Research Article
Hydrodynamic Characteristics of Semi-circular Breakwaters: Review Article
School of Civil Engineering, SASTRA University, Thanjavur 613402, Tamilnadu, India
LiveDNA: 91.324
The Semicircular Breakwater (SBW) is a composite breakwater consisting of a semicircular caisson resting on a rubble mound. The SBW function as a barrier dissipates the incident wave energy and creates tranquility on its leeside. A detailed survey of literature on the wave structure interaction problem is discussed below.
Sasajima et al. (1994) have reported the results obtained on measured pressures and forces on the rear wave dissipating type SBW constructed at Miyazaki port in Japan. The variation of measured highest 1/3 wave pressure, pressure at the time to maximum force and maximum wave pressure at different elevations along the wall have been compared to the modified theoretical formulation of Goda and Suzuki (1976). Sundar and Raghu (1997) from their model tests on a solid type SBW subjected to regular waves concluded that the reflection coefficient, Kr for a solid SBW varied from 0.5 to 0.9 for waves with steepness, H/L upto 0.12 for relative water depths, hw/L ranging from 0.1 to 0.4 where, H is wave height, L is wave length and hw is the water depth. The results also indicated that the variation of Kr with H/L was less than its variation with hw/L. The measured dynamic pressures on the seaward face was reported to be lesser at still water level (SWL) and greater at locations below SWL compared to their corresponding theoretical values of the semi empirical formula of Goda and Suzuki (1976). This trend in the variation of pressures was found to be for intermediate water depths, whereas, a reverse trend in their variation was noticed for deepwater conditions. Priya et al. (2000) claimed that their experimental results on the variation of the dynamic pressures on an impermeable SBW compared well with the two dimensional finite element model of Sundar et al. (2001). However, their results indicated that the measured values were less than the modified formulation of Goda and Suzuki (1976), particularly closer to the SWL, similar to the conclusions drawn by Sundar and Raghu (1997). Further, the dimensionless pressures were found to reduce with increase in the scattering parameter, ka, where, k is the wave number and a is the radius of the semicircular caisson. In addition, the pressures were reported to be less for higher hw/ht, where, ht is the total height of the model, that is, the height of the rubble mound plus the height of the semicircular caisson.
In many cases, the design of breakwater is difficult since the construction takes place in severe environment caused by high waves and poor ground conditions. Due to advances in the design and construction, several new concepts of breakwater are being introduced. One such concept is the Semicircular Breakwater in which, many researchers are focusing, especially in Japan and China. Jia (1999) obtained numerical solution for incident stokes waves passing the submerged obstacles and extended the method the calculation of wave run-up on a slope for estimation of over topping. Xie (1999) has given the new calculation method to estimate the wave forces acting on a submerged semicircular breakwater and verified with the results of seven related physical model tests and adopted in the design of south estuary jetty of the Yangstze river estuary of China. It is cast as different elements and made of prestressed concrete. As the caisson is a prefabricated structure, it can easily be transported, handled and placed at site. In addition the above, it has got excellent hydraulic characteristics compared to other types of breakwaters like, greater sliding stability against waves, horizontal component of a wave force applied to semicircular surface is smaller than that of applied to an upright wall, light in weight (since the structure is hollow), the soil sub grade reaction is less and ideally suited for poor ground conditions and curved structure provides increased member strength.
Gunaydin and Kabdasli (2004) investigated the performance of solid and perforated U-type breakwaters subjected to both regular and irregular waves for different immersion depths. They concluded that, the results of irregular wave tests are higher than those of regular wave tests for both solid and perforated model. Vijayalakshmi et al. (2007) studied the regular wave interaction with a twin concentric porous circular cylinder system consisting of an inner impermeable cylinder and an outer perforated cylinder through physical and numerical models. They concluded that, the maximum wave runup on the perforated cylinder is almost same as the incident wave height. Liu et al. (2007) studied the hydrodynamic performance of a breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them based on an analytical solution. They concluded that, with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient would be always rather small if the relative wave absorbing chamber width exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity. Liu et al. (2008) examined the hydrodynamic performance the breakwater with an upper submerged horizontal porous plate and a lower submerged horizontal solid plate using eigen function expansion method and calculated reflection, transmission, energy-loss coefficients and also the wave forces acting on the plates. They concluded that, the transmission coefficient will be always small if the dimensionless plate length exceeds a certain moderate value.
