Optimization of confined aquifer dewatering for long-deep excavation using simulation–optimization method

Abstract

The confined aquifer dewatering for longdeep excavations usually encounters challenges due to complicated geotechnical conditions, large excavation sizes, and high hydraulic pressures. To propose the most efficient scheme of confined aquifer dewatering for longdeep excavations, dewatering optimizations were performed using the simulationoptimization method. An open cut tunnel of the JiangyinJingjiang Yangtze River Tunnel Project was taken as an example. The methods of finite element and linear programming (LP) were combined to optimize the dewatering process. A threedimensional finite element model was developed. After simulating the pumping tests, hydraulic conductivity was inverted. Then, necessary parameters in the LP method were determined by simulating dewatering with each pumping well, and various LP models were developed based on some important influence factors such as dewatering sequence, considered pumping wells, and pumping rate limitation. Finally, the optimal pumping rates were solved and applied to the numerical model, with induced drawdown and ground settlement computed for comparison. The results indicate that the optimization can significantly reduce the required wells in the original design. Dewatering in the deepest zone exhibits the highest efficiency for longdeep excavations with gradually varying depths. For the dewatering sequence from the shallowest to the deepest zone, more pumping wells are required but less energy is consumed. Higher quantity and more advantageous locations of pumping wells in the LP model usually result in lower total pumping rate, drawdown, and ground settlement. If more pumping wells are considered in the deepest zone, pumping rate limitation of single well will only slightly increase the total pumping rate, number of required pumping wells, drawdown, and ground settlement.

Headnote

Abstract

The confined aquifer dewatering for longdeep excavations usually encounters challenges due to complicated geotechnical conditions, large excavation sizes, and high hydraulic pressures. To propose the most efficient scheme of confined aquifer dewatering for longdeep excavations, dewatering optimizations were performed using the simulationoptimization method. An open cut tunnel of the JiangyinJingjiang Yangtze River Tunnel Project was taken as an example. The methods of finite element and linear programming (LP) were combined to optimize the dewatering process. A threedimensional finite element model was developed. After simulating the pumping tests, hydraulic conductivity was inverted. Then, necessary parameters in the LP method were determined by simulating dewatering with each pumping well, and various LP models were developed based on some important influence factors such as dewatering sequence, considered pumping wells, and pumping rate limitation. Finally, the optimal pumping rates were solved and applied to the numerical model, with induced drawdown and ground settlement computed for comparison. The results indicate that the optimization can significantly reduce the required wells in the original design. Dewatering in the deepest zone exhibits the highest efficiency for longdeep excavations with gradually varying depths. For the dewatering sequence from the shallowest to the deepest zone, more pumping wells are required but less energy is consumed. Higher quantity and more advantageous locations of pumping wells in the LP model usually result in lower total pumping rate, drawdown, and ground settlement. If more pumping wells are considered in the deepest zone, pumping rate limitation of single well will only slightly increase the total pumping rate, number of required pumping wells, drawdown, and ground settlement.

Keywords: Dewatering; Confined aquifer; Simulationoptimization; Linear programming; Open cut tunnel

(ProQuest: ... denotes formula omitted.)

1 Introduction

To accommodate the rapid urbanization in cities along the Yangtze River, rivercrossing channels are being constructed at an increasing rate. The rivercrossing channels typically employ the scheme of either underwater tunnel or bridge. According to a layout plan proposed by the Chinese government in 2018, only 4 of the 13 existing rivercrossing channels in Jiangsu Province are underwater tunnels. By 2035, at least 36 rivercrossing channels will be in operation, with 66.67% of those under construction or planning to be underwater tunnels. The underwater tunnels are typically constructed by means of shield tunneling, with both ends of the tunnel excavated using the "cut and cover" method. Excavating open cut tunnels in strata with confined aquifers is challenging. In the process of excavation, once the gravity of the soils between the tunnel bottom and the confined aquifer is exceeded by the confined hydraulic pressure applied to the confined layer, uplift of the tunnel bottom and water inrush are likely to happen, which may result in engineering accidents (Hong & Ng, 2013; Xu et al., 2009). Therefore, the dewatering in confined aquifer is necessary for lowering confined hydraulic pressures and ensuring construction safety (Pujades et al., 2012). However, if the dewatering design is excessively conservative, it can lead to extra engineering costs and environmental effects. Jiangsu Province lies in the lower reaches of the Yangtze River. The complicated geological condition in the Yangtze River floodplain introduces new difficulties to the design and implementation of confined aquifer dewatering, particularly with the growth in excavation depths and tunnel sizes in engineering practices. Considering the increasing demand for underwater tunnels in the Yangtze River floodplain, the efficient dewatering scheme is of vital significance to reduce the engineering costs and environmental effects.

