k    CChhCChh mmmm ij1/2, kij ki ,1, j kij ,, kij,1/2, ki ,1, j k ,, ,    mmmm (4) CVhhCVhhi, jki ,1/2, jki ,1, jki ,, ,1/2, jki jki ,1, , jk    mm1 m hhi, j ,, ki , j k PhQi, j ,, ki ,, j ,ki j k Srcvi, j,kjik  ttmm 1 푚 where ℎ푖,푗,푘 is the head of the cell (i, j, k) at the time step m, (L); CR, CC, and CV are the hydraulic conductivity between adjacent nodes (L2 T−1); Pi, j, k is the sum of the head coefficients between the source and the sink (L2/T); and Qi, j, k is the sum of the constants of the source and the sink (L3/T). When Qi, j, k < 0, groundwater is exiting the system (e.g., pumping); when Qi, j, k > 0, groundwater is entering the system (e.g., injection). Si, j, k is the cell’s specific storage. ∆rj, ∆cj, and ∆vj are the 3D dimensions of the cube cell (i, j, k). tm 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. The calculation domain of seepage is discretized into a difference grid on the basis of Equation (4), and then the head of each element can be solved using an iterative algorithm [40].

3.2. Simplification of Model Parameters The numerical model is established on the basis of Equation (4). To investigate seepage characteristics, all of the field strata are summarized as three main layers in the model: The phreatic, aquitard, and confined aquifers. Table 2 provides the simplified parameters in the calculation model on the basis of the Fuzhou strata. The typical size of a rectangle station pit section is adopted in the calculation: L = 60 m, B = 20 m, and the depth of the retaining wall is 42 m (Mu = 18 m) with a short screen length of 8 m. Notably, the aforementioned parameters can be changed individually in Wateraccordance2019, 11, with 2182 the requirement. 6 of 19

3.3. Initial/Boundary Conditions Assume that the required sw is approximately 8 m and the maximum permeability coefficient of a confinedTo avoid aquifer thek boundaryis 36 m/d effect, based onSiechardt’s field conditions. empirical The formula influence is applied radius toR calculateis calculated the pumping as 480 m usinginfluence Equation radius (5)., as follows The model [38] 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 Figure4, the Rsk10 horizontal direction has 129 rows and 141 columns.w A fine mesh is found around the excavation area(5) andwhere gradually sw is the becomes drawdown a coarse of the mesh pumping from thewell, excavation and k is the center aquifer’s outward. permeability In the vertical coefficient direction,. the model of the three strata is divided into 22 layers and the confined aquifer is calculated in 18 layers.

Water 2019, 11, x FOR PEER REVIEW 6 of 19

(a)

(b)

(c)

Figure 4.4. Finite didifferenceﬀerence mesh:mesh: (a) Three-dimensionalThree-dimensional ( (3D)3D) view of the mesh; (b) planplan viewview ofof thethe mesh aroundaround thethe pit;pit; ((cc)) centralcentral cross-sectioncross-section ofof thethe mesh.mesh.

Table 2. Simplified parameters in the calculation model.

No. Soil Layer M (m) kh (m/d) kv (m/d) Ss (1/m) Phreatic 1 6 8.64 8.64 - aquifer 2 Aquitard 18 0.005 0.001 5E-4 Confined 3 36 24 24 2E-4 aquifer

Assume that the required sw 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. Taking the ground surface as the reference datum, the initial hydraulic head of the phreatic aquifer and aquitards is located at 2 m below the ground surface (BGS); for the head of the confined aquifer, it is 7.0 m BGS. Constant head boundaries are set in the calculation edge elements to simulate hydraulic recharge, which is equal to the initial head of each layer. The rectangle barrier is simulated

Water 2019, 11, 2182 7 of 19

Taking the ground surface as the reference datum, the initial hydraulic head of the phreatic aquifer and aquitards is located at 2 m below the ground surface (BGS); for the head of the confined aquifer, it is 7.0 m BGS. Constant head boundaries are set in the calculation edge elements to simulate hydraulic recharge, which is equal to the initial head of each layer. The rectangle barrier is simulated 5 by the impermeability elements (10− m/d) in the model. The location of the pumping wells and the observation points are shown in Figure4b,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 The link between the seepage field distribution and dewatering efficiency is obtained by adjusting Qw until sw reaches 8 m and by changing the dewatering parameters individually within a reasonable range, as shown in Figure5. The seepage field distribution is reflected by the measured drawdowns, 3 2 and the improved dewatering efficiency is defined by a less qw ((m /d)/(m m)), as follows: ·

qw = Qw/(L B sw) (6) × × (1) Permeability coefficient (k): k is applied to homogeneous aquifers. As shown in Figure5a, water table remains unchanged when k increases but qw increases linearly. In addition, this coefficient satisfies the linear relationship between k and qw in Darcy’s law. The result indicates that k affects dewatering efficiency only by changing flow velocities instead of the seepage field distribution. (2) Permeability anisotropy (kv/kh): 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 qw 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. (3) Aquifer thickness (M): Water table rises as M increases, and the Mu/M ratio remains fixed (0.5), while qw 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. (4) Insertion depth of the barrier (Mu): The penetration of curtains generates the blocking effects (i.e., flow direction transfer, flow path lengthening, and seepage area reduction). Water table rises, and qw is reduced gradually when Mu 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 Figure5d 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]. (5) Pumping well screen length (ls): The design value of ls relies on field conditions, such that a small ls will produce a small qw with the water table maintained outside. Thus, minimal influence is exerted on the seepage field distribution outside with various ls values, but a long flow path is produced inside. From the analysis of the different seepage characteristics, the effects of the parameters on the seepage field can be summarized as follows: (1) The variation of flow velocities and (2) the deformation of the 3D seepage field. When a single parameter changes, flow velocity (k) or seepage field distribution (M, Mu, ls) changes separately or both factors are influenced (kv/kh); thus, dewatering efficiency is significantly affected. Water 2019, 11, x FOR PEER REVIEW 7 of 19

by the impermeability elements (10−5 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 The link between the seepage field distribution and dewatering efficiency is obtained by adjusting Qw until sw 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 qw ((m3/d)/(m2∙m)), as follows:

qQLBswww /   (6)

(1) Permeability coefficient (k): k is applied to homogeneous aquifers. As shown in Figure 5a, water table remains unchanged when k increases but qw increases linearly. In addition, this coefficient satisfies the linear relationship between k and qw in Darcy’s law. The result indicates that k affects dewatering efficiency only by changing flow velocities instead of the seepage field distribution. (2) Permeability anisotropy (kv/kh): 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 qw 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. (3) Aquifer thickness (M): Water table rises as M increases, and the Mu/M ratio remains fixed (0.5), while qw 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. (4) Insertion depth of the barrier (Mu): The penetration of curtains generates the blocking effects (i.e., flow direction transfer, flow path lengthening, and seepage area reduction). Water table rises, and qw is reduced gradually when Mu 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]. (5) Pumping well screen length (ls): The design value of ls relies on field conditions, such that a small ls will produce a small qw with the water table maintained outside. Thus, minimal influence is Waterexerted2019, 11 on, 2182 the seepage field distribution outside with various ls values, but a long flow 8 path of 19 is produced inside.

