Author(s): Mario Oertel; Hanna Brandt; Yola Patzwahl

Linked Author(s): Mario Oertel

Keywords: Pile breakwater experimental model drag force energy dissipation wave damping

Abstract: Efficiency of Pile Breakwaters in Experimental Model Tests Mario OERTEL1, Hanna BRANDT2, Yola PATZWAHL3 1,2, 3 Hydraulic Engineering Section, Mechanical and Civil Engineering Department, Helmut-Schmidt-University Hamburg, Germany email: mario. oertel@hsu-hh. de Abstract Breakwaters are important coastal structures to prevent coastlines from damage and major erosion due to wave impact. The chosen type of the structure depends on various boundary conditions and the need of energy dissipation, translation or reflection. A permeable breakwater structure can exist of several vertical piles with predefined pile distances and heights as well as number of piles. The current study deals with experimental tests in a laboratory flume to investigate the efficiency of pile breakwaters for various configurations. Therefore, wave damping and drag forces are analyzed within a scaled physical model to allow statements and recommendations for minimum number of piles and maximum pile distances in lateral direction. Keywords: Pile breakwater; experimental model; drag force; energy dissipation; wave damping. Introduction The morphology of the coastline has changed considerably over time. In addition to the tidal currents, the incoming waves have a considerable influence on this process. Considering the growing impact of climate change and the associated rise in sea levels, this issue is becoming increasingly significant (Schumacher 2022; Sterr 2007). A significant amount of wave energy is dissipated along the coastline. In order to minimize or even prevent coastal erosion, a wide variety of methods and structures have been developed over time. Such protective measures include the construction of breakwaters (Pasche and von Lieberman 2008). The selection of the appropriate type of structure is dependent upon several factors, including the boundary conditions and the requirements for energy dissipation, translation or reflection. According to Brinkmann (2005), the following types of breakwaters can be distinguished: rubble mound breakwaters, vertical breakwaters, composite breakwaters, and special constructions. Pile breakwaters are a type of permeable breakwater and can consist of several vertical piles with predefined pile distances and heights as well as number of piles. They offer an effective form of protection for a section of a coastline and, furthermore, permit the circulation of water within the protected region, thereby facilitating the maintenance of a healthy marine ecosystem (Zhu and Xie 2015). In the process of dimensioning breakwaters, several factors must be taken into account. In addition to the wave force of the acting wave, the effects of wave run-up and wave damping are also significant (Sorensen 1997; Brinkmann 2005). The latter can be determined using the wave transmission coefficient, Kt (Eq. (1) ). K_t=H_t/H_i (1) where Kt = transmission coefficient [-], Ht = height of the transmitted wave [m], Hi = height of the incident wave [m]. The wave damping is complementary to the wave transmission and is represented by the value 1 – Kt. Wiegel (1964) establish the relationship between the transmission and the distance b and diameter D of the piles and developed Eq. (2) for the transmission coefficient. K_t=b/ (b+D) (2) where Kt = transmission coefficient [-], b = distance between piles [m], D = diameter of the piles [m]. However, the findings by Wiegel (1964) indicated that the measured transmitted wave height in the model was approximately 25% greater than the transmitted wave height predicted by Eq. (1). The discrepancy was attributed to the effects of diffraction of waves (van Weele and Herbich 1972). A considerably more complex formula for wave attenuation was established by Hayashi et al. (1966). K_t=4e ∙h/H_i ∙ (-e+√ (e^2+H_i/2h) ) (3) where Kt = transmission coefficient [-], e = empirical parameter [-], h = water depth [m], Hi = height of the incident wave [m]. Parameter e can be calculated by: e= (C ∙b/ (b+D) ) ⁄√ (1- (b/ (b+D) ) ^2) (4) where e = empirical parameter [-], C = discharge coefficient of each space of piles [-], b = distance between piles [m], D = diameter of the piles [m]. The hydraulic properties of a configuration of closely spaced circular piles functioning as breakwaters were examined theoretically and experimentally by Hayashi et al. (1966). The findings indicated that the efficacy of the breakwater decreased with the increase of space (b/D) between the piles. Van