Usually, an "equivalent well method" is used to design the dewatering scheme (L. Liu et al., 2019). The excavation zone enclosed with waterproof curtain is considered a large well with an equivalent diameter, and the water inflow can be calculated using Dupuit's equation. The number of the pumping wells can be roughly estimated based on the ratio of water inflow to the capacity of single well. However, Dupuit's equation is insufficient for considering complicated geological conditions, irregular excavation shapes, or partially penetrated waterproof curtains. Consequently, the computed total water inflow and pumping rate of each well are often overestimated, potentially resulting in additional engineering costs and more severe ground subsidence. Numerical simulation has been demonstrated to be a superior tool for investigating dewatering problems, provided that the model and parameters have been validated (Luo et al., 2008; Pujades et al., 2016; Su et al., 1998; Wang et al., 2012, 2013; Zhang et al., 2013; Zhou et al., 2011). If a construction project is deemed of importance, numerical simulation is typically employed to evaluate (Peng et al., 2021; Pujades et al., 2016; Wang et al., 2012; Xie et al., 2021; Zhang et al., 2013; Zhou et al., 2011) and improve (Luo et al., 2008; Ro´zkowski et al., 2021; You et al., 2018) the designed dewatering scheme. A limited number of dewatering schemes are simulated, and the results are compared to select the most efficient one. This is a typical procedure for improving a dewatering scheme using the numerical simulation method. As this procedure is not guided by optimization theory, the dewatering scheme can be further optimized.

For the purpose of further optimization, a simulationoptimization method has been developed. Optimization theory is used to optimize the dewatering scheme, whereas the numerical simulation provides the parameters necessary for the optimization theory. Over the past decades, the simulation–optimization method has been used to optimize various groundwater problems, including dewatering (Ayvaz, 2018; Jiang et al., 2012; Mansour & Aly, 2020; Shourian & Davoudi, 2017; Tokgoz et al., 2002), irrigation management (Hallaji & Yazicigif, 1996; Y. Liu et al., 2019), and groundwater remediation (Ayvaz, 2010; Erickson et al., 2002; KazemzadehParsi et al., 2015; Singh & Chakrabarty, 2010). However, there are some deficiencies in the existing studies. Firstly, most of the studies have focused on optimizing unconfined aquifer management, rather than confined aquifers. Secondly, the studies have often concentrated on applying new optimization methods to specific problems, whereas the results have limited general applicability to the problems of similar type. Thirdly, some critical influencing factors have not received sufficient attention, such as dewatering sequence for largescale excavations, considered pumping wells in optimization procedure, and pumping rate limitation. Finally, there is a lack of reported study on dewatering optimization problems related to longdeep excavations, such as open cut tunnels with partially penetrated waterproof curtains. Therefore, the most efficient dewatering scheme needs to be proposed urgently to meet the increasing construction demand for underwater tunnels in the Yangtze River floodplain.

This study aims to propose the most efficient dewatering scheme for longdeep excavations and investigate the effects of some important influencing factors, in order to provide instructions to the dewatering design and implementation in similar engineering projects. The simulation–optimization method combining finite element method (FEM) and linear programming (LP) method was used, and an open cut tunnel constructed in the Yangtze River floodplain was taken as an example. To determine the parameters required for the LP model, the simulation of dewatering with each well was performed using the hydraulic conductivity inversely computed by simulating pumping tests. LP models were developed and solved considering different dewatering sequences, considered pumping wells, and pumping rate limitations, with the optimal pumping rate of each well computed. The drawdowns and ground settlements induced by dewatering for different schemes were compared and the effects of the investigated factors were discussed. The findings of this study can be used to guide the confined aquifer dewatering for the longdeep excavations, particularly for projects involving underwater tunnels constructed in the Yangtze River floodplain.

2 Project background

2.1 Brief of the project

The JiangyinJingjiang Yangtze River Tunnel is located in Jiangsu Province, China. Its construction aims to connect Jingjiang City and Jiangyin City, with the objective of alleviating the traffic burden borne by the Jiangyin Bridge, which is located to the east of the tunnel at a distance of 5 km. The main line of the tunnel, which spans approximately 6445 m in total length, is divided into three sections: the northern open cut tunnel, the shield tunnel, and the southern open cut tunnel, as depicted in Fig. 1(a) and (b). The northern open cut tunnel comprises the shield shaft and the subsequent open cut tunnel, with an overall length of 713 m. Excavation depth of the northern open cut tunnel reaches its maximum at the shield shaft, peaking at 29.4 m, and decreases gradually northwards along the tunnel. Several structures, including diaphragm walls, soil mixing wall (SMW) piles, and Larsen steel sheet piles, have been used as retaining structures as well as waterproof curtains. The longitudinal profile and the location of the project, along with the plane view of the northern open cut tunnel, are depicted in Fig. 1. The profile of the tunnel in section 110 shown in Fig. 1(c) is depicted in Fig. 2.