Sundar et al. (2001) reported the results of hydrodynamic characteristics of impermeable SBW. Dhinakaran et al. (2002, 2008, 2009, 2010) reported the results of various hydrodynamic characteristics of surface piercing and submerged SBW and their study concentrated on effect of perforations, water depth and rubble mound height and concluded that effect perforations played vital role compared to effect of water depth and rubble mound height. An optimum percentage of perforations and height of the SBW were arrived.
EXPERIMENTAL INVESTIGATIONS
Test facility: The detailed experimental studies were carried out in a 72.5x2.0x2.7 m sized wave flume in the Department of Ocean Engineering, Indian Institute of Technology Madras, India and is capable of generating both regular and random waves. The water depth in this flume can be varied from 0.4 to 2 m. One personal computer, which is connected to servo actuator, is used to give the input values like wave height and wave period to the wave maker and the same is used for data acquisition of the signals from wave probes and pressure transducers through an amplifier. The details of the flume along with the positions of the wave gauges and the model are shown in Fig. 1.
Test model: The model basically consists of two parts, the bottom frame and the top semicircular shaped caisson. The caisson was made with 1 mm thick aluminium sheet rolled into a semicircular shape of radius 0.5 m. This sheet is fixed to a bottom frame of 50 mm height made up of ISA (Indian Standard Angle) 50x50. Rods of 12 mm diameter as stiffeners were provided at ends and at the center of the hollow semicircular caisson in order to provide the necessary rigidity for the wall of the model. A 30x3 mm flat was provided along the inner surface of the semicircular caisson to retain its shape. The caisson was fabricated in two units to facilitate easier handling. The central part of the caisson of about 200 mm width was fabricated using 4 mm thick perspex sheet onto which the Churchill runup meter was fixed.
Fig. 1: | Experimental setup for the study |
Fig. 2: | Isometric view of the Seaside perforated SBW model |
The bottom frame was fabricated using channels ISMC (Indian Standard Medium Channel) 100x50. It was ensured that this frame did not have contact with the flume sidewalls or with the flume floor. The scale adopted for the study was 1:20 and is derived from the rear dissipating SBW available in Miyazaki port, Japan. The mound was formed using coarse aggregates (granite stones) of weight varying from 50 to 100 g. The slope on both sides was maintained the same as 1 in 2. The weight of stones in model is the cubic root of weight of stones in prototype. Two frames of width 25 mm and height 120 mm were initially fabricated and kept on either side of the caisson. A gap of 5 mm was maintained between the caisson and the frames on either side. By providing a gap of 5 mm gap between the frame in which rubble mound was placed and the caisson, it was ensured that the force exerted on caisson only measured by the six component force balance. Rubble mound was placed on this frame, thus its height, hr being maintained at 120 mm. Hence, for this model its total height, ht is equal to hr plus radius of the caisson, hs plus height of the bottom frame of 50 mm (0.12+0.5+0.05 = 0.67 m). Four more frames each of 100 mm high were also fabricated. After the tests with hr equal to 120 mm, the rubble mound was removed and the additional frames were placed on which the rubble stones were placed. In this way tests were also carried out with hr equal to 220 and 320 mm. Isometric view of the SBW model is shown in Fig. 2.
Instrumentation: In order to obtain the incident and reflected wave heights from the structure, three wave gauges were positioned in front of structure at 7 m away from the breakwater model. The distances between the gauges, which were a function of the wave period, were calculated by considering the requirements as proposed by Mansard and Funke (1980). Three set-ups were calculated for the frequencies ranging from 0.50 to 0.60, 0.70 to 0.90 and 1.0 to 2.0 Hz. The positions of the wave gauges were changed accordingly. One wave probe was kept on the leeward direction of the model to register the transmitted wave height. The SBW model was subjected to the action of regular and random waves, of periods ranging from 0.8 to 2 sec at intervals of 0.2 sec. For each period atleast five different wave heights ranging from 0.03 to 0.18 m at intervals of 0.03 m were generated.
Fig. 3: | Details of 6-component force balance |
Thus, one test setup of the model was subjected to about 35 combinations each for regular and random waves. Details of six-component force balance are shown in Fig. 3. The experiments were performed with model mounted on the six-component force balance. The force balance R67 measures 6 components in a rectangular co-ordinate system. The resolution of the resulting force to be measured into the 6 components is effected mechanically by way of spring joints and measurement of the individual components unaffected with the help of strain gauge type force transducers.
