THE EVOLUTION TREND OF A BEACH IN CONSEQUENCE OF THE BUILDING OF COASTAL STRUCTURES Pasquale Filianoti, Università Mediterranea di Reggio Calabria, filianoti@unirc.it Luana Gurnari, Università Mediterranea di Reggio Calabria, luana.gurnari@unirc.it ABSTRACT The shoreline deformation produced by the interaction between waves and coastal structures have been analyzed by comparing two different analytical solutions. Starting from the same assumption, they converge to different profiles, according to the different way to take in account the phenomenon of the wave diffraction induced by the structure. INTRODUCTION The first mathematical model to foresee long-term shoreline change was the one-line shoreline model introduced by Pelnard-Considere (1956). Since then, different models have been developed to simulate shoreline change. The history of the one-line theory was summarized in Larson et al. (1997). The analytical solutions derived from the mathematical models are either unrealistic or are unable to provide quantitatively accurate results of beaches involving complicated initial and boundary conditions, such those generated by the presence of coastal structures. However, they exhibit several advantages. They can reveal the essential response features of the shoreline using basic physics, which produces results more rapidly than the complex numerical and physical modeling. Moreover, the analytical solutions avoid inherent numerical stability and numerical diffusion problems, which are uncertainties in all the mathematical models (Larson et al., 1997). Despite many models have been developed on the concept of one- line model, nowaday four have become the standard applied for engineering applications since the 1980s, including GENESIS (Hanson and Kraus, 1989); UNIBEST (WL, 1992); LITPACK (DHI, 2001); and GenCade (Frey et al., 2012). A comprehensive comparison among them can be found in Thomas and Frey (2013) and Townsend et al. (2014). The mathematical approach proposed here moves from the same hypotheses of one-line models and considers the beach as an ideal absorber, which does not alter the wave motion in front of it. Therefore, it does not reflect nor transmit energy. With this assumption, we calculate the evolution trend of the shoreline in consequence of the realization of coastal structures. THE LONGSHORE TRANSPORT AND BEACH PLANFOM EVOLUTION The governing equation of the one-line model is given by   =− 1    . (1) It states that the alongshore variation in the longshore sand transport rate Q, determines a change in shoreline position y. [D is the sum of the berm height and the depth of closure.] The derivative   ⁄ gives the evolution trend. If   ⁄ is positive the dry beach grows; if   ⁄ is negative the dry beach gets narrower; the largest the absolute value of   ⁄ , the larger is the deformation of the dry beach. Q depends mainly on the shear force <  >, exerted by the wave motion on the seabed. The bulk longshore sediment transport rate depends on the shear force exerted by the wave on the seabed. It can be expressed as   =    <  > √  , (2) where k depends on the size of the sand, on the specific weight on the sand and on the sediment porosity ; √  is the wave celerity at the breaking depth, and a is the specific weight of the water. According to Larson et al. (1997), the shear stress force can be evaluated as <  >= 1 32   2 sin(2  ), (3) being H b, the wave height at the breaking depth and b, the angle at the breaking depth formed by the direction of wave advance and the shoreline alignment, assumed parallel to the x-axis. Note that Eq. (3) is valid under the hypothesis of contour lines straight and parallel to the shoreline, in the case of natural diffraction phenomena. Assuming that the beach acts as an ideal absorber, and applying the linear momentum equation to a control volume with one side adjacent to the absorber, it can be shown that <  >= −  , (4) where   is the longshore component (i.e. x-component) of the radiation stress of the wave field in the presence of the coastal structure. Hence, by means of Eqs (4) and (5), we get   ≅ −const    . (5) The radiation stress can be obtained analytically for a few configuration of basic interest (i.e. a detached breakwater or a groin) or numerically, for more complex planform configurations of the structures. With this approach, it is possible to estimate the wave diffraction produced by structures placed near the coast, which is the main phenomenon responsible for the beach deformation. SHORELINE DEFORMATION PRODUCED BY A BREAKWATER Fig. 1 shows the evolution trend of a shoreline in consequence of the realization of a detached barrier