Effect of mixed physical barrier on seawater intrusion and nitrate accumulation in coastal unconfined aquifers

Physical barrier has been proven to be one of the most effective measures to prevent and control seawater intrusion (SWI) in coastal areas. Mixed physical barrier (MPB), a new type of physical barrier, has been shown to have higher efficiency in SWI control. As with conventional subsurface dam and cutoff wall, the construction of MPB may lead to the accumulation of nitrate contaminants in coastal aquifers. We investigated the SWI control capacity and nitrate accumulation in the MPB using a numerical model of variable density flow coupling with reactive transport, and performed sensitivity analysis on the subsurface dam height, cutoff wall depth and opening spacing in the MPB. The differences in SWI control and nitrate accumulation between MPB and conventional subsurface dam and cutoff wall were compared to assess the applicability of different physical barrier. The numerical results show that the construction of MPB will increase the nitrate concentration and contaminated area in the aquifer. The prevention and control efficiency of MPB against SWI is positively correlated with the depth of the cutoff wall, reaching the highest efficiency at the minimum effective dam height, and the retreat distance of the saltwater wedge is positively correlated with the opening spacing. We found a non-monotonic relationship between the change in subsurface dam height and the extent of nitrate accumulation, with total nitrate mass and contaminated area increasing and then decreasing as the height of the subsurface dam increased. The degree of nitrate accumulation increased linearly with increasing the height of the cutoff wall and the opening spacing. Under certain conditions, MPB is 46–53% and 16–57% more efficient in preventing and controlling SWI than conventional subsurface dam and cutoff wall, respectively. However, MPB caused 14–27% and 2–12% more nitrate accumulation than subsurface dam and cutoff wall, respectively. The findings of this study are of great value for the protection of coastal groundwater resources and will help decision makers to select appropriate engineering measures and designs to reduce the accumulation of nitrate pollutants while improving the efficiency of SWI control.


Introduction
Coastal areas are not only the most densely populated regions but also among the most economically active regions in the world. Reportedly, 50-70% of the global population resides in coastal plain areas, which occupy a mere 5% of the Earth's surface (Board and National Research Council 2007). Groundwater is a critical resource for human survival and serves as a primary source of freshwater in coastal areas, providing a vital water source for human activities, such as agriculture and industry. However, human activities, such as excessive use of fertilizers and discharge of domestic and industrial wastewater, have significantly increased the nitrate content in groundwater, leading to severe pollution (Lu and Tian 2017;Fang et al. 2020;Xin et al. 2019Xin et al. , 2021. Nitrate pollution in groundwater is a global environmental concern (Cui et al. 2014;Jang et al. 2017;Nai et al. 2020;Torres-Martínez et al. 2021). Despite the development of various measures to control nitrate pollution in groundwater (Gibert et al. 2019;Hu et al. 2019;Zhang et al. 2019;Zambito Marsala et al. 2021;Gao et al. 2023), effectively controlling the increasing nitrate levels in groundwater remains a persistent and challenging issue.
At the same time, coastal areas are currently facing an increasingly serious threat of seawater intrusion (SWI) (Fig. 1a). Overexploitation of groundwater in these areas has caused a decline in groundwater levels, which, combined with sea level rise caused by global climate change, has made SWI the primary cause of freshwater resource deterioration in coastal aquifers (Werner and Simmons 2009;Rozell and Wong 2010;Werner et al. 2013;Walther et al. 2017). Controlling SWI through effective and reasonable methods is critical for the sustainability of coastal areas and ensuring water availability (Abarca et al. 2013;Lu et al. 2016). Various measures have been proposed to control SWI, including artificial groundwater recharge, hydraulic barrier, air barrier, and physical barrier Ebeling et al. 2019;Wang et al. 2020;Wu et al. 2020;Zang and Li 2021). Subsurface physical barrier has become the most popular strategy and have been widely studied due to their low operating costs, high stability, and ability to store fresh groundwater resources Chang et al. 2019;Wu et al. 2020;Yan et al. 2021). Since the 1980s, subsurface physical barrier has been used globally (Nawa and Miyazaki 2009;Senthilkumar and Elango 2011). Japan, China, and the USA have built a series of subsurface physical barrier for SWI control with remarkable results (McAnally and Pritchard 1997;Japan Green Resources Agency 2004;Kang and Xu 2017;Zhang et al. 2021). The two main types of physical barrier are subsurface dam and cutoff wall (Abdoulhalik and Ashraf 2017;Gao et al. 2021). Cutoff wall is constructed in the upper part of the aquifer, and groundwater is discharged through openings in the lower part of the aquifer (Fig. 1b). Subsurface dam is built at the bottom of the aquifer, and groundwater is discharged through openings in the upper part of the aquifer (Fig. 1c) (Gao et al. 2021;Sun et al. 2021).
The feasibility of using physical barrier to inhibit SWI has been well established (Abdoulhalik and Ashraf 2017;Shen et al. 2020;Wu et al. 2020). However, the construction of physical barrier, particularly subsurface dam, can hinder the hydraulic connection between upstream and downstream, leading to high concentrations of residual saltwater being trapped behind the dam. As a result, residual saltwater has become a serious problem that limits the development of fresh groundwater in coastal areas. Luyun et al. (2009) showed that the time required to remove residual saltwater in the upstream aquifer after the construction of subsurface dam is considerably longer than the intrusion time of saltwater. Moreover, the removal time of residual saltwater decreases as the height of the dam decreases. At the field scale, Zheng et al. (2020) found that complete desalination of residual saltwater trapped upstream of subsurface dam could take several decades, significantly impacting the availability of fresh groundwater. Abdoulhalik and Ashraf (2017) used laboratory tests and numerical techniques to demonstrate that aquifer stratification patterns play a crucial role in determining the effectiveness of subsurface dam in removing residual saltwater. They also found that layered heterogeneity can significantly prolong the cleanup time of residual saltwater compared to homogeneous aquifers.
The construction of physical barrier that obstruct fresh groundwater flow to the ocean may also impact the transport of contaminants in the aquifer, leading to their retention in the aquifer (Gao et al. 2022;Fang et al. 2022). Nitrate has been identified as a major pollutant that poses a threat to freshwater resources and coastal marine ecosystems (Abarca et al. 2013;Anwar et al. 2014). Numerous studies have investigated the impact of physical barrier on nitrate fate in aquifers (Yoshimoto et al. 2013;Kang and Xu 2017) and have confirmed that subsurface physical barrier hinders nitrate discharge to the ocean, exacerbating nitrate pollution of groundwater. For instance, the studies by Yoshimoto et al. (2013) and Kang and Xu (2017) found that the construction of cutoff wall led to a notable increase in the average concentration of nitrate in groundwater. Other studies have examined the influence of factors such as barrier physical parameters, aquifer properties, and nitrate sources on nitrate accumulation in aquifers (Sun et al. , 2021Ke et al. 2021;Gao et al. 2022). Sun et al. (2019) investigated the factors affecting nitrate emission in aquifers impeded by subsurface dam through experimental and numerical analysis and concluded that wall height and aquifer permeability are the key factors determining nitrate accumulation. Ke et al. (2021) examined the impact of hydraulic gradients, nitrate contaminant source concentrations, relative height and location of subsurface physical barrier, as well as the condition of the physical barrier and cutoff wall on groundwater nitrate contamination. Their results indicated that the hydraulic gradient and the relative height of the subsurface physical barrier was the main factors influencing nitrate accumulation, and that the cutoff wall had a more pronounced effect on nitrate retention than the subsurface dam. Sun et al. (2021) considered the effect of denitrification and investigated the mechanisms by which physical barrier affects SWI and NO 3 − accumulation. They showed that the greater the barrier height, the closer the barrier location to the sea, the greater the concentration of infiltrated nitrate, and the lower the inflowing DOC (dissolved organic carbon) concentration, the greater the degree of nitrate accumulation. Gao et al. (2022) investigated the dynamic mechanisms of nitrate accumulation and denitrification in a layered heterogeneous aquifer situation under the influence of a cutoff wall and showed that the stratification pattern greatly disrupted groundwater flow and significantly increased nitrate accumulation.  recently proposed a new approach to control SWI using a mixed physical barrier (MPB) that combines an impermeable cutoff wall and a semi-permeable subsurface dam (Fig. 1d). Gao et al. (2021) investigated the effect of a more realistic MPB, which combines impermeable cutoff wall and subsurface dam, on residual saltwater removal based on approach of . Their results showed that MPB is 40%-100% and 0%-56% more effective in removing residual saltwater than conventional subsurface dam and cutoff wall, respectively. MPB has great potential for protecting coastal freshwater resources from SWI. However, the study of Gao et al. (2021) on residual saltwater removal by MPB was limited to a few tens of centimeters, and the total removal process lasted only a few hours. This is not representative of reality, as the natural removal time of residual saltwater often extends from years to decades. Furthermore, previous studies have only examined the mechanisms of the effects of single cutoff wall and subsurface dam on nitrate pollution accumulation. The process of NO 3 − accumulation in aquifers due to MPB construction remains unclear (Fig. 2).
This study investigated the SWI control performance of MPB and their effects on NO 3 − accumulation in aquifers using numerical simulations. The specific objectives were (1) to assess the performance of MPB in preventing and controlling SWI by measuring residual saltwater removal efficiency and saltwater wedge reduction rate; (2) to compare and analyze the differences in total NO 3 − and contaminated area in coastal aquifers before and after MPB installation; (3) to evaluate the impact of MPB structure variables on SWI control performance and NO 3 − accumulation mechanisms; and (4) to compare the differences between MPB and traditional single physical barrier in terms of SWI control performance and NO 3 − pollution accumulation effects. These results will assist decision-makers in selecting appropriate engineering measures and barrier types during physical barrier construction to safeguard subsurface freshwater resources in coastal areas.