All parts of the force balance are made of hard steel with good corrosion resistance against water. The six transducers are water proofed and can be used to a depth of 5 m. The balance, which is to be mounted in a recess at the bottom of the flume floor, has a platform of 850x850 mm flush with flume floor. The platform is suspended with 6 coupling rods with flexures at the both the ends and six force transducers. The force transducers are connected to a frame. This frame has to be fixed to the foundation at its four corners. In the direction of wave propagation, one force component X is measured. Vertically, the three components Z1, Z2 and Z3 are measured which are at a distance of 900 mm between each other. The side of the force balance with the Z3 transducer is placed towards the wave maker. The force transducers are connected to a data acquisition system through carrier frequency amplifiers. The sensitivity of the transducers at their rated loads is about ±2 m v/v, which means that, even for much smaller forces than the rated loads, the amplifiers can give full scale indication. The force balance is initially calibrated before starting the experiments and again after completing the experiments. Both the calibration values are one and the same. The calibration of force balance was done by placing known weights and recording the corresponding voltages. A spring balance is made use of to measure the horizontal pull and the corresponding voltage is noted. The model is fixed to the force balance consisting of a machined stainless steel plate of about 12 mm thickness with 36 threaded borings using M12 stainless steel bolts.
In this study selected results on various hydrodynamic characteristics of SBW for surface piercing and submerged conditions are presented to make potential reader/researcher to understand the effect on various parameters. The experiments are conducted for 7, 11 and 17 percentages of perforations provided on seaward side (front dissipating type) and on both sides (fully perforated type).
Surface piercing breakwater
Reflection characteristics
Effect of perforations and water depth: The variations of Kr (reflection coefficient) with hw/L for SBW0, SBW7, SBW11, SBWf7, SBWf11 and SBWf17 models for hw/ht = 0.6, 0.7 and 0.8 for a constant hr/ht = 0.18 due to regular waves are reported in Fig. 4a-c. The value of Kr varies from 0.5 to 0.9 for SBW0, whereas these values are 0.35 to 0.65, 0.28 to 0.51, 0.3 to 0.57, 0.24 to 0.49, 0.2 to 0.39 and 0.15 to 0.33 for SBW7, SBW11, SBW17, SBWf7, SBWf11 and SBWf17 respectively. The results indicate that Kr increases with an increase in hw/L for all the hw/ht tested and for all the models of seaside and fully perforated SBWs tested. When the waves of shorter wave length run over the curved surface, they feel the presence of perforations on the caisson for a shorter distance, because of which the energy dissipated due to the turbulence is less and hence the reflection is more for higher hw/L. In the case waves of long period, it runs over a curved surface for a greater distance and energy dissipated is more and hence lesser reflection. The reflection coefficient, Kr decreases with an increase in perforation upto 11 percentage and it increases with a further increase in perforations to 17 percentage. For the SBW models upto 11 percentage perforations, the energy is dissipated irrespective of wave periods, whereas, for the model with 17 percentage perforations, waves of smaller periods dissipates lesser energy and hence more reflection for this model.
Fig. 4: | Effect of perforations on Kr due to regular waves. (a) hw/ht = 0.6, (b) hw/ht = 0.7 and (c) hw/ht = 0.8 |
Even long period waves dissipate lesser energy in the case of SBW17 because of its size of perforation compared with models upto 11percentage perforations.
It is observed that, Kr decreases with an increase in hw/ht. For hw/ht = 0.6, only smaller height of the semicircular portion of the caisson is exposed to waves, that is, the effect of curvature is less pronounced, thus, resulting lesser dissipation and more reflection. This trend is reversed for higher hw/ht. i.e., for higher water depth condition, in which case, the waves are exposed to greater area of perforations leading to greater dissipation of energy and there by, resulting in lesser reflection. In addition, the effect of curvature also plays a role in dissipating more energy by permitting waves to run over a longer distance. Especially for hw/ht = 0.8, a partial over topping of waves also permitted which caused the reduction of Kr. However, the rate of reduction in reflection coefficient due to the effect of water depth is not that significant, compared to the effect of perforations.
It is also to be noted that, the values of Kr increase while perforation ratio increases from 11 to 17 percentage in the case of seaside perforated SBW and shows reverse trend for fully perforated SBW (i.e., Kr decreases from perforation ratio 11 to 17 percentage). It is due to fact that, increase in perforation ratio from 11 to 17 effected decrease in energy dissipation with higher percentage of perforation ratio in the case of seaside perforated SBW, whereas in the case fully perforated SBW, the scenario is different. Though perforation ratio increases, openings on the shoreward side of the breakwater permits higher amount of energy through transmission, the values of Kr gets reduced in SBWf17 compared to SBWf11. This is one reason why SBWf17 was not recommended due to large transmission of energy, which will definitely affect the tranquillity condition of the harbour.