2.2 Geotechnical and hydrogeological conditions

The project site exhibits an average ground elevation of +3.5 m and is characterized by a multilayered soil structure, with various layers ranging from miscellaneous fill (labelled as 11), plain fill (12), silty clay (21), mucky silty clay (22), silty clay (221), silty mealy sand (23), silty fine sand (24), silty clay (31), silty clay (321), silt (32), silty mealy sand (33), silty fine sand (34), medium sand (342), silty clay (42), silty clay (43), silty fine sand (44), etc. The soil strata are featured as a typical alternated multiaquiferaquitard system. The groundwater system encompasses a phreatic aquifer (labelled as Aq01) and three confined aquifers (AqIAqIII), which are separated by three aquitard layers labelled as AdI–AdIII. The phreatic aquifer Aq01 comprises layers 11, 12 and 21; AqI comprises layers 23 and 24; AqII comprises layer 32–342; and AqIII comprises layer 44 and the underlying sand layers. The average elevation of the phreatic water level is +2.33 m, whereas those of the confined water levels for AqI, AqII, and AqIII are +1.18, +0.72, and +0.67 m, respectively. AqI and AqII have direct connections with the Yangtze River, whereas AqIII mainly lies below its riverbed. The confined aquifers demonstrate high recharge rates. Figure 2 depicts the profile of the strata along section 110 , and Fig. 3 depicts the properties of distinct soil layers. Note that the thickness and parameter values of these soil layers in Fig. 3 were averaged based on the data collected from various boreholes at the investigated site.

2.3 Dewatering system

When the hydraulic pressure surpasses the soil weight between the bottom of the tunnel and the top surface of the confined aquifer, the confined water level should be lowered. To prevent hydraulic uplift, the acceptable drawdown can be determined with Eq. (1) (MOHURD, 2011).

... (1)

where hi represents the soil thickness of the ith layer between the bottom of the tunnel and the top surface of the confined aquifer; csi represents the unit weight of the ith soil layer between the bottom of the tunnel and the top surface of the confined aquifer; Hw0 represents the initial pressure head of the confined aquifer; s represents the drawdown at the top surface of the confined aquifer; cw represents the unit weight of water; Fs represents safety factor, which was taken as 1.1 in this study.

The drawdown requirements within the scope of the northern open cut tunnel were examined using Eq. (1). The calculation results indicate the necessity of dewatering in all confined aquifers when the tunnel is excavated to the bottom. Based on the dewatering requirements of different confined aquifers, the area requiring confined aquifer dewatering can be divided into three segments, as depicted in Fig. 1(c). In this study, only the segment necessitating dewatering in AqII was investigated, owing to its relatively larger span as compared to other segments, which makes it the most representative for analysis purposes.

The segment requiring dewatering in AqII was artificially separated into four excavation zones (Zone I–Zone IV) with varying excavation depths. In the original dewatering design, there were 17 pumping wells labelled as J1J17 within the segment. The plane layout of the pumping wells is depicted in Fig. 4(a), whereas the pumping well structures and the insertion depths of the waterproof curtains in different zones are depicted in Fig. 4(b).

3 Pumping test and parameter adjustment

In order to ascertain the hydraulic conductivity K of AqII, pumping tests were performed on the project site. Three wells, including a pumping well (P1) and two observation wells (OB1 and OB2), were arranged linearly from east to west, positioned approximately 50 m from the shield shaft along the direction of tunnel advancement. The two observation wells OB1 and OB2 were 10.1 and 4.2 m away from the P1, respectively (see Fig. 4(a)). The structure of P1 is depicted in Fig. 4(b).

The pumping rates Q of 141.0, 90.0, and 51.5 m3 /h were orderly applied to P1, with the corresponding drawdowns at approximately steady state being observed at P1, OB1, and OB2. Figure 5 shows the observed pumping ratedrawdown (Qs) curves for various pumping rates. The K value of AqII was calculated using the Dupuit's equation expressed in Eq. (2) (Dupuit, 1863) and was determined as about 10.50 m/d.

... (2)

where K represents the hydraulic conductivity of the confined aquifer; Q represents the pumping rate; Ma represents the thickness of the confined aquifer; sw represents the drawdown at the pumping well at steady state; R represents the influence radius at steady state; r represents the radius of the pumping well.

Prior research efforts (Wang et al., 2013, 2019; You et al., 2018) have indicated that the hydraulic conductivity value obtained from pumping tests requires adjustment for further use in the numerical simulation. In this study, the FEM was employed to model the pumping tests using a K value of 10.50 m/d at first. Discrepancies between the Qs curves for observation and simulation are depicted in Fig. 5. It is evident that the simulated drawdowns are lower than the observed ones, indicating the conservative results of further analyses and the necessity of the parameter adjustment.

The K value was varied from 7 to 10 m/d with an increment of 1 m/d, and the simulated drawdowns for varying K is depicted in Fig. 6. Each curve represents the simulated drawdowns with a specific Q for varying K. The K value corresponding to the intersection point of the observed drawdown and simulated curve is considered as an appropriate value. The adjusted K, namely the average of all appropriate K values, was determined to be 9.45 m/d. The simulated Qs curves for different wells with adjusted K value of 9.45 m/d are also depicted in Fig. 5, which are highly consistent with the observed ones. In subsequent analyses, the adjusted K will be used.