(a) 1 Retaining wall 1 Mu = 18m M = 36m (b) 1 M = 18m 1 0 k = k = k l = 8 m 0 Retaining wall u M = 36m Initial hydraulic head v h s 0 0 -1 -1 Initial hydraulic head kh = 24 m/d ls = 8 m -1 -1 -2 -2 -2 -2 -3 Upper part hydraulic head -3 -3 Upper part hydraulic head -3 -4 (steady state) -4 -4 (steady state) -4 -5 -5

q -k -5 q -(k /k ) -5 w Permeability coefficient w v h -6 1.0 -6

1.0 Permeability anisotropy

3 k = 6m/d -6 -6 3

-7 /m 0.8 -7 0.8 ) kv/kh=0.2

k = 12m/d -7 /m -7

)

/d 3

Water table (m) 0.6

/d 0.6

-8 -8 3 Water table (m) k /k =0.4

m k = 18m/d -8 v h -8

(

( 0.4

0.4 w

-9 -9 w

q k = 24m/d k /k =0.6 -9 q 0.2 v h -9 -10 0.2 k = 30m/d -10 -10 0.0 kv/kh=0.8 -10 0.0 0.2 0.4 0.6 0.8 1.0 6 12 18 24 30 36 k = 36m/d -11 -11 k /k =1.0 -11 kv / kh v h -11 k (m/d) -12 -12 -12 -12 -500 -400 -300 -200 -100 0 100 200 300 400 500 -500 -400 -300 -200 -100 0 100 200 300 400 500 Water 2019, 11, x FOR PEER REVIEW 8 of 19 Distance from the foundation pit center (m) Distance from the foundation pit center (m)

(c) 1 M / M = 0.5 1 Retaining wall u ls = 8 m (d) 1 1 0 0 Retaining wall l = 8 m M = 36m Initial hydraulic head k = 24 m/d (isotropy) 0 s 0 -1 -1 Initial hydraulic head k = 24 m/d (isotropy) -1 -1 -2 -2 -2 -2 -3 -3 -3 Upper part hydraulic head -3 -4 -4 Upper part hydraulic head -4 (steady state) Insertion depth of -4

-5 -5 the barrier

(steady state) -5 -5 qw-M M = 14m

-6 -6 u 1.0 -6 q -M -6 Aquifer thickness 1.0 w u M = 18m

-7 3 -7

0.8 -7 u -7 3

/m 0.8

) M = 36m

Water table (m) /m

-8 -8 M = 22m ) /d 0.6 -8 u -8

3 0.6

M = 32m Water table (m) 3

( m -9 0.4 -9 0.4 M = 26m ( u

w -9 -9 M = 28m

q w -10 0.2 -10 q 0.2 M = 30m M = 22m -10 u -10 0.0 0.0 -11 20 24 28 32 36 -11 12 16 20 24 28 32 36 M = 34m M (m) M = 18m -11 u -11 Mu (m) -12 -12 -12 -12 -500 -400 -300 -200 -100 0 100 200 300 400 500 -500 -400 -300 -200 -100 0 100 200 300 400 500

Distance from the foundation pit center (m) Distance from the foundation pit center (m) (e) 1 1 Retaining wall M = 18m M = 36m 0 u 0 Initial hydraulic head k = 24 m/d (isotropy) -1 -1 -2 -2 -3 -3 -4 Upper part hydraulic head -4

(steady state) -5 -5 1.0 q -l -6 w s -6

3 0.8

-7 Screen length -7 /m ) 0.6 l = 4m

/d s

-8 3 -8 Water table (m) m 0.4 ( l = 8m s -9 w -9 q 0.2 l = 12m -10 s -10 0.0 4 6 8 10 12 14 16 l = 16m -11 s -11 ls (m) -12 -12 -500 -400 -300 -200 -100 0 100 200 300 400 500

Distance from the foundation pit center (m) FigureFigure 5. 5Water. Water table table on the on central the centralcross-section cross with-section variation with dewatering variation dewatering parameters: parameters: (a) Permeability; (a) (bP)ermeability; permeability (b anisotropy;) permeability (c) aquiferanisotropy; thickness; (c) aquifer (d) insertion thickness; depth (d) insertion of barriers; depth (e) screen of barriers; length (e of) pumpingscreen length well. of pumping well.

4. QuantiﬁcationFrom the analysis of Blocking of the Edifferentﬀects seepage characteristics, the effects of the parameters on the

seepageThe wall–well field can design be summarized of the dewatering as follows: control (1) scheme The must variation obtain ofQ floww in advance. velocities The and formalized (2) the inflowdeformation prediction of the formulas 3D seepage are established field. When on a the single basis paramet of seepageer changes, characteristic flow analysisvelocity by(k) quantifyingor seepage thefield link distribution between dewatering (M, Mu, ls) changes parameters separately with Q orw. both factors are influenced (kv/kh); thus, dewatering efficiency is significantly affected. 4.1. Equivalent Pumping Well Inflow 4. Quantification of Blocking Effects For reference, equivalent inflow QT is proposed under the hypothesis of parallel flow, in which the pitThe is regarded wall–well as a design full penetrating of the dewa pumpingtering well control in the scheme absence must of 3D obtain flow, Q asw shownin advance. in Figure The6. formalized inflow prediction formulas are established on the basis of seepage characteristic analysis by quantifying the link between dewatering parameters with Qw.

4.1. Equivalent Pumping Well Inflow

For reference, equivalent inflow QT 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.

Water 2019, 11, 2182 9 of 19 Water 2019, 11, x FOR PEER REVIEW 9 of 19

The equivalent (a) pumping well (b) R r Ground surface

r Initial head B s

Depressurization head

Equivalent well L

FigureFigure 6. The 6. Theequivalent equivalent pumping pumping well: well: (a) C (aross) Cross-section;-section; (b) vertical (b) vertical section. section.