Weele and Herbich (1972) investigated the wave reflection and transmission for pile arrays. It was observed that the reflection coefficient decreased with an increase in the longitudinal and transverse spacing between piles. However, it became evident that the longitudinal spacing b is of equal, if not greater, significance than the transverse spacing B, regarding the reflection coefficient of pile groups. The transmission of random waves through pile breakwaters was investigates by Truitt and Herbich (1987). It was found that the ratio of water depth to wave height (d/H) affects the transmission coefficient to a certain extent. However, the impact of the breakwater geometry, specifically the ratio of spacing to diameter (b/D), is more significant. The wave runup on circular cylinders was the subject of an investigation by Niedzwecki and Duggal (1992). In a laboratory investigation conducted by Rao et al. (1999), the transmission of waves through two rows of perforated hollow piles was studied. The influence of various factors, including water depth, incident wave steepness, clear spacing between the piles (b) and the spacing of pile rows (B), on the transmission coefficient was examined. Huang and Yuan (2010) investigated the transmission of tsunami waves through a row of circular cylinders. It has been demonstrated that the distance between two adjacent piles represents a significant controlling factor in the transmission of solitary waves through pile breakwaters. Mojtahedi et al. (2020) studied pile breakwater consisting of nine piles arranged in two rows. Their findings suggest that, in this configuration, the reflection coefficient for the square cross-section pile is greater than that of the cylindrical pile. Suvarna et al. (2021) conducted a laboratory investigation with the objective to enhance the hydraulic efficiency of a pile breakwater by expanding the structure in the vicinity of the free surface and incorporating perforations. Experimental Setup General remarks Laboratory tests for this study were carried out at Helmut-Schmidt-University Hamburg’s Hydraulics Laboratory. The wave channel has a length of 20 m, a width of 0.8 m and a height of 1 m. The lateral walls are constructed from glass to ensure a smooth surface. Waves are generated by a piston wave paddle. To minimize reflections within the experimental flume, wave absorbers have been installed behind the paddle as well as at the opposite end of the flume. The wavemaker can generate waves of varying heights between H = 2 cm and 10 cm. The wave period (P) can range from 0.5 to 2 s. The piles were installed at a distance of 10 m from the paddle. To record the wave height, three ultrasonic sensors (fabricate: Microsonic, type: mic+130/IU/TC, accuracy  1 %) were positioned along the channel. USS 1 is situated at a distance of 0.2 m in front of the breakwater structure. USS 2 and USS 3 are positioned at a distance of 0.5 m and 0.8 m, respectively, behind the piles. USS 2 is positioned in the center, while USS 3 is offset by 0.2 m to avoid negative interference effects. The forces acting on the piles were measured by four load cells (fabricate: Tedea-Huntleigh, type: 1040, accuracy  0.02 %). Figure 1 illustrates the configuration of the wave flume, including the placement of the measurement devices. The pile structures were constructed utilizing PVC pipes with a length of 0.5 m and a diameter of 50 mm. In order to ensure the accuracy of force measurements, it is essential that the piles with load cells attached are positioned at a sufficient distance from the channel floor to prevent any influences by shear stresses at the channel bottom. To prevent any movement, piles without load cells were fixed to the channel floor. The data were recorded using a HBM QuantumX device. Fig. 1. Top view of the experimental setup. Model runs In total 29 model runs were conducted. For each model run, ten distinct waves were recorded, with a total of 20 waves of a specified height and period generated in sequence. The parameters of the measured waves are presented in Table 1. The measurements were conducted using a variety of pile configurations and distances b. These are dependent on the pile diameter D and are provided in Table 2. A maximum of four load cells were installed. It was ensured that as many different areas of the breakwater as possible were covered. The measured data was analyzed and outliers were removed. Table 1. Wave parameters and associated wave theory. Number Wave period T [s] Wave height H [cm] Wave theory 1 0.6 0.28 Linear wave theory 2 0.8 0.30 Linear wave theory 3 1.0 1.10 Stokes 2nd order 4 1.0 3.06 