4 Simulationoptimization method for dewatering

4.1 Dewatering optimization framework with the LP method

Typical pumping ratedrawdown curves are depicted in Fig. 7 (Fang et al., 1987; Wang et al., 2017). Curve I represents the linear correlation of the pumping rate and drawdown for confined aquifer dewatering, which is expressed in Eq. (3); Curve II represents the pumping ratedrawdown relation for phreatic aquifer dewatering; Curve III represents the condition when the water recharge is weak; Curve IV represents the condition when the water recharge is exhausted. According to the principle of flow superposition, the drawdown induced by multiple pumping wells can be linearly superposed by the drawdowns induced by all individual wells (Ayvaz, 2018). Therefore, drawdown at point j during confined aquifer dewatering can be expressed with Eq. (4).

... (3)

... (4)

where sj represents the drawdown at point j; sji represents the drawdown at point j induced by well i; Qi represents the pumping rate at well i; aji represents the ratio of sji to Qi

During the dewatering process, the drawdown at point j should not be lower than the required drawdown for engineering safety, as expressed in Eq. (5). However, examining every location within the excavation zone using Eq. (5) is impractical. Restricted to the limited number of points to be examined, sufficient control points can be chosen, assuming that the meeting of Eq. (5) for all the chosen control points represents the safety of the whole excavation zone.

... (5)

where sj,min represents the required drawdown at point j and takes the lowest valid s value in Eq. (1).

If the pumping rate of a well is sufficiently large so that the water level elevation at this well is under the top of the confined aquifer, the Qs curve pattern will shift from linear to a nonlinear type, represented by Curve II as depicted in Fig. 7. Since the LP method is inappropriate for optimization purposes in a nonlinear scenario, it is necessary to ensure that the drawdown at each well is not higher than the initial pressure head at the top of the confined aquifer, as expressed in Eq. (6):

... (6)

where sk represents the drawdown at well k; Hw0k represents the initial pressure head at the top of the confined aquifer where well k is located.

Similar to Eq. (4), the ratio of sk to Hw0k can be expressed by the linear summation of the ratio of the drawdown at well k induced by well i to Hw0k, as expressed in Eq. (7):

... (7)

where ski represents the drawdown at well k induced by well i; bki represents the ratio of ski/Hw0k to Qi

Each well's pumping rate has a minimum limit of zero and a maximum limit (pumping rate limitation, Qi,max), which is determined by the water pump's work rate or an artificially defined value.

Based on the aforementioned conditions, the LP model for optimizing confined aquifer dewatering can be formulated as follows:

... (8)

... (8a)

... (8b)

... (8c)

where Qtotal represents the total pumping rate; Ncw represents the number of the considered pumping wells; Ncp represents the number of the control points.

Equation (8) represents the objective function of the LP model, which aims to minimize the total pumping rate of all wells under the constraints formulated in Eq. (8a)(8c). Equation (8a) is the constraint on the drawdown at each control point, referring to Eqs. (4) and (5). Equation (8b) is the constraint on the drawdown at each well, referring to Eqs. (6) and (7). Equation (8c) is the constraint on the pumping rate of each well.

The parameters required to solve the LP model are sj,min, aji, bki, and Qi,max. sj,min can be computed with Eq. (1), whereas aji and bki can be obtained with numerical simulation. The values of Qi,max are determined based on the actual conditions. The optimal pumping rate of each well can be further computed by solving the LP model.

4.2 Procedures of the simulation–optimization method

Figure 8 illustrates the procedures of the simulation–optimization method. Initially, the required drawdowns at the chosen control points within the excavation zone are computed. Next, the quantity and locations of the pumping wells, as well as the sizes and depths of the well screens, are preliminarily determined following the typical design procedures. Note that a larger quantity of the pumping wells are preferred so that the pumping wells with higher efficiencies can be easily selected by optimization algorithm, as will be discussed later. Subsequently, the numerical model is developed based on the designed dewatering system, and the parameters aji and bki can be determined by simulating the dewatering with each well independently. Considering different dewatering schemes, a series of LP models can be developed and solved to determine the optimal pumping rate of each well. The optimal pumping rates are then applied to the numerical model and the induced drawdowns and ground settlements can be further computed. The total pumping rates Qtotal, the number of activated pumping wells Naw, the induced drawdowns s and the ground settlements dv for different LP models are compared. The ideal dewatering scheme will be chosen based on the comparison of the results and specific demands in engineering practices.

5 Development of LP models

5.1 Control points and drawdown requirements

The minimum drawdown always appears at one of the corner points if a pumping well is located inside the excavation zone. Therefore, the corner points of different excavation zones can be chosen as the control points to ensure that the drawdowns within the excavation zone will meet the drawdown requirements if the drawdown at each control point exceed the required drawdown sj,min. Figure 4(a) illustrates the definitions of ten control points. The value of sj,min at each control point can be obtained using Eq. (1). It should be noted that the maximum excavation depth of each zone was taken as the excavation depth of the zone in this study. The sj,min values at all control points are specified in Table 1.