Governing equations
In this study, we utilized the finite element software COM-SOL Multiphysics to establish a two-dimensional variabledensity flow and reactive transport model. This model simulated the variable-density groundwater flow, salt transport, and reactive solute transport in unconfined coastal aquifers under static oceanic boundary conditions. The model couples unsaturated porous medium flow, based on the Richards equation, with solute transport, based on the convection-dispersion-reaction equation:

3
where ρ is the fluid density; S e denotes the effective saturation, which is related to the pore water pressure (Eq. 7); S denotes the water storage coefficient; C m is the specific moisture capacity, which is related to the variation of water content (Eq. 5); k s is the permeability of the sediment at full saturation calculated from the hydraulic conductivity coefficient (K) (Eq. 3); k r is the relative permeability depending on the effective saturation Se (Eq. 4); μ is the hydrodynamic viscosity; P and Z are the pressure and elevation, respectively; g is the acceleration of gravity; Q m is the fluid mass source term that is related to the tidal effect; θ is the water content; C i is the solute concentration of species i; D is the hydrodynamic dispersion tensor; and R i is the reaction rate of the ith reactant. The sediment storage properties caused by the compressibility of water and solid substrates and the additional source/sink terms generated by tidal load effects are neglected in Eq. 1 (Reeves et al. 2000;Wilson and Gardner 2006).
The numerical model utilized the Van Genuchten (1980) model to establish the intrinsic correlations between the relative permeability (k r ), specific moisture capacity (C m ), effective saturation (S e ), and pore water pressure (P): (1) where θ s and θ r are the saturated liquid volume fraction and residual liquid volume fraction, respectively; the intrinsic relationship constants α and n are derived from the study conducted by Shen et al. (2019).
In the mixing process of salt and fresh water, the density of pore water varies with the salt concentration in the pore water, and the fluid density is based on the density function of salinity C in the pore water is expressed as follows.
(3) where f is the density of freshwater, taken as 1000 kg/m 3 ; ∂ρ/∂C is the rate of change of fluid density, taken as 0.7143; C is the salinity of pore water.

