Hydrodynamic studies on vertical seawall defenced by lowcrested breakwater

This paper presents results obtained from a series of experiments conducted in wave flume to assess the influence of the offshore lowcrested breakwater as a defence structure in reducing the wave forces on vertical seawall. The main aim of the tests was to know the effect of crest elevation of the offshore lowcrested breakwater as a rehabilitation structure for the existing damaged shore protection structures. In this study five relative breakwater heights are used and associated flow evolution was analyzed. With the sections proposed in this study, it is possible to achieve considerable reduction of wave force on the seawall. Modification factor is proposed to estimate the shoreward force on the seawall defenced by lowcrested breakwater.

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/237227831 Wave pressure reduction on vertical seawalls / caissons due to an offshore breakwater Article in Indian Journal of Geo-Marine Sciences · December 2004 DOI: 10.1115/OMAE2003-37074 CITATIONS READS 329 2 authors, including: Subramaniam Neelamani Kuwait Institute for Scientific Research 92 PUBLICATIONS 590 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Environmental& Economic values of native life View project All content following this page was uploaded by Subramaniam Neelamani on 01 December 2014 The user has requested enhancement of the downloaded file ARTICLE IN PRESS DTD Ocean Engineering xx (xxxx) 1–18 www.elsevier.com/locate/oceaneng Note 11 12 M.G Muni Reddya, S Neelamanib,* 14 15 a Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036, India Coastal Engineering and Air Pollution Department, Environmental and Urban Development Division, Kuwait Institute for Scientific Research, P.O Box 24885, 13109 Safat, Kuwait b 16 Received 21 January 2004; accepted July 2004 17 18 23 24 25 26 27 28 29 30 31 D This paper presents results obtained from a series of experiments conducted in wave flume to assess the influence of the offshore low-crested breakwater as a defence structure in reducing the wave forces on vertical seawall The main aim of the tests was to know the effect of crest elevation of the offshore low-crested breakwater as a rehabilitation structure for the existing damaged shore protection structures In this study five relative breakwater heights are used and associated flow evolution was analyzed With the sections proposed in this study, it is possible to achieve considerable reduction of wave force on the seawall Modification factor is proposed to estimate the shoreward force on the seawall defenced by low-crested breakwater q 2005 Published by Elsevier Ltd TE 22 EC 21 Abstract R 19 20 Keywords: Low-crested breakwater; Shoreward force; Overtopping; Submerged breakwaters; Seawall; Modification factor R 32 39 40 41 42 43 44 45 C 38 N 37 Coastal erosion is one of the challenging coastal engineering problems faced by human being around the world This calls for the proper remedial measures to protect valuable properties situated along the coast Many seawalls and vertical caisson breakwaters (CIRIA, 1986b; Oumeraci, 1994) around the world are being damaged Such failures are U 35 36 Introduction O 33 34 PR 13 O O 10 Hydrodynamic studies on vertical seawall defenced by low-crested breakwater * Corresponding author Tel.: C965 483 6100x5351; fax: C965 481 5192 E-mail addresses: reddy_muni@hotmail.com (M.G Muni Reddy), nsubram@kisr.edu.kw (S Neelamani) 0029-8018/$ - see front matter q 2005 Published by Elsevier Ltd doi:10.1016/j.oceaneng.2004.07.008 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 O O 58 PR 56 57 D 55 TE 54 EC 53 R 52 R 51 O 50 C 48 49 mainly caused by extreme wave actions, through displacement of the entire structure, or progressive failure starting from locally weak point, or through overall foundation failures, or through overtopping and toe erosion It may be economical to allow the less frequent storm wave to spill over the crest of the seawall rather than to its full height to reflect fully all the waves The disadvantage, however, is that overtopping waves plunge over the crest and inundates lee side leading to high economical loss The need for force reduction on these structures to increase the life span has resulted in different force reduction techniques like, introduction of porosity at the front face of the caisson, slotted seawalls, construction of horizontally composite caissons and construction of low-crested caissons etc Introduction of porosity into the structure leads to reduction of the strength of the structure Construction of horizontally composite structure in dynamic environment is risky Low-crested breakwater attracts lesser forces but the overtopping of waves create significant disturbance on the lee side These drawbacks can be overcome by constructing a low-crested breakwater in front of these structures to reduce the incident wave energy levels The offshore breakwater can be constructed after installation of caisson without much risk for floating vessels and caisson For existing weak or damaged structures construction of a protection structure such as submerged offshore breakwater is relatively an easy task Submerged breakwaters with deeper submergence would give larger wave energy transmission, which might eventually lead to failure in sheltering function of the breakwaters Therefore how to reduce the incident wave energy levels becomes a great challenge for