During the first 1980s, Danish Geotechnical Institute (DGI) installed a water filtration system at Hirtshals, pumping water from buried drain tubes along (and close to) the shoreline. Curtis and Davis
[78][58] reported that during the 8 months of the survey campaign the shoreline propagated seaward, even in the winter season. Though, in this period, the system did not manage to prevent erosion for severe storms. Nonetheless, the positive results boosted further studies and field campaigns. Later, since the positive results of the first experience, a seven years (1985–1991) campaign was led in Danmark by DGI at Thorsminde
[31,79,80][31][59][60] resulting in a total accretion of the beach of 30 m
3
/m (i.e., per unit meter along the beach) over 7 years, while the neighborhood beaches experienced 25 m
3
/m of erosion in the same period. The system was patented in 1987
[28] with the name of Beach Management System
® (BMS). Under that license, another installation was done at Sailfish Port (Florida) by CSI (Coastal Stabilization Inc.) with the American name of STABEACH
®. The system worked for at least 7 years, with some alternating performances. After about 2 years the installation, Dean
[81][61] independently reported that the beach resulted to be in local moderate accretion with a generalized more stable shoreline with respect to the control transects. Instead, different behaviors were exhibited by the northern and southern control sections during the following years. The system however was stopped during the years 1991–1992–1993 in the summer months due to the sea turtles’ nesting period, so it was not possible to study its capabilities on recovering, other than on preventing erosion. Moreover, an accretionary event was recorded even when the system was off. Turner and Leatherman
[27] concluded that it was difficult to discern any net positive effect, above all because the system was installed in the transition zone among two sections that experienced different trends of erosion and accretion. In the 1990s this method was investigated through both field and laboratory campaigns. During that period further investigations about the interaction between seepage and swash motion were performed (e.g.,
[55,57,82][62][63][64]), enhancing the knowledge about their correlation and their function on the sediment particles mobility within the swash zone. The commercial installation of STEABEACH
® was deployed at Nantucket beach, Florida. The project experienced a series of maintenance problems. The pumps did not work as expected, due to sand buildup within the pipes
[83][65]. Even after an increase in the pump size, the dewatering system achieved little success, and consequently, it has been removed by the local government, never reaching its potentiality due to maintenance issues. However, during the operative period of the system, Curtis et al.
[84][66] reported that it had no bad consequences on the local environment, vegetative communities, and public freshwater aquifer.
A field test was carried out by Davis et al.
[85][67] at Dee Why Beach, Australia. The drainage in this experiment was not pumped: they installed the type of drain commonly used for roads, laid vertically. The whole apparatus was surveyed for 18 months, stressing that it did not stop working, even though, due to some damages, the system reduced its efficiency. They stressed, in addition, that gravity drainage is a highly cost-effective means of beach stabilization, prone to extending the life of beach nourishment programs.
Katoh and Yanagishima
[32] used an alternative way to drain the sand, by means of a geotextile layer. The field survey was led, after laboratory tests
[67][47], at Kashima (Japan) in an already stable beach. It resulted that in the drained beach the speed of foreshore erosion in a storm slowed down and, in addition, the eroded foreshore is recovered quickly after a storm.
Another field campaign followed in the next years at Kashiwabaru Beach
[86][68], where a 2 years survey was carried out. The drains were laid parallel to the foreshore. From the comparison between the drained part and undrained part of the beach, it appeared that profile changes did not show any definite differences, although a small difference was found in the seaward area of the pipes. Analyzing that small difference, the amount of sand gained by the drain system was estimated as being roughly 5 m
3for 20 m of beach width.
The commercial installations of BMS or ECOPLAGE had been installed in the following years in different sites, i.e., France
[87,88[69][70][71],
89], Italy
[35,90[35][72][73][74],
91,92], Spain
[93][75]. French ECOPLAGE received good feedback from the site-installation local surveys. Unfortunately, international publications that confirmed the results did not follow, except for some documents (also in the French language) that are redacted by the constructors. The Spanish experience confirmed that beach drainage stops shoreline retreat and enhances quick recovery from storm erosion events. Regarding the systems installed in Italy, inconclusive results had been gained. In Alassio, both Ciavola et al.
[35] and Bowman et al.
[90][72] recognized the main role of the system in stabilizing the beach under normal to medium energy conditions, while under high energy conditions positive shoreline accretion trends faded. Again, Ciavola et al.
[35] reported the case of Procida (the beach did not benefit from the system and it was early abandoned) and of Bibione (where the survey campaign was interrupted). At Metaponto, as well, the monitoring did not continue as long as it should have to gain certain results. The same issue was for the Ostia site. Vicinanza et al.
[92][74], reporting in detail the case of Procida Island, expressed their not particularly positive opinion about such a system.