Model setup
Groundwater flow and salt transport model The model area represents a cross section of a two-dimensional homogeneous beach aquifer, as shown in Fig. 3. The boundary conditions of groundwater flow and salt transport model were set to simulate the natural forcing conditions acting on the beach aquifer. The aquifer is assumed to be located on bedrock, and the aquifer basement is considered impermeable with no flow boundary and zero salt flux boundary. The freshwater boundary on the left is a constant flow and salt concentration boundary with a flow rate of 0.4 m 3 /day (Q f ) and a salt concentration of 0 ppt. Infiltration zones with a constant salt concentration of 0 ppt were established along specific areas of the upper boundary, with the infiltration zone length (Ln) and infiltration rate (R) based on Sun et al. (2019Sun et al. ( , 2021. Other permanently exposed upper surfaces were set up as no-flow boundaries and zero salt flux boundaries, without considering precipitation and evaporation effects. The seaward boundary on the right is a permeable boundary with an external head equal to the sea level head and an open boundary with an external concentration equal to seawater salt concentration. The boundary condition is specified by the following equation: where n f is the normal vector of the boundary; R b is the conductivity, defined as the ratio of the hydraulic conductivity coefficient K to the coupling length scale D l ; H b is the sea level head and H w is the groundwater head. Equations 10 and 11 reveal that (1) when H b is higher than H w under saturated conditions, the head difference between the overlying surface water and the interfacial sediment will determine the water flux at the boundary; (2) under saturated conditions, when H b is lower than or equal to H w , a seepage surface forms along this boundary (Abarca et al. 2013;Chui and Freyberg 2009);and (3) under unsaturated conditions, when the pressure head is less than 0, the conductivity value (R b ) is set to 0, causing the boundary to become a no-flow boundary (Chui and Freyberg 2009).
Salt transport at the open boundary is determined by the direction of groundwater flow at the boundary, as indicated by Eqs. 12 and 13. Specifically, nodes flowing into the aquifer are assigned a seawater concentration of 35 ppt, while nodes flowing out of the aquifer have a zero-concentration gradient (Cardenas et al. 2015;Shen et al. 2019).
The physical barrier is simulated by setting specific areas as inactive units. The subsurface dam and cutoff wall thickness are fixed at 0.6 m, while the depth, height, and opening spacing of the MPB are variable and denoted by Hc, Hd, and Ls, respectively. Table 1 lists the model parameters related to groundwater flow and salt transport. The simulation area measures 90 × 23 m 2 and is discretized by a uniform grid with a size of Δx × Δy = 0.3 m × 0.25 m. This grid spacing satisfies the Péclet number criterion, ensuring that the mathematical model is numerically stable. The Péclet number is defined as follows (Voss & Souza 1987): where Δx is the grid size in the x-axis direction and α L is the dispersion coefficient in the x-axis direction.

Reaction transport model
Reactive solute transport in the aquifer is calculated based on the velocity field of the variable density groundwater flow model. The bottom of the model domain ( Fig. 3) is subject to a flux-free boundary condition. Specific areas along the upper boundary are designated as NO 3 − permeability zones, Sun et al. (2019Sun et al. ( , 2021. The remaining upper surface is subject to no-flow and zero-flux boundaries. The land side of the simulation area is subject to a constant concentration boundary condition. Similar to the salt transport model, an open boundary on the seaward side (right-hand side in Fig. 3) specifies an external concentration equal to the solute concentration in seawater. Seawater entering the simulated area through the aquifer-ocean interface is the source of O 2 , while DOC is present in fresh groundwater inflow from the land boundary, as shown in Fig. 3.
The aerobic respiration and denitrification processes involved in this model follow Heiss et al. (2017) and Bardini  Table 2, and the reactant concentrations and reaction kinetic parameter values are shown in Table 1. A fully coupled solver is used to solve the multi-physics field coupled equations, which simultaneously solve for groundwater flow, solute transport, and reactions. The simulation consists of four steps: First, groundwater flow and salt transport are calculated without a physical barrier and with an initial value of 0 until the steady-state head and salt concentration are achieved. Second, using the steady-state results from the first step as initial values, the SWI removal process is calculated with the installation of physical barrier. Third, the initial value of reactive solute concentration is set to 0, and 2000 days of variable density water flow and non-reactive transport of multiple solutes are simulated to ensure steady-state head and solute concentration. Finally, the reaction rate of the reactive solute is added to the results of the third step to simulate another 2000 days until the reactive solute reaches equilibrium.
This study compared the effect of the MPB on SWI and nitrate accumulation by first considering the no physical barrier case (case A) and the base case (case B). Next, a sensitivity analysis was conducted based on case B to explore the effects of variations in the height, depth, and opening spacing of MPB on SWI and nitrate accumulation. Table 3 summarizes the simulated cases for the sensitivity analysis. Finally, to determine the value of MPB applications, the differences in SWI control performance and nitrate accumulation between the MPB and single physical barrier (subsurface dam and cutoff wall) were compared.

Measurable diagnostics
To assess the effectiveness of physical barrier in SWI control performance, two dimensionless parameters were introduced: the saltwater wedge length reduction rate (R S ) and the post-barrier residual saltwater removal rate (R M ). R S and R M are expressed as, respectively: where L 0 is the initial length of the saltwater wedge before MPB installation and L f is the length of the saltwater wedge after MPB installation. M 0 is the initial residual total salt mass trapped in the inland aquifer before MPB installation. M 0 is constant for a dam installed at a fixed position while it has various values for dams installed at different positions. M is the residual total salt mass in the inland aquifer after MPB installation. A seawater salinity of 0.5 ppt was used as a threshold to define the total amount of saltwater water behind the barrier, and the toe location was determined by the isoline of 50% seawater salinity.
To compare the effect of physical barrier on nitrate accumulation in aquifers, two parameters were used: the total nitrate mass accumulation rate (TNM) and the nitrate contaminated zone area increase rate (VNM). The TNM and VNM are described below:  where TNM W and VNM W are the total nitrate amount and nitrate contaminated area of the aquifer after physical barrier installation, respectively, and TNM N and VNM N are the total nitrate amount and nitrate contaminated area of the aquifer before physical barrier installation. According to WHO standards, a NO 3 − concentration of 11.3 mg/L is used as a threshold to define the nitrate pollution zone. Figure 4 shows the steady-state cross-sectional distributions of salinity, NO 3 − concentration, and DOC concentration in the aquifer under two conditions: no physical barrier installation (case A) and MPB installation (case B). Without physical barrier, a saltwater wedge about 57 m long was formed along the bottom of the aquifer side against the sea due to the difference in density and hydraulic gradient of salty and freshwater. The subsurface fresh water moved upward under the effect of buoyancy and eventually sank into the ocean. NO 3 − seeping from the surface formed a semi-elliptical pollution zone in the aquifer, while the distribution of DOC entering the aquifer from the landside boundary was

