Performance Optimization of a Floating Breakwater Model Using SPH Method, with a Practical Application

Performance Optimization of a Floating Breakwater Model Using SPH Method, with a Practical Application D. Alejandro Rueda Duran Final Report of the Master Thesis Directed By Dr. Germán Rodríguez Rodríguez Dr. Alejandro Jacobo Cabrera Crespo UNIVERSIDAD DE LAS PALMAS DE GRAN CANARIA FACULTAD DE CIENCIAS DEL MAR LAS PALMAS DE GRAN CANARIA 2013 Performance Optimization of a Floating Breakwater Model Using SPH Method with, a Practical Application Alejandro Ruedaa, Germán Rodrígueza, A.J.C. Crespob aDepartamento de Física, Universidad de Las Palmas de Gran Canaria, 35017 - Las Palmas de Gran Canaria, Spain ([email protected]). bEnvironmental Physics Laboratory, Universidad de Vigo (Campus de Ourense) - Facultade de Ciencias, As Lagoas, 32004 - OurenseSpain ([email protected]). ABSTRACT The use of a floating breakwater, as an environmentally friend structure, is suggested as a coastal protection structure for the EGSAM pier in Santa Marta Bay, Caribbean Colombian coast. A large number of floating breakwater structures existing in the literature are examined and compared to define the structure to be used in the studied case. The selection of the more adequate structure is mainly based on two aspects, their dimensions and efficiency, in terms of the wave energy transmission. The efficiency assessment, as a function of the incident wave period and the distance between the floating breakwater and the pier, has been carried out by means of the smoothed particle hydrodynamic (SPH) method, a free-mesh numerical method. Results reveal that SPH method properly simulates the interaction between water waves and a coastal protection structures. Nevertheless, 3D numerical experiments require considerable computational cost, whereas the use of 2D experiments alleviates these drawbacks but include unrealistic effects, mainly due to the presence of closed, non dissipative, boundaries. The proposed structure for the EGSAM pier reveals considerable advantages in contrast with conventional coastal protection structures, which must be evaluated in a wave channel, as part of the design process. Key Words: Floating Breakwater, Smoothed Particle Hydrodynamic, Waves and Coastal Structures 1 1. INTRODUCTION A large number of coastal structures to protect human goods against wind-wave attack, including port facilities both commercial and recreational, have been built during recent decades along the Colombian coasts, especially on the North of the Caribbean coast. However, despite such structures successfully protect coastal zones against waves, mainly due to reasons concerning the preservation of the coastal environment and of aesthetic character, there is an increasing strong negative public reaction to the emplacement of classical rubble-mound breakwaters along the coast. This has led engineers to look for more soft and “environment friendly” coastal protection structures, while ensuring proper safety levels and functionality. The indiscriminate use of rubble-mound breakwater during the last forty years, as the only alternative to protect small piers, marinas and beaches from erosion, has generated important environmental problems, mainly associated with the interruption or alteration of littoral drift, erosion and pollution. This fact has stimulated interest and research activities for the development of efficient structures helping to preserve the coastal environment. In particular, the use of floating breakwaters (FB hereafter), an old idea (i.e. De la Sala, 1873), has been revisited and picked up as an alternative to protect coastal areas and for generating sheltered areas. The existence of improved facilities to implement more realistic physical models, as well as the development of numerical models and computational capabilities has supported advances in this field. 