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Performance of a circular cross-section moored floating breakwater Whiteside, Wesley Neal 1994

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PERFORMANCE OF A CIRCULAR CROSS-SECTIONMOORED FLOATING BREAKWATERbyWESLEY NEAL WHITESIDEB.Sc. in Mechanical EngineeringUniversity of Alberta, 1992A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CIVIL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNWERSITY OF BRITISH COLUMBIAApril, 1994(c) Neal Whiteside, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_____________________Department of C4The University of British ColumbiaVancouver, CanadaDate 4P,’,L 25’, /99L/DE-6 (2188)TABLE OF CONTENTSABSTRACT iiLISTOFTABLES viLIST OF FIGURES viiLIST OF SYMBOLS xACKNOWLEDGEMENT xiiCHAPTER 1: INTRODUCTION 11.1 Floating Breakwaters in Coastal Engineering 11.2 Floating Breakwater Designs in Use 21.3 Performance of Existing Floating Breakwaters 41.4 Motivation for Study 51.5 Organization of the Thesis 5CHAPTER 2: SCOPE OF WORK 72.1 Attributes of Proposed Breakwater 82.2 Design Variables 92.3 Dimensional Analysis 11CHAPTER 3: WAVE FLUME TESTING 15in3.1 Experimental Facilities and Measurement Equipment 153.2 Model Breakwater 163.3 Experimental Program and Procedures 17CHAPTER 4: WAVE BASIN TESTING 194.1 Experimental Facilities and Measurement Equipment 194.2 Model Breakwater 204.3 Experimental Program and Procedures 21CHAPTER 5: EXPERIMENTAL RESULTS 235.1 Brealcwater System Characteristics 235.2 Breakwater Motions 275.2.1 Wave Flume Results and Observations 285.2.2 Wave Basin Observations 305.3 Wave Attenuation 305.4 Mooring Line Forces 325.5 Breakwater Internal Stresses 335.6 Comparison to Rectangular Caisson Results 33CHAPTER 6: NUMERICAL MODEL 356.1 Hydrodynamic Analysis 35iv6.1.1 Incident Potenti. 386.1.2 Scattered Potential 386.1.3 Forced Potentials and Body Motions 386.2 Mooring Analysis 396.3 Numerical Results 406.4 Comparison of Numerical and Experimental Results 43CHAPTER 7: EVALUATION OF PERFORMANCE 457.1 General Conclusions 457.2 Performance of Numerical Model 467.3 Potential for Improvement and Further Study 47BIBLIOGRAPHY 49VLIST OF TABLES2.1 Comparison of Reynolds numbers between prototype and model states3.1 Experimental program for wave flume tests4.1 Experimental program and results for wave basin tests5.1 Summary of experimental results from wave flume tests5.2 Estimation of the natural frequencies in heaveviLIST OF FIGURES1.1 Cross-sections of typical bottom founded breakwaters, [25].1.2 Floating tire breakwater, [7].1.3 Equiport breakwater, [27].1.4 Tethered float breakwaters, [14].1.5 Log bundle floating breakwater, [4].1.6 Various reflective floating breakwater cross-sectional geometries.1.7 Comparison of transmissibility of rectangular caisson and tire breakwaters, [15].1.8 Comparison of transmissibility of various caisson breakwater types, [3].2.1 Definition of design parameters for proposed breakwater system.2.2 Mooring line attachment point arrangements.2.3 Importance of inertial and viscous effects, [24].3.1 Experimental set-up used in wave flume tests.3.2 Schematic layout of wave generation and data collection hardware.3.3 Photograph of wave probes.3.4 Photograph of a load cell.3.5 Photograph of model breakwater used in wave flume tests.4.1 Photograph of wave basin.4.2 Experimental set-up used in wave basin tests.4.3 Arrangement of strain gages.vii4.4 Photograph of model breakwater used in wave basin tests.5.1 Definition sketch for six degrees of freedom.5.2 Response of a SDOF system to periodic forcing, [23].5.3 Wave flume test results for base case with chain. (a) transmission coefficient,(b) motion amplitudes.5.4 Wave flume test results for base case with nylon. (a) transmission coefficient,(b) motion amplitudes, (c) mooring line forces.5.5 Wave flume test results showing the influence of wave steepness H/L for the case ofnylon mooring lines. (a) transmission coefficient for DIL = 0.116 and 0.173, (b)motion amplitudes for D/L = 0.116, (c) motion amplitudes for DIL = 0.173, (d)mooring line forces for D/L = 0.116 and 0.173.5.6 Wave flume test results showing the influence of relative draft h/D for the case ofnylon mooring lines. (a) transmission coefficient, (b) surge RAO, (c) heave RAO, (d)roll RAO.5.7 Wave flume test results showing the influence of line slackness s/so for the case ofchain mooring lines. (a) transmission coefficient, (b) surge RAO, (c) heave RAO, (d)roll RAO.5.8 Wave flume test results showing the influence of mooring line attachment points ontransmission coefficient. (a) chain mooring lines, (b) nylon mooring lines.5.9 Wave basin test results showing the influence of the angle of wave incidence.(a) transmission coefficient, (b) mooring line forces, (c) horizontal bending moments,(d) vertical bending moments, (e) torsion.5.10 Record of mooring line forces for wave flume test 2.5.5.11 Comparison of transmission coefficients between rectangular and circular caissonbreakwaters.5.12 Comparison of observed breakwater motions; (a) surge, (b) heave, and (c) roll.viii6.1 Numerical results for base case with chain mooring lines. (a) transmissioncoefficient, (b) motion amplitudes, (c) mooring line forces.6.2 Numerical results for base case with nylon mooring lines. (a) transmissioncoefficient, (b) motion amplitudes, (c) mooring line forces.6.3 Numerical results showing the influence of relative draft h/D for the case of chainmooring lines. (a) transmission coefficient, (b) surge RAO, (c) heave RAO, (d) rollRAO, (e) upwave mooring line force, (f) downwave mooring line force.6.4 Numerical results showing the influence of wave steepness H/L for the case of chainmooring lines. (a) upwave mooring line force, (b) downwave mooring line force.6.5 Numerical results showing the influence of line slackness s/so for the case of chainmooring lines. (a) upwave mooring line force, (b) downwave mooring line force.6.6 Numerical results showing the influence of mooring line attachment points for thecase of chain mooring lines. (a) upwave mooring line force, (b) downwave mooringline force.6.7 Wave flume test results compared with numerical results for base case with chain.(a) transmission coefficient, (b) surge RAO, (c) heave RAO, (d) roll RAO.6.8 Wave flume test results compared with numerical results for base case with nylon.(a) transmission coefficient, (b) surge RAO, (c) heave RAO, (d) roll RAO.ixLIST OF SYMBOLSA Cross-sectional area of mooring lineb Horizontal spacing between adjacent mooring line attachment pointsD Breakwater diameterd Water depthMooring line elasticity per unit length of breakwater (EA/b)E Young’s modulus of mooring lineF Mooring line pretension (at breakwater attachment point)F’ Mooring line pretension per unit length of breakwater (F/b)g gravitational constant (9.81 mis2)H Wave heightH Incident wave heightHr Reflected wave heightHt Transmitted wave heighth Breakwater draftI Moment of inertia of breakwaterL WavelengthL0 Deep water wavelengthM Mass of breakwaterMh Horizontal bending moment induced in breakwaterMt Torsion induced in breakwaterM Vertical bending moment induced in breakwaterMass of mooring line per unit lengthm” Mass of mooring line per unit length and per unit length of breakwater (m’/b)Il Normal vector to the body surfaceS Surface of the bodys Unstretched length of mooring lineso Distance between anchor point and attachment point on breakwaterT Wave periodw’ Mooring line submerged weight per unit length of linew” Mooring line submerged weight per unit length of line and per unit length ofbreakwater (w’/b)horizontal span of mooring linexV kinematic viscosity of water0 incident wave directionp density of waterpartial potential (complex function of space only)total potential (function of space and time)maximum mooring line tensions: j = 1, upwave line; j =2, downwave linehorizontal static offset of breakwaterbreakwater motion amplitudes: i = 1, sway; i =2, heave; i = 3, rollxiACKNOWLEDGEMENTThe author would like to acknowledge and thank several individuals and institutions whichwere integral to the completion of this research. First, the