Effect of rubble mound height: The effect of rubble mound height on the reflection characteristics of the surface piercing seaside perforated SBW models were studied for three different hr/ht ratios of 0.18, 0.29 and 0.36 with a constant water depth, hw of 0.54 m. In this case, the rubble mound heights (hr) were changed from 0.12 to 0.32 m. The variation of Kr for various SBW models subjected to regular waves due to the effect of rubble mound height is reported in Fig. 5a-c. The value of Kr varies from 0.34 to 0.74 for SBW0, whereas these values are 0.24 to 0.54, 0.16 to 0.44, 0.18 to 0.48, 0.19 to 0.34, 0.14 to 0.33 and 0.12 to 0.27 for SBW7, SBW11, SBW17, SBWf7, SBWf11 and SBWf17, respectively. The results clearly indicate that, the rate of reduction in reflection coefficient is significant from hr/ht = 0.18 to 0.29 and is less significant from when hr/ht is changed from 0.29 to 0.36. It is understood that for higher hr/ht of 0.36, the rubble mound action is predominant. The rate of reduction due to increase in hr/ht is less in the case of seaside perforated semicircular breakwaters compared to an impermeable SBW, since the combination of rubble mound height and perforations play a dominant role in the dissipation of energy in former type of breakwater.
Runup characteristics
Effect of perforations and water depth: The variations of dimensionless run-up, Ru/Hi with hw/L for SBW0, SBW7, SBW11, SBW17, SBWf7, SBWf11 and SBWf17 models for hw/ht of 0.6.0.7 and 0.8 for a constant hr/ht of 0.18 due to regular waves are reported in Fig. 6a-c. The Ru/Hi decrease with an increase in hw/L due to the fact that, for long period waves more run-ups occurs on the caisson. In the case of lesser period waves (larger hw/L), most the energy contained in the incident waves gets reflected as discussed earlier and hence only lesser energy will be available for the run-up.
Fig. 5: | Effect of rubble mound height on Kr due to regular waves. (a) SBW7, (b) SBW11, (c) SBW17, (d) SBWf7 (e) SBWf11 and (f) SBWf17 |
Fig. 6: | Effect perforations on Ru/Hi due to regular waves. (a) hw/ht = 0.6, (b) hw/ht = 0.7 and (d) hw/ht = 0.8 |
This explains the phenomena of run-up decreasing with an increase in hw/L. The results also demonstrate that Ru/Hi decreases with an increase in hw/ht due to the reason that as hw/ht increases, the effect of curvature is more pronounced and hence lesser run-up. This can be as explained below. For higher hw/ht, though the distance travelled over the caisson is more, the run-up being a vertical projection will be less. In addition, for higher hw/ht, larger area of the structure exposed to waves, which leads to more energy dissipation and subjected to lesser run-up. The Ru/Hi also decreases with an increase in percentage of perforations up to 11. Further increase in the perforation to 17 percentage results in an increase in the run-up, where as in case of fully perforated SBWs, run-up values gets reduced with increase in perforations even up to 17 percentage, due to reason that, it permits more transmission.
The rate of reduction in dimensionless runup is calculated by taking SBW0 as the reference and calculated for seaside perforated and fully perforated SBWs. The percentage of reduction in dimensionless run-up compared to an impermeable type (SBW0) varies from 19 to 40% for seaside perforated SBWs and 35 to 68% in the case of fully perforated SBWs for lower hw/ht. These reductions vary from 48 to 60% for seaside perforated SBWs and 47 to 76% for fully perforated SBWs for higher hw/ht. For hw/ht = 0.8, the free board is only 13 cm, some of the waves longer wave periods and heights, over top the crest in case of an impermeable SBW (SBW0) and hence higher reduction run up was observed in perforated SBWs. Among the three water depths tested, hw/ht = 0.7 exhibits considerable reduction in runup, which will reduce the force experienced by the caisson. By taking effect of perforation in reduction, SBW11 and SBWf11 cause higher reduction in the case of seaside and fully perforated SBWs, respectively.
Effect of rubble mound height: The variations of dimensionless run-up, Ru/H with hw/L for SBW0, SBW7, SBW11, SBW17, SBWf7, SBWf11 and SBWf17 models for hr/ht of 0.18, 0.29 and 0.36 for a constant hw = 0.54m due to regular waves are reported in Fig. 7a-f. The Ru/Hi decreases with an increase in the rubble mound height, since rubble mound absorbs certain amount of energy leading to lesser energy available for run-up on the semicircular caisson. The rate of reduction in dimensionless run-up is similar as seen earlier and confirming the variation of Kr.
