Reshaping berm breakwaters: A physical model study
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(2) JANARDHAN et al.: RESHAPING BERM BREAKWATERS. A review of the available literature underlines the potential advantage of berm breakwater over conventional breakwater and emphasizes the interest of the scientific community in developing a design procedure for the design of berm breakwater. The present paper focuses mainly on the stability of statically stable reshaping berm breakwaters with artificial armour units. The shape of armour units considered for present investigations is a cube. Cubes are selected because of its massive structure that satisfies the requirement of an armour unit. In addition, production of cubes is economical than other artificial armour units like Accropode and Core-loc11. The specific objectives of the present investigation are (1) to investigate the static stability of breakwater with reduced armour weights under varying wave climate (2) Study the effect of wave steepness on wave run-up and run-down (3) Estimate the damage in terms of berm recession. Materials and Methods An important and simple measure for the reshaping of a berm breakwater is the recession of the berm (Rec)12 (Fig. 1). Failure is typically defined as when RecB, where B is the berm width. Numerous empirical formulae are available to evaluate the recession of the berm7,13,14,15. In the present analysis, all of the listed simple regression models have been evaluated. Experimentally, recession was measured using a profiler system. The initial and final profile of the breakwater before and after the test was taken and plotted together to obtain the recession. Wave run-up (Fig. 2) is another important design criterion for several types of coastal structures such as revetments, breakwaters and dikes. Wave run-up is a phenomenon in which an incoming wave crest runs. Fig. 1 — Definition sketch of recession. Fig. 2 — Illustration of wave run-up and wave run-down 16. 1051. up along the slope up to a level that may be higher than the original wave crest. The vertical distance between SWL and the highest point reached by the wave tongue is called the run-up (Ru). Run-up can be indirectly used to estimate the risk of damage to the inner slope of the structure. Wave run-up can be evaluated by the equations in CEM16 developed by Waal and Van der Meer17. %. =. 1.5𝜉 𝛾 𝛾 𝛾 𝛾 = 1.5𝜉 𝛾 𝛾 𝛾 𝑓𝑜𝑟 0.5 < 𝜉 3.0𝛾 𝛾 𝛾 𝑓𝑜𝑟𝜉 > 2. ≤2 . … (3) Where, r = influence of surface roughness given in Table VI-5-3 of CEM, 2006. b = influence of berm 𝜉 𝛾 = = 1 − 𝑟 (1 − 𝑟 ) 0.6 ≤ 𝛾 ≤ 1.0 𝜉 𝑡𝑎𝑛𝛼 𝑑 𝑟 =1− , 𝑟 = 0.5 ,0 ≤ 𝑟 ≤ 1 𝑡𝑎𝑛𝛼 𝐻 h = influence of shallow water [16]. = influence of approaching wave angle [17]. Wave run-down (Rd) is defined as the vertical distance between the SWL and maximum down rush of the wave impinging on the structure. It is important from the structural stability point of view. If run-down is high, there may be chances of armour units being dragged down the slope which may reduce the stability of the structure. Equivalent surf similarity parameter (ξeq) can be calculated using the method explained in CEM16, for different wave heights and wave periods considered for the study. Following equation was used to estimate ξeq. tan eq … (4) eq Ho Lo The experiments were carried out in a long twodimensional wave flume. The waves were passed through a filter made up of thin parallel asbestos sheets placed at definite interval to produce smooth regular waves by reducing turbulence. Three wave probes installed in the flume, were used to measure the wave characteristics18. The experiment was then conducted for a specific storm duration. The data were recorded and used to analyze the influence of various non-dimensional parameters on the values of recession, wave run-up and wave run-down..