guidance of his advisor, Dr.Michael Isaacson, has been critical to the progress of the research throughout and is deeplyappreciated. As well, the financial and technical support from Hay & Co. Consultants Inc.,in particular Mr. Bob Gardiner, who provided the original motivation for the research isgratefully acknowledged. The author would also like to thank several individuals within theCivil Engineering Department for help in completing the numerical and physical testing; Mr.Kurt Nielson for assisting with the assembly of physical models, Mr. Ron Dolling forassistance in providing instrumentation, Mr. Sundar Prasad for help in setting up dataacquisition for the experiments, and Mr. John Baldwin for providing numerical results. Theauthor would also like to thank his peers in the hydrotechnical engineering group for helpduring physical testing, in particular Mr. S.S. Bhat, Mr. A. Kennedy, and Mr. A. Phadke.Funding from the Natural Sciences and Engineering Research Council in the form of ascholarship is gratefully acknowledged.xliCHAPTER 1: INTRODUCTION1.1 Floating Breakwaters in Coastal EngineeringMany marinas, fishing harbours, and aquaculture operations are partially protected fromwave action by natural topographic features such as islands, shoals, and spits. Due to theminimal fetch and wind speeds required to generate water waves of a magnitude largeenough to limit such operations, most such sites require additional protection. Therefore, thenatural wave protection found at a site is often augmented by the construction of abreakwater. The term breakwater refers to a class of structures whose main function isattenuating wind or ship generated water waves.The oldest and most common breakwaters are bottom-founded structures. Breakwaters suchas the rubble-mound or caisson types (see Fig. 1.1) provide excellent harbour protection astransmission of waves occurs only by diffraction around the ends of the breakwater.However, as water depth increases the cost of a bottom-founded system can becomeprohibitive. Bottom-founded breakwaters also reduce water circulation in the protected area,possibly creating a sedimentation problem where dredging may be required to maintainnavigable channels. Also, reduced flushing may lead to increased concentrations ofpollutants within the protected area.In some locations floating breakwaters have been used with good success in preference totraditional bottom-founded breakwaters, avoiding many of the problems outlined above.Sites where floating breakwaters may be preferable to traditional structures are characterizedby a moderate wave climate sheltered from long period waves by surrounding land masses,and large tidal fluctuations and/or a steeply sloping seabed which would make a bottomfounded structure very expensive. Floating breakwaters allow water circulation under the1structure reducing the siltation and pollution problems alluded to earlier. Floatingbreakwaters are also somewhat portable. This can be a tremendous advantage in situationswhere only temporary or seasonal protection is desired.Due to the very nature of floating breakwaters, they become unfeasible as design waveperiods increase beyond 5-6 seconds. For longer period and hence longer wavelength wavesa floating breakwater will respond much like a ball in the ocean moving up and down inphase with the incoming waves. To be effective the breadth and/or depth of the breakwatermust be of the same order of magnitude as the wavelengths of the incoming waves.1.2 Floating Breakwater Designs in UseA diverse variety of floating breakwaters have been developed and used, ranging from verysimple schemes to complex and expensive designs. A report produced by the U.S. Navy [121lists 52 different floating breakwater concepts for which either numerical or physical studieshave been carried out. All of these structures use one or a combination of the following threebasic mechanisms to reduce wave heights within the protected area:(i) wave reflection, a portion of the incident wave energy is reflected from theface of the breakwater as if it were a fixed obstacle;(ii) energy transformation, where incident wave energy excites breakwatermotions forcing radiated waves which are out-of-phase with the incident waveforcing because of the response characteristics of the system;(iii) energy dissipation, where turbulence induced by either wave breaking orwave-structure interaction effects causes dissipation of incident wave energy.The first two mechanisms can be modelled by ideal fluid theory and approximated by linearpotential theory. The third mechanism is a result of viscous dissipation and nonlinear wave2breaking mechanisms, and as such can not be readily dealt with using ideal fluid theory. Thediverse variety of breakwater types can be classified into two broad categories, pontoonbreakwaters (which rely primarily on the first two mechanisms), and dissipative breakwaters.Dissipative breakwaters rely primarily on wave-induced turbulence in order to dissipate waveenergy and typically consist of flexible interconnected units. The most common breakwaterof this type is a floating tire breakwater (Fig. 1.2). Other promising designs include equiportbreakwaters (Fig. 1.3), tethered float breakwaters (Fig. 1.4), and flexible log rafts [12]. Adissipative floating breakwater has the advantage of not significantly increasing wave heightson the upwave side of the structure. This feature is advantageous for navigation in and out ofmarinas for instance. However in reviewing the literature, few systems of this type havebeen implemented compared to reflective breakwaters. This can be attributed to severaldisadvantages of dissipative breakwaters:(i) they require a large amount of material and space to be effective,(ii) high maintenance costs and/or a short service life,(iii) they may be aesthetically unappealing.All that is required of a reflective floating system is sufficient size and inertia to reflect asignificant portion of the incoming wave energy. Generally breakwaters of this type arerigid, wall-sided structures. Makeshift breakwaters of this type have been constructed fromsuch diverse material as log bundles (see Fig. 1.5), partially submerged scrapped barges andrail cars, and even out-of-service floating bridges. These designs were economically feasibleand hence successful due to the relatively low cost of the raw materials. However, as well asbeing perhaps aesthetically unappealing, it is not always possible to find such suitableinexpensive structures.Many specially manufactured reflective floating breakwaters with different cross-sectionalgeometries and/or mooring arrangements have been put to use in harbours. Even more3designs have been either numerically or laboratory tested. Some of the common cross-sectional geometries found in the literature are shown in Fig. 1.6. The most common andsimplest of these is the rectangular pontoon breakwater.Two main types of restraint have been used; either mooring lines or piles. Piles have theadvantage that they restrict surge and roll motions almost completely which should result inlower transmission coefficients. However, breakwaters with pile restraints have sufferedfrom wear problems at the point of contact between the piles and the breakwater. Thisproblem has resulted in higher initial design and manufacture costs and reduced service lifeand/or increased maintenance costs. As well, the design and installation of pile restraints canbe complicated by poor soil conditions and/or the depth of the water at the site. For theforegoing reasons, mooring lines are the most common constraint used with floatingbreakwaters. The two most popular mooring line materials are steel chain and nylon cable.Chain mooring lines are usually slack to allow for tide fluctuations. Occasionally suspendedweights are used somewhere along the length of the mooring line to increase the stiffness ofthe mooring system. Nylon cables have been installed pretensioned to ensure that the cableis in tension at all tide levels. This has been possible due to the relatively large elasticelongation these cables can withstand before