5.2 Numerical simulation of singlewell dewatering

A threedimensional (3D) FEM was developed for simulating dewatering in AqII with each well to determine parameters aji and bki, using the finite element software ABAQUS. The details of the model are as follows.

5.2.1 Geometry, mesh, and boundary conditions

The influence radius of dewatering R can be estimated as 403.9 m using Eq. (9) (Wang et al., 2019):

... (9)

In numerical model, the soil domain was expanded 1000 m outward from the tunnel's plane modelling scope, which far exceeds the calculated R. The plane size of soil domain is 2327 m long and 2056 m wide, whereas the depth is 100 m. Figure 9 illustrates the model's geometry.

The waterproof curtains located to the north of Zone IV are not included in the investigated zones nor do they penetrate into AqII, having minimal impact on seepage flow. For the sake of simplicity, they were excluded in modelling. The waterproof curtain was discretized using 8node linear 3D Langrangian elements with reduced integration (C3D8R), consisting of 2402 elements and 4086 nodes. The soil body was discretized using 6node linear triangular prism elements coupled with pore pressure (C3D6P), consisting of 473 834 elements and 252 666 nodes. Mesh sizes were refined within the confined aquifer AqII, especially for the zones within the scope of the tunnel. With increasing distance from the abovementioned zones, the mesh sizes were controlled to increase in the vertical and horizontal directions. The overall and local refined meshes are depicted in Fig. 9.

Displacement boundary conditions were imposed on the lateral and bottom surfaces of the soil body to restrict motion in the normal direction, whereas the top surface was free to move. The initial water levels of the phreatic and confined aquifers were set based on the water level elevations detailed in Section 2.2. The hydraulic heads at the lateral boundaries of the aquifers were fixed, matching the initial water levels (Dirichlet boundary condition). A seepage velocity v, which can be calculated using Eq. (10), was applied to the well screen surface to simulate the dewatering with a constant pumping rate (Neumann boundary condition).

... (10)

where v represents the seepage velocity; S represents the area of the well screen.

5.2.2 Parameters

The soil layers of 11, 12, and 21 were modeled using the Mohr–Coulomb (MC) model for easy convergence, whereas the underlying soil layers were modeled using the modified CamClay (MCC) model. Adjacent soil layers with similar parameter values were merged into a single layer. The stress ratio M was calculated using Eq. (11) according to the equivalent area circle yield criterion (Deng et al., 2006), which can describe the strength of soil more precisely since the area of the equivalent area circle in the deviatoric plane is exactly the same with the area enclosed by the yield surface of the MC model. The soils were assumed to be isotropic, thus the hydraulic conductivity of each layer took the higher value between the Kv and Kh as depicted in Fig. 3, expect for AqII of which the hydraulic conductivity was adjusted to 9.45 m/d. The parameters of soil layers used in numerical simulation are summarized in Tables 2 and 3.

... (11)

where M represents the stress ratio at critical state; u΄ represents the effective internal friction angle.

The waterproof curtain (diaphragm wall) was described using the linear elastic model. The parameters were set as c = 24 kN/m3 , E = 30 GPa, and t = 0.15, which were referred to the values of C30 concrete.

5.2.3 Contacts

The contacts between the curtain and soil materials were described using the surfacetosurface contact. The hard contact was used to describe the normal behavior and the penalty contact algorithm was employed to simulate the tangential behavior between the soil materials and the curtain. The relationship between the normal stress and shear stress at soilstructure interface can be expressed in Eq. (12) (Gennaro & Frank, 2002):

... (12)

where smax represents the interface shear stress at failure state; rn represents the normal stress applied to the interface; uint represents the angle of interface friction.

According to previous research works, the ratio of uint/ u΄ for saturated sandconcrete interface is about 0.89–0.90 (Potyondy, 1961) and was set to 0.9 in this study, whereas that for silt clayconcrete interface ranges from 0.95 to 1.04 (Konkol & Mikina, 2021; Wang et al., 2020) and was set to 1.0 in this study. Therefore, the friction coefficients (namely tanuint) of the interfaces between various soils and waterproof curtain were set according to the abovementioned uint/u΄ values and the corresponding u΄ described in Fig. 3.

5.3 Simulated results of dewatering with single pumping well

The parameters aji and bki were obtained by simulating the dewatering with each single well. The serial number of the wells and control points are depicted in Fig. 4(a). The values of aji and bki are stored in the following matrixes [aji] and [bki] respectively.