NO 3 − accumulation under MPB
limited by the saltwater wedge and NO 3 − , and most of it was consumed by denitrification and oxidation reactions. When the MPB was constructed, the toe of the saltwater wedge receded to the location of the subsurface dam, and the subsurface freshwater sank into the ocean through the opening between the subsurface dam and the cutoff wall. Compared to case A, the NO 3 − contaminated area and the total NO 3 − mass on the left side of the subsurface dam increased significantly, especially in the deeper part of the aquifer. However, the NO 3 − contamination above the subsurface dam decreased slightly due to the increased flow velocity in the vertical direction, which inhibited the downward transport and diffusion of NO 3 − . The DOC in the deep part of the aquifer pushed toward the ocean and filled the lower part of the aquifer due to the retreat of the saltwater wedge toward the ocean.
We used the metrics TNM, TNM', VNM, and VNM' (where TNM' and VNM' denote TNM W , TNM N , and VNM W , VMN N ) to quantify the effect of the MPB on NO 3 − accumulation in case A and case B. Figure 5a demonstrates the evolution of TNM and TNM' over time for both cases. Prior to considering biochemical reactions, TNM' gradually increased until it reached a steady state as vertical infiltration of NO 3 − occurred, which resulted in values of 48.21 kg and 63.42 kg for case A and case B, respectively. At stabilization, the TNM index was approximately 31.57%. Throughout the experiment, TNM rapidly increased, followed by a slow decrease before gradually increasing and stabilizing at Fig. 4 Cross-sectional distributions of salinity, NO 3 − and DOC for the case without physical barrier (case A) and the case with MPB installed (case B), the distributions for each case are shown in the left and right columns, respectively. The arrows indicate the flow direction and velocity magnitude. Purple, green, and yellow colors indicate the 10%, 50%, and 90% salinity contours, respectively. The white columns are the subsurface dam and cutoff wall of the MPB, which are 17 m and 25 m from the sea-side boundary, respectively. Realistic scales are used for the length units in [m] a steady state. TNM was always greater than zero during the entire process, indicating that MPB facilitated NO 3 − accumulation. After biochemical reactions were coupled, total NO 3 − went through a short decline phase due to mass consumption but ultimately returned to a stable phase. This caused the TNM' values for Case A and Case B to slightly decrease to 48.0 kg and 63.22 kg, respectively, compared to their pre-reaction counterparts. Meanwhile, TNM was slightly larger after considering biochemical reactions, reaching 31.69%. Figure 5b displays the transient processes of VNM and VNM' over time in the aquifers of case A and case B from the initial conditions to reaching a steady state. Before considering the reaction, the size of the contaminated zone, VNM', increases with time until it reaches a steady state. In the early stage of NO 3 − infiltration (the first 250 days), the growth rate and value of VNM' in case A were slightly larger than in case B. This was due to the interception wall in case B blocking the transport diffusion of NO 3 − in the horizontal direction and the slower increase in the transport rate of NO 3 − in the vertical direction in the initial stage. With continued NO 3 − infiltration, the growth rate and value of VNM' in case B gradually became larger than in case A until it reached a steady state. After stabilization, the VNM' of case A and case B were 562.02 m 2 and 722.45 m 2 , respectively, and the VNM was stabilized at 28.8%. After considering the consumption of NO 3 − by the reaction, the NO 3 − contaminated area in the aquifer underwent a brief decline phase at the beginning, but then returned to the stabilization phase after 1000 days. The stabilized VNM' were 557.48 m 2 and 716.99 m 2 , respectively, and the VNM was equal to 28.61%.
The processes of TNM, TNM', VNM, and VNM' indicate that nitrate pollution growth in the aquifer follows similar trends in both cases. However, installing MPB inhibits the seaward discharge of NO 3 − , increases the total amount of NO 3 − in the aquifer, expands the NO 3 − pollution zone, leads to more severe nitrate accumulation, and deteriorates the subsurface freshwater resources.

SWI control performance
The saltwater removal process is calculated after installing the MPB while assuming that the barrier installation is transient and does not affect the initial pressure and salinity distribution of the aquifer. Figure 5c displays the variation process of R M and R S over time after the installation of MPB. During the period from the initial moment to day 600, R M increases to over 50% as a nearly linear function, and its rate of increase gradually slows down after day 600. After approximately 1200 days of MPB installation, the R M value increases to over 70% and then increases at a decreasing rate until it reaches stability on day 4650. The R S increased rapidly during the first period of saline clearance (first 400 days), after which its growth rate gradually diminished until day 2100 when there was an abrupt change in the growth rate, and the R S rapidly increased in a short period of time before reaching stability on day 2200. The sudden change in the R S growth rate in the later stage is mainly due to the disappearance of the 50% salinity contour behind the dam when the saline water decreases to a certain level, and the salinity contour is truncated due to the non-existence of salinity in the area where the subsurface dam is located. Figure 6 illustrates the concentration distribution of residual saltwater at different stages after MPB installation. Once SWI has occurred, saturated aquifers can typically be divided into saline, freshwater, and mixed zones. The mixing zone is the transition zone between brackish and freshwater areas, and when the salinity of seawater is standard salinity, the area with salinity between 10 and 90% is generally considered to belong to the mixing zone (Lu & Luo 2010;Lu et al. 2009). We divided the mixing zone into a high salinity mixing zone (HCMZ) with a salinity range of 50 to 90% and a low salinity mixing zone (LCMZ) with a salinity range of 10 to 50% ). The LCMZ is the primary channel for saltwater discharge, and the efficiency of saltwater desalination behind the dam is dominated by the concentration gradient between the LCMZ and HCMZ and the LCMZ at the dam with respect to the dam height, which is dominated by the relative height. As shown in Fig. 6, the area of the mixing zone near the subsurface dam and the toe of the saltwater wedge increased significantly during the initial period after MPB installation (day 200). The 10% salinity contour moved upward at the location of the subsurface dam and to the right of the dam, and was depressed to the left of the dam, with no significant change in the location of the 10% contour at the salt toe. The 50% and 90% salinity contours experienced significant retreat. At days 600 and 1200 after MPB installation, the mixing zone area decreased relative to the initial moment, but the 10% salinity contour remained higher than the subsurface dam, and the 10%, 50%, and 90% salinity contours all experienced significant retreat. On day 2000 after MPB installation, the HCMZ almost disappeared, and only a small amount of low concentration saltwater was retained upstream, with the 10% salinity contour level with the top part of the subsurface dam, and its 10% and 50% salinity contours receded significantly less relative to the first 1200 days.
The analysis demonstrates that the desalination mechanism of MPB is in line with the proposals of Zheng et al. (2020) and Gao et al. (2021). That is to say, when the HCMZ is large and the LCMZ exceeds the dam, the salt in the HCMZ is dispersed into the LCMZ at a faster rate, while low concentration saltwater is more easily discharged across the dam to the sea boundary, resulting in higher desalination efficiency and quicker decay of residual saltwater mass and area. However, when only a small amount of low concentration saltwater is retained behind the dam and the 10% salinity contour is lower than the dam, the rate of internal salt dispersion to the outside is The white columns are the subsurface dam and cutoff of MPB, which are 17 m and 25 m from the sea-side boundary, respectively. Purple, green, and yellow solid lines represent the salinity contours of 10%, 50%, and 90% of seawater, respectively greatly reduced, and the saltwater needs to flow vertically from the bottom to the top of the dam. Therefore, the saltwater removal rate decreases significantly, and the residual saltwater quality and area decay slowly.