failure.1.3 Performance of Existing Floating BreakwatersFigure 1.7 is reproduced from [12] and shows the transmission coefficients measured forvarious rectangular caissons breakwaters and floating tire breakwaters (here B is thebreakwater width and L is the wavelength of incident waves). Clearly, the caissonbreakwater types have better transmission characteristics.Figure 1.8 shows the transmission characteristics measured for a variety of caissonbreakwater types. The catamaran configuration performed best for these tests. These results4also examine the effectiveness of an intermediate skirt in reducing wave transmission. Theresults show that a substantial skirt (such as configuration no. 6) reduce wave transmission.However, the advantage of a skirt may be nullified by higher construction and maintenancecosts due to more complex construction and larger internal stresses.1.4 Motivation for StudyAlthough considerable expertise has been acquired with regard to their efficiency,construction, and maintenance, a truly satisfactory floating breakwater system has yet to bedeveloped. It is hoped that the proposed circular-section breakwater may be an affordablealternative to existing floating breakwaters without some of the problems of existing designs.Local concrete manufacturers presently have the capability of producing circular concretepipe with cross sectional areas comparable to existing rectangular caisson type breakwaters.It is believed there is a potential for considerable cost savings by using circular concrete pipein preference to rectangular cross sections because it has a simpler manufacturing procedure.As well, the nature of circular sections should preclude the development of significanttorsion and corner stress concentrations that are induced by wave action on rectangularsections. As well, it may be possible to construct a long flexible breakwater by post-tensioning sections of the concrete pipe together.1.5 Organization of the ThesisThe preceding sections described various types of breakwaters and introduced the circularcross-section floating breakwater concept. Chapter 2 defines the scope of work which theresearch encompasses and the goals of the research. As well, the design variables aredefined. Chapters 3 and 4 describe the two and three dimensional physical testingrespectively, including details concerning the facilities, measurement equipment, data5acquisition, the model breakwaters, and the testing programs. Chapter 5 gives the results ofboth the 2-D and 3-D physical modelling and the meaning of the results is discussed. Alsoin Chapter 5, a comparison is made between experimental results from this study and studiesdone with a rectangular caisson breakwater. Chapter 6 includes a description of thenumerical model used in the research and a overview of the numerical results obtained.Chapter 7 summarizes some important conclusions about the breakwater system proposedand the performance of the numerical model. As well, improvements to the design aresuggested and variables not examined are noted. Tables and figures follow the main text ofthe thesis.6CHAPTER 2: SCOPE OF WORKA new floating breakwater concept based on a circular cross-section with a draft determinedby the weight of fluid contained within the section has been proposed. Two and threedimensional laboratory model tests were completed in order to provide generic performancecharacteristics which could subsequently be applied to specific design situations. Anumerical analysis of the breakwater based on linear potential theory was also used to obtainsimilar results. This allowed a comparison between results from numerical and physicalmodeling and an assessment of the accuracy of the numerical model.Specific goals of the analytical and physical model studies of the circular cross-sectionfloating breakwater were to:(i) evaluate the efficiency and practicality of the circular cross-section floatingbreakwater proposed compared to existing breakwaters;(ii) establish criteria with regards to mooring line forces and wall stresses to aid inthe design of a floating breakwater of the type studied;(iii) better understand the role of design parameters in effecting the performance offloating breakwaters;(iv) identify potential improvements to the proposed breakwater,(v) evaluate the suitability of applying a linear potential theory model for thedesign of a floating breakwater.72.1 Attributes of Proposed BreakwaterThe proposed breakwater design consists of a large diameter concrete pipe (D > 2m) mooredwith either nylon cable or steel chain. A cross-sectional view of the proposed breakwatersystem defining the design parameters is shown in Fig. 2.1. The necessary buoyancy wouldbe provided by a low density material such as extruded polystyrene sheet attached to theinside of the breakwater. The remainder of the volume inside the breakwater would be filledwith water to add inertia to the system. The use of a low density material has two keyadvantages over using entrapped air for buoyancy: a secondary compartment which enclosesthe entrapped air does not have to be fabricated, and the breakwater does not have to besealed to prevent sinking.When designing the breakwater for a particular location, a suitable draft must be selectedwhich is a compromise between excessive overtopping caused by too deep of a draft and theadvantages of the added inertia at deeper drafts. One of the goals of this study is to providedata to aid the engineer in this design decision. The mooring lines chosen and their proposedconfiguration are similar to the mooring systems used for existing rectangular caissonbreakwaters.The prototype proposed breakwater consists of several sections of concrete pipe posttensioned together at the installation site forming a long flexible breakwater. This featureallows the breakwater sections to be easily transported and also gives the design anadvantage over present configurations which have gaps between breakwater sections.However, the present work concentrates on the performance of a single section of breakwaterand does not address the design of connections between breakwater sections.82.2 Design VariablesA complete listing of all the parameters considered when modeffing the proposed breakwateris given in the list of symbols on pp. ix-x. To better understand the role of all of the relevantparameters and variables, it is useful to group the factors into the following categories:(i) independent wave parameters:p, water density;v, dynamic viscosity;g, gravitational acceleration;H, incident wave height;T, wave period;d, water depth;0, incident wave angle.(ii) independent breakwater geometry parameters:h, breakwater draft;D, breakwater diameter.(iii) independent mooring line parameters:w’, mooring line submerged weight per unit length of line;s, unstretched length of mooring line;s0, distance between anchor point and attachment point;EA, mooring line elasticity;b, mooring line spacing.9(iv) dependent variables known by definition from above three categories:E’, mooring line elasticity per unit length (EA/b);I, breakwater moment of inertia;L, wavelength;M, mass of breakwater.