coastal engineers In the present study an offshore low-crested rubble mound breakwater is considered as a defence structure to reduce the incident wave energy levels that reach the vertical impervious structure viz., seawall/caisson This type of protection can also be used in situations wherein it is required to reduce the wave forces to enhance the functional life of protection structures that are damaged by extreme wave forces, as a rehabilitation structure A theoretical analysis of the present problem is cumbersome Due to the complexity of the physical processes at the submerged breakwaters, physical modeling is necessary to define the site-specific interactions between the structure and the local wave climate The defence structure may become submerged or emerged during the tidal variation Low-crested rock structures can be classified (van der Meer and Daemen, 1994) as dynamically stable reef breakwaters, statically stable low-crested breakwaters and statically stable submerged breakwaters A reef breakwater is low-crested homogenous pile of stones without a filter layer or core and is allowed to be reshaped by wave attack (Ahrens, 1987) Statically stable low-crested breakwaters are close to non-overtopping structures, but are more stable due to the fact that large part of the wave energy can pass over the breakwater (Powell and Allsop, 1985) All waves overtop statically stable submerged breakwaters and the stability increases remarkably if the crest height decreases Submerged breakwaters have been widely used as wave energy dissipaters Efficiency of the submerged breakwaters depends on the crest free board, crest width and permeable material characteristics Many investigators like Newman (1965); Dick and Brebner (1968); Dattatri et al (1978); Losada et al (1997), have studied the wave transmission and reflection characteristics The stability and wave transmission characteristics of N 47 U 46 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 O O 93 94 the low-crested rubble mound breakwaters were investigated by Allsop (1983); Ahrens (1989); van der Meer and Pilarczyk (1990); van der Meer and d’Angremond (1991); Seabrook and Hall (1998), and Yamashiro et al (2000) and, the design formulae were developed by van der Meer and Daemen (1994) by analyzing the data sets of various investigations Behavior of the deeply submerged breakwaters with multi vertical sliced permeable structure was investigated by Twu et al (2000) Based on the monitoring results of a submerged breakwater and resulted model studies, Dean et al (1997) have reported that detached breakwater modifies both the wave and current fields depending substantially on the crest elevation relative to the still water level However, not much study on the present topic except the work by Gonzleg Madrigal and Olivares Prud’homme (1990) on the reduction of forces on vertical breakwater defenced by seaward submerged breakwater For partial barrier of any configuration, irrespective of the porosity and flexibility, full reflection always occurs when the distance between the end-wall and the barrier is an integer multiple of half-wave length and hence overturning and moment will vanish (Yip et al., 2002) Many investigators have studied analytically and numerically the wave transmission and reflection characteristics of the submerged breakwaters Yet these mathematical models cannot reproduce some of the features observed such as strong mean water level gradients on the submerged breakwater, pumping effect of the submerged breakwater and vertical circulation induced by breaking waves on the submerged breakwater PR 92 D 91 113 Experimental procedure and investigation 115 120 121 122 EC 119 Experiments have been carried out in a 30 m length m wide and 1.7 m deep wave flume at Indian Institute of Technology Madras, Chennai, India Seawall was fixed (Fig 1) over a six-component force balance (GmbH R67) Top level of the force balance is flushed with the flume bed The sensitivity of the transducers (strain gauge type) of six-component force balance at rated loading is about G2 mV/V Force balance consists of a stainless steel platform 850!850 mm size, below which force transducers were fixed to a rigid frame of 900!900 mm2 This frame was R 117 118 R 116 123 O 124 C 125 126 127 131 132 U 130 N 128 129 TE 112 114 133 134 135 Fig Experimental set-up for the present study OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 O O 140 PR 138 139 tightly fixed to the flume sidewalls to arrest the movement of force balance Seawall model was mounted on top of the steel platform so that the force on the seawall will be transferred to the transducers The height of the seawall model was fixed based on the theoretically estimated maximum run-up over the seawall, to ensure no overtopping of waves Crest width of the offshore low-crested breakwater was chosen as 0.40 m The stable weight of the armour unit of the breakwater was estimated by using the van der Meer (1987) formulae for statically stable low-crested and submerged breakwater Here our aim was not the damage of the low-crested breakwater, so a stable armour weight was used Breakwater was constructed with two layers, an armour layer and core Weight of the armour stone was 14.70–19.62 kN [This was arrived at for the inputs significant wave height ‘Hs’Z0.29 m, zero crossing period ‘Tz’Z3.0 s, damage level ‘S’Z2, number of waves ‘N’Z3000 and gsZ 26.5 kN/m3 for plunging breaking] The weight of the core