2 A clear example of the need to protect a port facility is that of the Santa Marta Coast Guard Station - EGSAM, unit located inside the bay of Santa Marta, which is dedicated to safeguard human life at sea and control illegal activities in the north of the Caribbean coast of Colombia. This pier built in 2005 was designed with the optimum characteristics for mooring, giving service and maintenance of the fast boat assigned to this military unit. However, due to the change in sediment rate of the Manzanares River, which after six seasons of heavy rainfalls has increased its rate of sediment supply and disposal in the zone, leading to a process of accretion under the pier of the EGSAM and inducing a change in the breaking zone position towards the berthing area. As a result, the structure is now partially useless. The aims of this study is to explore the possibility of improving operating conditions in the EGSAM pier by using a FB, under certain restrictions concerning the fraction of wave energy transmission. For this, numerical experiments, based on the use of the Smoothed Particle Hydrodynamics (SPH) methodology, are performed to simulate monochromatic incident waves and examine the FB efficiency. The final goal is to suggest some efficient FB structure to protect the study case facility. The remainder of the thesis is structured as follows. Main geographical and climatic conditions of the study area are introduced in section 2. A brief review of the development and main characteristics of FB is presented in section 3. Theoretical basis of the SPH methodology, as well as experimental set-up are described in section 4. Preliminary results derived from numerical simulation concerning wave energy transmission trough the selected 3 floating breakwater geometry are discussed in section 5. Finally, conclusions are summarized in section 6. 2. STUDY AREA Santa Marta bay is located in the Southwestern side of the Caribbean Sea (11°14’44.98N, 74º13’11.11W), approximately, see Fig. 1. Figure 1. Location map of the Santa Marta bay. According to the final report of weather conditions for Colombian Caribbean ports, presented by the Center for Hydrographic and Oceanographic Researches (CIOH) in 2010, at a large scale, its weather is influenced by fluctuations in the Azores high pressure system the Inter-tropical Convergence Zone positions. During the dry season (December to April) The Azores high pressure system moves toward lower latitudes leading to an increase in the wind intensity, reaching values over to 3.0 m/s. The predominant direction is determined by the effect of the trade winds, mainly in the dry season, flowing from north and northeast directions during 26% and 15% of the time, respectively (See Table 1). The modal mean wave direction in the zone is from NE, while more severe sea states come from ENE (See N N 4 Lat. 11°14´05.74N Long. 74°13’16.09W Table 1). Due to fetch restrictions the remainder directional sectors present a very low or null frequency of occurrence. Data presented in table 1 have been derived from a hindcasting study developed by CIOH for the Colombian Caribbean area covering a period of 32 years, by using the third generation WAM model. Table 1. Mean wind direction and wave conditions in Santa Marta bay. A recently acquired bathymetry (Colombian Navy Oceanographic and hydrographic Research Center, CIOH, 2012), as well as a recent aerial photo of the study area are shown in Figure 2(a) y 2(b), to facilitate identification of the major geographic features of the zone. Average temperature is about 28 ° C, and relative humidity is close to 79%. Average rainfall levels are in the order of 98 mm/month, but can change drastically during the rainy season, reaching values close to 330mm/month, in the surroundings to the Sierra Nevada de Santa NE 5.0 -7.0 7.0 -9.0 5.0 -7.1 3.0 -3.5 ENE Wave