(v) dependent variables whose relationship to the independent variables isrequired:Ht, transmitted wave height;Mh, horizontal bending moment induced in breakwater,Mt, torsion induced in breakwater;M, vertical bending moment induced in breakwater;aj. mooring line forces: j = 1, upwave line; j =2, downwave line;j, breakwater motions: i = 1, sway; i = 2, heave; i = 3, roll.The mooring line pretension, F, should be used as an alternate independent variable insteadof the unstretched cable length, s, when a pretension is present in the mooring lines.However, pretensioning of the mooring lines is only seen as a possibility for nylon mooringlines since chain does not have enough elasticity to accommodate changes in the still waterlevel due to tidal fluctuations. In fact, during model testing any initial pretension placed inthe nylon lines disappeared after the breakwater was exposed to waves due to plasticelongation of the nylon cables and hence no testing was done with mooring lines inpretension. The ability of prototype-scale nylon lines to maintain pretension in fieldsituations was not investigated in any of the literature reviewed.In addition to the parameters considered above, the location of the mooring attachment pointsto the breakwater may also have an influence on the breakwater’s response. In the presentstudy, three arrangements (shown in Fig. 2.2) have been examined. These correspond to an10attachment point at the bottom of the breakwater, and a pair of attachment points subtendinga 6O angle at the centre of the breakwater, with the mooring lines either uncrossed orcrossed.When considering three-dimensional conditions, two additional independent parametersbecome relevant, the overall breakwater length and the specific mooring line arrangement.Only one breakwater length and mooring line arrangement were considered in testing. Theexperimental setup for these parameters was similar to that of existing rectangular caissonbreakwater installations. It is hoped therefore that actual field designs will not be sufficientlydifferent in these two respects so as to significantly affect their performance.2.3 Dimensional AnalysisAs a preliminary to canying out the laboratory tests and applying the numerical model, it isuseful to carry out a dimensional analysis of the wave-breakwater interaction in order to:(i) identify the governing dimensionless groupings influencing the breakwatereffectiveness and response;(ii) provide a basis for model scale selection;(iii) plan for the selection of the experimental test program.There are a total of 14 independent variables, and on the basis of a 3 unit system (mass,length, and time), there should be 11 dimensionless groups influencing each dependentvariable. For example, a dimensional analysis for the transmission coefficient, Kt, providesthe following relationship:21 K_1t_ hdIIjR E’ bs0s8(•)11where Re, the Reynolds number, is based on the maximum horizontal velocity of the waterparticles at the still water level as given by linear potential theory:D (icH 1 “D(2.2) Re=U—=1—. I—rnaxV T tanhkd}vDifferent functions with the same form as Eqn. 2.1 apply to the other dependent variablesexpressed in their non-dimensionlized forms. The non-dimensional groupings used for eachof the remaining dependent variables are as follows:(2.3) Kr=(2.4) RAO= 11,12for i = 1 (surge), i =2 (heave)(2.5) RAO• = for i =3 (roll)H/2(2.6) CFJ= pgHDbforj = 1 (upwave), j =2 (downwave)27 C- Mh c- c- MMh— pgHDb2 ‘ Mv — pgHDb2 ‘ Mt— pgHDb2The significance of the dimensionless parameters in Eqn. 2.1 is as follows. D/L representsthe breakwater size to wave length ratio and accounts for the influence of wave length orwave period on the breakwater response. h/D represents the relative draft of the breakwater,and is an indirect indication of the inertia of the breakwater. d/D represents the influence ofwater depth and is expected to be significant only for shallower water as d/D becomessmaller. HjIL is the wave steepness, which should not significantly influence thoseparameters which vary linearly with wave height. As HilL and h/D increase and/or D/Ldecreases the propensity of the breakwater to overtopping increases. The remainingparameters, except for the Reynold’s number, represent a characterization of the mooringline properties and configuration: b/D is the mooring line spacing ratio, w”/pgD represents12the relative submerged weight of the mooring lines; E’/p gD2 represents the relative elasticityof the mooring lines; and sdd and s/s0 are dimensionless parameters describing the mooringline slope and slackness.The Reynolds number which is an indication of viscous effects is not expected to influencethe breakwater response strongly. In modeling the breakwater in physical tests it was notpossible to match the Reynolds number and the other parameters concurrently. Hence, waveflume, wave basin, and prototype states do not have matching Re. The Reynolds number forseveral prototype scenarios and their corresponding model states are presented in Table 2.1.The Keulegan-Carpenter number, K, is an indicator of the importance of inertial and viscouseffects and is defined as:(2.8) K = UmaxT/DFigure 2.3 shows the relative importance of inertial (diffraction) and viscous (flowseparation) effects as K and D/L vary. By comparing this figure with values of K and D/Lfrom Table 2.1, it is concluded that inertial effects will be the dominant factor in determiningthe breakwaters response. This serves as a justification for the use of the potential theorymodel described in Chapter 6. For long period waves, D/L decreases and hence theimportance of diffraction decreases.Typical values of the dimensionless parameters may be estimated on the basis of prototypeconditions corresponding to D = 3.21 m, T = 2.0 - 6.0 sec, and mooring lines made of 1inch stud link anchor chain (w’ 140 N/rn, EA 2 x 108 N) and 2 inch double-braided nylonrope (w’ 2 N/rn, EA 2 x 106 N), and spaced 5 m apart. On this basis, typical values ofthe dimensionless parameters are as follows:13D/L0.1-0.5, h/D=0.6-1.0,d/D 2- 20, H/L 0.01 - 0.1,4, s/s0 = 1.00- 1.06,w”/pgD 900 x 10.6 for chain, E’/pD2 4000 for chain,w”/pgD 130 x 10-6 for nylon, E’IpgD2 40 for nylon.On the basis of Eqn. 2.1, which corresponds to Froude scaling, the scale factors of thevariables can be expressed in terms of the length scale factor, Ki, as follows. Note that thesubscripts m and p denote variables corresponding to the model and prototype respectively.(29)D H d hA!, Sp(2.10)(2.11)w E(2.12) (EA) =K13(EA)In a presentation of numerical results, it is convenient to present the results in the form ofcurves of transmission coefficient, response amplitude operators, and mooring line forcecoefficients as functions of D/L for given values of the other parameters (b/D, H/L, 5/5, andso on); and to examine the influence of each of these other parameters in turn on such curves.In planning the physical and numerical experiments, it is not feasible to consider all ranges ofeach variable. Instead, one or more base cases were considered, and the influence of eachvariable was considered in turn.14CHAPTER 3: WAVE FLUME TESTING3.1 Experimental Facilities and Measurement EquipmentThe two-dimensional laboratory tests were carried out in the wave flume of the HydraulicsLaboratory in the Department of Civil Engineering at the University of British Columbia.The flume is 0.62 m wide and 20 m long from the wave paddle to the holding tank at the farend. The flume was operated with a water depth of 0.6 m. A 7 m long artificial beachconsisting of plywood set at a 1:15 slope covered with artificial hair matting extends fromthe end of the tank. The beach combined with the holding tank at the end of the flumeeffectively absorb and dissipate wave energy preventing significant wave reflection. Theflume is equipped with a computer controlled wave generator capable of producing regularand random waves. A one-tenth scale model of the proposed breakwater was centered 10.8m down from the wave paddle. Figure 3.1 shows a sketch of the experimental set-up.Figure 3.2 shows a schematic layout of the apparatus used for acquiring water surfaceelevation, force and motion records during the experiments. The main components are thevideo camera and recorder, wave probes, load cells, amplifiers, signal cables, analog-to-digital (A/D) converter, and computer. The latter is a Digital Equipment Corporation (DEC)VAXstation 3200 computer and was used to control the experiment. The GEDAP(Generalized Experiment control, Data acquisition and Analysis Package) library of softwareand associated RTC (Real Time Control) programs developed at the Hydraulics Laboratoryof the National Research Council of Canada were used to control the wave generation anddata acquisition processes. This system allowed simultaneous sampling of the wave probeand load cell signals. Data was recorded at a sampling frequency of 100 Hz so that spikes inthe load cell records would not be lost.15Capacitance-type wave probes (see Fig. 3.3) were used for measurements of the watersurface elevation. The wave probes exhibited a linearity