stone was 1.96–2.45 kN (gsZ29.5 kN/m3) Five crest level configurations (two emerged, two submerged and one at still water level) were used in this study A stable slope of 2H:1V was adopted as the effects of breakwater slope on the wave transformation were found to be relatively unimportant (Seabrook and Hall, 1998) Ratio of the breakwater height to water depth h/d is varied from 0.66 to 1.33, keeping the water depth ‘d’ constant at 0.30 m and varying the height of the breakwater, ‘h’ from 0.20 to 0.40 m with 0.05 m increment This simulates the investigation on site where the tidal fluctuations are insignificant Two pool lengths, Lp (Lp is the distance between the toe of the lowcrested breakwater and seawall, Fig 1) 0.50 and 1.0 m were used D 137 158 159 2.1 Data collection and analysis procedure 160 166 167 168 169 170 171 EC R 165 R 164 O 162 163 The wave synthesizer (WS4) involving an application software package, along with analogue-digital and I/O modules installed in personal computer was employed in the measurement and analysis The software is capable of controlling the wave paddle and at the same time acquires data from sensors used in the tests The force balance transducers are connected to the data acquisition system through carrier frequency amplifiers Each set of data for regular wave was sampled at frequency of 40 Hz The filtered signals are analyzed using the wave synthesizer It contains the options for synthesis of regular and random 2D waves Regular waves of different predetermined wave period and wave amplitude combinations are generated for the testes The horizontal force (force in the direction of wave propagation), vertical force on the seawall, run-up on the wall and wave elevations in front of the model were acquired C 161 172 175 176 177 178 179 180 N 174 2.1.1 Range of inputs Relative wave height, Hi/d Relative depth, d/L Wave steepness, Hi/L Relative breakwater height, h/d Non-dimensional pool length, Lp/L Relative breakwater width, B/d U 173 TE 136 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 0.15–0.51 0.025–0.192 0.003–0.058 0.66–1.33 0.035–0.641 1.33 Here L is the deep-water wavelength and Hi is the incident wave height OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 O O 188 PR 187 D 186 TE 185 EC 183 184 2.1.2 Data analysis The data collected were converted to physical variables by using the corresponding calibration constants/coefficients The raw data (in the form of time series) were analyzed in time domain to get the clear understanding of the phenomenon under investigation The measured wave height, wave periods and forces were obtained by analyzing the measured time histories of wave surface elevations and force amplitudes using the thresholdcrossing analysis The threshold-crossing option is a generalization of classical zerocrossing analysis For a pre-defined reference level, the input time series is divided into events For each event, the peak–peak value, the minimum and maximum values, and the duration are determined The time series of the different parameters stated earlier were viewed to pickup the part of time series with regular trend by omitting the transient part This also ensures that no rereflected waves were present in the selected window of the time series The regular time series of force was then subjected to threshold-crossing analysis to get the mean amplitude of the time history The mean of the all amplitudes above the reference level in a time series is taken as a positive or shoreward force Similarly mean of all the amplitudes below the reference level on a time series is taken as negative or seaward force The mean amplitudes of measured hydrodynamic force were obtained using the above procedure for each test run ½F x Šshore is the ratio of shoreward force in the direction of wave propagation in the absence of the low-crested breakwater to shoreward force in the direction of wave propagation in the presence of low-crested breakwater ½F x Šsea is the ratio of seaward force in the direction opposite to wave propagation in the absence of the breakwater to the seaward force in the direction opposite to wave propagation in the presence of the breakwater These forces are obtained using procedure for the respective case of with and without low-crested breakwater Incident wave elevations are measured using DHI capacitance wave gauges in the absence of model in the flume, for pre-determined sets of different wave period and wave height combinations This procedure is repeated thrice and the average value is taken for the wave height for that particular combination It is done with a view to check the repeatability of wave heights at the same point later when tests are conducted with the model in position R 182 R 181 213 O 214 Results and discussion 217 3.1 General 221 222 223 224 225 The non-breaking wave forces on seawalls are pulsating A substantial portion of the horizontal momentum of the wave is imparted to the wall Methods to calculate the wave forces for simple vertical structures and pulsating wave conditions are relatively well established and are described by Goda (1985) According to Goda (1985) U 220 N 218 C 215 216 219 Fh Z 0:5ðp1 C p2 Þh C 0:5ðp1 C p4 ÞhÃc OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 (1) ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 p1 Z 0:5ð1 C cos bÞða1 C a2 cos2 bÞrw gHmax (2) 228 229 p2 Z p1 =ẵcosh2ph=Lị (3) 230 p Z a p1 (4) 226 227 231 ( 232 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 