Direction Significant Wave Height Wave Period 1.5 - 2.0 2.0 -2.5 Direction % N26 NE 15 E 4 SE 3 S10 SO 9 O 8 NO 8 Calm 14 Santa Marta Wind Direction 5 Marta, giving rise to a significant increase of the average flow of the rivers in the area, see Figure 3(a-d). Figure 2. (a) EGSAM Bathymetry (depth in m), (b) Santa Marta Aerial Photo (a) Year 2006 (b) Year 2009 (c) Year 2011 (d) Year 2012 Figure 3. Effects of Manzanares River sediment rate discharge variability (2006 to 2012). EGSAM Pier Manzanares River N N N N 6 2.1 FLOATING BREAKWATERS: A SHORT REVIEW Floating breakwaters (FB) can provide an alternative coastal protection solution with low environmental impact, because its main purpose is to reduce the wave energy transmission to a required level, providing a dynamic equilibrium of the shoreline to preserve existing or artificially nourished beaches, as well as to avoid stagnation zones, by allowing water flow circulation below their bottom tip and the sea bed. A concise definition of floating breakwater was provided by Hales[1]: “The basic purpose of any Floating breakwater is to protect a part of shoreline, a structure, a harbor, or moored vessels from excessive incident wave energy. Are passive systems; i.e., no energy is produced by the device to achieve wave attenuation. The incident wave energy is reflected, dissipated, transmitted, or subjected to a combination of these mechanisms. The interference of a floating breakwater with shore processes, biological exchange, and with circulation and flushing currents essential for the maintenance of water quality is minimal”. The efficiency of FB is commonly determined by means of the relationship between the incident wave height (Hi) and the transmitted wave (Ht), known as the transmission coefficient (Kt): 𝐾𝑡=𝐻𝑡 𝐻𝑖 (1) Assume a FB with rectangular prism (Poonton type) form and considering a twodimensional view along the wave propagation axis, such as depicted in Figure 4. The water column in the surrounding area can be divided into three sections; (1) a zone before the structure; (2) other just below; and (3) other after the FB. Wave energy approaching to the structure is a function of Hi, while the energy fraction transmitted towards the area to be 7 protected will depend on Ht. Wave energy transmission will also depend, among other factors, on the wavelength, λ, the FB height, Zr, draft, Dr, and width W, as well as of the water depth, h. Figure 4. Geometric characteristics of a simple FB. The use of floating breakwaters as coastal protection structures date back, at least to 1811, when a floating structure was installed to protect the Plymouth Bay (Massachusetts). In that case, a floating breakwater with iron frames of nine feet wide and six feet high, fixed to the bottom with anchors, was used. Used materials were wood and iron, which made its life time very short due to corrosion and biological activity. There are records documenting at least three attempts to use this protection method in the bays of Plymouth and Brighton between 1811 and 1844, De la Sala (1873). The shape of the structures used was very different, but all of them had in common the use of iron frames to contain wooden boxes, and even iron pipes in wooden boxes (see Figure 5), so that the final result was not different to that of their predecessors. It was not until World War II when the FB use was diversified and began its real optimization from "Phoenix" and "Bombardon" models, developed by the Allies for the 1) 2) Dr Zr M.S.L. Ht H i λ W z x h 3) 14 Figure 7. Sketch of the influence domain of a particle. The approximation (2), in discrete notation, leads to the following approximation of the function at the particle (interpolation point) a: 𝐴𝑎=∑𝑚𝑏𝐴𝑏 𝜌𝑏𝑊𝑎𝑏𝑏 (3) where the summation is overall the particles (b) within the region of compact support of the kernel function, fixed by h. The mass and density