Then,Then, the thefollowing following Thiem Thiem equation equation [43] [ 43is ]selected is selected to calculate to calculate the theQT QvalueT value of the of theequivalent equivalent pumpingpumping well: well: 2πkMs 2πTs Q =22kMsTs = (7) T 2 QT ln(R/r) ln(2.25Tt/2 S sr ) (7) ln(/)ln(2.25/)RrTtSr s where k is the permeability coefficient under Dupuit’s assumption for the equivalent well and wherinhomogeneouse k is the permeability aquifer, k coefficient= kh; s is the under drawdown Dupuit’s inside assumption the equivalent for the well equivalent and is substituted well and by inhomogeneousthe average drawdown aquifer, k = onkh; s the is the confined drawdown aquifer’s inside top the inside equivalent the pit, well as shownand is substituted in Figure6b; by rtheis the averageinner drawdown radius of the on equivalent the confined well aquifer’s that can top be determined inside the pit, using as theshown formula in FigLureB 6=b;2 rπ isr2 ,the as showninner in × radiusFigure of 6thea; andequivalentT is the well transmissivity that can be of determined the aquifer. using the formula L × B = 2πr2, as shown in Figure 6However,a; and T is Thiemthe transmissivity equation reflects of the aquifer. the influence of flow velocity (k) but not of seepage field distortion.However, The Thiem parallel equation flow is reflects transferred the influence to the 3D of flow flow near velocity the curtains (k) but and not causes of seepage seepage field field distortion.deformation. The parallel Thus, theflow distortion is transferred of the to 3D the seepage 3D flow field near should the curtains be quantified. and causes seepage field deformation. Thus, the distortion of the 3D seepage field should be quantified. 4.2. 3D Seepage Field Distortion Function 4.2. 3D Seepage Field Distortion Function Dewatering under the barriers is divided into four stages [35]—that is, stage I: Groundwater withdrawalsDewatering onlyunder come the frombarriers aquifers is divided inside into pits andfour drawdownstages [35]— developsthat is, withstage noI: G barrierroundwater influence; withdrawalsstage II: Groundwater only come from withdrawals aquifers inside come pits from and aquifers drawdown inside develops and outside with pits no barrier and drawdown influence; is in stageinfluenced II: Groundwater by the presence withdrawals of barriers; come from stage aquifers III: Groundwater inside and withdrawals outside pits areand supplied drawdown by is outside in influencedaquifer onlyby the and presence drawdown of barriers;time curvestage III: isparallel Groundwater to the nowithdrawals barrier condition; are supplied stage by IV: outside Pumping − aquiferreaches only the and stable drawdown state and−time drawdown curve is becomesparallel constant.to the no Onbarrier the basiscondition; of the stage empirical IV: P dewateringumping reachesscheme, the stable when statet = 100 and d, drawdo the transientwn becomes flow enters constant Stage. On IV. the At basis this point,of the itempirical closely approachesdewatering the scheme,steady when state t (error = 100< d,5%). the The transient numerical flow results enters of Stage the Q IVc–s. curveAt this are point, obtained it closely under approaches various conditions the steadyby adjusting state (error inflow <5%). inthe The numerical numerical model. results The of inflow the Q modificationc–s curve are factor obtainedQd of the under equivalent various well conditionswith barriers by adjusting can be calculated inflow in under the numerical a particular model. drawdown The inflows as follows: modification factor Qd of the equivalent well with barriers can be calculated under a particular drawdown s as follows: Qd = Qc/QT (8) QQQdcT / (8) 4.2.1. Normalized Form

4.2.1. NormalizedTo generalize Form the calculation results, the parameters affecting the seepage field distributions are converted to their normalized form. This form contains the relative barrier ratio b (Mu/M), To generalize the calculation results, the parameters affecting the seepage field distributionsd are non-standard thickness coefficient Md (36/M), permeability anisotropy coefficient kd (kd/kh), and well converted to their normalized form. This form contains the relative barrier ratio bd (Mu/M), non- screen insertion ratio ld (ls/Mu). In the standard state, the normalized parameters are set as kd = 1, standard thickness coefficient Md (36/M), permeability anisotropy coefficient kd (kd/kh), and well screen ld = 1, and Md = 1 (M = 36 m). insertion ratio ld (ls/Mu). In the standard state, the normalized parameters are set as kd = 1, ld = 1, and Md 4.2.2.= 1 (M Standard = 36 m). Curve

4.2.2. StandardIn the standard Curve state, the numerical results (Qc–s) with diﬀerent bd and Thiem results (QT–s) can be obtained by specifying an inﬂow set, as shown in Figure7a. The resulting curves show the linear In the standard state, the numerical results (Qc–s) with different bd and Thiem results (QT–s) can be obtained by specifying an inflow set, as shown in Figure 7a. The resulting curves show the linear

Water 2019, 11, 2182 10 of 19 Water 2019, 11, x FOR PEER REVIEW 10 of 19

distribution but with different slopes. All the slopes of the numerical result curves are greater than 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 bd gradually increases the curve slope of the numerical that of the Thiem result curve. An increase in bd gradually increases the curve slope of the numerical results. Such increase shows that a large bd will enhance sensitivity between inflow and drawdowns. results. Such increase shows that a large bd will enhance sensitivity between inflow and drawdowns. The Qd–bd curves can be calculated using Equation (8) by setting different s values, and all the curves The Q –b curves can be calculated using Equation (8) by setting different s values, and all the curves underd differentd s values converge to a single curve, as shown in Figure 7b. Such convergence indicates under different s values converge to a single curve, as shown in Figure7b. Such convergence indicates that the inflow reduction caused by the 3D flow is uniform under different drawdowns in a particular 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 Qd as Qs in this state, a state. By regarding this converged curve as the standard curve and writing Q as Q in this state, a separate nonlinear function of the standard curve can be expressed by artificiallyd definings the line separate nonlinear function of the standard curve can be expressed by artificially defining the line type type boundary (bd = 0.75) as follows: boundary (bd = 0.75) as follows: 0.7160.3750.75bifbdd   0.7160.3750.206bd i f bd 0.75 Qs   1 bd  (9) Q = 0.6950.75−( )0.206 ifb ≤ (9) s  1 bd 0.039 d  0.6951.223− b 0.039 i f bd > 0.75  1.223bdd

(a) 14 b = 0 b = 0.28 (b) d d b = 0.39 b = 0.50 d d 0.6 12 bd= 0.61 bd = 0.72

bd = 0.78 bd = 0.83 b = 0.89 b = 0.75 10 d d b = 0.94 d 0.5 bd = 0.97 8

(m) c

s Numerical results

6 Q 0.4

4 0.3 2 Thiem equation result

0 1200 2400 3600 4800 6000 7200 8400 9600 10800 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 3 Qw (m /d) b d

FigureFigure7. 7. VariationVariation resultsresults inin thethe standardstandard state: ( a) Qw––ss curvecurve with with different diﬀerent bbd;d (;(bb) )standard standard curve. curve.

However,However, this formula formula can can only only be be applied applied to the to thestandard standard state state but not but to not conditions to conditions with non with- non-standardstandard parameters parameters (Md, (kMd, dand, kd ,l andd). Thus,ld). Thus,additional additional distortion distortion functions functions are required. are required.