O O PR 243 D 242 TE 241 p1mod Z 0:5ð1 C cos bÞa1 rw gH Fhmod Z 0:5ðp1mod C p2mod Þh C 0:5ðp1mod C p4mod ÞhÃc EC 240 where Fh, total horizontal force per meter length of the wall/caisson; hb, water depth at a location at a distance of 5H1/3 seaward of the breakwater; a2, pressure coefficient (varies from to 1.0); b, angle between the direction of wave approach and a line normal to the breakwater; d, depth above the armour layer of the rubble foundation; hc, crest elevation of the breakwater above the bottom of the upright section; h*, elevation at which the wave pressure exerted; hÃc , min{h*, hc}; Hmax, maximum or design wave height p1, p2, p3 and p4 are the representative wave pressure intensities Pressure coefficient a2 represents the tendency of the pressure to increase with the height of the rubble mound foundation The coefficient a2 (Eq (6)) becomes zero, as hb and water depth d are the same in the present study Hence the Eqs (1) and (2) can be written as (7) (8) p1mod is less than p1 in Eq (2) because of additive term a2 cos2 b vanishes From Eqs (3) and (4) it can be observed that the magnitude of p2 and p3 reduces hence horizontal force Fh in Eq (8) The measured shoreward forces (without breakwater) are compared (Fig 2) with Eq (8) for validation of the present shoreward force measurements The measured forces are more than the estimated forces Increase of wave pressure/force due to the presence of a rubble foundation may regarded as the result of the change in the behavior of wave from non-breaking to breaking although actual waves never exhibit such marked changes Most design methods for caisson and the other vertical wall concentrate on forces that act landward, usually termed as positive forces It has however, been shown that some breakwaters/walls failed by sliding or rotation seaward indicating that net seaward forces may indeed be greater than positive forces The time series of incident wave height and wave force on the wall for different relative breakwater height ‘h/d’ ratios are shown in Fig Quantitative reduction in force on the seawall with increased h/d is very clear The time series of wave forces on the seawall defenced by an low-crested breakwater show that the wave breaking on the breakwater generates high frequency waves on the lee side of breakwater, which results in irregular force time series consisting of superposition of fundamental wave R 239 (6) R 238 È É a2 Z ẵhb K dị=3hb Hmax =dị2 ; 2d=Hmax O 236 237 (5) : h à % hc C 235 p1 ð1 K hc =hÃ Þ : hà O hc N 234 p4 Z U 233 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 271 272 273 274 275 276 277 278 279 280 O O 281 282 283 285 Fig Comparison of non-dimensional shoreward force on vertical seawall with Goda’s (1974) formulae [dZ 0.30 m, Hi/dZ0.29K0.48] PR 284 286 287 293 294 295 296 297 298 299 300 301 302 D TE 292 EC 291 R 289 290 frequencies and the higher wave frequencies It would be worth mentioning at this point, the effect of wave set-up or pumping effect (Drei and Lamberti, 2000) or the piling-up (Diskin, 1970) of water behind the protected area creates a difference in mean water level inside the protected area and that of open sea This component is inherent in the time series shown in the Fig It is difficult to quantify this component in the force measurement, because the force balance measures total effect For laboratory measurements this effect is unavoidable due to the fact that the water will confine between the sidewalls of the flume and between two structures and there will be very little scope for water to escape In the field situations, in open sea this effect will not be of much significant as there will be sufficient space for water to escape laterally between the two structures It should be noted that experiments were conducted in the two-dimensional flume, and thus the values of mean water levels may be overestimated in comparison with the values of mean water levels in three-dimensional wave field About 14% deviation observed from the forces estimated by Eq (8) and the forces measured from the experiments R 288 303 308 309 310 311 312 313 314 315 O C 307 Fig provides the effect of h/d on fore ratio ½F x Šshore for different incident wave steepness Force ratio 1.0 means that the breakwater has no effect on the reduction of forces on the caisson and zero means 100% protection of the caisson by low-crested breakwater The value of force ratio lies in-between zero and 1.0 Oscillatory nature of force ratio ½F x Šshore is observed when the h/d is varied from 0.66 to 1.33 The amplitude of the oscillation decreases with increase of h/d The high value of force ratio for h/dZ0.83 is due to wave jetting on the seawall after overtopping over the low-crested breakwater This increased force is unwarranted for the general presumption that as the barrier height increases force will have to decrease correspondingly Designers and N 305 306 3.2 Effect of relative height of the breakwater, h/d on the normalized wave forces on the seawall U 304 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 316 317 318 319 320 321 322 323 324 325 O O 326 327 328 329 PR 330 331 332 333 D 334 335 336 TE 337 338 339 340 EC 341 342 343 344 R 345 346 R 347 348 Fig Typical force time series for different relative breakwater height h/d [HiZ0.152 m, dZ0.3, d/LZ0.059, B/dZ1.33, Lp/LZ0.071–0.64] C 350 351 O 349 352 353 356 357 358 359 360 coastal engineers should take care of this while decision making in