are denoted by 𝑚𝑏 and 𝜌𝑏 respectively and 𝑊𝑎𝑏 =𝑊(𝑟𝑎−𝑟𝑏,ℎ) is the weighting function or kernel between two particles a and b. • Kernel function The performance of SPH models depends on the choice of the weighting function, which should satisfy several conditions such as: o Positivity: 𝑊(𝑟𝑎−𝑟𝑏,ℎ)≥0 in the domain Ω o Compact support: 𝑊(𝑟𝑎−𝑟𝑏,ℎ)= 0 out the domain Ω o Normalization:∫𝑊(𝐫𝒂−𝐫𝑏,ℎ)𝑑𝐫𝑏= 1 Ω o Delta function behavior: limℎ→0𝑊(𝐫𝒂−𝐫𝑏,ℎ)𝑑𝐫𝑏=𝛿(𝐫𝒂−𝐫𝑏) o Also 𝑊𝑎𝑏 must be monotonically decreasing within creasing distance from particle a. r Point r´ Influence d Domain Ω 15 Kernels depend on the smoothing length, h, and the non-dimensional distance between particles given by 𝑞=𝑟𝑎𝑏 ℎ � where 𝑟𝑎𝑏 is the distance between particles a and b �𝑟𝑎𝑏=𝑟𝑎−𝑟𝑏�. The Lagrangian form of the Navier-Stokes set equation is written as follows: • Momentum equation The momentum conservation equation in a continuum field is: 𝐷𝑣 𝐷𝑡=−1 𝜌𝜵𝑃+𝐠+𝜣 (4) where v is the velocity, P y ρ are pressure and density, g = (0,0,-9.81)ms-2 is the gravitational acceleration and Θ refers to the diffusion terms. The pressure term is expressed in SPH notation as: −1 𝜌𝜵𝑃=−�𝑚𝑏�𝑃𝑎 𝜌𝑎2+𝑃𝑏 𝜌𝑏2�𝜵𝑎𝑊𝑎𝑏 𝑏 (5) where 𝑃𝑏 y 𝜌𝑏 are pressure and density corresponding to a particle a and b and 𝑊𝑎𝑏= 𝑊(𝑟𝑎−𝑟𝑏,ℎ) is the kernel function. Then, the SPH momentum equation, Monaghan (1992) becomes: 𝑑𝐯𝒂 𝑑𝑡 =−�𝑚𝑏�𝑃𝑎 𝜌𝑎2+𝑃𝑏 𝜌𝑏2�𝜵𝑎𝑊𝑎𝑏+𝐠 𝑏 (6) Different approaches, based on various existing formulations of the diffusive terms, can be considered in the SPH method to describe the momentum equation. • Viscosity Two different options for diffusion can be used in SPH: artificial or laminar viscosity. 16 o Artificial Viscosity The artificial viscosity proposed by Monaghan (1992) has been used very often due to its simplicity. In SPH notation Eq. (6) can be written as: 𝑑𝐯𝒂 𝑑𝑡 =−∑𝑚𝑏�𝑃𝑎 𝜌𝑎 2+𝑃𝑏 𝜌𝑏 2+Π𝑎𝑏�𝜵𝑎𝑊𝑎𝑏+𝐠 𝑏 (7) where Πab is the viscosity term: Π𝑎𝑏=�−𝛼𝑐𝑎𝑏𝜇𝑎𝑏 𝜌𝑎𝑏 ,𝑖𝑓 𝐯𝑎𝑏·𝐫𝑎𝑏< 0 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (8) with 𝜇𝑎𝑏=ℎ𝐯𝑎𝑏·𝐫𝑎𝑏 𝐫𝑎𝑏 2+𝜂2 (9) where 𝜌𝑎𝑏=1 2(𝜌𝑎+𝜌𝑏), 𝑐𝑎𝑏=1 2(𝑐𝑎+𝑐𝑏); 𝜂2= 0.01ℎ2; α is a free parameter that can be changed according to each problem. o Laminar Viscosity The momentum conservation equation with laminar viscous stresses is given by: 𝐷𝐯 𝐷𝑡=−1 𝜌𝜵𝑃+𝐠+𝜐0𝛻2𝐯 (10) where the laminar stress term simplifies Morris et al., (1997), Lo and Shao (2002) to: (𝜈0𝛻2𝐯)𝑎=∑𝑚𝑏�4𝜈0𝐫𝑎𝑏𝜵𝑎𝑊𝑎𝑏 (𝜌𝑎+𝜌𝑏)|𝐫𝑎𝑏|2�𝐯𝑎𝑏𝑏 (11) where 𝜈0 is the kinetic viscosity of laminar flow (0.893·10-6 m2/s). So, in SPH notation, Eq. (11) can be written as: 𝑑𝐯𝑎 𝑑𝑡 =−∑𝑚𝑏�𝑃𝑎 𝜌𝑎 2+𝑃𝑏 𝜌𝑏 2�𝜵𝑎𝑊𝑎𝑏𝑏+ +𝐠+∑𝑚𝑏�4𝜈0𝐫𝑎𝑏𝜵𝑎𝑊𝑎𝑏 (𝜌𝑎+𝜌𝑏)|𝐫𝑎𝑏|2�𝐯𝑎𝑏𝑏 (12) • Continuity Equation Changes in the fluid density are calculated in DualSPHysics using: 𝑑𝜌𝑎 𝑑𝑡 =∑𝑚𝑏𝐯𝑎𝑏𝜵𝑎𝑊𝑎𝑏𝑏 (13) 17 instead of using a weighted summation of mass terms (Monaghan, 1992), since it is known to result in an artificial density decrease near fluid interfaces. • Equation of State The fluid in the SPH formalism can be treated as weakly compressible. This facilitates the use of an equation of state to determine fluid pressure, which is much faster than solving an equation such as the Poisson´s equation. Following (Monaghan et al., 1999; Batchelor, 1974), the relationship between pressure and density is assumed to follow the expression: 𝑃=𝐵��𝜌 𝜌0�𝛾−1� (14) where B is a constant related to the modulus of compressibility of the fluid, 𝜌0= 1000.0 𝐾𝑔𝑚3 � being the reference density, usually at the free surface and γ is a constant between 1 and 7 (although 7 is used in most of the oceanic applications). The speed of sound c, depends on the derivative of pressure with respect to density: 𝑐2(𝜌)=𝜕𝑃 𝜕𝜌=𝐵𝛾 𝜌0�𝜌 𝜌0�𝛾−1=𝐵𝛾 𝜌0𝛾𝜌𝛾−1 (15) 𝑐02=𝑐2(𝜌0) = 𝜕𝑃 𝜕𝜌|𝜌=𝜌0=𝐵𝛾 𝜌0 (16) where c0 is the speed of sound at the reference density; 𝐵=𝑐02𝜌0𝛾 ⁄. Additionally, B provides a limit for the maximum allowed change of density in each simulation. 