Influences of subsurface dam height
In this subsection, we simulated a series of MPB cases with varying subsurface dam heights (Table 3) while maintaining Hc and Ls at the same levels as the base case (case B). The objective was to study how the subsurface dam height, Hd, affects the performance of SWI control and the extent of NO 3 − accumulation. Figure 7 illustrates the distributions of nitrate and DOC for different subsurface dam heights (Hd) at steady state. As shown in Fig. 7, the height of the subsurface dam has some effect on the distribution of NO 3 − . As Hd increases, the depth of the nitrate pollution zone on the left side of Fig. 7 Cross-sectional distribution of salinity, NO 3 . − and DOC for MPB using different subsurface dam heights under stable conditions. The purple, green and yellow colors indicate the concentration contours of 10%, 50%, and 90%, respectively. The white bars are the subsurface dam and cutoff wall of the MPB, which are 17 m and 25 m from the sea-side boundary, respectively. Realistic scales are used for the length units in [m] the MPB opening (as indicated by the 10% concentration contour position) gradually increases. When Hd = 12 m, the depth of nitrate pollution is at its maximum, and when Hd ≥ 12 m, the depth of the nitrate pollution zone gradually decreases. The area of the nitrate mixing zone (10 to 90% concentration contour range) on the left side of the opening does not show significant changes due to the increase in Hd. Above the subsurface dam, the depth of nitrate contamination decreases in steps with increasing Hd. The relationship between nitrate distribution on the right side of the opening and Hd is different from that on the left side. The 90% concentration contour on the right side of the opening shifts upward with increasing dam height, while the 10% and 50% concentration contours are depressed near the subsurface dam, and the depth of the depression is proportional to Hd. The area of the nitrate mixing zone on the right side of the opening changes significantly with increasing Hd, and the area of the mixing zone increases with increasing Hd. Figure 8a Fig. 8a and b, it can be observed that when Hd is below 10 m, TNM and VNM gradually increase with increasing Hd. When Hd exceeds 10 m, TNM and VNM gradually decrease. Overall, it exhibits a trend of initially increasing and then decreasing. The reasons for this trend may be as follows: (1) when MPB fails to effectively control SWI, the depth of nitrate transport is limited by the residual saltwater. However, when Hd increases to 10 m, the residual saltwater is completely removed, resulting in a significant increase in the depth of nitrate transport, and the amount of nitrate in the region to the left of the MPB increases. Although the Hd increase causes a decrease in the nitrate amount on the right side of the MPB, the overall increase in nitrate exceeds the decrease. Thus, both the R M and R S values gradually increase as Hd increases from 8 to 10 m. (2) Once Hd exceeds 10 m, the amount of nitrate pollution in the left region of the MPB is primarily controlled by the cutoff wall, and the increase in Hd does not significantly affect the nitrate quantity in this area. However, the nitrate quantity on the right side of the MPB decreases with the Hd increase, especially in areas with high nitrate concentrations. Therefore, when Hd exceeds 10 m, both the R M and R S values gradually decrease with the Hd increase. Figure 7 shows that when the height of the lower dam is 8 m, the barrier fails to completely control the SWI, and residual saltwater still exists behind the dam. When the dam height is greater than 8 m, the SWI can be effectively controlled. Figure 8c and d illustrate the course of R M and R S with time for different dam heights, respectively. When Hd exceeds 8 m, the R M values gradually increase with time until the residual saltwater inland is completely removed (R M = 1), and the rate of increase gradually decreases with time. When Hd = 8 m, the R M value still increases gradually with time, but the residual saltwater behind the dam cannot be completely removed (as shown in Fig. 7), and the R M finally stabilizes at 0.84, indicating that the barrier cannot effectively control the SWI. When MPB can effectively control SWI, the R M growth rate decreases with increasing dam height, and the time for complete removal of residual saltwater increases with increasing dam height. For instance, after 1000 days of MPB installation, the R M values for subsurface dam heights of 10 m, 12 m, 14 m, and 16 m were Fig. 8 a Variation of TNM, the accumulation rate of total nitrate mass in the aquifer, with subsurface dam height, and Hd equals 0 corresponding to case A. b Variation of VNM, the increase rate of nitrate contaminated area in the aquifer, with subsurface dam height, and Hd equals 0 corresponding to case A. c Post-barrier residual salt removal rate R M versus time using MPB with different subsurface dam heights. d Saltwater wedge length reduction rate R S versus time using MPB with different subsurface dam heights 1 3 0.76, 0.72, 0.68, and 0.66, respectively, corresponding to complete residual saltwater removal times of 4050, 4650, 4850, and 5000 days, respectively. The R S values follow a similar pattern to R M . When Hd is greater than 8 m, R S values increase with time and eventually reach a stable value of 1.0 (where the 50% salinity contour corresponds to the salt toe reaching the location of the subsurface dam), and when Hd is equal to 8 m, R S eventually stabilizes at 0.49. The rate of increase of R S decreases with increasing Hd, and the elapsed time for the salt toe to reach the location of the subsurface dam increases with increasing dam height. The increased height of the subsurface dam lengthens the residual saltwater removal time due to the extended transport path of salts in the low salinity zone. The difference in the variation of R M and R S values for different dam heights indicates that the SWI can be effectively controlled only when the dam height of MPB is slightly higher than the 50% salinity contour, and at this time, the residual saltwater removal efficiency is optimal.