(3) 1052. INDIAN J. MAR. SCI., VOL. 47, NO. 05, MAY 2018. Fig. 3 — Definition of equivalent and average slope17. Fig. 4 — Longitudinal section through the experimental setup. The longitudinal section of wave flume facility is shown in Fig. 4. The wave flume is 50 m long, 0.71 m wide and 1.1 m deep. It has a 41.5 m long smooth concrete bed. It has a 6.3 m long, 1.5 m wide and 1.4 m deep chamber at one end where the bottom hinged flap generates waves. Gradual transition is provided between normal bed level and that of generating chamber by ramp. About 15 m length of the flume is provided with glass panels on one side to facilitate observations and photography. Spending beach consists of granite stones laid in 1:12 slope, which act as wave absorber behind the flap in the generating chamber. The wave generator system consists of a bottom-hinged flap, which is moved back and forth by induction motor of 11 kW, 1450 rpm. This motor is regulated by Kirloskar made inverter drive (0 to 50 Hz), to rotate with a speed range of 0 – 155 rpm. Regular waves of 0.08 m to 0.24 m heights and of periods 0.8 sec to 4.0 sec in a maximum water depth of 0.5 m can be generated with this facility. The choice of scale, for the model test, is often limited by constraints put by experimental facilities available. Within this constraint, an optimum scale should be selected by comparing the economies of the scale model with that of the experiment19,20. To simulate the field conditions of wave height, period and water depth, by the application of Froude's Law20, a geometrically similar scale of 1:30 was selected. This scale is within the scale selected for rubble mound breakwater model tests conducted in majority of the laboratories around the world and is good enough to give reasonable and satisfactory results compared to those of the prototype20.. Dimensional analysis is a rational procedure for combining physical variables into non-dimensional parameters, thereby reducing the number of variables that need to be considered. The non-dimensional quantities obtained from experiments may be easily correlated to the corresponding quantities in the prototype. The primary variables and the nondimensional parameters derived along with their range as applicable for the experimental study are given in Tables 1 and 2, respectively as shown below. The important non-dimensional input terms were selected based on the PCR analysis24. The berm breakwater of 0.45m wide berm was designed for significant wave height 0.10 m, with a uniform slope of 1V:1.5H above and below the berm. The weight of concrete cube armour unit (W) was determined using Hudson’s formula9. The mass density of the concrete armour unit was 24 kN/m3 and KD was 5.5. In the present study breakwater models with reduced armour weight were tested. The weights of armour were reduced by 25%, 40% and 50% of the weight obtained by Hudson formula. To attain the density of concrete, 20% by weight of sand was replaced by iron ore filings in 1:3 cement mortar with a water cement ratio of 0.4. The various structural parameters are tabulated in Table 3. The primary armour layer was divided into three zones; crest ward slope, berm and toe ward slope and the units in these regions were coloured as white, red and grey respectively to identify the movement of cube in each Table 1 — Primary variables considered for non – dimensional analysis Primary variables Wave height Wave period Water depth Storm duration Angle of wave attack Position of berm from sea bed. Symbol H T D N hb. Range 0.1 – 0.16 m 1.6 – 2.6 sec 0.30 – 0.45 m 3000 waves 900 0.45 m. Table 2 — Non – dimensional parameters along with their range Non- dimensional parameter. Symbol. Range. Period Stability number Stability number Relative berm position Relative wave steepness Relative wave run-up Relative wave run-down Dimensionless recession Relative recession. HoTo 61 – 194 Ns 2.2 – 4.0 hb/d 1.0 – 1.5 H/gT2 1.32*10-3 – 6.90*10-3 Ru/H – Rd/H – Rec/Dn50 – Rec/B –.
(4) 1053. JANARDHAN et al.: RESHAPING BERM BREAKWATERS. Table 3 — Structural parameters and their ranges Variable Slope Armor type Mass Density Armor cube weight. Expression. Size of armor cube. Dn50. Berm width Berm position from sea bed Crest width Crest height. B. Value 1V: 1.5H Concrete cube 2.4 g/cc 106, 79.5, 63.6, 53 g 0.0353, 0.0325, 0.0298, 0.0285 m 0.30, 0.35, 0.40, 0.45 m. hB. 0.45 m. ---. 0.10 m 0.70 m. -γr W50. (a). Fig. 5 — Berm breakwater model. region. Regarding the placement of the armour units, a casual placement of each individual cube was done to obtain fitted surface. Fig. 5 shows a model diagra diagram of berm breakwater. The wave flume was filled with fresh water to the required depths. Before the model was tested, the flume was calibrated to produce the incident waves of different combinations of wave heights and wave periods. Combinations that produced the secondary waves in the flume were not considered for the experiments. The wave probes were calibrated in the beginning and at the end of the each test run. Before starting the experiments the initial seaward profile of the breakwater was recorded using a surface profiler system. The probes kept on the seaside of model were used for acquiring incident wave characteristics. The wave run-up up and run run-down were measured over the breakwater on the graduated scale fixed over the glass panels of the flume. Occasionally, the wave heights were measured manually and were found ound to be tallying with the instrumental data. The stability of statically stable reshaping berm breakwater is defined based on the recession of the berm. The damage number is not considered since reshaping is allowed. Therefore, if recession is less than the berm width then the structure is safe. Further, the exposure of the secondary layer is also considered as damage to the structure.. (b). (c) 2. Fig. 6 (a) — (c) Effect of variation in Ho/gT on Rec/B, Ru/Ho and Rd/Ho with varying armour weights. Results and Discussion The experiments were conducted with reduction in primary armour weight by 25%, 40% and 50%. Effects of various parameters like relative wave steepness on berm recession, wave run-up run and wave run-down down are discussed separately in detail deta in the following sections. The effect of Ho/gT2 on Rec/B, Ru/Ho and Rd/Ho for a water depth of 0.40 m and berm width of 0.45 m (B/d = 1.13) are presented in Fig. 6 (a) – (c). The Rec/B increases with Ho/gT2. Short steeper waves dislocate the armour unit and subsequent wave will bring that armour unit down even before it settles back thus causing higher damage.