Stokes 2nd order 5 1.2 4.38 Stokes 2nd order 6 1.4 3.39 Stokes 2nd order 7 1.4 7.76 Stokes 3rd order 8 1.6 6.30 Stokes 3rd order 9 1.8 1.72 Stokes 2nd order 10 2.0 8.35 Stokes 3rd order Table 2. Distance between piles b and porosity ε. Ratio b/D b [mm] ε [-] 0.1 5 0.33 0.3 15 0.50 0.5 25 0.67 1.0 50 0.77 2.0 100 0.91 Results Wave damping During the measurements, the wave heights were measured at two different positions behind the breakwater, as described in Section 2.1. When analyzing the influence of the wave height measurement position, it was determined that the discrepancies between the sensors are minimal, and thus, the data of the ultrasonic sensor 2 will be utilized in the further course of the study. As already established in previous studies, the distance between the piles has a significant influence on wave attenuation. It can be observed that the impact of the distance increases as the number of piles increases. The influence of pile distance is negligible when only two piles are present. A difference can be determined starting from a number of four piles. As the number of piles increases, the discrepancy between the values of distance b = 2D and those of distance b = 0.1D also increases. The impact of varying the number of piles is recognizable, particularly at smaller distances. The discrepancy between the data sets comprising two and twelve piles at a distance of b = 0.1D is approximately 0.375 (Fig. 2). Fig. 2. Wave attenuation dependent on the distance ratios between the piles (for visual support, Kt = β1- (b/D) β2+β3 functions were used). Drag forces The results demonstrate that the maximum force acts on the central pile. Consequently, the maximum force and the data from the central sensor are employed in the subsequent assessment of the impact of other parameters. It is evident from previous research that the distance between piles has an influence on the maximum force that acts on a pile in a pile breakwater. At a distance of b = 2D, the forces are observed to be between approximately 0 N and 1.5 N. In comparison, the maximum force at a distance of b = 0.1D is approximately 8.5 N. Similar to wave damping, the influence of the pile distance increases with decreasing distance. It can be stated that the piles influence each other starting at a distance of b = 0.5D. Outlook For further investigations, the influence of the wave parameters and the number of piles on the wave attenuation will be analyzed. Furthermore, the results obtained will be compared with the current state of the art. With regard to the drag force, the influence of the wave parameters will be analyzed. In addition, the force over the width of the breakwater will be investigated. This will be followed by a comparison with the current state of the art. References Brinkmann, B. (2005) Seehafen: Planung und Entwurf, Springer, 459 pp. Hayashi, T. ; Hattori, M. ; Kano, T. ; Shirai, M. (1966) Hydraulic Research on the Closely Spaced Pile Breakwater, Coastal Engineering in Japan, 9 (1), 107–117 Huang, Z. ; Yuan, Z. (2010) Transmission of solitary waves through slotted barriers: A laboratory study with analysis by a long wave approximation, Journal of Hydro-environment Research, 3 (4), 179–185 Mojtahedi, A., Beiragh, M. S., Farajpour, I. und Mohammadian, M. (2020) Investigation on hydrodynamic performance of an environmentally friendly pile breakwater, Ocean Engineering 217,107942 pp. Niedzwecki, J. M. ; Duggal, A. S. (1992) Wave Runup and Forces on Cylinders in Regular and Random Waves, Journal of Waterway, Port, Coastal, and Ocean Engineering, 118 (6), 615–634 Pasche, E. ; von Lieberman, N. (2008) Kustenschutz, Beton Kalender 2008. Hrsg. von K. Bergmeister K. ; Worner, J. -D., 291–356 Schumacher, L. (2022) Das Recht der Kustenanpassung, Springer, 17 pp. Sorensen, R. M. (1997) Basic Coastal Engineering, Boston, MA: Springer US. Sterr, H. (2007) Folgen des Klimawandels fur Ozeane und Kusten, Humboldt-Universitat zu Berlin, Mathematisch-Naturwissenschaftliche Fakultat II, Geographisches Institut, 86–97 Truitt, C. L. ; Herbich, J. B. (1987) Transmission of Random Waves Through Pile Breakwaters, 20th International Conference on Coastal Engineering, Taipei, Taiwan, 2303–2313 van Weele, B. J. ; Herbich, J. B. (1972) Wave Reflection and Transmission for Pile Arrays, Int. Conf. Coastal. Eng. (Coastal Engineering Proceedings), 13 Wiegel, R. L. (1964) Oceanographical Engineering. Prentice-Hall, New Jersey, 532 p. Zhu, D. T. ; Xie, Y. f. (2015) Hydrodynamic characteristics of offshore and pile breakwaters, Ocean Engineering, 104,257–265

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Year: 2025