... (13)

... (14)

5.4 LP models for different dewatering schemes

A series of LP models were developed based on various dewatering schemes. The dewatering schemes were basically distinguished by the dewatering sequences, considered pumping wells in the LP model, and pumping rate limitations of single well. Three sets of the considered wells and three dewatering sequences were combined to construct nine LP models. In addition, the dewatering practices typically adhere to the principle of using multiple pumping wells and maintaining low pumping rates for individual wells (Zhou et al., 2011), in case some of the wells may malfunction and the consequences are difficult to be predicted and controlled with high pumping rates. Therefore, additional LP models (LP4–LP6) considering pumping rate limitation of single well Qi,max were also developed. All LP models are summarized in Table 4.

Dewatering sequence S represents dewatering synchronously in the zones (Zones I–IV) depicted in Fig. 4 (a). Dewatering sequence DS represents dewatering from the deepest zone to the shallowest zone, namely, from Zones I–IV. Dewatering sequence SD represents dewatering from the shallowest zone to the deepest zone, namely, from Zones IV–I. For the DS and SD dewatering sequences, the dewatering is implemented in four stages, with each zone being gradually dewatered following the prescribed order. In addition, once the drawdown requirement of a specific zone is met in a stage, it still has to be met in all subsequent stages. For the consistency of the analyses, the S dewatering sequence was also divided into four equivalent stages. Based on the actual construction process of Zone I–IV, the duration of the whole dewatering process was set to 60 d, with each stage lasting for 15 d.

The parameter values of aji and bki for the LP models were obtained by extracting the corresponding elements of the considered pumping wells from the matrixes [aji] and [bki]. The sj,min values at all stages for the S dewatering sequence are summarized in Table 1, whereas the sj,min values at Stages 1–4 for the DS and SD sequences are summarized in Table 5 and Table 6, respectively.

6 Results and discussions

6.1 Optimal pumping rates

The "linprog" function incorporated in software MATLAB was used to solve the LP models. The optimal pumping rates, activated pumping wells, and total pumping rates are summarized in Fig. 10. The optimal pumping rates were further applied to the corresponding pumping wells in the numerical model. The drawdowns at the top of AqII and the ground settlements at the end of each stage along the sections defined in Fig. 9(b) for various LP models were compared, with the effects of different influencing factors discussed.

6.2 Effects of the dewatering sequence

As shown in Fig. 10(a)–(c), owing to the same drawdown requirements, the activated pumping wells and optimal Qi for the DS and SD dewatering sequences at Stage 4 are identical to those for the S dewatering sequence at all stages. Although the drawdown requirements for the DS dewatering sequence differ across stages as summarized in Table 5, the dewatering configurations remain unchanged, which can be explained as follows. The excavation depth varies along the length of the tunnel. The much deeper excavation depth of Zone I represents much higher drawdown requirement than the other zones. Hence, meeting the drawdown requirement of Zone I facilitates the fulfillment of drawdown requirements in other shallower zones with the induced groundwater depression cone. Therefore, the drawdown requirements at all stages for the DS dewatering sequence are equivalent and are governed by the drawdown requirement of the deepest zone, which will be discussed later. From this perspective, dewatering in the deepest zones is the most efficient. This finding can be demonstrated by the optimization results that the activated wells at Stage 4 of all LP models are mainly located in Zone I, particularly for LP3 that all the activated wells at Stage 4 are in Zone I. In addition, The highest insertion ratios of the waterproof curtains in Zone I also contribute to the highest efficiency of dewatering in Zone I, since the drawdown inside the excavation area increases with increasing insertion ratio (Wang et al., 2019; Wu et al., 2017). Based on the results, the drawdown requirement of the deepest excavation zone should be met in priority to achieve the highest dewatering efficiency for the longdeep excavations with varying excavation depths.

The comparisons of the numbers of the activated wells Naw and the considered wells Ncw are also depicted in Fig. 10. For the S and DS dewatering sequences, relatively low ratios of Naw to Ncw indicate that dewatering optimization can significantly decrease engineering costs.

Compared with S and DS dewatering sequences, the optimal dewatering configurations for the SD dewatering sequence vary across different stages. Since the drawdown requirement is usually not met for the deeper zone when it is just met for the shallower zone, the adjustment of dewatering configuration is necessary in subsequent stages, potentially resulting in deactivating certain wells and activating new ones. Consequently, the value of Naw for the SD dewatering sequence is much higher than those of the other two dewatering sequences, as depicted in Fig. 10. In addition, since Qtotal at Stages 1–3 for the SD dewatering sequence are much lower than those of the other two dewatering sequences, the energy consumed by water pumping is lower, provided that the total dewatering time for different dewatering sequences is equal.