(5) 1054. INDIAN J. MAR. SCI., VOL. 47, NO. 05, MAY 2018. to the structure. Further, the short steeper waves are obstructed and broken efficiently by the berm and hence, the low wave run-up and run-down. In Fig. 6 (a) all the models with 25% (Wo =0.75W) and 40% (Wo =0.60W) reduced armour weight were found safe for all wave conditions. The model with 50% (Wo =0.50W) reduced armour weight was unsafe for many of wave conditions. Further, from Fig. 6 (b) and (c) it can be observed with the decrease in armour weight the wave run-up and run-down decreases with increase in Ho/gT2 and increased reduction of armour weight. The failure of the structure and increased runup and run-down for models with lighter armour weight is due to decrease in the porosity with smaller armour size. In addition, with the reduction in size, the armour units get packed closely decreasing the gap between the units and subsequently increasing run-up and run-down and reducing the wave energy dissipation. As 25% reduction (Wo = 0.75W) was found totally safe, same armour weight is maintained for further investigations. Effect of stability number (Ns) on Rec/B in water depth of 0.40 m and 25% reduced armour weight (Wo =0.75W) can be noticed in Fig. 7 (a). The effect of Ho/gT2 on Ru/Ho and Rd/Ho for the similar conditions considered above is shown in Fig. 7 (b) – (c). With the increase in Ns it is noticed that there is an increase in berm recession (Fig. 7 (a)). This increase is attributed to higher energy of the wave. In addition, from Fig. 7 (b) and (c) it is noticed that both wave run-up and run-down reduces with the increase in wave steepness. Same effect was also observed in Fig. 6 (b) and (c). The wave run-up and run-down ranges from 0.929 – 1.1235 and 0.752 – 1.085 for 0.40 m water depth respectively. The model with B/d = 0.75 (B = 0.30 m) for a wave period of 1.6 s and wave height of 0.16 m showed failure with (Rec/B) reaching a value of 1.0 as observed in Fig. 7 (a). All the other models were found safe (with Rec/B < 1) for the test conditions. It is also observed from Fig. 7 (b) and (c) that in all the cases wave run-up and run-down is low for higher berm width. Larger berm width reduces damage to the structure by absorbing most of the wave energy and helps in reducing run-up and run-down by acting as a “stilling basin”. A safe berm width (B) of 0.40 m is adopted for further studies. Influence of thickness of primary layer on berm recession, wave run-up and run-down. Effect of Ho/gT2 on Rec/B, Ru/Ho and Rd/Ho for a reduced armour weight of 0.75W, berm width and. (a). (b). (c) Fig. 7 (a) — (c) Effect of variation in Ns on Rec/B and Ho/gT2 on Ru/Ho and Rd/Ho for different berm widths. water depth of 0.40 m (B/d =1.00) with varying thickness of primary layer are illustrated in Fig. 8 (a) – (c). A slightly lower berm recession, a large reduction in wave run-up and small difference in run-down is observed for n = 3 when compared with that of n = 2. For both the layers, Rec/B is less than 1 for all the considered test conditions. Lower recession, wave run-up and run-down is due to the increase in the area available for dissipation of energy. A clear decreasing Ru/Ho and Rd/Ho with increasing Ho/gT2 can be observed in Fig. 8 (b) and 7 (c) respectively which is same as in the previous sections. With the increase in thickness of primary layer, there is about 11.6%, 4.1% and 1.5% reduction.