3.2 Box Model Design and code validation The problem to study presents a 3D nature. However, to reduce the computational time, several experiments were carried out in a 2D domain. The main goal of these 2D simulations has been to assess the usefulness and possible limitations of the methodology to explore the 18 problem under study, especially in terms of the bathymetry. After these, the final steps of the study have been developed by using a 3D domain. The following dimensions have been used for the box model design: 300m long, 100m wide (3D) and 45m depth (see Figure 8). The wavemaker in the numerical tank is a piston-type wave generator. Separation between particles has been established as 0.25m. The number of particles used in the 2D model is 121.812 and 7.264.747 in 3D experiments. Figure 8. Configuration of the 2D numerical tank. It is important to remark the hypothesis underlying the experiments: (a) the FB has a position which is fixed in space, so that the possibility of energy radiation is eliminated, and (b) the FB is infinitely long in alongshore direction in 2D, (c) due to shoaling effects, the wave propagation direction is almost perpendicular to the beach. Hence, all simulations were carried out with the FB located parallel to pier line, d) the structures were designed using a reference depth of h = 20m and a period T = 7s. Furthermore ideal and weakly compressible fluid and irrotacional flow are assumed, as well as the applicability of lineal wave theory. The FB structure used to validate the applicability of the methodology to tackle the proposed study, has been that proposed by Bruce (1985). A total of 90 simulations were carried out in 19 2D with the aid of two Graphic Processing Units (GPU) with the support from the Environmental Physics Laboratory of the University of Vigo. The first problem evidenced while carrying out 2D experiment has been the large importance acquired by wave reflection, since in this case the box model behaves like a closed box. Progressive input of wave energy to the numerical wave tank and successive reflections will give rise to harbor agitation problems which, for some incident wave periods can give rise to resonance conditions. Naturally, these phenomena are frequent in the nature when wave energy propagates into or towards a closed or semi-enclosed basing. However, in the present simulations, these are mainly an artifact generated by using a 2D box model. Note that in a 2D model, the lateral boundaries, especially those constituted by the wavemaker and the pier fully close the domain of study, such that energy cannot be properly dissipated, as occurs in the beach placed behind the pier in nature (Fig. 1). The validation procedure consisted of six different simulation experiments: a) without bathymetry, b) bathymetry with constant slope of 9%, c) bathymetry with constant slope of 18%, d) a bathymetry designed to strokes, e) Santa Marta's actual bathymetry and, f) bathymetry with constant slope of 16%, without pier, X = 350m and a 50m length beach. The latter case was considered to enhance wave energy dissipation, reducing reflection effects. Points to measure wave height have been placed at 1.5, 25, 165 and 200m separated from the pier. The values wave heights were numerical measured by using post-processing tools of the DualSPHysics code. 20 Each experiment has been performed for 160s of physical time. Since average wave period in Santa Marta is around T = 7s, simulations were performed for periods T = 6, 7 and 8 s. The FB efficiency was evaluated at four different distances (50, 75, 100 and 150 m) from the EGSAM pier. The existence of harbor oscillations induced by incident and reflected waves in simple geometries can be predicted by means of the Merian formula (ie., Sorensen, 1993), which in two-dimensional conditions is given by: 𝑇𝑛=2𝐿 𝑛�𝑔ℎ (16) where 𝑇𝑛 is the natural period of oscillation, L is the length of the domain, n