Modellazione matematica di un sistema di drenaggio di una spiaggia: aspetti idrodinamici

Among the soft coastal defense systems it is possible to include the beach drainage system (BDS). It is a low visual impact system, whose functioning is based on the interaction between the groundwater dynamic at coast and the swashing waves on the foreshore. It consists of a series of buried pipes in the sand, that aim to lower the groundwater table. The basic idea is that, by artificially drying the groundwater table in the swash zone, the fluidization of the particles is discouraged as well as the capability of the waves of washing them out. Acting on the influence that the groundwater dynamics (forced by both tides and waves) has on the sand particle mobilization, this tool presents the strong potentiality to be applied as a soft engineering method to stabilize the shoreline, and to be applied, if not alone, at least coupled with other methods (i.e. beach nourishment) in order to increase their life time and to guarantee them better economical and efficient performances. Nontheless, different and controversial results have been obtained from its application during the years around the world, hence progressively it has been leaving. This thesis aims to mathematically investigate the influence of the drain on the groundwater dynamics, in order to estimate its influence on groundwater table, so that it is possible to eventually correlate the drain characteristics to the sediment transport rate. Only the hydrodynamics aspect of the BDS are taken into account herein. The present work deals with the analytical and numerical modeling of the waves-driven hydrodynamics at coast in presence of a BDS. The groundwater dynamics is firstly modeled by a novel analytical simplified approach: a linear equation is applied to finite length domains. Two different boundary conditions are considered: a wall boundary condition is applied in order to simulate the presence of deepen foundations and a drain-like effect boundary condition is applied to take into account the lowered level of the groundwater table. The analytical approach, even if simplified, makes possible to consider the behavior of the groundwater table for a general set of cases, that, if not allow to get a general solution, at least they make possible a comparative analysis. On the other hand, in the second part of the thesis a numerical approach is used to simulate the influence of the BDS on the groundwater dynamics. The numerical modeling of the sandy porous medium has been achieved by means of the open-source OpenFoam$\textsuperscript{\textregistered}$ solver, IHFoam, capable to account for both porous medium and waves generation and absorption. The model was developed in the first place to account for coarse size porous medium, hence a validation activity for finer material has been carried out. The numerical results have been compared against experimental data collected within the frame of a novel experimental campaign, carried out at LIam (Laboratorio di Idraulica ambientale e marittima) of the University of L'Aquila. The presence of the drain was tested and validated as well, by mean of small scale 3D simulations. In the end, the model has been applied to prototype scale cases. The overall results of the thesis are intended to be useful for the technical design of real case BDS projects, then solving the controversial performance observed in the past.