4.2.3. Distortion Function 4.2.3. Distortion Function

(a) Permeability coefficient (k): The Qd–bd curves with different k values are presented in Figure8a (a) Permeability coefficient (k): The Qd–bd curves with different k values are presented in Figure using8a using the the same same analysis analysis method method as thatas that for for the the standard standard curve. curve. The The results results show show that that all all the the curves curves are consistentare consistent with with those those of the of standard the standard curve, curve, indicating indicating that k thatis a non-disturbingk is a non-disturbing factor forfactor the for seepage the fieldseepage distribution. field distribution. Modification Modification is unnecessary is unnecessary because because only flow only velocity flow velocity is changed. is changed. (b) Permeability anisotropy coefficient (k ): Similarly, the Q –b curves under different k values (b) Permeability anisotropy coefficient (kdd): Similarly, the Qd–bdd curves under different kd dvalues areare establishedestablished andand shownshown inin FigureFigure8 8b.b. AA decreasedecrease inin kd increasesincreases the the deviation deviation between between QQd dandand QQs, s, butbut linearlinear deviationsdeviations (the(the ooffsetffset valuevalue <<10%)10%) occur occur as as kkdd approachesapproaches 0.2 0.2 and and below. below. By By disregarding disregarding thisthis linearlinear deviationdeviation andand modifyingmodifying Qss to Qd under the the corresponding kkdd, ,the the distortion distortion function function of of permeabilitypermeability anisotropyanisotropy isis constructedconstructed as follows:

1111 2020 α= (kd ) (10(10))

d d d (c)(c) Non-standardNon-standard thicknessthickness coecoefficientfficient ((MMd): Fig Figureure 88cc presentspresents the QQd––bb dcurvescurves under under different different Md values. The figure shows that the Qd–bd curves diverge as Md changes with a similar line type. Md values. The figure shows that the Qd–bd curves diverge as Md changes with a similar line type. When Md > 1, the curve moves upward; otherwise, it shifts downward. By quantifying the variation When Md > 1, the curve moves upward; otherwise, it shifts downward. By quantifying the variation of theof the standard standard curve, curve, the the distortion distortion function function of aquiferof aquifer thickness thickness is givenis given as: as:

0.2415lnMd 0.7734   Md  (11)

Water 2019, 11, 2182 11 of 19

Water 2019, 11, x FOR PEER REVIEW 11 of 19 0.2415 ln Md+0.7734 β = (Md)− (11) (d) Well screen insertion ratio (ld): To utilize the wall–well effects, a short screen length is (d) Well screen insertion ratio (ld): To utilize the wall–well effects, a short screen length is provided provided in the field to lengthen flow path. The Qd–bd curves at different ld values are shown in Figure in the field to lengthen flow path. The Qd–bd curves at different ld values are shown in Figure8d. 8d. The line type of the curves remains, but the curves move downward with decreasing ld values. The line type of the curves remains, but the curves move downward with decreasing ld values. The variation can be quantified using the following distortion function of screen length: The variation can be quantified using the following distortion function of screen length: l 51 d l  0.781 51 d (12) η = 0.781 40 (12) · 40

0.65 k = 0.1 (a) (b) d 0.7 k = 0.2 0.60 d bd = 0.75 bd = 0.75 kd = 0.4 0.6 k = 0.6 0.55 d kd = 0.8 0.5 k = 1.0 0.50 d Stantard curve

d 0.45 d 0.4 k = 6 m/d

Q Q k = 12 m/d 0.40 0.3 k = 18 m/d k = 24 m/d 0.35 0.2 k = 30 m/d 0.30 k = 36 m/d Standtard curve 0.1 0.25 0.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 b b d d

(d) (c)0.9 0.6 bd = 0.75 bd = 0.75 0.8

0.7 0.5

d 0.6 d

Q 0.4 0.5 ld = 0.1 0.4 l = 0.4 0.3 d l = 0.7 0.3 Md = 3.0 Md = 1.8 d Md = 1.29 Md = 1.0 ld = 1.0 0.2 Md = 0.82 Md = 0.69 0.2 Stantard curve Standard curve 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 b b d d

Figure 8. Variation curve of Qd–bd with varying dewatering parameters: (a) Permeability coefficient; (b) Figure 8. Variation curve of Qd–bd with varying dewatering parameters: (a) Permeability coefficient; permeability anisotropy coefficient; (c) non-standard thickness coefficient; (d) well screen insertion ratio. (b) permeability anisotropy coefficient; (c) non-standard thickness coefficient; (d) well screen 4.2.4.insertion Inflow Prediction ratio. with Partial Penetrating Curtains

4.2.4.To Inflow increase Prediction the similarity with betweenPartial Penetrating inﬂow prediction Curtains and actual conditions, Qs can be approximately modiﬁed to Qd by multiplying it to the normalized distortion function as follows: To increase the similarity between inflow prediction and actual conditions, Qs can be

approximately modified to Qd by multiplyingQ =it toQ stheα β normalizedη distortion function as follows:(13) d · · · QQds (13) Furthermore, the empirical inflow prediction formula of the overall station pit that is suitable for the sandFurthermore, and gravel the strata empirical (i.e., MAS) inflow with prediction high permeability formula of is the established overall station as follows: pit that is suitable for the sand and gravel strata (i.e., MAS) with high permeability is established as follows: Qw = QT Q (14) · d QQQw T d (14) Combined with Equations (13) and (14), the inflow of steady flow can be effectively calculated Combined with Equations (13) and (14), the inflow of steady flow can be effectively calculated using the formalized equations with the determined predesign parameters. using the formalized equations with the determined predesign parameters.

5. Field Application

5.1. Design Method of the Dewatering Scheme

Water 2019, 11, 2182 12 of 19

5. Field Application

5.1.Water Design 2019, 11 Method, x FOR PEER of the REVIEW Dewatering Scheme 12 of 19

OnOn the the basis basis of the of preceding the preceding empirical empirical prediction prediction equations, equations, the design the method design of method the dewatering of the schemedewatering with scheme barriers with in the barriers sand andin the gravel sand strata and gravel is presented strata is in presented Figure9, wherein Figure the 9 increment, where the in ∆incrementMu is determined in ∆Mu is through determined design through precision design and precision hydraulic and conditions. hydraulic conditions.

Design Preparation Dewatering Scheme Design Scheme Determining Multiple schemes Wall design increment ΔM Formation generalization u designed by Eq. (14) Optimal dewatering scheme Field pumping Laboratory test (1) ... test Dewateing Schemes with (2) (3) (n) Deviation analysis of designs Hydraulic and formation different Mu Q Q Q Q Parameters of the aquifer w1 w2 w3 ... wn Mu1 Mu2 Mu3 Mun Calculating QT of each scheme Pumping wells location Seepage-pressure by Eq. (7) balanced method Schemes comparison Safe uplift water pressure Calculating normalized functions of on the aquifer top each scheme by Eq. (8-13)

FigureFigure 9. 9.Dewatering Dewatering schemescheme design method with with partial partial penetrating penetrating curtains curtains..