With the optimal pumping rates applied to the numerical model, the drawdowns and ground settlements along different sections were computed. Taking LP1 as an example, the drawdowns at different stages along Sections I, II, and III are depicted in Fig. 11. The drawdown curves for the SD dewatering sequence (LP13) develop gradually at different stages, and at Stage 4, they almost overlap with the curves for the other two dewatering sequences. This result is expected since the dewatering configurations for all three sequences are identical at the final stage. As depicted in Fig. 11(c), at all stages, the required drawdowns along Section III are entirely enveloped by the drawdown curves. At Stage 4, it is evident that the required drawdowns are precisely met at the boundary between Zone I and II, whereas those of Zones II–IV are much lower than the corresponding drawdowns. These observations lead to the deduction that ignoring the drawdown requirements of Zone II–IV does not influence the optimization results for all stages of the S and DS dewatering sequences as well as Stage 4 of the SD dewatering sequence. In other words, once the drawdown requirement of Zone I is met, so are those of Zones II–IV. The observations also demonstrate the previous explanation of why the dewatering configurations of DS dewatering sequence remain unchanged across different stages. Note that for the DS dewatering sequence if the required drawdowns of Zones II–IV are not completely enveloped by the drawdown curve at Stage 1, Qtotal will increase and even extra wells may be required in the later stages. Consequently, the dewatering configurations for the DS dewatering sequence will vary across different stages.

Figure 12 depicts the ground settlements at different stages along Sections I, II for LP1. Settlement troughs are observed and the maximum ground settlements occur at some distance from the waterproof curtain, which can be attributed to the reduction in soil deformation near the curtain due to the frictional force between the curtains and the surrounding soils. The ground settlements gradually develop across different stages. The ground settlements for the SD dewatering sequence differ significantly across different stages compared with the other two dewatering sequences, which can mainly be attributed to the distinctive dewatering configurations at different stages. At the same stage, the ground settlements for the SD dewatering sequence are the lowest. There are two main explanations for this phenomenon. First, the drawdowns at Stages 1–3 are much lower for the SD dewatering sequence than those for the other two dewatering sequences, leading to lower compressions of the AqII. Second, although the hydraulic conductivities of the confined layers of AqII are relatively low, the vertical seepage flows towards AqII do exist and contribute to the compressions of other layers. Compared with the other two dewatering sequences, the drawdowns for the SD dewatering sequence are lower in Stages 1–3, resulting in lower hydraulic gradients between AqII and its confined layers for most of the time, thereby inducing less evident vertical seepage flows and lower compressions of the other layers.

Figure 13 illustrates the developments of maximum ground settlements (dvm) outside the waterproof curtain along Sections I and II for LP1, LP2, and LP3. For the S and DS dewatering sequences, the values of dvm increase rapidly during the first stage, whereas the growth rates evidently decline in subsequent stages. Conversely, the growth rates of dvm for the SD dewatering sequence are relatively lower during early stages, but increase evidently during Stage 4. The values of dvm at the end of Stage 4 for SD dewatering sequence are approximately 20.6%–24.5% lower than those for the other two dewatering sequences. The results indicate that controlling ground settlements for the SD dewatering sequence is simpler because dvm develops in a predictable and gradual manner.

6.3 Effects of the considered pumping wells

There are four wells considered in LP1. Based on LP1, four extra wells are added to LP2, whereas all the designed wells are included in LP3. According to Fig. 10(a)–(c), the Qtotal values for LP1, LP2, and LP3 at Stage 4 are in descending order, whereas the trend of Naw is different from that of Qtotal. It is indicated that higher Ncw results in lower Qtotal and higher Naw, which can be explained as follows. When pumping with a single well, the drawdown generally decreases with increasing distance from the well. If more wells are considered in the LP model, some wells may be closer to a specific control point. Therefore, the drawdowns induced by these wells at the control point are higher, representing higher pumping efficiencies on the control point. Since the control points are scattered with specific distances from one another, the most efficient wells relative to different control points are different. Consequently, more wells are likely to be selected by the optimization algorithm to achieve higher global pumping efficiency, resulting in lower Qtotal and higher Naw. However, when the value of Ncw is relatively low, there may be exception. For instance, the Ncw values of LP1 and LP2 are different, whereas the Naw values are equal. Nonetheless, the exception does not alter the overall conclusion. The conclusion is also valid for the LP models with Qi,max. As shown in Fig. 10(d), the Qi,max values for LP4 and LP5 are both 50 m3 /h. Since more pumping wells are considered in LP5, the Qtotal value is lower and Naw value is higher.

Figure 14 shows the drawdowns at Stage 4 along Sections I, II for LP1, LP2, and LP3, whereas Fig. 15 shows the drawdowns at different stages along Section III for the SD dewatering sequence (LP13, LP23, and LP33). The drawdown values for LP1, LP2, and LP3 are generally in descending order and the results are positive correlated to Qtotal. Figure 16 shows the ground settlements dv outside the waterproof curtain at Stage 4 along Sections I and II. The relationship of dv for LP1, LP2, and LP3 is consistent with those of the pumping rate and drawdown, which indicates that higher Ncw resulted in lower ground settlement. Based on the results, it can be concluded that the pumping wells with more advantageous locations result in lower Qtotal, drawdown, and ground settlement. Increasing the Ncw value in the LP model improves the probability of locating more efficient pumping wells.

