Underground Barriers Could Unlock Safer Groundwater Pumping on Coasts, New Math Shows

Coastal aquifers are among the most contested water resources on Earth. Beneath many of the world’s shorelines, a delicate balance holds between fresh groundwater flowing from the land and denser seawater pushing in from the ocean. When wells pump too hard, that balance collapses: the salty wedge creeps inland, wells turn brackish, and communities lose the freshwater reserves they depend on. A new study published in Hydrogeology Journal by Benoît Dewandel, Augustin Gouy and Nicolas Frissant of the French Geological Survey (BRGM) and the University of Montpellier offers a fast, mathematically elegant way to predict exactly where that boundary between fresh and salt water will sit when engineers install an underground barrier and run a pumping well at the same time.

The work addresses a technology that has quietly become one of the most promising defenses against seawater intrusion: the underground physical barrier, sometimes called a subsurface dam or cutoff wall. These are impermeable structures built into the aquifer itself, typically from the ground surface down to the impermeable basement, designed to block or slow the landward migration of seawater while allowing freshwater to pool behind them on the inland side. Japan has built such structures for decades in the Ryukyu Arc, and interest has surged worldwide as rising seas and growing coastal populations intensify pressure on shallow groundwater. Yet, as the authors note, most previous analyses have treated barriers in two dimensions only, examining cross-sections perpendicular to the coast and ignoring what happens along the barrier’s length.

That simplification matters because real barriers are finite. They have a measurable length running parallel to the shoreline, and water can flow around their ends. A barrier that looks impregnable in a two-dimensional cross-section may leak saltwater around its flanks, and a well placed near its edge may behave very differently from one placed at its center. The new study tackles this three-dimensional reality head-on. Dewandel and colleagues derived steady-state semi-analytical solutions for the shape of the sharp freshwater–seawater interface in a sloping coastal aquifer containing a finite-sized, impermeable rectangular barrier that fully penetrates the aquifer, with or without a pumping well operating nearby.

The technical machinery behind the solutions combines two classical ideas with one modern numerical trick. First, the authors adopt the Dupuit–Forchheimer assumption, which treats groundwater flow as essentially horizontal in aquifers whose lateral extent greatly exceeds their thickness, and the sharp-interface approximation, which treats fresh and saline water as immiscible fluids separated by a discrete boundary rather than a gradual mixing zone. These assumptions, long the backbone of coastal aquifer analysis dating back to the Ghyben–Herzberg principle and Strack’s single-potential formulation, reduce a fiendishly complex variable-density flow problem to a tractable one. Second, to handle the flow disturbance created by the rectangular barrier, the team employed the Method of Fundamental Solutions, a boundary-type numerical technique in which the solution is built from a superposition of analytical point sources, or image wells, whose strengths are adjusted to satisfy the boundary conditions on the barrier’s faces.

A crucial innovation is the inclusion of an inland boundary flow condition in all of the solutions. Many earlier analytical treatments assumed either constant hydraulic head or an infinite aquifer inland, which obscures the role of the natural hydraulic gradient that drives freshwater toward the sea. By specifying the inland flux, the new solutions explicitly account for both the regional hydraulic gradient and the slope of the aquifer’s impermeable basement. This makes them applicable to realistic sloping coastal settings rather than idealized flat ones, and it allows the researchers to capture how the ambient groundwater flow interacts with the barrier and the pumping stress. Separate solutions are provided for unconfined aquifers, where the water table is free to rise and fall, and for confined aquifers, where the saturated thickness is fixed by overlying impermeable layers.

Because the saturated thickness of an unconfined aquifer changes wherever the water table is drawn down or mounded, the underlying flow equations are nonlinear. The authors discuss two linearization strategies for handling this. The first, an h-linearization, assumes the deviation of the saturated thickness from its undisturbed value is small, which is reasonable when the barrier and well sit near the coastline, since the sea acts as a constant-head boundary that limits water-table fluctuations. The second, an h²-linearization, relaxes that restriction and remains valid as long as the thickness change does not exceed half the undisturbed thickness. In the more general formulation, a linearization constant is refined through successive iterations until the strength coefficients of the image wells converge, a process the authors note can take from an hour to several hours of computation depending on barrier size, though the simplified near-coast version runs almost instantly.