5.2.5.2 Dewatering. Dewatering Design Design ofof thethe ShuibuShuibu MetroMetro Station 5.2.1. Hydrogeological Conditions of the Area 5.2.1. Hydrogeological Conditions of the Area The dewatering scheme combining partial penetrating curtains and wells is selected for groundwater The dewatering scheme combining partial penetrating curtains and wells is selected for control during the excavation of this case. The hydrogeological conditions of the area are presented groundwater control during the excavation of this case. The hydrogeological conditions of the area in Figure 10. Possible connection regions in the silty clay layers are blocked via grouting to reduce are presented in Figure 10. Possible connection regions in the silty clay layers are blocked via grouting hydraulic recharge from the aquifers. Then, the strata are generalized again during the design period, to reduce hydraulic recharge from the aquifers. Then, the strata are generalized again during the as shown in Figure 11. Before curtain construction, field pumping and laboratory tests are conducted to design period, as shown in Figure 11. Before curtain construction, field pumping and laboratory tests obtain permeability in various directions as follows: kh = 24.5 m/d and kv = 15 m/d. are conducted to obtain permeability in various directions as follows: kh = 24.5 m/d and kv = 15 m/d. 5.2.2. Depressurization Requirements The depressurization requirements of uplift pressure can be calculated using the classic soil–pressure balanced method [33]. The calculated safe drawdown (s) of the west and east sections is 6.68 m and 7.53 m, respectively.

5.2.3. Dewatering Scheme Design The designed length of the reinforced diaphragm wall for load bearing is 31.5 m in engineering applications. For groundwater blocking, non-reinforced concrete curtains should be added at the wall’s bottom. The multiple schemes and corresponding inflow are determined as follows. (a) On the basis of ∆Mu (2 m), as set by construction organizations, various alternative schemes with different Mu (integers) are presented in Figure11. (b) The short well screen ( ls = Mu/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 3 3 Equation (5). (d) QT is calculated using Equation (7) with a value of 4328 m /d (west) and 5187 m /d (east). (e) The distortion functions (normalized) and inflow of each scheme are presented in Table 3 (a) and Figure 12, respectively. Bury depth of water table Elevation (m) A—A 20 WulongjiangTable 3. Normalized seepageMinjiang field distortion function. Flow path 0.5 River Shuibu station 10 2.4 1.5 1.4 1.2 River 2.1 2.3 3.7 1.2 Aq.I Aq.I Aq.I 1.8 1.8 Partial penetrating 0 Ad.I retaning wall Ad.I Section Lp Qs α β η Ad.IIQd SectionAd.II Lp Qs α β η Qd -10 Aq.II Aq.II Ad.II -20 Ad.I0 0.634Aq.II 0.76 1.60 1.18Ad.I 0.916 0 0.601 Pumping0.76 1.52 1.02 0.711 well -30 2.5 0.575 0.76 1.60 0.99 0.699 Ad.II2.5 0.549 0.76Ad.II 1.52 0.94 0.598 -40 4.5 0.529 0.76 1.60 0.94 0.604 4.5 0.507 0.76 1.52 0.90 0.533 Aq.III Aq.IV Aq.II West-50 6.5Aq.IV 0.482 0.76 1.60 0.90 0.531 East 6.5 0.466Ad.III 0.76 1.52Aq.IV 0.88 0.478 Ad.III Aq.IV Ad.III -60 8.5 Aq.I 0.435 Ad.I0.76 1.60Ad.II 0.88 0.468Aq.II Aq.III 8.5 0.424weathered0.76 granite 1.52 0.87micro-weathered0.427 Aq.IV Ad.III 10.5filling0.372 soft0.76 soil 1.60clay 0.87 0.393sand gravel 10.5 0.363(intensely)0.76 1.52 0.86granite 0.361 Perched phreatic water Porosity confined water in loose rock mass Fissure confined water in magmatic rock mass 12.5 0 0.76 1.60 0.86 0 12.5 0 0.76 1.52 0.85 0 (b)

Figure 10. Hydrogeological conditions of the area: (a) Hydrogeological map of Fuzhou basin and coastal plain; (b) hydrogeological profile of the metro line.

Water 2019, 11, x FOR PEER REVIEW 12 of 19

On the basis of the preceding empirical prediction equations, the design method of the dewatering scheme with barriers in the sand and gravel strata is presented in Figure 9, where the increment in ∆Mu is determined through design precision and hydraulic conditions.

Figure 9. Dewatering scheme design method with partial penetrating curtains.

5.2. Dewatering Design of the Shuibu Metro Station

5.2.1. Hydrogeological Conditions of the Area The dewatering scheme combining partial penetrating curtains and wells is selected for groundwater control during the excavation of this case. The hydrogeological conditions of the area are presented in Figure 10. Possible connection regions in the silty clay layers are blocked via grouting to reduce hydraulic recharge from the aquifers. Then, the strata are generalized again during the Waterdesign2019 period,, 11, 2182 as shown in Figure 11. Before curtain construction, field pumping and laboratory13 tests of 19 are conducted to obtain permeability in various directions as follows: kh = 24.5 m/d and kv = 15 m/d.

Water 2019, 11, x FOR PEER REVIEW 13 of 19

5.2.2. Depressurization Requirements The depressurization requirements of uplift pressure can be calculated using the classic soil– pressure balanced method [33]. The calculated safe drawdown (s) of the west and east sections is 6.68 m and 7.53 m, respectively.

5.2.3. Dewatering Scheme Design The designed length of the reinforced diaphragm wall for load bearing is 31.5 m in engineering applications. For groundwater blocking, non-reinforced concrete curtains should be added at the wall’s bottom. The multiple schemes and corresponding inflow are determined as follows. (a) On the basis of ∆Mu (2 m), as set by construction organizations, various alternative schemes with different Mu (integers) are presented in Figure 11. (b) The short well screen (ls = Mu/3) is selected to enhance the wall–well effect. (c) R is set as 330 m (west) and (370a) m (east) on the basis of the field pumping tests 3 Bury depth and Equation (5). (d) QT is calculated using Equation (7) with a value of 4328 m /d (west)of water tableand 5187 Elevation (m) A—A m3/d (east).20 (e) TheWulongjiang distortion functions (normalized)Minjiang and inflow of each scheme areFlow pre pathsented in 0.5 River Shuibu station 10 2.4 1.5 1.4 1.2 River 2.1 2.3 3.7 1.2 Aq.I Aq.I Aq.I 1.8 1.8 Table 3 and Figure 12, respectively. Partial penetrating 0 Ad.I retaning wall Ad.I Ad.II Ad.II -10 Aq.II Aq.II Ad.II -20 Ad.I Aq.II Ad.I Pumping Table 3. Normalized seepage field distortion functionwell . -30 Ad.II Ad.II -40 p s d p s d Section L Q α β Aq.IIIη Q Section Aq.IVL Q α Aq.II β η Q -50 Aq.IV Ad.III Aq.IV 0 Ad.III 0.634 0.76 1.60 1.18 Aq.IV0.916 0 0.601 0.76 1.52 Ad.III1.02 0.711 -60 Aq.I Ad.I Ad.II Aq.II Aq.III weathered granite micro-weathered 2.5 0.575 0.76 1.60 0.99 0.699 2.5 Aq.IV0.549 0.76 1.52Ad.III 0.94 0.598 filling soft soil clay sand gravel (intensely) granite 4.5Perched phreatic0.529 water 0.76 1.60Porosity confined0.94 water in0.604 loose rock mass 4.5 0.507Fissure confined0.76 water in magmatic1.52 rock mass0.90 0.533 West 6.5 0.482 0.76 1.60 0.90 0.531 East 6.5 0.466 0.76 1.52 0.88 0.478 (b) 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 Figure 10. Hydrogeological conditions of the area: (a) Hydrogeological map of Fuzhou basin and 12.5 0 0.76 1.60 0.86 0 12.5 0 0.76 1.52 0.85 0 coastalFigure plain;10. Hydrogeological (b) hydrogeological conditions proﬁle of of the the area metro: (a line.) Hydrogeological map of Fuzhou basin and coastal plain; (b) hydrogeological profile of the metro line. The west zone The east zone depth (m) depth (m) 0 0 I: Fill 6.0 6.0