(6) 1055. JANARDHAN et al.: RESHAPING BERM BREAKWATERS. (a). (a). (b). (b). (c). (c) 2. Fig. 8 (a) — (c) Effect of variation in Ho/gT2 on Rec/B, Ru/Ho and Rd/Ho with varying thickness of primary armor layer. Fig. 9 (a) – (c) Effect of Ho/gT on Rec/B, Ru/Ho and Rd/Ho for varying water depths. in berm recession, wave run-up and run-down respectively. However, as the breakwater is safe for n = 2, it is recommended that only 2 layers be used for primary armour. The effect of Ho/gT2 on Rec/B, Ru/Ho and Rd/Ho for a reduced armour weight of 0.75W, berm width of 0.40 m with varying water depth are presented in Fig. 9 (a) – (c). Position of berm from the seabed (hb) is located at a height of 0.45 m. From Fig. 9 (a) it is observed that berm recession, wave run-up and rundown are maximum, when water level is equal to the berm position (i.e., hb/d = 1) for all test conditions and they are reduced as the water level in front of the structure falls and are minimum when hb/d = 1.50.. This is because, when berm level equals water level, waves directly attack the berm, run up and dislodge the armour units and further the return flow of the water pull back the dislodged armour units along with it thus increasing erosion. However, as water level falls the berm restricts the movement of the wave onto the upper slopes and hence the return flow will be less thus reducing the berm erosion, wave run-up and run-down. Further, wave run-up and run-down for 0.30 m water depth (hb/d = 1.50) is more than 0.35 m depth. This is because for lower water depth, the effect of berm is not felt and the wave impinges directly on lower slope without reaching the berm thus increasing wave run-up..
(7) 1056. INDIAN J. MAR. SCI., VOL. 47, NO. 05, MAY 2018. It is clear from the Fig. 10 that most of the settlement and movement of the armour takes place within the first 2000 waves and mild increase in recession can be observed from 2000 to 3000 waves for higher wave heights. Increase in berm recession with increasing wave height and decreasing wave period is observed. Further, 90% of the berm recession occurred within 2000 waves (4.4 hrs to 7.2 hrs) for higher wave heights (H = 0.14 m, 0.16 m) and within 1000 waves (2.2 hrs to 3.6 hrs) for lower wave heights (H = 0.10 m, 0.12 m). This is similar to the findings of many researchers15, 20. All the test data for different configurations of berm breakwater were combined into suitable dimensionless terms and are represented in Fig. 11. The figure shows the experimental data for 540 test runs and the best-fit curve with a correlation coefficient of 0.8251. From Fig. 11, the equation for berm recession in statically stable reshaped berm breakwater is derived as:. R ec D n 50 0 .1 N s A 0 .2 N. 2 3 Where, A H o gT *10 n * B d * h b d . … (5) 0.1. … (6). Similarly, equations for prediction of wave run-up and run-down are also developed which are given as: 2.449 eq Ru … (7) H o 1 1.681 eq 1.680 eq Rd … (8) H o 1 1.133 eq Fig. 12 shows the comparison between the measured berm recession and the calculated berm recession. A good R2 of 0.821 is obtained with a. Fig. 10 — Effect of no. of waves on berm recession for varying deepwater wave steepness. Fig. 11 — Stability equation for berm breakwater. Fig. 12 — Comparison of measured and calculated berm recession, wave run-up and wave run-down.
(8) JANARDHAN et al.: RESHAPING BERM BREAKWATERS. standard error of 0.199. Comparison between the measured wave run-up and the calculated wave runup using Eq. 7 showed a better R2 of 0.821. Similarly, the comparison between the measured wave run-down and the calculated wave run-down using Eq. 8 showed a better R2 of 0.822. Conclusions The following conclusions were drawn from the present study: (1) Berm recession, wave run-up, rundown and exposure of secondary layer are influenced by armour weight, berm width, wave height, period and depth, and storm duration. (2) Structure with reduced armour weight by 25% and 0.45 m berm width is safe for all the parameters considered in the present investigation. (3). Breakwater model with 25% reduced armour weight, 0.40 m berm and 2 layers of primary armour is totally safe for almost all the test conditions except for extreme waves of 0.16 m height and 1.6 s period. (4) As relative berm position (hb/d) parameter increases from 1.00 to 1.50, the berm recession decreased by up to 77%. Also, the wave run-up and run-down decreases by 7% and 14% respectively. (5) A