Validation came from comparison with spatially distributed numerical modeling, including simulations with the USGS MODFLOW 6 code and with published three-dimensional results from earlier barrier studies. Across test cases spanning different hydraulic conductivities, aquifer thicknesses, hydraulic gradients, barrier lengths and well positions, the semi-analytical interface predictions tracked the numerically simulated salinity distributions closely, both in cross-sections through the center of the barrier–well system and along its edges. The agreement held for confined conditions as well, and the authors reproduced the behavior seen in independent published simulations of finite-length barriers placed at varying distances from the shoreline, lending confidence that the new equations capture the essential physics despite their simplifying assumptions.

The practical payoff of the study is a set of design rules that emerge directly from the mathematics. The analysis shows that the maximum pumping rate a well can sustain without drawing seawater into its capture zone, the so-called maximum safe or critical pumping rate, increases both with the length of the barrier and with the barrier’s distance from the coast. In other words, a longer wall shields more of the aquifer’s freshwater lens, and a wall set farther inland leaves more room for a well to operate on the protected side before the interface toe reaches it. The solutions also quantify how much the barrier improves on the no-barrier baseline, expressing the gain in safe yield as a function of barrier dimensions, well placement and aquifer properties, information that is invaluable when weighing the considerable cost of constructing an underground cutoff wall against the water it secures.

Because the equations rest on the Dupuit–Forchheimer and sharp-interface assumptions, the authors are careful to position them as a first-order tool rather than a replacement for detailed simulation. They deliberately exclude dispersion-driven mixing at the interface, aquifer heterogeneity and transient effects, all of which a full three-dimensional variable-density model can represent. But that is precisely their strength. Where a numerical model may take hours to set up and run, the semi-analytical solutions evaluate in seconds, making them ideal for the preliminary design stage: screening dozens of candidate barrier lengths, positions and well configurations, and identifying the handful of options worth subjecting to rigorous numerical analysis. The authors also provide a corrected formulation incorporating an empirical density correction factor to account for the mixing that real interfaces exhibit, tightening the link between the idealized sharp interface and observed salinity profiles.

The timing of this work could hardly be better. The growing trend of saltwater intrusion, driven by over-pumping, reduced recharge and sea-level rise, threatens coastal agriculture and drinking water supplies on every inhabited continent, and the coastal groundwater squeeze between rising seas and intensifying demand is now recognized as a defining water-management challenge of the century. Tools that let engineers quickly and reliably size a subsurface barrier, place a well at a safe distance and estimate the sustainable yield of the protected freshwater body could turn a promising but underused technology into standard practice. With this study, the French team has extended the analytical toolkit for coastal aquifer management from the flat, two-dimensional world of textbook theory into the sloping, finite, three-dimensional world where real barriers and real wells actually operate.

Subject of Research: Semi-analytical modeling of the freshwater–seawater interface controlled by underground barriers and pumping wells in sloping coastal aquifers

Article Title: Steady-state semi-analytical solutions for assessing the shape of the freshwater–seawater interface induced by a finite-sized underground physical barrier and a pumping well in a sloping coastal aquifer

Article References: Dewandel, B., Gouy, A., & Frissant, N. (2026). Steady-state semi-analytical solutions for assessing the shape of the freshwater–seawater interface induced by a finite-sized underground physical barrier and a pumping well in a sloping coastal aquifer. Hydrogeology Journal. https://doi.org/10.1007/s10040-026-03177-1

Image Credits: AI Generated

DOI: 10.1007/s10040-026-03177-1

Keywords: seawater intrusion, coastal aquifer, underground barrier, subsurface dam, freshwater–seawater interface, pumping well, semi-analytical solutions, Method of Fundamental Solutions, Dupuit–Forchheimer, hydrogeology, groundwater management, safe pumping rate