choosing the range h/d values For h/dO1.0, the wave energy is effectively dissipated which result in significant wave force reduction on the seawall When h/dZ1.0, the reduction in average shoreward or positive force is 66% (standard deviation is 0.097) as Hi/L is varied from 0.003 to 0.058 for the range of Lp/LZ0.035–0.321 Percentage decrease in the magnitude of peaks of force ratio is ½F x Šshore found to increase with h/d The following wave-structure interaction processes were identified during the experimental N 355 U 354 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 361 362 363 364 365 366 367 368 369 370 O O 371 372 373 374 376 377 PR 375 Fig Variation of shoreward force ratio with relative reakwater height h/d for three different wave steepness [Lp/LZ0.198, B/dZ1.33, d/LZ0.059] 378 investigations, which are explained below for the type of normalized wave force trend observed: D 379 380 381 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 TE EC 389 R 387 388 R 386 O 385 C 384 (a) For offshore breakwater with more submergence (say h/dZ0.66), the wave transmit freely, reflects from the seawall These reflected waves contribute significantly for the amplification of waves and the corresponding wave forces on the seawall/ caisson (b) For offshore breakwater with smaller submergence (say h/dZ0.83), the propagating wave on the breakwater attains the characteristics of wave breaking and the overtopping jet of mass acts on the seawall/caisson resting behind the breakwater and imparts higher order of forces (c) For the case of offshore breakwater with crest level flushing with still water level (h/dZ1.0), most of the interacting energy is expected to be dissipated on the crest of the breakwater and hence the wave force reduction is significant (d) For the offshore breakwater with less emergence i.e crest located just above the still water level (here h/dZ1.16), the dominant mode of wave transmission is by run-up and overtopping and the efficiency of transmission process increase as wave height increases The energy available with this overtopping water mass imparts forces on the seawall The wave energy dissipation due to the interaction with the breakwater reduces to the significant overtopping processes (e) For the offshore breakwater with significant emergence of the crest (h/dZ1.33), overtopping will be prevented for most of the waves and the waves may be allowed to transmit through the pores of the breakwater The energy available with this transmitted wave imparts forces on the rear side structures N 383 U 382 A through analysis of Fig with this understanding gives a clear answer why a force ratio variation is oscillatory with increased h/d It was observed that the force ratio at any OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 10 407 408 409 Table Measured mean force ratios for two pool lengths h/d Lp/LZ0 035–0 32, Hi/ LZ0 003–0.09 ½F x Šshore Standard deviation ½F x Šsea Standard deviation Lp/LZ0 071–0 641, Hi/ LZ0 003–0.09 ½F x Šshore Standard deviation ½F x Šsea Standard deviation 1.33 1.16 1.00 0.83 0.66 0.17 0.31 0.33 0.63 0.55 0.066 0.069 0.097 0.113 0.108 0.25 0.35 0.39 0.62 0.56 0.106 0.106 0.110 0.180 0.110 0.20 0.34 0.31 0.52 0.48 0.08 0.12 0.09 0.16 0.12 0.29 0.46 0.43 0.64 0.60 0.15 0.18 0.15 0.13 0.13 410 411 412 413 414 415 416 417 418 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 PR D 426 TE 424 425 EC 423 R 422 R 421 h/d is the minimum when the waves acting on the system are steeper This point must be given due attention, since the design is carried out for steeper waves The results plotted in Fig are typical for a d/L value of 0.058 The results for the other values were also observed to follow the same trend In order to bring out the cumulative effect of range of heights and periods used in the study, a table containing the force ratio information is prepared Table is provided to visualize the force ratio for two pool lengths and for a wide range of wave steepness Both shoreward and seaward force ratios are provided in the table The mean and the standard deviation of the wave force ratios are tabulated Mean of the shoreward force amplitude and seaward force amplitude and the corresponding standard deviations are provided in this table For example, the shoreward force ratio value for h/dZ1.33 is given as 0.17, which is the average value for a number of wave heights and periods The standard deviation for this set is 0.066 (i.e., the ratio of standard deviation and the average is about 38.8%) This table is mainly provided for an overall understanding of the effect of pool length and relative height of the breakwater on wave force reduction on the seawall From this table it is clear that the shoreward force ratio for the case of smaller pool length (Lp/ LZ0.035–0.32), is from 0.17 to 0.55 when h/d is varied from 1.33 to 0.66 This means that the mean wave force reduction of the order of 83–45% is possible for this case For the large pool length ratio (Lp/LZ0.07–0.64), the shoreward force ratio ranges from 0.2 to 0.48 for the same range of h/d The seaward force ratio is ranging from 0.29 to 0.60, which is significantly higher than the shoreward force ratio The average value of force ratio along with the standard deviation can be used for the selection for appropriate vale of h/d O 420 C 419 442 445 446 447 448 449 450 N 444 3.3 Effect of wave period and wave height on wave force ratio Fig shows the effect of variation of wave period on shoreward