better than 98.5% and a resolutionbetter than 1 mm. Two sealed shear beam load cells (see Fig. 3.4) were placed in series withthe mooring lines near the connection points with the breakwater in order to measuretensions in the upwave and downwave mooring lines. The load cells have a 50 lb (222 N)capacity with 99.5% linearity through their working range.A Super VHS camera and recorder was used to record the motions of the breakwater in roll,surge and heave with respect to a grid placed on the side of the flume.3.2 Model BreakwaterThe prototype breakwater being proposed would be constructed of concrete pipe. Presentlypipe diameters up to 3.5 m can be produced by local concrete manufacturers using existingequipment. Assuming a prototype diameter of 3.21 m, a 1:10 scale model was constructedfor the two dimensional (2-D) tests. The scale chosen allowed for model tests at UBC’swave flume over the anticipated range of full scale wave periods and heights.Figure 3.5 is a photograph of the model used. The model consists of a 321 mm diametercircular PVC cylinder of a width slightly narrower than that of the flume. The draft of thebreakwater was altered by the addition of lead bars fixed inside the cylinder. Three ballbearings were connected to each end of the breakwater so the model could move freely alongthe sides of the flume. The bearings served the additional purpose of limiting undesirablepitch, yaw, and sway motions and reducing the necessary clearance between the breakwaterand the sides of the flume thereby limiting the amount of wave energy diffracted.The model breakwater was restrained by four mooring lines (two upwave and twodownwave). The mooring line spacing of 0.3 m corresponds to a 1:16.7 scale ratio based ona typical prototype spacing of 5 m between adjacent mooring lines. Two different sets of16mooring lines were used during the tests, one modeling 1” (25 mm) stud link anchor chain,and the other modeling 2” (51 mm) double-braided nylon cable. Several connection pointson the breakwater enabled tests to be carried out with the mooring lines connected at thebottom of the breakwater; and at the sides of the breakwater as shown in Fig. 2.2. All testswere conducted with a water depth of 0.6 m.3.3 Experimental Program and ProceduresAll wave flume tests were performed with monochromatic regular wave conditions. A totalof 70 tests were performed with varying wave conditions and breakwater characteristics. Asummary of the experimental program devised for the wave flume tests is shown in Table3.1. The parameters varied in the experimental program included wave period, wave height,breakwater draft, and mooring line type, slackness, and connection points. Parameters heldconstant were water depth and breakwater diameter. The testing program was divided intosets of thals which focus on the effects of the variation of one of the design variables. Forexample, tests 4.1 to 4.16 focus on the effect of breakwater draft on breakwater efficiencyand motions. The experimental program was organized to achieve two purposes; (i) to gain abetter physical understanding of the effect of each parameter on the breakwater’sperformance, and (ii) to enable the evaluation and calibration of the numerical model.Originally the following parameters were to be measured in each test:H1 incident wave heightHr reflected wave heightHt transmitted wave height,horizontal static offset of breakwater,breakwater motion amplitudes (surge, heave, and roll),maximum mooring line tensions (upwave and downwave).17The incident and reflected wave height were to be interpolated from three wave elevationrecords taken from wave probes placed upstream of the breakwater. The analysis was to becarried out using the GEDAP analysis program REFLM. After the first set of tests it wasapparent that REFLM would not give reliable results given the short duration of the tests.Hence the reflected wave height was not measured for the remainder of the tests. Waveheights were obtained from water elevation records using the GEDAP program ZCA (ZeroCrossing Analysis). The incident wave height was measured in calibration tests with themodel removed from the water. An average transmitted wave height was calculated fromthree wave elevation records obtained by wave probes downwave of the breakwater.Due to the limited length of the flume, after a time a partial standing wave would set-upbetween the wave paddle and the breakwater. This condition was especially pronounced intrials with short period waves where significant wave reflections from the breakwater werepresent. To avoid contaminating the results, the duration analyzed for each test was limitedaccordingly.As described earlier, the breakwater motions were measured from VCR records of the tests,with a grid placed in the field of view. The accuracy of the video record in assessingbreakwater motions is estimated to be ± 0.5 cm, allowing for constraints of resolution, framespeed, and undesirable pitch, yaw, and sway motions. The load cells used to measuremooring line tension were calibrated by hanging weights from the load cells. The calibrationcurves were very linear and consistent indicating good accuracy. Using 10 volts DCexcitation and amplifying the signal l000x, it was possible to obtain a signal resolution ofbetter than 0.5 N.To determine the natural periods of the wave flume model, the breakwater model was giveninitial displacements in the surge, heave, and roll directions in turn and the resultingoscillations were recorded with an accelerometer fixed to the breakwater.18CHAPTER 4: WAVE BASIN TESTING4.1 Experimental Facilities and Measurement EquipmentThe wave basin used for the testing shown in Fig. 4.1 has dimensions 13.7 m long by 4.5 mwide and 0.55 m deep. A variable speed, electrically driven flap-type wave generator at oneend of the basin is capable of producing uniform long-crested waves with periods rangingfrom 0.4 to 2.0 s. The wave period and height have to be set manually by setting the speedcontrol and altering the stroke of the wave paddle, respectively. A 1:3.5 slope, permeablebeach consisting of a timber frame covered with 1” artificial hair matting was constructed atthe opposite end of the wave basin to reduce wave reflection. Two movable dividing wallswere constructed to isolate the breakwater so accurate readings of the transmitted andincident wave heights could be obtained. The dividing walls were also covered with artificialhair matting.Figure 4.2 shows a sketch of the experimental set-up. The same capacitance-type waveprobes and load cells described in Chapter 3 were used again for measurements of watersurface elevation and mooring line tension, respectively. Two wave probes were used tomeasure the incident wave height and one to measure transmitted wave height.In addition, the model breakwater was machined and instrumented with three strain gagebridges to measure vertical bending moment, horizontal bending moment, and torsion in thewalls of the breakwater. Each of the three bridges was designed so it would only sensemoments in the desired direction (either horizontal bending, vertical bending, or torsion) andignore moments in other directions and any axial tension or compression. The strain gagebridges were installed at the midpoint between two mooring lines to capture the maximummoments. The arrangement of the strain gage bridges is shown in Fig. 4.3.19A Super VHS camera was used to record breakwater motions for all tests. Unlike the waveflume testing, the video record was only used to gain a qualitative understanding of thebreakwater motions.4.2 Model BreakwaterA 15.1 cm diameter aluminum tube 1.98 m long was used as a model breakwater (see Fig.4.4) corresponding to a 1:21.3 scale based on a prototype diameter of 3.21 m. Aluminumwas chosen as a material on which to mount the strain gages because of its uniformproperties, machinability, and relatively low modulus of elasticity. The tubing had a nominalwall thickness of 1/8” (3.2 mm). The tube was machined down to 1/32” (0.8 mm) wallthickness where the strain gages were mounted to increase the output from the gages.The model breakwater