III: Silt 14.0 18.0 Pit bottom

IV: Silt sand Reinforced concrete continuous wall 26.0 28.0 31.5 34.0 36.0 V: Sand 38.0 40.0 42.0 44.0 44.0 44.0 VI: Silty clay and grouting Non-reinforced 50.0 concrete wall 50.0 VII: Gravel 54.0 56.0 VIII: Granite

Figure 11. Strata generalization and designed curtain schemes. Figure 11. Strata generalization and designed curtain schemes.

Water 2019, 11, 2182 14 of 19 Water 2019, 11, x FOR PEER REVIEW 14 of 19

6000 5500 5000 Inflow Prediction by 4500 empirical equations 4000

/d)

3 3500

(m 3000 Uncertainty

2500 Water 2019, 11, x FOR PEER REVIEW2000 14 of 19 1500 West section East section 1000 6000 500 5500 0 5000 0 2 4 Inflow6 Prediction8 10 by 12 14 4500 empirical equations Lp (m) 4000

/d) FigureFigure 3 1 12.23500. PumpingPumping rate rate prediction prediction of of various various schemes schemes..

(m 3000 Uncertainty

Q 5.2.4.5.2.4. C Comparisonomparison of of Dewatering Dewatering 2500Control Control S Schemeschemes 2000 Completely blocking seepage using the 12.5 m non-reinforced concrete curtain is impossible due Completely blocking seepage1500 using the 12.5 West m section non-reinforced concrete curtain is impossible due to the layer fluctuations and dispersions ofaquitards. East section The inevitable partial blocking leads to an to the layer fluctuations and dispersions1000 of aquitards. The inevitable partial blocking leads to an uncertainuncertain inflow inflow with with large large errors. errors. 500Moreover, Moreover, the the microflow microflow with with a a large large flow flow velocity velocity poses poses a a risk risk of of formationformation damage damage.. Th Thee water water pressure pressure0 difference difference of of curtains curtains is is difficult difficult to to release release without without sufficient sufficient groundwater flow and may cause leakage0 at2 vulnerable4 6 points8 of the10 curtains.12 14 Therefore, a scheme groundwater flow and may cause leakage at vulnerableL points(m) of the curtains. Therefore, a scheme of 10.5 m non-reinforced concrete curtain with a controllablep prediction Q of 2450 m3/d (west) and of 10.5 m non-reinforced concrete curtain with a controllable prediction Qww of 2450 m3/d (west) and 3 26942694 m m3/d/d (east) (east) is is selected. selected. Figure 12. Pumping rate prediction of various schemes. 5.2.5. Deviation Control Curves 5.2.5.5.2.4. Deviation Comparison Control of C Dewateringurves Control Schemes TwoCompletely types of design blocking deviations seepage areusing proposed the 12.5 bym non considering-reinforced field concrete conditions. curtain is (a) impossible The layer due fluctuation(a) may cause changes in the actual Mu, and 10% deviations are set in this study. (b) The to5000 the layer Normal fluctuations state WEST and SECTION dispersions of ( aquitards.b)5000 The Normal inevitabl state e partial blocking leads to an partial failure Mu of 10% non-reinforced decrease concrete curtains changes the M 10% blocking decrease effects,EAST SECTION and curtains with uncertain inflow with large errors. Moreover, the microflowu with a large flow velocity poses a risk of M 10% increase M 10% increase half-part failureu (5 m) are assumed to be the limit state. Hence, deviationu control curves are calculated formation4000 non-reinforced damage wall. Th failuree water pressure difference4000 of curtains non-reinforced is difficult wall failure to release without sufficient

usinggroundwater the inﬂow predictionflow and may formulas cause shownleakage in at Figure vulnerable 13. On points this basis,of the threecurtains. levels Therefore, of dewatering a scheme /d)

/d) 3000 3 system3 3000 states are presented: Wall-failure, layer-ﬂuctuation, and normal states. The upper limits of the

of 10.5 m non-reinforced concrete curtain with a controllable prediction Qw of 2450 m3/d (west) and (m deviation(m control3 curves are presented in Figure 13. Cautious schemes are then adopted on the basis

w 2000 w 2694 m /d (east) is selected.

2000 Q of theQ crossover points of the deviation control curves and safe drawdown lines. In this project, the Safe drawdown corresponding control inﬂow is 3600, 3000, and 2400 m10003/d under safeSafe drawdown drawdowns. 5.2.5.1000 Deviation Control[ sC] urves= 6.68m [s] = 7.53m 0 (a)4 5 6 7 8 9 4 5 6 7 8 9 Normal state WEST SECTION (b)5000 Normal state 5000 M 10% decreases(m) s(m) EAST SECTION u Mu 10% decrease Mu 10% increase Mu 10% increase 4000 non-reinforced wall failure 4000 non-reinforced wall failure

Figure 13. Deviation control curves: (a) West section; (b) east section. /d)

/d) 3000 3 3 3000

Two types of design deviations are proposed by considering field conditions. (a) The layer (m

w 2000

fluctuationw 2000 may cause changes in the actual Mu, and 10% deviations are set in this study. (b) The Q

Q partial failure of non-reinforced concreteSafe drawdown curtains changes the1000 blocking effects,Safe drawdown and curtains with half- part failure1000 (5 m) are assumed to[s ]be = 6.68mthe limit state. Hence, deviation [controls] = 7.53m curves are calculated 0 using the inflow4 prediction5 6 formulas7 8shown9 in Figure 13. On 4this basis,5 three6 level7 s of8 dewatering9 system states are presented: Ws(m)all-failure, layer-fluctuation, and normal states. sThe(m) upper limits of the deviation control curves are presented in Figure 13. Cautious schemes are then adopted on the basis Figure 13. Deviation control curves: (a) West section; (b) east section. of the crossover points ofFig theure deviation13. Deviation control control curves curves: and (a) Wsafeest drawdownsection; (b) east lines. section In this. project, the corresponding control inflow is 3600, 3000, and 2400 m3/d under safe drawdowns. Two types of design deviations are proposed by considering field conditions. (a) The layer 5.2.6. Location of Pumping Wells fluctuation may cause changes in the actual Mu, 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 m3/d under safe drawdowns.