Transmission characteristics
Effect of perforations and water depth: In case of fully perforated SBW the transmission of waves take place since both seaside and leeside are perforated. The variations of transmission coefficient, Kt with hw/L for SBWf7, SBWf11 and SBWf17 models for hw/ht of 0.6.0.7 and 0.8 for a constant hr/ht of 0.18 due to regular waves are reported in Fig. 8a-c. The value of Kt varies from 0.2 to 0.43 for SBWf7, whereas these values are 0.23 to 0.49 and 0.32 to 0.59 for SBWf11 and SBWf17 respectively for regular waves. In the case of SBWf17, the energy transmitted exceeds 50 percentage of the incident energy, which will affect the tranquility condition inside the harbor. The increase in perforation ratio from 7 percentage to 17 percentage decreases the energy loss in general. The Kt increases and Kl decreases with increase in percentage of perforations. It is also observed that, higher the hw/ht, higher the transmission. However, the reduction in Kl for the fully perforated SBW models is less significant. From the three models tested with different hw/ht ratios, SBWf11 gives the optimum results both in terms of reflection and transmission point of view.
Fig. 7: | Effect of rubble mound height on Ru/Hi due to regular waves. (a) SBW7, (b) SBW11, (c) SBW17, (d) SBWf7 (e) SBWf11 and (f) SBWf17 |
Fig. 8: | Effect perforations on Kt due to regular waves. (a) hw/ht = 0.6, (b) hw/ht = 0.7 and (d) hw/ht = 0.8 |
Fig. 9: | Effect of rubble mound height on transmission coefficient due to regular waves. (a) SBWf7, (b) SBWf11 and (c) SBWf17 |
Effect of rubble mound height: The variations of transmission coefficient, Kt with hw/L for SBWf7, SBWf11 and SBWf17 models for hr/ht of 0.18, 0.29 and 0.36 for a constant water depth of 0.54 m due to regular are reported in Fig. 9a-c. In general, increase in perforation ratio increases transmission and for SBWf17 the energy transmitted exceeds more than 50 percentage of incident wave energy, which will affect the tranquillity condition of any harbour and an optimal transmission occurred in SBWf11. Considering the effect of rubble mound height for all the cases fully perforated SBW cases, the rate of reduction is significant, when hr/ht increased from 0.18 to 0.29 and insignificant from 0.29 to 0.36. It was understood that, when hr/ht increased from 0.29 to 0.36, the rubble mound action was predominant than that of composite action and hence hr/ht = 0.29 is an optimal value from the experiment s conducted.
Forces on the semicircular caisson
Effect of perforations and water depth: The shoreward horizontal force, [Fh]max and vertical force, [Fv]max exerted on the semicircular caisson in the presence of the submerged mound measured, were normalized by dividing them by [γalHi]. The variation of the dimensionless shoreward horizontal force [Fh]non = [(Fh)max/(γalHi)] and vertical force [Fv]non = [(Fv)max/(γalHi)] on SBW0, SBW7, SBW11, SBW17, SBWf7, SBWf11 and SBWf17 for three different hw/ht ratios are shown in Fig. 10a-c and 11a-c due to regular waves. The horizontal force component is found to decrease with increase in hw/L irrespective of the type of SBW. It is due to fact that, long period waves exert more force on the caisson and short period waves transfer lesser force. The increase in hw/ht increase forces on the semicircular caisson due to a fact that, higher the water depth, higher the area of the SBW model exposed to wave action and hence the increase in hw/ht causes increase in [Fh]non. The percentage of reduction is about 55 to 76% for seaside perforated SBWs for all hw/ht tested and this percentage of reduction of dimensionless forces varies from 75 to 95% in case of fully perforated SBWs while comparing with SBW0. Hence it is understood that, effect of perforations plays a major role in reduction of forces on semicircular caisson.
Effect of rubble mound height: The variation of dimensionless horizontal and vertical force due to regular waves are depicted in Fig. 12a-f and 13a-f to understand the effect of rubble mound height for all the perforated SBWs. Both [Fh]non and [Fv] non decrease with increase in hw/L.