Influences of cutoff wall depth
To investigate the effect of cutoff wall depth on SWI and NO 3 − accumulation, a series of MPB cases with different cutoff wall depths (Hc values) were simulated while keeping Hd and Ls the same as the base case (case B) (as shown in Table 3). Figure 9 displays the distributions of nitrate and DOC for different cutoff wall depth (Hc) conditions at steady state. As shown in Fig. 9, the range of NO 3 − and DOC distribution is greatly affected by the depth of the cutoff wall. As Hc increases, the depth reached by the nitrate contamination zone on the left side of the opening (10% concentration contour position) gradually increases, and the area of DOC distribution near MPB decreases. The area of the nitrate mixing zone on the left side of the opening (10 to 90% concentration contour range) decreases with the increase of Hc. The 90% concentration contour near the opening moves upward in the vertical direction with increasing wall depth and closer to the cutoff wall in the horizontal direction. As Hc increases, the 90% concentration contour on the right side of the opening moves upward, the position of the 50% concentration contour remains almost unchanged, and the position of the 10% concentration contour moves downward. The area of the nitrate mixing zone on the right side of the opening changes significantly with the increase of Hc, and the area of the mixing zone increases with the increase of Hc. Figure 10a and b demonstrate the effect of Hc values on nitrate accumulation. The variation curves of TNM and VNM follow a linear increase with increasing Hc. The TNM values for cutoff wall depths of 9 m, 11 m, 13 m, 15 m, and 17 m were 27.48%, 31.69%, 36.10%, 40.10%, and 43.68%, respectively, corresponding to VNM of 24.62%, 28.61%, 32.88%, 37.13%, and 41.30%, with growth rates of about 2.03% and 2.09%, respectively. Comparing the effect of subsurface dam height on nitrate accumulation, it can be observed that the changes in TNM and VNM values are more significant when the depth of the cutoff wall is increased compared to the change in subsurface dam height. Figure 9 illustrates the salinity distribution under different cutoff wall depth conditions at the steady state. As shown in Fig. 9, barrier with varying Hc values can entirely control the SWI, and the mixing zone area after SWI stabilization significantly reduces compared to that before MPB installation. The variation process of R M and R S with time for different cutoff wall depths is presented in Fig. 10c and d. When the cutoff wall depth was large, the R M values showed rapid growth, such as the saltwater removal rate exceeding 0.9 on day 600 for the first 600 days at Hc = 17 m. As the cutoff wall depth decreased, the growth rate of R M decreased. For example, after 600 days of MPB installation, the R M values for cutoff wall depths of 17 m, 15 m, 13 m, 11 m, and 9 m were 0.91, 0.83, 0.67, 0.53, and 0.44, respectively. This suggests that the efficiency of residual saltwater removal by MPB decreases with decreasing Hc. The time for complete removal of residual saltwater increases with decreasing cutoff wall depth, and the time for complete removal of residual saltwater is 1750, 2050, 3100, 4650, and 5900 days for cutoff wall depths of 17 m, 15 m, 13 m, 11 m, and 9 m, respectively. The variation pattern of R S values is similar to that of R M , where R S values increase with time and eventually reach stability. The rate of increase of R S increases with increasing Hc, and the elapsed time for the salt toe to reach the location of the subsurface dam decreases with increasing Hc. Combining Figs. 8 and 10, it is evident that the effect of the change in cutoff wall depth on the R L and R M values is more significant than the change in the height of the subsurface dam, consistent with the findings of Gao et al. (2021).

Influences of MPB spacing
Previous studies have indicated that the location of subsurface dam may significantly impact the performance of barrier against SWI Zheng et al. 2020;Fang et al. 2021) and affect the exchange of material from the aquifer to the ocean (Fang et al. 2023). In this subsection, we use case B as the base case for Hd, Hc, and different Ls to analyze the impact of MPB opening spacing Ls on nitrate accumulation in the aquifer and the control of saltwater wedge performance. Unlike the setup of Gao et al. (2021), we define the MPB by the location of the cutoff wall instead of the location of the subsurface dam (Gao et al. 2021). We maintain the location of the cutoff wall constant and create two physical barrier spaced Ls by adjusting the location of the subsurface dam. Figure 11 displays the steady-state distributions of nitrate and DOC for different MPB opening spacing conditions. As shown in Fig. 11, the impact of Ls on the NO 3 − distribution on the left and right sides of the opening varied, and generally, the change in NO 3 − distribution on the right side was more significant than that on the left side. With an increase in Ls, the depth of the nitrate contaminated area to the left of the opening also increased, and the area of DOC distribution decreased slightly. However, the change was negligible. The area of the nitrate mixing zone (10 to 90% concentration contour range) on the left side of the opening did not exhibit significant alterations due to the increase in Ls. The 10%, 50%, and 90% concentration contours near the opening shifted downward with increasing spacing in the vertical direction and further away from the cutoff wall in the horizontal direction. As Ls increased, the Fig. 9 Steady-state cross-sectional distributions of salinity, NO 3 . − and DOC for MPB using different cutoff wall depths. The purple, green, and yellow colors indicate the concentration contours of 10%, 50%, and 90%, respectively. The white columns are the subsurface dam and cutoff wall of the MPB, which are 17 m and 25 m from the sea-side boundary, respectively. realistic scales are used for the length units in [m] Fig. 10 a Variation of TNM, the accumulation rate of total nitrate mass in the aquifer, with depth of the cutoff wall, and Hc equals 0 corresponding to case A. b VNM, the increase rate of nitrate contaminated area in the aquifer, versus depth of the cutoff wall, and Hc equals 0 corresponding to case A. c The relationship between the rate of residual salt removal R M after the barrier with different cutoff wall depths and time. d The variation of the rate of reduction of saltwater wedge length R S with time using different cutoff wall depths Fig. 11 Cross-sectional distribution of salinity, NO 3 . − and DOC at different MPB opening spacing after reaching steady state. The purple, green, and yellow colors indicate the concentration contours of 10%, 50%, and 90%, respectively. The white columns are the subsurface dam and cutoff wall of the MPB, which are 21 m, 19 m, 17 m, and 15 m from the sea-side boundary, respectively. Realistic scales are used for the length units in [m] 90% concentration contour on the right side of the opening moved down gradually, the position of the 50% concentration contour did not change significantly, and the position of the 10% concentration contour gradually moved up. The area of the nitrate mixing zone on the right side of the opening changed significantly due to the increase in Hc, and the area of the mixing zone decreased with the increase in Ls. Figure 12a and b illustrate the effect of the change in Ls value on nitrate enrichment. It can be observed that TNM and VNM are linearly and positively correlated with Ls, i.e., the larger the Ls, the larger the TNM and VNM. The TNM values corresponding to MPB spacing of 4 m, 6 m, 8 m, and 10 m are 25.32%, 28.57%, 31.69%, and 34.74%, respectively, and the corresponding VNM are 23.84%, 26.32%, 28.61%, and 31.22%, with TNM and VNM growth rates of approximately 1.57% and 1.23%, respectively.