5.2.6. Location of Pumping Wells

Water 2019, 11, 2182 15 of 19

Water 2019, 11, x FOR PEER REVIEW 15 of 19

Water5.2.6. 2019 Location, 11, x FOR PEER of Pumping REVIEW Wells 15 of 19 Pumping wells are located in accordance with the control inflow of the three level states. As 3 shownPumpingPumping in Fig wellsur wellse 1are4, are fourlocated located pu mpingin inaccordance accordance wells (Y: with with 600 the them control/d) control are inflowlocated inﬂow of of inside the the three three each level level section states. of As Asthe shown pit to 3 showninensure Figure in itsFig 14 constructionur,e four 14, pumpingfour pusafetymping wells under wells (Y: normal 600 (Y: m600 /stated) m3 are/d) (2400 locatedare locatedm3/d). inside For inside eachthe eachwall section -sectionfailure of theofstate, the pit twopit to ensureto reserved its 3 ensureconstructionpumping its construction and safety observation undersafety normalunderwells normal(G: state 600 (2400 statem3/d) (2400 m are/d). addedm For3/d). the For(total wall-failurethe of wall 3600-failure m state,3/d). state, Given two two reserved the reserved high pumping porosity 3 3 pumpingand observationco mpressibilityand observation wells of wells (G:the 600silty (G: m 600sand/d) m 3 arelayer,/d) are added observationadded (total (total of ofwells 3600 3600 m(SW) m3//d).d). outside Given Given thethe the high pit high areporosity porosity installed and to andcompressibilityobserve compressibility head changes of of the the siltyin silty the sand siltysand layer, sandlayer, observationlayer observation with high wells wells external (SW) (SW) outside outsidesensitivity. the the pit pit are are installed installed to to observe observehead changeshead changes in the in silty the sandsilty sand layer layer with with high high external external sensitivity. sensitivity. The retaining wall The middle partition wall SW-1 The retaining wall The middle partition wall SW-9 SW-1 SW-3 SW-5 SW-7 SW-3 SW-5 SW-7 SW-9 The west zone The east zone The west zone The east zone Y-1 Y-2 Y-3 Y-4 Y-5 Y-6 Y-7 Y-8

Y-1 G-1Y-2 Y-3 Y-4G-2 Y-5 Y-6G-3 Y-7 Y-8G-4 19.7m

G-1 G-2 G-3 G-4 19.7m SW-4 SW-6 SW-8 SW-2 SW-4 SW-6 SW-8 SW-10 SW-2 SW-10 88.3m 81.3m 88.3m 81.3m Y--The pumping well G--The inner observation well WG--The outer observation well Y--The pumping well G--The inner observation well WG--The outer observation well FigureFigureFig 1ure4. Loc 14.14ation. LocationLoc ationof the ofwells the. wells.wells.

A numericalA numerical model model was was performed performed to check to check the ef the thefectiveness ef eﬀfectivenessectiveness of the ofdesigned the the designed designed dewatering dewatering dewatering system. system. system. ConsideringConsidering the the possible possible adverse adverse conditions conditions caused caused by the by wall the construction wall construction defects, defects, the failure the failureand and leakingleaking of of6 of m 6 6 nonm m nonnon-reinforcedreinforced-reinforced bottom bottom bottom wall wall was wall takenwas was taken into taken consideration into into consideration consideration in the numericalin the in numerical the model. numerical model.The model. The simulatioThesimulatio simulationn ofn oftwo two of-stage two-stage-stage dewatering dewatering dewatering with with wall with -wallfailure wall-failure-failure state statewa states conductedwa wass conducted conducted according according according to the actualto to the actual excavationexcavation sequences sequences (west (west to east), to east), east), as presented as as presented presented in Fig in inure FigureFig 15ure. The 1515. .numerical The numerical results results show the show the calculatedcalculated average average average drawdown drawdown drawdown (6.8 (6.8 (6.8 m) m) waswa m)s almost waalmosts almost consistent consistent consistent with with prediction withpredicti predicti resultson resultson during results during dewatering during dewateringinsidedewatering the inside west-subsection inside the the west west-subsection excavation.-subsection excavation. With excavation. the developmentWith Wtheith developmentthe of the development subsequent of the of dewatering subsequent the subsequent inside dewatering inside east-subsection excavation, all the wells were gradually activated. The excessive east-subsectiondewatering inside excavation, east-subsection all the excavation wells were, graduallyall the wells activated. were gradually The excessive activated. drawdowns The excessive were drawdowns were caused by dewatering inside the two subsection excavations, which may induce causeddrawdown by dewaterings were cause insided by dewatering the two subsection inside the excavations, two subsection which excavation may induces, which large may settlements induce large settlements outside. Thus, the control of both the amount of pumping wells and dewatering outside.large settlements Thus, the outside control. Thus, of both the the control amount of both of pumping the amount wells of and pumping dewatering wells time and needsdewatering to be time needs to be carried out during the actual excavation dewatering. carriedtime needs out duringto be carried the actual out during excavation the actual dewatering. excavation dewatering.

Retaining wall Retaining wall Middle wall Drawdown curves Middle wall Retaining wall Retaining wall Middle wall Drawdown curves Middle wall

West section East section Pumping well Pumping well Pumping well Drawdown curves (closed) (opened) (opened) West section East section Pumping well Pumping well Pumping well Drawdown curves (closed) (opened) (opened)

(a) (b) (a) (b) Figure 15. Numerical simulation of the dewatering system: (a) West section dewatering; (b) overall Figure 15. Numerical simulation of the dewatering system: (a) West section dewatering; (b) overall pit dewatering. pitFigure dewatering. 15. Numerical simulation of the dewatering system: (a) West section dewatering; (b) overall pit dewatering. 5.35.3.. Field Field Verification Veriﬁcation 5.3The. FieldThe observation V observationerification data data inside inside the west the west section section are gathered are gathered for analysis for analysis due to duethe impervious to the impervious dewatering process, the inflow and corresponding head variations are shown in Figure 16. With the dewateringThe observation process, the data inﬂow inside and the corresponding west section headare gathered variations for are analysis shown due in Figure to the 16impervious. With the pumping wells successively turning on, the uplift head inside the west section exhibits a segmented pumpingdewatering wells process, successively the inflow turning and corresponding on, the uplift head head inside variations the west are shown section i exhibitsn Figure a16 segmented. With the downward trend during pumping, as shown in Figure 16a, and displays evident depressurization pumping wells successively turning on, the uplift head inside the west section exhibits a segmented downward trend during pumping, as shown in Figure 16a, and displays evident depressurization

Water 2019, 11, 2182 16 of 19

Water 2019, 11, x FOR PEER REVIEW 16 of 19 downward trend during pumping, as shown in Figure 16a, and displays evident depressurization eeffect.ffect. Meanwhile, the measured heads at (G (G-1)-1) and (G (G-2)-2) are approximately uniform throughout the entire dewatering process. Thus, introducing the average drawdown s insideinside isis reasonable.reasonable. When 3 seepage approaches a steadysteady state, s finallyfinally reaches 8.3 m with an inflowinflow of 24002400 mm3/d/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 + 10%) deviation control curve shown in Figure 13a. Hence, a 25% design safe curve and the (Mu + 10%) deviation control curve shown in Figure 13a. Hence, a 25% design safe margin is set for the westwest sectionsection dewateringdewatering design. For the head variations in the upper aquitard outside the pit, FigureFigure 1616b shows the measured data during pumping.pumping. Drawdowns are around 1 m and 0.5 m near the west and east sides,sides, respectively. These findings findings satisfy the the control value (2 (2 m) required byby constructionconstruction safety. safety. Moreover, Moreover, several several heads heads outside outside return return to theirto their initial initial states states due due to the to powerfulthe powerful recharge recharge of aquifers. of aquifers. The constant The constant stability stability of the excavation of the excavation surface in the surface entire in construction the entire processconstruction verifies process the reliability verifies the of thereliability design of method. the design method.