6.4 Effects of the pumping rate limitation

The considered pumping wells of LP2 and LP4 are the same, whereas Qi,max for LP2 (positive infinity) is higher than that for LP4 (50 m3 /h). The results of LP2 and LP4 indicate that lower Qi,max results in higher Naw and Qtotal, as depicted in Fig. 10(d). A similar conclusion can be drawn from the comparison among LP3, LP5, and LP6, which can be explained as follows. Consider a scenario in which the activated wells and the corresponding optimal pumping rates have already been computed with the optimization algorithm. When a sufficiently low Qi,max value is introduced, the drawdown requirements may not be met solely by the previously determined activated wells. As a result, less efficient wells have to be activated, resulting in the increases of both Naw and Qtotal. The difference in Qtotal between LP2 and LP4 is more significant than those among LP3, LP5, and LP6, which can be explained as follows. All the designed wells are considered in LP3, LP5, and LP6, whereas less wells are considered in LP2 and LP4. When Qi,max is introduced, the less efficient wells required to be further activated for LP3, LP5, and LP6 are right in or close to the deepest zone (Zone I), indicating relatively similar efficiencies of the activated wells for LP3, LP5, and LP6 compared with those for LP2 and LP4. Hence, the differences in Qtotal among LP3, LP5, and LP6 are less significant, which are less than 2.3%.

Figure 17 shows the drawdown curves at Stage 4 along Section III for the LP models with Qi,max. With the same considered pumping wells, introducing Qi,max results in evidently higher drawdown values, except for the almost overlapped curves of LP3 and LP5. It can be explained as follows. Zone I can be regarded as a large well since all the activated wells for LP3 and LP5 are located in it. The seepage flowing towards the "large well" for LP3 and LP5 shows minimal differences due to the nearly identical Qtotal values (see Fig. 10), resulting in extremely close drawdown curves along Section III. Comparisons between Fig. 17(a) and (b) indicate that the differences between the drawdown curves for different Qi,max are smaller when including more pumping wells in the most efficient dewatering zone. The comparisons of ground settlements at Stage 4 are depicted in Figs. 18 and 19. It can be deduced that the effects of Qi,max on ground settlement are consistent with those on Qtotal and drawdown.

In dewatering practice, using a larger number of pumping wells with lower pumping rates for each well is preferable, in case some wells malfunction which will result in consequences difficult to be predicted and controlled. Based on the results, the pumping wells are more favorable to be located in the deepest excavation zone to minimize the adverse effects of Qi,max on Qtotal, drawdown, and ground settlement.

7 Conclusions

In this study, the simulation–optimization method was used to optimize confined aquifer dewatering for the longdeep excavations, taking the northern open cut tunnel of JiangyinJingjiang Yangtze River Tunnel Project as an example. The hydraulic conductivity of the confined aquifer was adjusted by simulating the pumping tests using FEM. The parameters required for optimization were determined by simulating the dewatering with each well, based on which a series of LP models characterized by different influencing factors were developed. The optimal pumping rate of each well was computed and applied to the numerical model, with the drawdowns and ground settlements induced by different dewatering schemes computed and compared. The key findings of the study are summarized as follows:

(1) Dewatering optimization can significantly reduce the number of activated wells. Dewatering in the deepest excavation zone is the most efficient for the longdeep excavation with gradually varying excavation depths. The drawdown requirements of the whole excavation zone may be met only with the pumping wells in the deepest excavation zone activated.

(2) For the investigated case, dewatering synchronously is equivalent to dewatering from the deepest zone to the shallowest zone. Dewatering from the shallowest zone to the deepest zone consumes less energy and induces lower ground settlements compared with the other two dewatering sequences; however, it requires a higher number of activated wells.

(3) More advantageous locations of the pumping wells result in lower total pumping rates, drawdowns, and ground settlements. Increasing the quantity of pumping wells in the LP model facilitates the selection of wells in more advantageous locations.

(4) Applying a pumping rate limitation to individual wells typically results in increases in the total pumping rate, number of activated wells, induced drawdown and ground settlement. Nevertheless, the adverse effects of the pumping rate limitation can be mitigated by including an adequate number of pumping wells in the deepest zone in the LP model.

CRediT authorship contribution statement

Yanxiao Sun: Conceptualization, Methodology, Software, Investigation, Visualization, Validation, Writing – original draft. Zhenxiong Jiang: Project administration, Resources, Investigation, Data curation. Liyuan Tong: Funding acquisition, Writing – review & editing. Jiawei Sun: Software, Visualization. Jia Cui: Investigation, Data curation. Xin Zhou: Investigation, Data curation. Songyu Liu: Conceptualization, Supervision, Funding acquisition, Resources, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 41972269 and 52178384), and the Project of Jiangsu Provincial Transportation Construction Bureau, China (Grant No. 2021QD05).

Sidebar

Received 23 June 2023; received in revised form 30 August 2023; accepted 22 November 2023

Available online 24 January 2024

Footnote

* Corresponding author.

Email address: [email protected] (S. Liu).

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