force ratio The variation of wave period is presented in terms of relative water depth, d/L This plot is given for the case of larger pool length (Lp/LZ0.07–0.64), h/dZ1.0 and for three different range of wave heights in terms of relative wave heights, Hi/d The force ratio has oscillating character when the d/L changes from 0.021–0.192 Theoretical results of Yip et al (2002) on the interaction of wave on vertical walls U 443 O O 406 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 11 451 452 453 454 455 456 457 458 459 460 O O 461 462 463 464 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 PR D TE 473 EC 472 R 471 R 469 470 protected by a thin porous barrier also shows similar trend on wave reflection Since the wave reflection and wave forces are related, the present trend can say to be acceptable Also, it is to be noted that the response of the seawall depends entirely on the response of the pool, which is bounded by two bodies (wall and breakwater) Hence the pool is expected to resonate when situation arises In general, it is found that the force ratio is smaller for high waves compared to the wave of smaller heights This is due to the predominant wave breaking and the consequent dissipation of waves This sort of trend is good for the design of seawall/caisson, since the design is governed by high wave actions It is also reported that the wave damping effects of breakwaters increases with increasing wave steepness (Johnson et al., 1951) This phenomenon suggests the submerged breakwater behaves as a filter, attenuating steeper waves with higher energies The peak value of force ratio is about 0.4, which occurs at d/LZ0.083 For high waves, i.e., Hi/dZ0.45 this clearly proves that the force can be reduced to the order of 50% when h/dZ1.0 A cost estimate of the seawall without defence structure and that with defence structure and its comparison is required for finalizing the selection of the option with defence structure Further investigation and analysis is required in this direction Fig shows the variation of seaward or negative force ½F x Šsea ratio for the same input condition The trend of variation of force ratio is similar to that of Fig The difference is the maximum value of the force ratio, which is of the order of 0.8 for smaller Hi/d and is about 0.4 for higher Hi/d Fig is similar plot as shown in Fig 5, but for h/dZ0.66 Again the oscillating nature of wave force with increased d/L persists However, the major difference between the Figs and is the value of force ratio, which is about 0.5 for Hi/dZ0.45, whereas for the same condition with h/dZ1.0, the force ratio is only about 0.4 That means the force ratio has increased by an about 10% due to the submergence of the breakwater from h/dZ 1.0 to h/dZ0.66 Fig is a similar to Fig 6, but for h/dZ0.66 Here again it is found that O 468 C 467 Fig Variation of shoreward force ratio with relative water depth d/L [h/dZ1.0, B/dZ1.33, Lp/LZ0.071– 0.641] N 466 U 465 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 12 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 496 497 498 499 500 501 502 503 504 505 O O 506 507 508 509 513 514 515 516 517 518 PR 512 Fig Variation of seaward force ratio with relative water depth d/L [h/dZ1.0, Lp/LZ.071–0.641, B/dZ1.33] the maximum force ratio for Hi/dZ0.45 is about 0.7, compared to 0.4 for the same Hi/d for h/dZ1.0 Once the value of h/d is selected, one can select the value of force ratio for a given wave period and height The actual force acting on the seawall can now be estimated by multiplying the force ratio with the force on the seawall without defence structure D 511 TE 510 519 521 522 523 524 3.4 Influence of pool length (Lp) on wave forces on the seawall defenced by low-crested breakwater EC 520 Some of the hydrodynamic phenomena found in the area between the breakwater and seawall are wave height and period evolution, wave reshaping and possible R 525 526 R 527 528 O 529 C 530 531 532 535 536 537 538 539 540 U 534 N 533 Fig Variation of shoreward force ratio with relative water depth d/L [h/dZ0.66, Lp/LZ0.071–0.641, B/dZ 1.33] OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 13 541 542 543 544 545 546 547 548 549 550 O O 551 552 553 554 Fig Variation of seaward force ratio with relative water depth d/L [h/dZ0.66, Lp/LZ0.071–0.641, B/dZ1.33] PR 555 556 561 562 563 564 565 566 D 559 560 wave breaking, interference with waves reflected from seawall Wave reflection and re-reflection between the caisson and breakwater depends on distance between the barrier and end wall is called pool length and this is required for effective location of offshore breakwater A typical plot Fig shows the effect of relative pool length, Lp/L on wave forces In general, we have the wave force reduces to the extent of 10–30% when then relative pool length is reduced from 0.16 to 0.08 It is to be recalled that in the real field situation, it is always better to place the breakwater closer to the seawall, since the water depth is expected to be small and hence the quantity of stones required for TE 558 EC 557 567 568 569 R 570 571 R 572 573 O 574 C 575 576 577 580 581 582 583 584 585 U 579 N 578 Fig Effect of pool length (Lp) on shoreward force with relative Breakwater height, h/d [B/dZ1.33, Hi/LZ0.015 and d/LZ0.048] OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 14 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 586 587 588 589 590 591 592 593 594 595 O O 596 597 598 599 604 605 