7 2 Y-2 Y-1 Y-3 Y-4 (a) Y-2 Y-1 Y-3 Y-4 G-1 (b) turn on turn on turn on turn on turn on turn on G-2 6 0 initial head 5 -2 4 -4

8.3m

6.68m

s = s = 3 SW-1 -6 SW-2 SW-3

2 Groundwater levels(m) Groundwater Groundwater levels(m) Groundwater SW-4 -8 safe head SW-5 1 SW-6 -10 monitoring head SW-7 SW-8 0 4/5 4/10 4/15 4/20 4/25 4/30 5/5 -- 4/5 4/10 4/15 4/20 4/25 4/30 5/5 Date Date

FigureFigure 16.16. GroundwaterGroundwater level variation during excavation: ( (aa)) A Aquiferquifer top within the pit; ( b) upperupper aquitard outside the pit.pit. 6. Discussion 6. Discussion Partially penetrating curtains in the seepage field generate considerable head differences between Partially penetrating curtains in the seepage field generate considerable head differences the outside and inside of the aquifer. Such differences indicate that the 3D seepage field formed by between the outside and inside of the aquifer. Such differences indicate that the 3D seepage field the wall–well effects plays an important role in groundwater control during excavation. Drawdowns formed by the wall–well effects plays an important role in groundwater control during excavation. are concentrated in the aquifer bottom and the curtain-enclosing scopes because of the vertical Drawdowns are concentrated in the aquifer bottom and the curtain-enclosing scopes because of the flow anisotropy of the aquifer. The distribution induces the water pressure to satisfy the uplift vertical flow anisotropy of the aquifer. The distribution induces the water pressure to satisfy the uplift pressure requirement outside and the decompression requirement inside. Furthermore, water pressure pressure requirement outside and the decompression requirement inside. Furthermore, water differences are reduced at the bottom of curtains to prevent damages and leaks. Thus, the 3D flow pressure differences are reduced at the bottom of curtains to prevent damages and leaks. Thus, the enables the appropriate distribution of the pressure head in dewatering construction. 3D flow enables the appropriate distribution of the pressure head in dewatering construction. However, an empirical prediction may not completely fit the observation data. The following However, an empirical prediction may not completely fit the observation data. The following simplified hypotheses should be further discussed in establishing inflow formulas that result in simplified hypotheses should be further discussed in establishing inflow formulas that result in uncertain deviations between predictions and reality. uncertain deviations between predictions and reality. 1. AA quantitative quantitative analysis analysis is is based based on the assumption that aquifer permeability is uniformly distributeddistributed at at each each point point in the influenceinfluence domain. However, However, many many deep deep structures (e.g., pile foundationsfoundations and and high-rise high-rise building building basements) basements) have have dispersed dispersed clay and clay grouting and grouting structures structures around aroundthe pumping the pumping influence influence area; this area; condition this condition reduces reduces the regional the regional permeability permeability of aquifers of aquifers [35]. [When35]. When these these obstructions obstructions are located are located in regions in regions with with dense dense flows flows (e.g., (e.g., foundation foundation pit scope pit scope and andcurtain curtain bottom), bottom), dewatering dewatering efficiency efficiency is substantially is substantially improved improved due due to flow to flow blocking. blocking. 2. NonNon-Darcy-Darcy flow flow occurs occurs with with a a fast fast flow flow velocity [ 34] that is evident at the wall bottom and near thethe pumping well. well. Moreover, Moreover, the the wall–well wall–well eff ects effects enhance enhance the non-Darcy the non-Darcy flow e flowffect and effect further and furtherpromote promote dewatering dewatering efficiency. efficiency. 3. TheThe parameter parameter coupling coupling effect effect is not considered in formula establishment. For example, when kkdd decreasesdecreases and and the the other other parameters parameters vary vary to to extend the vertical flow flow path, groundwater control efficiency may be improved rather than the multiplication of distortion functions caused by the separate variation of parameters.

Water 2019, 11, 2182 17 of 19

eﬃciency may be improved rather than the multiplication of distortion functions caused by the separate variation of parameters.

Thus, the aforementioned cumulative effects lead to conservative prediction values. Consequently, the measured drawdowns are nearly 1.6 m higher than the prediction in the field. However, detecting a particular distribution of the overall strata at limited cost is nearly impossible using existing technologies. Moreover, the exact range of non-Darcy flow is uncertain because of the unclear boundaries of the nonlinear laminar and the laminar [36]. Hence, quantifying the non-Darcy flow effect is difficult. For the algorithm that considers multi-parameter coupling, a complex algorithm is inappropriate for field application. To ensure safety, the preceding simplified hypotheses are applied to field dewatering design, in which they are reasonable and provide safe construction conditions within engineering accuracy.

7. Conclusions This study presents a formalized inflow formula for pits with partial penetrating curtains based on seepage characteristic analysis. The corresponding design method is further developed for the dewatering scheme design in sand and gravel strata and applied to a field case for verification. The following conclusions are drawn.

1. 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 Qw. Among the parameters, k plays a key role in flow velocity. Meanwhile, the other parameters, such as kv/kh, M, Mu, and ls, change the seepage field distribution. 2. 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 Qd–bd curve and quantifying seepage deformation. 3. 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: Conceptualization, L.L.; investigation, L.L.; methodology, C.C.; resources, C.S.; writing—original draft, L.L.; writing—review and editing, M.L. Funding: Projects funded by the National Natural Science Foundation of China (No. 51978669, U1734208), the Natural Science Foundation of Hunan Province, China (No. 2018JJ3657), and the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts294) are gratefully acknowledged. Acknowledgments: The authors are grateful for the funds provided by Guangzhou Metro Design & Research Institute Co., Ltd. and CCCC Strait Construction Investment and Development Co., Ltd. The authors also thank the 2nd Harbor Engineering Co., Ltd., of CCCC for cooperation in the field tests and data collection for this study. Conflicts of Interest: The authors declare no conflict of interest.

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