A commercial alternative version to the generic BDS is represented by PEM (Pressure Equalizing Modules), patented by
[29] and commercialized by EcoShore Inc. In this case, the essence of the tool does not change, except for the position whereby they are installed: they consist of 2 m long permeable tubes deployed vertically into the beach. They, as the name suggested, are placed in rows forming a matrix along the shoreline. They are vented at the top in order to make the pressure to be equalized. Jakobsen and Brøgger
[94,95][76][77] reported the three-years survey of the installation at Skodbjerge (Denmark), funded by the Danish Ministry of Transport. The functioning period ranged between January 2005 and 2008. At the end of that period, the analysis showed favorable performances. Actually, the report lacks deep analysis and information, above all about the average climate as well as recorded extreme events. The coast of Skodbjerge, historically in erosion, seemed to show a rising level of the beach in the area in front of the PEM, with an accumulation rate greater than 50% with respect to the reference areas (the neighbor check areas where the system was not installed), coming from long-shore sediment transport current. The same system has been deployed also in Malaysia
[96][78], and in Florida
[97][79]. In Malaysia, PEM combined with beach nourishment was installed in a pocket beach, most of it exposed to the main direction of the northeast monsoon. After three years it resulted to be stabilized, even with no natural sediment input: the losses are estimated as 25% of the total amount nourished at the beginning of the survey campaign. The critically eroding Hillsboro Beach (Florida), even with a delay with respect to the expectations, probably due to a reduced depth of the sand than usual, showed an undoubtedly accretive behavior (8.2 m in three years of the campaign; from 2008 to 2011). The survey dealt also with the influence of the system on the local fauna: no negative impacts were recorded.
The latest two field campaigns, independently documented, are
[98[80][81],
99], with two opposite interpretations of the results. The first one describes 4 years of survey in the Netherlands of a passive vertical drainage system. It resulted that no measurable influence on the beach and dune volumes variations were recorded. In
[99][81], on the other end, after five years of “classical” BDS survey on a macro-tidal beach in France, it seemed that the beach drainage allows faster recovery of the upper part of the shoreface after a storm.
4. Mathematical modeling
The water table is defined as the surface where the pore pressure is atmospheric. Above the free surface, a layer of unsaturated medium is present: the pores between the solid grains are not full of water, but it results to be a three-phase area: liquid (water), solid (grains), and gas (air). The mathematical modeling of the groundwater motion in an unconfined aquifer (i.e., a flow whose upper boundary is represented by a water table) follows the classical approach of the continuum medium for irrotational flow. The simplest approach for the unconfined unsteady flow (since the presence of the time-dependent forcing) is the one-dimensional linearized Boussinesq equation [100][82], i.e. the combination of Darcy’s law and the mass conservation equation, considering the Dupuit’s assumption [101][83], which assumes equipotential lines as vertical and streamlines as horizontal and hence a hydrostatic pressure distribution.
Even if the first approach on modeling the groundwater dynamics at the coast is analytical
[102,103,104,105,106[84][85][86][87][88][89],
107], only Fischione et al.
[108][90], according to the best authors knowledge, engaged to analytically model a beach drained by BDS. They solved the classical Boussinesq equation
[109][91] in an idealized finite-length rectangular domain with a simplified boundary condition to take into account the presence of the drain: a constant groundwater level has been imposed at the shoreward boundary, at a certain distance from the shoreline (i.e. the seaward boundary), where the effect of the waves has been modeled as a periodic function of the water table.
On the other hand, groundwater dynamics has been widely investigated by means of numerical modeling. Dominick et al.
[110][92] were among the first ones that tried to numerically predict water table fluctuation due to waves by an implicit finite-difference solution. The groundwater response to tide-induced oscillations has been taken into account in their studies by
[47,111,112][93][94][95]. The “BeachWin” model
[113][96] links beach groundwater and swash, simulating interacting wave motion, beach groundwater flow, and sediment transport in the swash zone. The model uses simplified descriptions of the various processes and does not consider either the effect of vertical flow in porous media on the sediment immersed weight or the increase and decrease of the boundary layer. The model has been validated by Ang et al.
[114][97] for controlled boundary conditions against the experimental results, with no satisfactory results. The numerical work of Li et al.
[115][98] is worth to be mentioned when the numerical modeling of dewatering systems is concerned. They included the drainage effects for the macro-tidal beach, modifying the model presented in
[116][99]. Two different types of dewatering systems were investigated: artificial and gravity drained beaches. In the first place, the original model by
[116][99] included a modified kinematic boundary condition for the water table, which takes into account the capillarity effects as well. The new kinematic boundary condition was incorporated into a boundary element method model. Karambas and Ioannidis
[117][100] modified the numerical model proposed by Karambas
[118][101] in order to take into account the effect of the draining system. They coupled the Boussinesq type model for the propagation of the waves in the near field with a porous flow model capable to account for sediment transport. Vesterby et al.
[87][69] coupled the commercial model powered by Danish Hydraulic Institute MIKE SHE (for groundwater dynamics) and MIKE 11 (for sea-level fluctuations and wave run-ups) and applied them to the real case of Les Sables d’Olonne
[89][71]. Saponieri and Damiani
[119,120][102][103] solved Richard’s equation by means of HYDRUS-2D code
[121][104] to simulate the GWK prototype-scale experiments
[72][52]. They tested the model for the static case (i.e., with no waves) in order to check the capability of the model to catch the draining capabilities of the BDS, and eventually use it to optimize the position of the drain according to its best performances. Against the groundwater-coastal hydrodynamic coupling, the approach used by
[122,123][105][106] resorts to the power of the Computational Fluid Dynamics to model a fine porous medium in presence of wave-forced groundwater table, in presence of a drained beach. The OpenFOAM
® library has been used to solve the Volume-Averaged Reynolds Averaged Navier–Stokes equation
[124][107]. In
[122][105], different drain diameters have been compared in terms of groundwater table and discharge, while
[123][106] modeled three-dimensional small-scale numerical tests for different draining patterns and sand permeability. The dynamic inside the pipe has been studied and analyzed, to gain insight into its hydraulic regime and eventually to define appropriate configurations to prevent the pipe from pressurizing.