was ballasted with water and a made-to-fit insert made of styrofoamsheet was used for positive buoyancy. The ends of the breakwater were sealed, therebyeliminating any flow of air or water into the breakwater. This arrangement is a much betterrepresentation of the envisioned prototype ballasting than the 2-D model and hence shouldbetter represent the performance of the prototype breakwater. The relative draft of thebreakwater, h/D, was not altered during the testing and was measured to be 0.735.Six upwave mooring lines and six downwave mooring lines were used to restrain thebreakwater. This corresponds to a 7.1 mfline prototype spacing. The six mooring lines oneach side were connected uncrossed to three connection points on each side of thebreakwater located 30° from the bottom. Mooring lines of light steel chain of the correctweight to imitate 1” (25 mm) stud link anchor chain were used. The mooring line slackness,s/s0, was 1.02 for all the wave basin tests.204.3 Experimental Program and ProceduresThe angle of incidence is defined as the angle between the breakwater axis and the incidentwave crests. The angle of incidence was varied from 00 to 45° in the wave basin tests.Table 4.1 shows the testing program devised for three dimensional (3-D) testing. A total of24 tests comprised of 4 sets of tests at different angles of incidence were performed. The sixwave conditions tested in each set and the breakwater parameters other than angle ofincidence were not varied from set to set, as far as possible.Figure 4.5 is a photograph of the testing apparatus and breakwater model setup with an angleof incidence of 450 The load cells and the strain gage bridges were given 10 volt excitationand their corresponding signals were boosted by a factor of 1000 with amplifiers.Essentially the same data acquisition system as described in Sec. 3.1 was used for the wavebasin tests as well, with the exception that the wave generator had to be activated andcontrolled manually as mentioned earlier. Eight channels of data were recorded by the dataacquisition system at a sampling rate of 100 Hz. The data records tabulated for each testwere:llj(t) incident wave elevations (2 channels),flt(t) transmitted wave elevation (1 channel),o(t) mooring line tensions (2 channels),Mh(t),Mv(t), Mt(t) horizontal and vertical bending moments, and torsioninduced in the breakwater (3 channels).As in the wave flume testing, data was only analyzed over a limited duration to prevent theeffects of wave reflection from affecting test results. As well any high frequency noise(greater than 10 Hz) was filtered out using the GEDAP program FILTA. A measure of theincident and transmitted wave energy for each test was calculated using two methods; zerocrossing analysis and spectral analysis. For the zero-crossing analysis, the average wave21height and period for a record were determined using the program ZCA. For the spectralanalysis, the GEDAP program VSD was used with. a filter bandwidth of 0.05 Hz and a Cutoff frequency of 5 Hz to determine the record variance (proportional to H2) and spectral peakfrequency (111’). The maximum mooring line tensions and induced moments for each testwere determined by inspection of the individual records.22CHAPTER 5: EXPERIMENTAL RESULTSThis chapter summarizes the quantitative and qualitative experimental results obtainedduring wave flume and wave basin testing. As well, an attempt is made to explain therelevance of the results and the impact of the different dimensionless parameters onbreakwater performance. Table 5.1 is a summary of experimental results for the wave flumetest program and Table 4.1 contains results from the wave basin test program.When analyzing the data it was assumed that the response of the breakwater would beperiodic and of the same frequency as the incident waves. However, the inherentnonlinearities in the problem (particularly the nonlinear moorings) did result in somevariance from cycle to cycle in the recorded quantities (partially non-periodic response)which combined with the limited length of the tests is responsible for some scatter in thedat&5.1 Breakwater System CharacteristicsThe natural frequencies of a floating breakwater are of interest because the amplitudes of themotions are expected to increase as the frequency of the incident waves approach one of thenatural frequencies. If the breakwater is considered a 3-D rigid body then it should have sixnatural frequencies and six mode shapes corresponding to its six degrees of freedom: surge,heave, sway, roll, yaw, and pitch as defined in Fig. 5.1. Modelling the breakwater as a twodimensional body eliminates three degrees of freedom (DOFs) leaving only the surge, heave,and roll DOFs and hence the system should have only three natural frequencies and modeshapes.In a rigorous sense, to have well defined natural frequencies requires that the system has bothconstant inertia and linear stiffness. For the system studied, neither of these assumptions is23strictly satisfied. First, the mooring lines do not provide linear stiffnesses as there isgenerally some slack in the lines. As well, the vertical stiffness created by buoyancy forcesvaries as the floating breakwater is displaced from its equilibrium position. Finally, theadded mass which contributes to the inertia varies with the frequency of excitation.However, by exciting the floating breakwater with displacements of similar amplitude asthose experienced during testing, estimates of the natural frequencies may be made.It is useful to discuss the type of results that may be expected. First, by examining the two-dimensional model, the following results concerning its three mode shapes can be deduced.Since the model can move freely in the heave direction without eliciting motion in the rolland surge directions, the heave degree of freedom is uncoupled from the other two degrees offreedom. Therefore, heaving motion without roll or surge will constitute one of the modes.However, a displacement in the surge direction will result in a rolling motion as well unless arestraining moment is applied to the breakwater. The coupling of the roll and surge modesresults from the mooring line not being connected to the centre of the breakwater cylinder.However, the coupling of the surge and roll motions is not very strong. Therefore, one modethat is predominantly roll and another mode which is predominantly surge should beexpected. For convenience, these modes will be referred to as the roll mode and surge moderespectively, although they are actually coupled modes. The same reasoning can be extendedto the 3-D model with its extra degrees of freedom. The sway, yaw, and pitch motions arenot coupled to the heave, surge, and roll motions.Two types of restoring forces are present: mooring line forces and buoyancy I gravity forces.Because of the mooring lines’ slackness, the magnitude of the hydrodynamic forces shouldgenerally be much larger than the mooring line forces. Therefore, it is expected that motionswhich are restored by hydrodynamic forces should have larger spring constants and hencelower natural periods (i.e. the natural period of the heave mode should be lower than thenatural frequency in surge).24As a precursor to measuring the natural frequencies, the heave and roll natural frequencieswere calculated ignoring mooring line stiffness for both the 2-D and 3-D models. Thecalculation method for both heave and roll motions is based on the hydrodynamic stiffnessinduced by buoyancy and gravitational forces.For the heave mode, the inertia to motion is the sum of the mass of the body and the addedmass predicted by potential theory. For a system with a free surface, the added mass forheave has a dependence on the frequency of oscillation as shown by Vugts [26]. Resultsfrom [26] were extrapolated to give rough estimates of the added mass in heave for circularcylinders with h/D ratios differing from 0.5 (see Table 5.2). Using these approximate valuesfor the added mass, the predicted natural periods in heave for the 2-D and 3-D models were1.01 s and 0.84 s respectively. The natural periods differ because