the number of nodes, g the gravitational acceleration and h the basin depth. Furthermore, the critical ratio of resonance occurrence between the wavelength λ and the domain length L, in enclosed and semi-enclosed basins are given in Table 2 (Sorensen, 1993). Table 2. Critical values of λ/L inducing resonance conditions. Open-ended Basin Critical Periods 0.25 0.75 1.25 1.75 2.25 Closed Basin Critical Periods 0.5 1 1.5 2 2.5 To compare theoretical reflection and transmission coefficient with the values observed in the numerical wave tank, the following equations can be derived: 𝐻𝑅 𝐻𝑖=�𝐸𝑅 𝐸𝐼�12 �=�1−sinh�4∗𝜋 (ℎ−𝐷𝑟)/𝜆� sinh4𝜋ℎ/𝜆�12 � (17) 𝐻𝑡 𝐻𝑖=�𝐻𝑖2−𝐻𝑅2�12 �=�sinh�4∗𝜋 (ℎ−𝐷𝑟)/𝐿� sinh4𝜋ℎ/𝐿�12 � (18) where, 𝐸𝑅 y 𝐸𝑖 are the reflected and transmitted energy, respectively. 21 3.3 Floating Breakwaters Assessment The selection of the FB structure to be evaluated has been done after an in-depth literature review. Fourteen cases, including structural information of the FB and properly described wave conditions in physical, numerical or actual cases, were considered for further analysis, by taking into account the usefulness of the information provided (see Table 3). The numerical implementation of the FB structures in the model has been developed by using dimensionless relationships between geometrical dimensions of the structure, bathymetry and wave parameters given in Table 3. This methodology makes possible comparisons between structures with different dimensions. The efficiency of each one of the selected structures has been assessed by using the average wave and bathymetric conditions recorded in Santa Marta Bay. The efficiency of these fourteen selected structures was compared using a decision matrix in which the transmission coefficient Ktand volume of the structure are evaluated to select that offering a better balance between efficiency and geometrical dimensions, or cost. Table 3. FB Methodology Design References Thesis Code Place Height FB /Draft Zr/Dr Wide / Draft W/Dr Wave Height/ Depth H/h Depth/ Wave Lenght h/λ Wide/ Wave Lenght W/λ Draft / Depth Dr/h Wave Height/ Wave Lenght Hi/λ Dimentional Depth 2πh/λ Brebner (1968) Case 1 Physical Model 2,221844 7,5647092 0,200 0,345 0,383 0,147 0,069 2,167 Bruce (1985) Case 2 Olympia Harbor (Washington) 1,5714286 60,156 0,196 0,165 0,140 0,031 1,231 Torum (1987) Case 3 Physical Model 1,4285714 4,6869141 0,123 0,223 0,091 0,088 0,027 1,401 Manuel (1995) Case 4 Physical Model 1,3333333 20,032 0,620 0,248 0,200 0,020 3,895 Murali (1997) Case 5 Physical Model 1,4347826 2,826087 0,200 0,108 0,141 0,460 0,022 0,680 Sannasiraj (1998) Case 6 Physical and Numerical Model 4 4 0,019 0,510 0,087 0,043 0,010 3,203 Allyn (2004) Case 7 Physical Model 1,2352941 2,2941176 0,076 0,326 0,127 0,170 0,025 2,046 Fouster (2007) Case 8 Numerical Model 1,25 2,25 0,123 0,396 0,178 0,200 0,049 2,488 Martinelli (2008) Case 9 Physical Model 2,3333333 6,6666667 0,170 0,246 0,105 0,064 0,042 1,545 Elchahal (2009) Case 10 Numerical Model 1,1315789 0,6644737 0,050 0,401 0,101 0,380 0,020 2,518 Wang (2010) Case 11 Numerical Model 1,1111111 1,6 0,150 0,168 0,135 0,450 0,025 0,731 Yoon (2011) Case 12 Physical and Numerical Model 2,6666667 6,6666667 0,086 0,116 0,106 0,136 0,010 0,731 He (2012) Case 13 Physical Model 2,259887 8,7570621 0,044 0,225 0,388 0,197 0,010 1,414 Loukogeorgaki (2012) Case 14 Numerical Model 1,8181818 4,5454545 0,037 0,158 0,250 0,347 0,006 0,995 22 The three more efficient structures, in terms of wave energy reduction and dimensions, were considered to decide the geometrical shape of the FB to be suggested as an initial optimal infrastructure for the study area, both in 2D and 3D. For this, 75 numerical experiments were carried out in 2D. 4. RESULTS AND DISCUSSION A first observed result is that in 2D simulations the wave reflection from the front and backside boundaries plays a dominant role, due