Fig. 10: | Effect of perforations on dimensionless shoreward horizontal force due to regular waves (a) hw/ht = 0.6, (b) hw/ht = 0.7 and (c) hw/ht = 0.8 |
Fig. 11: | Effect of perforations on dimensionless shoreward horizontal force due to regular waves (a) hw/ht = 0.6, (b) hw/ht = 0.7 and (c) hw/ht = 0.8 |
Fig. 12: | Effect of perforations on dimensionless shoreward horizontal force due to regular waves (a) SBW7, (b) SBW11 and (c) SBW17, (d) SBWf7, (e) SBWf11 and (f) SBWf17 |
Fig. 13: | Effect of perforations on dimensionless shoreward horizontal force due to regular waves (a) SBW7, (b) SBW11 and (c) SBW17, (d) SBWf7, (e) SBWf11 and (f) SBWf17 |
It is due to a fact that higher the rubble mound height, higher the energy dissipation and lesser the energy transferred on the SBW model. Both in dimensionless horizontal and vertical forces the rate of reduction is more from hr/ht = 0.18 to 0.29 and further increase in hr/ht to 0.36 does not cause more reduction. It is clear that, the rate of reduction decreases from hr/ht 0.29 to 0.36. As seen in horizontal component, similar trend was observed in vertical component also.
Submerged breakwater
Reflection and transmission characteristics: The reflection coefficient, Kr was evaluated from the measured time histories for each of the tests based on the methodology of Mansard and Funke (1980) by decomposing the composite wave elevations measured the three wave gauges placed on the seaward side of the model. The transmission coefficient, Kt (Ht/Hi) was evaluated from the wave surface elevation obtained from the wave gauge positioned on the leeside of the structure. The loss coefficient, Kl is evaluated as
The variations of Kr with scattering parameter, ka, for SBW7, SBW11 and SBW17 obtained from the present study are compared with that of SBW0 for a constant hr of 0.12 m and for hw/ht = 1, hw/ht = 1.2 and hw/ht = 1.4 in Fig. 14a-c to study the effect of perforations. It is observed that Kr varies from 0.16 to 0.35 for SBW7, from 0.12 to 0.34 for SBW11 and from 0.15 to 0.32 for SBW17, whereas, Kr for SBW0 vary from 0.18 to 0.39. For a particular water depth, Kr is found to decrease with increase in percentage of perforations which is due to the fact that, provision of perforation dissipates more energy by creating turbulence and the curvature of the structure also enhances this phenomena. Furthermore, Kr is found to decrease with increase in scattering parameter, which clearly demonstrates that the structure reflects more energy for long period waves and lesser energy for short period waves. In addition, Kr decreases with increase in water depth due to a fact that, the effect of the structure on the propagating waves will be less pronounced, since the relative depth of submergence is more. The percentage reduction in Kr due to perforations compared to that for the impermeable SBW, [Kr]red is more for short period waves for SBW7, SBW11 and SBW17 models for hw/ht = 1.0, that is when the SWL is in level with the crest of the caisson. ([Kr]red or [Kt]red is the percentage of reduction in Kr or Kt of either SBW7 or SBW11 or SBW17 with respect to Kr or Kt of SBW0). For long period waves, wave energy dissipated is more irrespective of type of SBW and hence the [Kr]red is low for higher ka. However, for the cases, hw/ht = 1.2 and hw/ht = 1.4, the [Kr]red decreases with increase in scattering parameter, since smaller waves passes the structure without much attenuation.
It is observed from the Fig. 16, that Kt varies from 0.42 to 0.85 for SBW7 and from 0.21 to 0.80 for SBW11, 0.17 to 0.73 for SBW17 and from 0.46 to 0.91 for SBW0. For hw/ht = 1, the value of Kt decreases with increase in ka. The long period waves are expected to have larger displacements in the direction of wave propagation and the obstruction extending over the entire water depth would lead to substantial dissipation of orbital motions, leading to a lesser Kt for larger ka. However, for the conditions of hw > ht (i.e., hw/ht = 1.2 and hw/ht = 1.4), a greater amount of energy gets transmitted past the structure being greater in the case of longer period waves which explains the probable reason for the above stated phenomena. The [Kt]red for the SBW7, SBW11 and SBW17 compared to SBW0 clearly indicates that for ka >2.4, [Kt]red is more for SBW11 and for ka <0.3,[Kt]red is more for SBW17.
Fig. 14: | Effect of perforations on (a) Kr, (b) Kt and (c) K1 |
The rate of [Kt]red decreases with increase in water depth due to the fact that more transmission occurs irrespective of the type of SBW for higher relative depth of submergence. The values of Kl were calculated from the law of conservation of energy as stated above and are shown in Fig. 14. The energy dissipation is more in case seaside perforated SBW, in which the perforation plays a major role in dissipating the incident wave energy. The value of Kl varies from 0.49 to 0.91 for SBW7, 0.58 to 0.95 for SBW11 and for SBW17 it falls between SBW7 and SBW11where as for SBW0, it varies from 0.36 to 0.84. It is inferred from the results that in addition to the curvature, the effect of perforations plays a significant role.