new formula (Eq. 4) that includes the sea state and structural parameters is derived for estimating the berm recession. Berm recession is well predicted by the new formula for reshaping berm breakwaters. (6) The formulae show better estimation of wave run-up and wave run-down with R2 of 0.821 and 0.822 respectively. Acknowledgement Authors are thankful to the authorities of National Institute of Technology Karnataka, Suarthkal for the facilities provided for the investigations and for permitting to publish the results. The financial support by the Ministry of Water Resources through INCH is gratefully acknowledged. References 1 2 3 4 5. Priest M. S., Pugh J. W., and Singh R., Seaward profile for rubble mound breakwaters,Proc. 9thIntl. Conf. on Coastal Engg., ASCE,1964, 553–559. Baird W. F., and Hall K. R., The design of breakwaters using quarried stone,Proc. 19th Coastal Engg. Conf., ASCE, Houston, 1984. Kao, J.S., Hall, K.R., Trends in Stability of Dynamically Stable Breakwaters,Proc. 22th Intl. Conf. on Coastal Engg., Delft, 1990. Van der Meer, J.W., Stability of the seaward slope of berm breakwaters,Coastal Engg., 16 (1992), 205–234. Van Gent M .R. A.,Berm Breakwaters, Communications on hydraulic and geotechnical engineering, Delft University of Technology, 1993.. 6 7 8 9 10 11 12. 13 14 15. 16 17 18 19 20 21 22 23 24. 25. 1057. Lissev N., and Tørum A., Influence of core configuration on the stability of berm breakwaters, Coastal Engg., 1996, 1735–1747. Andersen L. T., and Burcharth H. F., A new formula for front slope recession of berm breakwaters,Coastal Engg., 57(4) (2010), 359–374. PIANC MarCom. State of the art of designing and construction berm breakwaters. Report of WG 40, International Navigation Association, Brussels, Belgium, 2003. Rao, S.,Pramod, and Rao,K. B., Stability of berm breakwater with reduced armour stone weight,Technical note, Ocean Engg.,31(2004), 1577–1589. Manu, Rao, S., Shirlal, K. G., Janardhan, P. and Rao, K. B., Physical Model Studies on Stability of Concrete Armoured Breakwaters, ISH J. of Hydraulic Engg., 17, sup 1 (2011), 51-60. Van der Meer J.W., Design of concrete armour layers,Proc. Coastal Structures '99, Santander, Spain. Losada (ed.), Balkema, Rotterdam, 1999, 213-221. Burcharth H. F. and Frigaard P, On 3-dimensional stability of reshaping breakwaters, Seminar for Berm Breakwaters: Unconventional Rubble-Mound Breakwaters, Ottawa, Canada, 1988. Hall K.R. and Kao J. S., A study of the stability of dynamically stable breakwaters, Canadian J. of Civil Engg.,18 (1991), 916-925. Menze A., Stability of multilayer berm breakwaters. Diploma thesis, University of Braunschweig, Germany, 2000. Torum, A., Krogh, S.R., Bjordal, S., Fjeld, S., Archetti, R., and Jacobsen, A., Design criteria and design procedure for berm breakwaters,Proc. Coastal Structures ‘99, Rotterdam, 1999, 331-341. Coastal Engineering Manual (CEM). Fundamental of Design. EM 1110-2-1100 (Part VI), U.S. Army Corps. of Engineers, 2006. De Waal J. P. and Van der Meer J. W., Wave run-up and overtopping on coastal structures,Proc. XXIII ICCE,Venice, 1992, 1758-1771. Mansard E.P.D. and Funke E.R., The measurement of incident and reflected spectra using a least squares method. Proc. 17th Coastal Engg. Conf., Sydney, Australia, 1980, 154–172. Chakrabarti S.K., Experimental techniques in offshore engineering, Proc., Intl. Conf. in Ocean Engg., COE-96, I.I.T. Madras, Chennai, 1996, 631-642. Hegde, A. V., Studies on deterministic optimum Computer Aided Design on non-overtopping rubble mound breakwaters, Ph.D. thesis, Mangalore University, Surathkal, India, 1996. Hughes, S.A.,Physical Models and Laboratory Techniques in Coastal Engineering,(World Scientific Publishing Co. Pte. Ltd., Singapore), 1993. Torum, A., On the stability of berm breakwaters in shallow and deep water,Proc. of the 26th Intl. Conf. on Coastal Engg., ASCE, Reston,(1998), 1435-1448. Torum, A., Kuhnen, F., and Menze A., On berm breakwaters. Stability, scour, and overtopping, Coastal Engg.,49(2003), 209-238. Janardhan, P., Harish, N., Rao, S., and Shirlal. K. G., Performance of Variable Selection Method for the Damage Level Prediction of Reshaped Berm Breakwater,Aquatic Procedia, 4 (2015), 302-307. Janardhan, P., Rao, S., Shirlal. K. G.,and Rao, K.B., Experimental studies on berm breakwater with different armour units,Proc. Nt. Conf. on Harbour and Ocean Engg., Goa, 2014..
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