SWI control performance
To evaluate the impact of Ls values on the performance of MPB-controlled SWI, we considered the formation of a steady-state saltwater wedge in case A and installing a physical barrier afterward. Figure 11 shows the SWI distribution after reaching a steady state, indicating that the area of the saltwater mixing zone significantly decreases after MPB installation. Additionally, the area of the saltwater mixing zone gradually decreases with an increase in Ls. The closer the subsurface dam is to the ocean boundary (i.e., the larger the Ls), the closer the low salinity mixing zone at the location of the subsurface dam is to the top part of the dam. The corresponding M 0 values are 5228.2 kg, 5840.5 kg, 6498.4 kg, and 7204.7 kg when the spacing between the cutoff wall and the subsurface dam is equal to 4 m, 6 m, 8 m, and 10 m, respectively, but the initial saltwater wedge L 0 value within the aquifer is the same at 57.2 m. Figure 12c illustrates the R M course over time for different Ls values. During the first 600 days, the post-dam saltwater removal rate increased rapidly with time for all MPB opening spacings. Then, it underwent a long period of slow increase, during which the growth rate of R M continuously decreased until all saltwater was removed (R M = 1). The R M change curves for Ls = 4 and Ls = 6 were almost identical. At the beginning of saline wedge removal (first 600 days), there was no significant difference in the R M change curves for Ls = 4, Ls = 6, and Ls = 8. Ls = 8 and Ls = 10 exhibited a longer slow-rise period compared to Ls = 6 and Ls = 4, with the longest slow-rise period for Ls = 10. The complete removal times of residual saltwater for MPB spacing of 4 m, 6 m, 8 m, and 10 m were 4400, 4400, 4650, and 5100 days, respectively. This is mainly due to larger Ls values trapping a greater total amount of saltwater behind the dam. Figure 12d presents the variation of R S with time for different Ls values. All R S values increased with time and eventually reached stability. During the first 400 days, R S values increased the fastest for Ls = 10. The overall increase in R S values during this period was characterized by a decreasing rate of increase with decreasing Ls. The rate of increase of R S values was almost the same for different Ls cases during the phase from day 400 to day 2000. There were some differences in the time for R S to reach stability for different Ls cases. When Ls = 4 and Ls = 6, the time for both R S values to reach stability was almost the same, 1900 and 1950 days, respectively. The time for R S to reach stability was longer for Ls = 8 and 10, 2100 and 2300 days, respectively. When the saltwater can be completely removed behind the dam, the length of the stabilized saltwater wedge is related to the location of the subsurface dam, and different Ls values lead to different Fig. 12 a Variation of TNM, the accumulation rate of total nitrate mass, with MPB opening spacing Ls. b VNM, the increase rate of nitrate contaminated area, versus MPB opening spacing Ls. c The relationship between R M , the rate of residual salt removal after the barrier with different Ls, and time. d The variation process of R S , the rate of reduction of saltwater wedge length with time using different Ls saltwater wedge setback distances. Therefore, the stabilized R S value increases with an increase in Ls.

Comparison with single physical barrier
We compared MPB with single subsurface dam and cutoff wall to evaluate the differences between MPB and single physical barrier in controlling SWI and nitrate pollution enrichment. We assessed the capability of physical barrier to control SWI using R M and R S , and analyzed the effect of various physical barrier on the degree of nitrate contamination in the aquifer using TNM and VNM.

Comparison of MPB and subsurface dam
A comparative analysis of MPB with subsurface dam at different dam heights was performed by adjusting the Hd values based on the baseline case (Fig. 13). From Fig. 13a and b, it is evident that both TNM and VNM of the MPB are significantly higher than those of the subsurface dam due to the nitrate enrichment exacerbated by the presence of the cutoff wall. The relationship between TNM and Hd under subsurface dam conditions is consistent with the findings of Sun et al. (2021), indicating that anomalously low TNM values occur when the subsurface dam fails to control SWI, and after Hd exceeds the minimum effective dam height, TNM gradually decreases with an increase in Hd. The relationship between VNM, TNM and dam height for both shows an increasing and then decreasing pattern with an increase in Hd. Specifically, TNM and VNM increase with an increase in Hd when Hd is less than 10 m. After Hd exceeds 10 m, TNM and VNM gradually decrease with an increase in Hd. The TNM values for the MPB case at dam heights of 8 m, 10 m, 12 m, 14 m, and 16 m were 30.02%, 33.58%, 31.69%, 29.31%, and 26.77%, respectively, corresponding to a VNM of 27.35%, 30.07%, 28.61%, 27.02%, and 25.69%, respectively. The TNM values for subsurface dam at the corresponding dam heights were 3.37%, 19.51%, 17.51%, 14.41%, and 10.80%, with corresponding VNM of 2.85%, 17.45%, 15.67%, 13.09%, and 10.39%, respectively. In other words, the enrichment effect of MPB on nitrate pollution is 14 to 27% higher than that of a single subsurface dam.
The MPB outperforms the subsurface dam significantly in terms of SWI control. From Fig. 13c and d, it is evident that both the MPB and the subsurface dam fail to control SWI effectively for Hd = 8, but there is a significant difference between them. When the R M and R S values reached stability, the MPB had significantly higher R M and R S values of 0.84 and 0.48 compared to the single dam's values of 0.21 and 0.07, respectively, indicating that the presence of the cutoff wall accelerated the saltwater removal rate. Both MPB and subsurface dam follow the characteristic that the rate of saltwater removal behind the dam decreases as Hd increases, which is consistent with the findings of Gao et al. (2021). The R M and R S rise rates were greater for MPB than for subsurface dam conditions at different dam heights. For the MPB case, saltwater removal times were 4050, 4650, 4850, and 5000 days for 10 m, 12 m, 14 m, and 16 m subsurface dam heights, respectively. The saltwater removal times for subsurface dam at the corresponding dam heights were 7900, 8600, 9650, and 10,700 days, respectively. Thus, the MPB removes saltwater 46 to 53% faster than the subsurface dam. Notably, Fig. 13 Comparison of the performance of MPB and single subsurface dam at different dam heights. a Total nitrate mass accumulation rate TNM, and Hd equals 0 corresponding to case A. b Increase rate of nitrate contaminated area VNM, and Hd equals 0 corresponding to case A. c Residual salt removal rate R M after the barrier versus time. d Variation process of saltwater wedge length reduction rate R S with time even when the dam height of the MPB is larger, its SWI control performance is still superior to that of the subsurface dam with a lower dam height. For instance, when the Hd of the MPB is 16 m and that of the subsurface dam is 10 m, at day 1000, the R M and R S of MPB are 0.66 and 0.39, respectively, while those of the subsurface dam are 0.44 and 0.22.