Fig. 15: | Effect of perforations on (a) [Fh]non and (b) [Fv]non |
Forces on the semicircular caisson: The peak shoreward horizontal, (Fh)max and vertical, (Fv)max forces exerted on the semicircular caisson in presence of the submerged mound measured using six component force balance, normalized by dividing the forces with [γalHi/2]. The variation of the dimensionless horizontal force, (Fh) non = (Fh)max/[γalHi/2] with hw/L for the SBW7 and SBW11 are compared with the results of SBW0 in Fig. 15a and b. It is seen that (Fh) non decreases with increase in ka, for all the three models, the rate of decrease being drastic particularly for SBW0. SBW7 is found to experience the least force for the three hw/ht tested. From the results, it seen that [Fh] red for SBW7 ranges from 41 to 59% for hw/ht = 1.0, 36 to 67% for hw/ht = 1.2 and 40 to 73% for hw/ht = 1.4. This reduction for SBW11 is found to range from 60 to 78% for hw/ht = 1.0, 53 to 82% for hw/ht = 1.2 and 68 to 80% for hw/ht = 1.4. It is seen that (Fv)non decreases with increase in hw/L, for all the three models, the rate of decrease reducing as the percentage of perforations increases. The SBW11 is found to experience the least force for the three hw/ht tested similar to the variation in the (Fh)non and hence dissipates maximum energy in seaside perforated SBWs. The [Fv] red in for SBW7 ranges from 22 to 47% for hw/ht, 32 to 56% for hw/ht = 1.2 and 20 to 36% for hw/ht = 1.4. This reduction for SBW11 is found to range from 70 to 80% for hw/ht = 1.0, 70 to 87% for hw/ht = 1.2 and 57 to 88% for hw/ht = 1.4. In addition, the percentage of reduction in forces for the seaside perforated SBW is found to slightly decrease with increase in ka due to fact that, for short period waves the force exerted on the structure is less, in general, irrespective of the type of SBW. The dimensionless forces also increases with increase in hw, that is, the structure experiences higher forces for higher water depths from hw/ht = 1.0 to 1.2 and decreases for further increase in hw/ht to 1.4. It is due to fact that, for hw/ht = 1.4, the dynamic action of waves influence the structure only to a lesser extent, since the depth of submergence above the model is about 40% of the total height of the model. The results clearly demonstrate that the percentage of reduction in forces for SBW11 is much greater than for SBW7. It may be recalled that the maximum percentage of reduction in Kr for SBW11 is greater than that for SBW7 as discussed earlier, which is the main attribute for the above trend. It is observed from the plots that, the rate of reduction due to increase in hw/ht on (Fv) non more for SBW0 and less for seaside perforated SBWs. The results clearly indicate that the effect of perforations play a vital role in the reduction of both horizontal and vertical forces on the caisson. The results show that the vertical force on the semicircular caisson significantly more than the horizontal force for the seaside perforated SBWs.
Dynamic pressures on SBW: The variations of dimensionless pressures, pc/γHi with ka for SBW7, SBW11 and SBW17 models for hw/ht = 1.2 compared with SBW0 for all the locations of relative depth of submergence of pressure port, z/hw is shown in Fig. 16 to understand the phenomena. The results clearly show that, the rate of reduction in the pressures is more for the location closer to the SWL and less for the location closer towards the seabed. The pressure decay from the SWL towards the seabed is also seen. By comparing the lines of best fit for each of z/hw superposed it is observed that the dimensionless shoreward pressure decreases with increase in ka for all z/hw in general. This only reflects that the pressures exerted by the long period waves are larger. Such a trend in its variation is seen for the three water depths tested. A significant scatter in pc/γH for the location closer to the SWL is observed for the model with hw/ht = 1.0 condition and is attributed to the intermittence effects, an aspect discussed by Mallayachari and Sundar (1995) and Isaacson and Subbiah (1991). The results indicate that the effect of the perforations is quite significant in reducing the pressures closer to the free surface. It is clearly observed the above results that, the structure for the condition hw/ht = 1.4, experiences least pressures among the three hw/ht tested due to reason that, relative depth of submergence is high in this case and effect of waves not much felt by the structure. It is inferred from the results that, submerged SBW will be ineffective in terms of hydrodynamic performance for a water depth (hw) of 1.4 times the total height of the model (ht).