606 607 608 609 610 611 612 613 614 the construction will be less, which will be economical Fig is only typical plot for one wave height and period In order to zero down to the cumulative effect of pool length, Fig 10 is plotted by keeping the force ratio on the x-axis and cumulative probability of force ratio on y-axis for two pool lengths In this plot all the ranges of wave heights, wave periods and relative breakwater heights of the present study are considered From this plot, it is found that 2% exceedence value of force ratio is 0.75 for Lp/LZ0.035–0.32 and 0.78 for Lp/LZ0.07–0.64 D 603 Fig 10 Cumulative probability of shoreward force ratio ½F x Šshore for different relative breakwater heights (h/dZ 0.66–1.33, including all wave heights and wave periods which are used for the investigation, thick line for Lp/LZ 0.071–0.641 and dotted line for Lp/LZ0.035–0.32 TE 602 3.5 Probability analysis on force ratio 620 621 622 623 624 625 626 627 628 629 630 R O 619 C 618 N 617 The probability of non-exceedence of force ratio ½F x Šshore for all wave heights (Hi/dZ0.15–0.51) and wave periods T(d/LZ0.021–0.192) is given in Fig 11 The value corresponding to 98% non-exceedence (2% exceedence) can be taken for the purpose of design of the seawall It is seen that when the seawall is defenced by the breakwater, 2% exceedence value of ½F x Šshore is 0.71, 0.81, 0.42, 0.38 and 0.29 when h/dZ0.66, 0.83, 1.0, 1.16 and 1.33, respectively, for Lp/LZ0.035–0.32 This clearly brings out the relative benefit of increasing the height of breakwater for the purpose of reduction of wave loads on the seawall It is also clear that one has to avoid h/d around 0.83, which induce plunging breaking over the breakwater and causes more force than the case for h/dZ0.66 Fig 12 shows the shoreward force ratio for 2% exceedence against h/d for the two pool lengths studied This is simple and consolidated plot but can be used reliably by the coastal community for the design of seawalls A cost benefit analysis is required to select a suitable h/d value It is to be remembered that if h/d is increasing the force ratio on the seawall will reduce, which will result in economic design of seawall but the cost of U 616 R 615 EC 601 PR 600 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 15 631 632 633 634 635 636 637 638 639 640 O O 641 642 643 644 646 Fig 11 Cumulative probability of shoreward force ratio ½F x Šshore for different relative heights (h/dZ0.66–1.33) of breakwater [Lp/LZ0.035–0.32] PR 645 647 649 650 defence structure will increase with increase in h/d Further optimization study for a typical site will be helpful for the user D 648 651 3.6 Modification factor (Sn) for shoreward force TE 652 653 655 656 657 658 Modification factor is proposed to estimate the shoreward force on the seawall defenced by low-crested breakwater After analyzing the influence of the non-dimensional parameters on shoreward force a modification factor (Sn) is derived from a non-linear optimization algorithm Modification factor is the ratio of shoreward force on the wall EC 654 659 R 660 661 R 662 663 O 664 C 665 666 667 670 671 672 673 674 675 U 669 N 668 Fig 12 2% non-exceedence of shoreward force ratio with relative breakwater height h/d for two pool lengths [Lp/LZ0.035–0.32 and Lp/L 0.071–0.64] OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 16 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 676 677 678 679 680 681 682 683 684 685 O O 686 687 688 689 Fig 13 Comparison of observed and predicted modification factor for different wave periods and wave heights PR 690 691 696 697 698 699 700 701 702 703 ½Fx Šshore Z Sn ẵFx Goda (9) ẵSn shore Z 0:1h=dịK0:41 Hi =dÞK0:60 ðLp =LÞK0:40 R 705 Concluding remarks 708 714 715 716 717 718 719 720 O C 713 N 712 Measurements of wave elevations and forces on the structures reveal that the flow behavior changes depending on the relative height of the breakwater for a given water depth, resulting in five characteristic phases: freely transmitting wave, overtopping, crest dissipation, predominant wave breaking and transmission over the breakwater as the breakwater crest level reduces form emergent to submerged Relative height of the breakwater, h/d, associated with the formation of standing wave and resonant conditions between the structures, is found to be important parameters for the oscillatory behavior of the force ratios, which also depends on wave period Average shoreward force ratio ½F x Šshore is more for h/dZ0.83 when compared to h/dZ0.66 for the range of pool length chosen in the experimental investigation This was not expected because as the relative breakwater height increases force ratio decreases, but the reason for such peculiar behavior is found out based on the experimental observations U 710 711 R 706 709 (10) Fig 13 shows the comparison of observed and measured modification factor This factor is more sensitive to relative breakwater height, h/d In the above equation Lp/L is influence of the wave period since Lp has taken as constant and, also decides the offshore location of the low-crested breakwater As shown in Fig force ratio increases at h/dZ0.83, but in the Fig 13 the modification factor is not depicting same trend because of combined influence of the other non-dimensional parameters Scatter in the points includes the same inherent error in measurement of force as explained in the Fig 704 707 D 694 695 TE 693 (with low-crested breakwater) to force estimated from Goda