of differences in scale sizeand relative draft. The natural periods for the 2-D and 3-D models can be translated intovalues for the prototype breakwater by applying the appropriate scale factor. For prototypescale breakwaters (D = 3.21 m) with draft ratios (h/D) of 0.579 and 0.735, the coffespondingnatural periods in heave would be 3.2 s and 3.9 s, respectively.The restoring force for roll motion is caused by the eccentricity of the centre of gravity fromthe centre of the cylinder. The moment of inertia of the cylinder in roll was the only inertiacomponent considered. Theoretically, a circular cylinder in roll should have no added mass.The natural periods in roll predicted for the 2-D and 3-D models were 0.72 s and 2.46 s. The3-D model had such a long natural period in roll because its centre of gravity was very closeto the centre of the cylinder and hence had a small spring constant. The 2-D model’s internalconfiguration and moment of inertia were not a good approximation to those of the proposedbreakwater, hence its roll response may not be indicative of the performance of the proposedprototype breakwater. However, the 3-D model was weighted properly so its roll responseshould approximate that of the prototype very well. The proposed prototype breakwater25should therefore have a natural period in roll of 11.4 s, much higher than the exciting periodof incoming waves (less than 6 s).The natural frequencies of the 2-D model were measured by exciting the model in each of itsthree DOFs and measuring the motion in the primary direction with an accelerometer. Theresulting motions were recorded and converted to provide frequency spectra. When excitedin heave, a natural period of 0.97 s was recorded, corresponding well with the estimate of1.01 s. When excited in the roll DOF, frequency peaks corresponding to the heave (T = 0.97s) and surge (T = 3 s) modes were detected. The natural frequency of the roll mode, whichwas expected to be 1.39 Hz (T = 0.72 s), could not be isolated. The most feasibleexplanation for this discrepancy is that the natural period in roll was close to the naturalperiod in heave and could not be distinguished. The natural period for surge motions variedfrom 3 s to 5 s depending on the mooring line properties particularly the amount of slack inthe lines.For the 3-D model, wave elevation records were used to obtain a plot of the response in thefrequency domain. A natural period of 0.83 s was recorded for the heave mode whichcompares well with the predicted value of 0.84 s. A natural period of 3.4 s was recorded forthe surge mode (with s/s0 = 1.02). A natural frequency could not be obtained for the rollmode since the rolling motion did not induce wave propagation. The other naturalfrequencies were heavily damped, approaching critical damping and records of sufficientlength to obtain a reliable frequency spectrum could not be obtained. However, it wasobserved that the sway, pitch, and yaw modes had natural periods of comparable length tothe natural period in surge (3.4 s).For the 2-D model, both the heave and roll modes are very important to the response of thebreakwater since their natural periods fall in the operating range of the breakwater (T = 0.97s corresponds to D/L = 0.22). Hence it should be expected that the heave and roll motionswill peak around D/L = 0.22 for the 2-D model.26For the 3-D model, which more truly represents the actual breakwater, the roll mode is not asimportant since its natural period in roll is considerably higher (approximately 2.46 s). Theheave mode can therefore be expected to be the dominant mode since its natural frequency isstill in the operating range of the breakwater (T = 0.83 s corresponds to D/L = 0.141).5.2 Breakwater MotionsThe importance of the breakwater motions is mainly due to their role in the transmission ofwaves past the breakwater. Incoming waves force heave, surge and other motions of thebreakwater which in turn create a radiation velocity potential which results in wavegeneration downwave from the breakwater. As well, the breakwater motions induce thetensions in the mooring lines.A body moving in the heave and surge directions in phase with incident waves (i.e. has samecircular or elliptical orbit as surrounding water particles) will not deter the propagation ofwaves past the body. This situation will arise when the body length is much smaller than thewavelength of the waves (D/L small). If however, the motion of the body is of a smalleramplitude or out-of-phase from the water particle orbits then part of the wave energy will bereflected and there should be a net reduction in wave height on the downwave side of thebreakwater. Ideally, the breakwater would have sufficient inertia to behave like a fixed bodyand wave transmission would occur only by overtopping of the breakwater and transmissionof energy under the breakwater.Some understanding of the situation can be gained by considering the response of a singledegree of freedom (SDOF) system. A SDOF system’s motion under periodic forcing isdetermined by the magnitude of the forcing and the frequency as shown in Fig. 5.2. Fourparameters, 8st (the static deflection produced by the magnitude of the force), o’i (frequencyof the forcing), o (the natural frequency of the system), and (the degree of damping) will27determine the amplitude and phase of the system’s response. A drastic reduction inamplitude and increase in phase shift occurs when the frequency of forcing is greater than thenatural frequency. For the case of a floating breakwater, the preceding statement suggeststhat if the frequency of the incident waves is greater than the natural frequencies of thebreakwater then wave transmission will be notably reduced.The situation under consideration is somewhat complicated by the additional degrees offreedom and the fact that the forcing is not independent of the motion. A more detailedmathematical description of the problem is given in Chapter 6. However, the SDOF systemcan still be useful in visualizing the response of the breakwater.5.2.1 Wave Flume Results and ObservationsFigure 5.3(b) shows the amplitude of the breakwater motions measured with the breakwatersecured by chain mooring lines. The data points on the graph correspond to test conditions1.1 to 1.8 and 7.1 to 7.5 as summarized in Table 5.1. For comparison purposes theamplitudes of motion are non-dimensionalized by the wave height. For D/L 0.15, surgeand heave motions are of approximately the same amplitude as the amplitude of orbit of awater particle at the water’s surface H/2). As well, the video record shows that themotions for these conditions were essentially in-phase with the incident wave train. Therewas little roll for these conditions because there was sufficient mooring line slack to allowthe centre of gravity to move freely within its orbit. Under these conditions, little or noreflection of the incoming waves should be expected. At about D/L 0.23, the breakwaterappears to undergo resonance in heave. At this frequency the orbit of the centre of gravity isnearly elliptical with the major axis inclined about 15° clockwise from the z-axis. The heaveamplitude is about 50% greater than the amplitude of the incident waves, whereas the surgeamplitude is considerably less than the amplitude of incident waves. As well, thebreakwater’s motion is almost completely out-of-phase with the incident wave train. For28tests performed at D/L >0.23, motions decreased dramatically as DIL increased and themotions continued to be out-of-phase with the incident waves.Figure 5.4(b) is a graph of the breakwater motions for essentially the same conditions exceptthe breakwater is constrained by nylon mooring lines. This data corresponds to tests 2.1 to2.8 and 8.1 to 8.5. At D/L 0.10, the breakwater appears to undergo resonance in asurge/roll mode. This resonant condition was not present with the chain mooring lines, andis almost certainly due to the added stiffness from the taut nylon lines. However thebreakwater’s motion was still fundamentally in-phase with the excitation. At larger D/L, thebreakwater’s response is essentially the