Fig. 16: | Effect of perforations on dimensionless pressure for hw/ht = 1.2 |
Detailed experimental study was carried out to investigate the reflection, transmission, runup characteristics, hydrodynamic pressure and forces on seaside perforated and fully perforated SBW models for three different perforations, water depths and rubble mound height for surface piercing and submerged condition. The salient conclusions for as follows:
Surface piercing SBW: The increase in percentage of perforations from 0 to 17 decreases the reflection coefficient and dimensionless runup and in the case of seaside perforated SBWs, for the 17 percentage perforation it shows reverse trend. The transmitted wave height on the seaside exceeds 50percentage of incident wave height in case of SBW17 almost in all the hw/ht ratios tested and concluded that SBW17 will affect the tranquility condition on the shoreward direction. Dimensionless runup decreases with increase in water depth and perforation and in case of higher water depth, there is no much reduction in values are observed among the different cases of seaside and fully perforated SBWs. The increase in rubble mound height resulted significant reduction in reflection and transmission coefficients and runups from hr/ht from 0.18 to 0.29 and it is less significant for further increase in hr/ht to 0.36. The effect of water depth on hydrodynamic characteristics of seaside perforated SBW models is less significant compared to the effect of perforations and the effect of rubble mound height. The comparison of transmission coefficient indicates that, for submerged condition, SBW transmits lesser energy than conventional rubble mound breakwater, whereas for surface piercing condition Kt value is on the higher side for SBW (till 11 percentage perforation) than rubble mound breakwater and is within the upper bound. The dimensionless vertical force are very much higher than the dimensionless horizontal force for the all the perforated SBW models tested and it is worthy to note that, vertical force acts on the semicircular caisson adds stability to the breakwater. The optimum percentage of perforation arrived in case of fully perforated SBW is 11 from the experiments conducted. The total height of the model recommended being about 1.25 times the water depth and height of the rubble mound which is 0.29 times the total height of the model. These values can be adopted in the field for a better performance of SBW.
Submerged SBW: Kr is found to decrease with increase in water depth and increase in perforations upto 11% and further increase in perforation shows a reverse trend and hence provision of perforations beyond 11% is not recommended from the experimental investigations. The maximum reduction of 41% in Kr for seaside perforated SBWs compared to SBW0 is obtained in SBW11 for hw/ht = 1.2. The increase in ka and percentage of perforations decreases both the dimensionless pressure and forces. The rate of decrease is more for dimensionless vertical force compare to dimensionless horizontal force. The increase in hw/ht from 1.0 to 1.2 increases the dimensionless forces, whereas further increase in hw/ht from 1.2 to 1.4 decreases the same for all the seaside perforated SBWs and hence hw/ht = 1.4 is not recommended. The seaside perforated SBW with 11% perforations is recommended for intermediate water depth conditions with the total height of breakwater equal to 0.83 times water depth to enable maximum energy dissipation resulting lesser pressures and forces on a structure or harbor on its leeward side.
The results reported in this study are a part of a joint research project between Indian Institute of Technology Madras, India and University of Leipzig, Germany. The writer is thankful to the Collaborating Institutes German Society for Technology Cooperation, Germany for the financial assistance and IIT Madras, India for the experimental facilities provided to carry out experimental investigations. Author is very much grateful to the management of SASTRA University for the sponsorship and the financial assistance during tenure of the research work.
NOTATIONS
a | = | Radius of semicircular breakwater |
Fh | = | Horizontal force |
Fv | = | Vertical force |
hw | = | Water depth |
hw/L | = | Relative water depth |
hs | = | Height of semicircular caisson |
hr | = | Height of rubble mound |
ht | = | Total height of the model |
Hi | = | Incident wave height |
Ht | = | Transmitted wave height |
k | = | Wave number = 2π/L |
ka | = | Scattering parameter |
Kr | = | Reflection coefficient |
Kt | = | Transmission coefficient |
Kl | = | Loss coefficient |
l | = | Width of the model across the flume |
L | = | Wavelength |
T | = | Wave period |
x12, x13 | = | Distance between wave gauges |
X | = | Horizontal force component in the direction of wave propagation |
Y1,Y2 | = | Force components rectangular to X component |
Z1,Z2,Z3 | = | Vertical components of force |
γ | = | Specific weight of water |
ABBREVIATIONS
SBW | = | Semicircular breakwater |
SBW0 | = | Semicircular breakwater with no perforations |
SBW7 | = | Semicircular breakwater with 7 percentage perforation ratio on its seaside |
SBW11 | = | Semicircular breakwater with 11 percentage perforation ratio on its seaside |
SBW17 | = | Semicircular breakwater with 17 percentage perforation ratio on its seaside |
SBWf7 | = | Fully perforated semicircular breakwater with 7 percentage perforation ratio |
SBWf11 | = | Fully perforated semicircular breakwater with 11 percentage perforation ratio |
SBWf17 | = | Fully perforated semicircular breakwater with 17 percentage perforation ratio |