formulae (Eq (8)) EC 692 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 722 723 724 725 726 727 728 729 730 731 732 Amplitudes of the force ratio decrease with increase in relative breakwater height and relative water depth Force ratios are small for steeper waves as the damping effect of breakwater increases for steeper waves due to depth limited breaking over submerged breakwater Influence of the pool length on reduction of force ratios is observed to be small (to the order of 5–10%) for two different ranges studied This needs investigation for more pool lengths to substantiate further Finally a modification factor is presented to estimate the shoreward force on the vertical structure defenced by an offshore low-crested rubble mound breakwater The results of this study can be used for rehabilitating the partially damaged seawalls and caissons or for the design of new seawall and caissons with offshore breakwater as a defence structure A cost benefit analysis by using the present results is required to select the optimum h/d values O O 721 733 734 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 PR D TE 743 EC 742 R 741 R 739 740 Ahrens, J.P., 1987 Characteristics of reef breakwaters Technical Report CERC-87-17, Vicksburg Ahrens, J.P., 1989 Stabilty of reef breakwaters J WW, Port, Coastal Ocean Eng 115 (2), 221–234 Allsop, N.W.H., 1983 Low-crested breakwaters, studies in random waves, Proceedings of Coastal Structure 1983, Arlington, Virginia 1983 pp 94–107 CIRIA, 1986b Sea walls: survey of performance and design practice CIRIA (Construction Industry Research and Information Association), London, Technical Note 125 Dattatri, J., Raman, H., Shankar, J.N., 1978 Performance characteristics of submerged breakwaters Proc 16th ICCE, ASCE 1978;, 2153–2171 Dean, R.G., Renjie Chen, Browder, A.E., 1997 Full scale monitoring study of a submerged breakwater, Palm Beach, Florida, USA Coastal Eng 129, 291–315 Dick, T.M., Brebner, A., 1968 Solid and permeable submerged breakwaters Proc 11th Conf Coastal Eng., ASCE 1968;, 1141–1158 Diskin, M.H., 1970 Piling-up behind low and submerged permeable breakwaters J WW Harbour Division, ASCE, WW2 96, 359–372 Drei, E., Lamberti, A., 2000 Wave pumping effect of a submerged barrie, Coastal Structures 99, vol 2000 pp 667–673 Goda, Y., 1985 Random Seas and Design of Maritime Structures University of Tokyo Press, Tokyo, Japan Gonzleg Madrigal, B., Olivares Prud’homme, J., 1990 in: Edge, Billy L (Ed.), Reduction of wave forces and overtopping by submerged structures in front of a vertical breakwater Coastal Engineering Proceedings, vol I and II, pp 1349–1361 Johnson, J.W., Fuchs, R.A., Morison, J.R., 1951 The damping action of submerged breakwaters Trans Am Geoph Union 32 (5), 704–717 Losada, I.J., Patterson, M.D., Losada, M.A., 1997 Harmonic generation past a submerged porous step Coastal Eng 31, 281–304 Newman, J.N., 1965 Propagation of water waves past long two-dimensionalobstacles J Fluid Mech., Cambridge, UK 23, 23–29 Oumeraci, H., 1994 Review and analysis of vertical breakwater failures—lessons learned Coastal Eng 22, 3–29 Powell, K.A., Allsop, N.W.H., 1985 Low-crested breakwaters, hydraulic performance and stability Report SR 57, HR Wallingford, England Seabrook, S.R., Hall, K.R., 1998 Effect of crest width and geometry on submerged breakwater performance 26th Int Conf Coastal Eng., Copenhagen, Denmark 1998;, 144–145 Twu, S.W., Liu, C.C., Hsu, W.-H., 2000 Wave damping characteristics of deeply submerged breakwaters J WW, Port, Coastal Ocean Eng 127 (2), 97–105 van der Meer, J.W., 1987 Stability of breakwater armour layers—design formulae Coastal Eng 11, 219–239 O 738 C 737 References N 736 U 735 17 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 ARTICLE IN PRESS DTD 18 766 767 768 769 770 771 772 773 M.G Muni Reddy, S Neelamani / Ocean Engineering xx (xxxx) 1–18 van der Meer, J.W., Daemen, I.F.R., 1994 Stability and transmission at low-crested rubble mound structures J WW, Port, Coastal Ocean Eng 120 (1), 1–19 van der Meer, J.W., d’Angremond, K., 1991 Wave transmission at low-crested structures, Coastal structures and breakwaters, ICE, Coastal structures and breakwaters, ICE 1991 pp 25–41 van der Meer, J.W., Pilarczyk, K.W., 1990 Stability of low-crested and reef breakwaters Proc 22th ICCE, ASCE 1990;, 1375–1388 Yamashiro, M., Yoshida, A., Irie, I., 2000 Experimental study on wave field behind a submerged breakwater., Coastal Structures 1999 Balkema, Rotterdam pp 675–682 Yip, T.L., Sahoo, T., Chwang, A.T., 2002 Trapping of surface waves by porous and flexible structures J Wave Motion 35, 41–54 774 775 O O 776 777 778 779 PR 780 781 782 783 D 784 785 786 TE 787 788 789 790 EC 791 792 793 794 R 795 796 R 797 798 O 799 C 800 801 802 N 803 804 806 807 U 805 808 809 810 OE 926—15/11/2004—12:42—ADMINISTRATOR—125109—XML MODEL – pp 1–18 View publication stats ... the caisson, slotted seawalls, construction of horizontally composite caissons and construction of low-crested caissons etc Introduction of porosity into the structure leads to reduction of the... reduction of forces on vertical breakwater defenced by seaward submerged breakwater For partial barrier of any configuration, irrespective of the porosity and flexibility, full reflection always occurs... series of wave forces on the seawall defenced by an low-crested breakwater show that the wave breaking on the breakwater generates high frequency waves on the lee side of breakwater, which results