Comparison of MPB and cutoff wall
Based on the baseline case, the MPB was compared with a single cutoff wall at different cutoff wall depths by adjusting the Hc value (Fig. 14). It should be noted that we placed the cutoff wall at the same location as the cutoff wall in the MPB, while M 0 was calculated using the residual saltwater behind the location of the subsurface dam in the MPB. Figure 14a and b reveal that the nitrate enrichment and contaminated area of both MPB and cutoff wall increased gradually with increasing depth of the cutoff wall, following a linear trend. Although both TNM and VNM of MPB are greater than those of the cutoff wall, the difference between them diminishes as the depth of the cutoff wall increases, indicating that the cutoff wall's contribution to nitrate enrichment increases with greater depth. The TNM values for the cutoff wall depths of 9 m, 11 m, 13 m, 15 m, and 17 m in the MPB case were 27.48%, 31.69%, 36.10%, 40.10%, and 43.68%, respectively, with corresponding VNM values of 24.62%, 28.61%, 32.88%, 37.13%, and 41.30%. For the cutoff wall, TNM values at corresponding depths were 3.37%, 19.51%, 17.51%, 14.41%, and 10.80%, with corresponding VNM values of 14.35%, 21.06%, 28.15%, 34.81%, and 40.61%, respectively. Consequently, the nitrate enrichment effect of MPB is 2 to 12% higher than that of a single cutoff wall. Figure 14c and d demonstrate that increasing wall depth improves the control performance of both the cutoff wall and MPB for SWI, with the R M and R S values of the cutoff wall reaching stability sooner than the MPB. However, the R M and R S values of MPB can reach 1.0 and 0.71, respectively, while the highest values for the cutoff wall are only 0.82 and 0.54, respectively, and even the stable R M and R S values are only 0.43 and 0.27 when the wall depth is small. This indicates that the MPB can increase the retreat distance of the saltwater wedge, decrease contamination by brackish water in the aquifer, and provide better protection for underground freshwater resources. The stable R M and R M values for various wall depths reveal that the MPB controls SWI more efficiently than the cutoff wall, with an improvement of 16 to 57%.
Comparing the MPB to a single physical barrier, the study found that the MPB was more prone to NO 3 − accumulation than the subsurface dam and the cutoff wall, with the obstructive effect of the cutoff wall being the primary cause of the increased NO 3 − pollutants. However, conventional physical barrier is inadequate for controlling SWI. Subsurface dam is unable to rapidly remove saltwater behind the dam, particularly at greater heights, and the removal of saltwater wedges can take decades. Cutoff wall is unable to stably and effectively control the intrusion distance of saltwater. In contrast, the MPB maintains high efficiency in removing saltwater and possesses stable and effective control performance of saltwater wedges, even at high dam heights or shallow cutoff wall depths.
It is clear that physical barrier is conflicting in controlling saltwater intrusion and nitrate pollution in the Fig. 14 Comparison of the performance of MPB and single cutoff wall under different cutoff wall depth conditions. a Total nitrate mass accumulation rate TNM, and Hc equals 0 corresponding to case A. b Increase rate of nitrate contaminated area VNM, and Hc equals 0 corresponding to case A. c Residual salt removal rate R M versus time. d Variation process of saltwater wedge length reduction rate R S with time aquifer. For this contradiction, Sun et al. (2021) concluded that although the accumulation of NO 3 − caused by subsurface dam is small, the removal of residual saltwater wedges after the dam is slow, and for areas where SWI has occurred, cutoff wall measures should be used in preference to the use of subsurface dam. Our study shows that when the depth of the wall is large, the cutoff wall is still weaker than MPB in controlling the saltwater wedge, while the degree of NO 3 − pollution accumulation generated is very close to that of MPB. Therefore, we believe that for areas where severe SWI exists, the use of MPB can strike a relative balance between accelerated aquifer saltwater removal and control of nitrate pollution. For areas where SWI has not occurred, subsurface dam should be used, which can provide good prevention of SWI while reducing the accumulation of nitrate pollution.

Conclusion
This study aimed to evaluate the performance of an MPB against SWI and its impact on nitrate pollution accumulation using numerical simulation. Through univariate analysis, we assessed how the performance of the MPB in controlling SWI and nitrate pollution accumulation is affected by subsurface dam height, cutoff wall depth, and opening spacing. We compared the differences between MPB and single physical barrier to assess the applicability of these three types of physical barrier. Our study draws the following conclusions: 1. The installation of MPB resulted in an increase in the total nitrate mass and the area of nitrate contamination in the aquifer. 2. In the MPB structure, the degree of nitrate enrichment did not follow a monotonous pattern as the dam height increased. As the subsurface dam height (Hd) increased from 8 to 16 m, the TNM and VNM values initially showed an increase (from 30.02 to 33.58% and from 27.35 to 30.07%, respectively), followed by a gradual decrease (from 33.58 to 26.77% and from 30.07 to 25.69%, respectively). If the dam height of the subsurface dam was too low, the MPB would not be able to effectively prevent and control SWI. Conversely, with an increase in dam height, the removal efficiency of saltwater behind the dam decreased. The degree of nitrate enrichment was directly proportional to the depth of the cutoff wall. TNM increased from 27.48 to 43.68%, and VNM increased from 24.62 to 41.30% as Hc increased from 9 to 17 m. Additionally, with an increase in Hc, the removal efficiency of post-dam saltwater improved, and the removal time decreased from 5900 to 1750 days. TNM and VNM showed a linear and positive correlation with the MPB opening spacing, and the stabilized saline wedge length decreased with an increase in Ls. 3. A contradictory relationship was observed between accelerated SWI removal and reduced nitrate pollution. MPB exhibits significant advantages in controlling SWI efficiency, which is 46 to 53% and 16 to 57% higher than that of conventional subsurface dam and cutoff wall, respectively. Nonetheless, the use of MPB results in more severe nitrate accumulation, which is 14 to 27% and 2 to 12% higher than that of subsurface dam and cutoff wall, respectively. In aquifers where SWI has occurred, MPB can be employed to strike a relative balance between improving SWI control efficiency and controlling nitrate contamination. Conversely, in areas where SWI does not occur, subsurface dam can effectively prevent SWI while reducing the accumulation of nitrate pollution.
In our study, we assumed that the aquifer is homogenous and isotropic, and we did not consider the tidal fluctuations of the ocean. Real-life aquifers are complex, possibly layered, anisotropic, and influenced by tides and waves. As a result, the process of nitrate accumulation and SWI removal is more complicated, and the current model needs refinement to accurately reflect such complexities. Our study provides valuable physical mechanisms and laws that can aid in the practical application of MPB and traditional physical barrier. Policy makers should evaluate the most appropriate physical barrier for their specific situation and strike a relative balance between SWI control efficiency and nitrate pollution.