to the lack of energy dissipating areas. Furthermore, it has been observed that wave conditions become stable after some transient period. Thus, only a final part of the total wave data record measured has been considered to examine the resulting conditions associated to each case. (See figure 9). Figure 9. Fraction of wave data series selected to be analyzed. When a wave train propagates towards beach and meets the FB, part of the incident energy is reflected. Another part of the fraction transmitted through the structure can be reflected at the sloped bottom, at the deck, and at the front boundary of the box model. In this sense, for all the studied cases, when the FB was placed at a distance of 50, 75 and 100m from the pier, the box model behaved like a semi-enclosed basin, with the reflection between FB and the pier been the most important effect. When the FB was located 150m apart from the pier, in the middle of the box model domain, the reflection effect was the same both between the 23 piston and the structure, as between the pier and the FB, so that in this condition the box model behaves in a similar way to a closed basin. All the simulations have revealed that wave energy transmission increases with the period of the incident waves. In other words, efficiency of FB decreases with the length of the incident waves. In the first simulation, carried out without bathymetry (see Figure 10a) it has been found that basin oscillations are considerable when the structure is separated 75m from the pier, for periods of 8 and 6 s, inducing oscillating modes close to T3 and T1, respectively. When the wave period is 7s, this phenomenon was mainly observed with the FB structure placed at 100 and 150m far from the deck. Adding a bottom slope of 9%, simulations of Figure 10b reveal that for shorter wave period, 6s, the effect of basin oscillation reduces because of this phenomenon is particularly relevant to long waves, and is intensified for longer periods. This enhancement is particularly notable for T=8s, due to the match with the critical period given by the Merian expression, (Sorensen 1993). By increasing the slope (see Figure 11a), it is observed that the transmission coefficient moderately reduces. This is probably due to the increase in wave energy dissipation by bottom friction. However, the general behavior remains similar and continues along validation test by using 2D numerical tank. 30 Figure 15. Case 15: FB Efficiency Comparison (2D vs. 3D) 5. CONCLUSIONS • The SPH method is adequate to simulate with accuracy the interaction between water waves and a coastal protection structure, including the effect of an irregular bathymetry. • However, physical phenomena, such as wave reflection, generated in 2D numerical wave tanks, are non realistic and must be carefully considered. Nevertheless, results derived with 2D models permits to assess efficiency of different structures with a low computational cost. • The efficiency, in terms of the transmission coefficient, of the floating breakwater structure selected for the study case, evaluated under almost real conditions, for incident waves of 7s, is considerable high. • It is shown that a structure with an area of 39 m2, or with a volume of 1560 m3, can protect adequately the pier with low environmental impacts. • The proposed structure for the EGSAM pier reveals considerable advantages in contrast with conventional coastal protection structures, which must be evaluated in a wave channel, as part of the design process. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0100 200 300 Kt Case 15 -2D Case 15 - 3D 31 6. REFERENCES 1. Adee, B., Floating Breakwater Performance. Coastal Engineering, 15, pp.2777-2791, 1976. 2. Allyn, N., Watchorn, ernie., Jamieson, W., and Yang, G., Port of Brownsville Floating Breakwater. Proc. 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