same as with chain mooring lines but with oneexception. At the heave resonance condition (D/L 0.23), the roll response is significantlyless. This also may be due to the taut mooring lines causing some shifting of the surge androll mode shapes.Figures 5.5(b) and 5.5(c) show the effect of wave height on the non-dimensional motions.Figure 5.5(b) is based on test results from 3.1 to 3.4 and Fig. 5.5(c) on 3.5 to 3.8. Thesefigures show that there is little or no dependence of the non-dimensionalized motions on theincident wave height (i.e. the actual motions have a nearly linear dependence on waveheight).Figures 5.6(b), 5.6(c) and 5.6(d) show the effect of relative draft on the surge, heave, and rollmotions, respectively. These figures were compiled from the results of tests 4.1 to 4.16. Ingeneral, the results indicate that the motions decrease as the relative draft and inertiaincrease, as expected. A few exceptions to this general trend are present in Fig. 5.6(c) andare associated with resonant peaks in the heave response at different drafts.Figures 5.7(b), 5.7(c) and 5.7(d) were taken from the results of tests 6.1 to 6.8 and show theresponse of the breakwater with chain mooring lines for different degrees of slack present inthe lines. Less slack in the mooring lines tended to result in decreased heave and surge29motions. As well, the roll response increased. Since the mooring lines are fastened at thebottom of the breakwater, larger moments were induced by the increased rigidity of thebottom of the cylinder resulting in greater roll motions. The increased roll motions allow thebreakwater’s centre of gravity to move in a larger obit.5.2.2 Wave Basin ObservationsAs alluded to earlier, the 3-D tests essentially consisted of the same six tests within the range0.1 D/L 0.6 repeated for four different angles of incidence. Yaw, pitch, and swaymotions were expected for angles of incidence other than zero. As the angle of incidencewas increased, the net amount of breakwater motion decreased markedly. Rolling motion inparticular was much less for 9 00.Pitch and yaw motions were especially noticeable for the longer period waves (when9 0°). When combined with the surge and heave motions, the pitch and yaw motionsallowed the breakwater’s orbit to nearly match the orbit of the water particles along most ofthe length of the breakwater for these long period waves. No noticeable sway oscillationswere detected for any of the tests.5.3 Wave AttenuationWave energy can pass a floating breakwater and contribute to the transmitted wave height bythree means: energy transmitted under the breakwater, energy transmitted over thebreakwater (overtopping), and by transferring energy through the breakwater via breakwatermotions. In the model tests, a fourth mechanism, diffraction between the ends of thebreakwater and the walls of the flume or wave barriers existed. Diffraction was limited bykeeping this gap as small as possible. At field breakwater sites, diffraction will occur aroundthe ends of the breakwater arrays and through gaps between breakwaters (if gaps exist).30However, diffraction considerations are not included in the calculation of wave transmissioncharacteristics here.The breakwater model was observed to use all three of the wave protection mechanismslisted in Sec. 1.2 (wave reflection, out-of-phase damping, and turbulence) to varying degrees.The most prevalent mechanism for short period waves (D/L 0.30) was wave reflection.Out-of-phase motion and turbulence were more pronounced for waves of comparable periodto the breakwater’s natural period in heave (D/L 0.20 — 0.25). Waves with longer periodstended to transmit nearly completely past the breakwater.Figures 5.3(a) and 5.4(a) show the transmission coefficients for chain and nylon mooringlines respectively. Both figures show that the breakwater is ineffective for D/L (relativediameters) less than 0.20. A distinct decrease in transmission coefficient occurs as therelative diameter parameter increases from 0.15 to 0.20. Still, wave transmission remainsquite large (between 40% and 60%) for relative diameters ranging from 0.20 to 0.50.Figure 5.5(a) shows the variance of the transmission coefficient caused by altering the wavesteepness for two wave periods. The figure shows that the wave steepness does notsignificantly effect the transmission coefficient.Figure 5.6(a) shows the effect of relative draft on wave transmission. In general wavetransmission was somewhat better for relative drafts varying from 0.55 to 0.70. Relativedrafts greater than 0.70 give rise to excessive overtopping, which results in highertransmission coefficients even though breakwater motions were reduced by the increasedinertia.Figure 5.7(a) shows the influence of line slackness on wave transmission. It was expectedthat a decreased line slackness would decrease the wave transmission. However, the resultsare non-conclusive, probably due to the effect of the mooring line slackness on the naturalperiods and the breakwater motions. Decreasing the wave slackness, increases the effect of31the nonhinearities in the mooring response making it difficult to define the net effect on thesystem. Figures 5.8(a)-(b) show the effect of the attachment point on the transmissioncoefficient. The uncrossed arrangement shown in Fig. 2.2 gave marginally better results. Ingeneral, the overall performance of the breakwater was insensitive to variations in themooring line parameters.Figure 5.9(a) shows the wave transmission coefficients recorded for the wave basin tests.The figure shows wave transmission improves dramatically as the angle of incidence isincreased. When the angle of incidence is significantly different from 00, wave crests andtroughs are hitting the breakwater at the same instant along the length of the breakwaterinducing forces in opposite directions. The net result is that breakwater motions are reducedand hence greater wave reflection and lower wave transmission is achieved.5.4 Mooring Line ForcesRecords of the mooring line tension for both nylon and chain lines showed the forces in themooring lines were typically close to zero for a portion of the cycle with one sharp spike percycle when the line became taut. As well, the peak mooring line force often variedconsiderably from cycle-to-cycle. These two observations indicate that the mooring lines’behavior was very nonlinear. Figure 5.10 shows typical mooring line forces experienced bythe load cells as recorded during test 2.5 of the wave flume experiments.Figure 5.4(c) shows the mooring line forces measured for the base case with nylon mooringsnon-dimensionalized as defined by Eqn. 2.6. The mooring line forces decreased withincreasing D/L, corresponding with the decreased breakwater motions.Figure 5.5(d) shows the influence of wave height on the maximum forces experienced withnylon moorings. The graph shows that the maximum mooring line forces at a particular D/Lvalue increase linearly with the wave height.32Figure 5.9(b) shows the influence of wave angle on the forces measured with chain mooringlines. Here too, with chain moorings, the breakwater forces decrease dramatically as DJLincreases. Mooring line forces are much less for wave angles other than zero.5.5 Breakwater Internal StressesFigures 5.9(c)-(e) show the bending moments and torsion (non-dimensionalized as definedby Eqn. 2.7) experienced by the wave basin model at different angles of incidence. There isconsiderable scatter in the data due to the difficulty in obtaining stress measurements of themagnitude experienced during testing. However, horizontal and vertical bending momentstended to decrease with increasing D/L (shorter periods) and increasing angle of incidence.No significant torsion was induced in the breakwater for any of the conditions tested.5.6 Comparison to Rectangular Caisson ResultsResults from Byres [4], Nece and Skjelbria [17], and Nelson and Broderick [18] for arectangular caisson breakwater are compared here to results obtained for the circular cross-section breakwater. The rectangular caisson breakwater considered in the studies cited had awidth to depth ratio of 3.2:1 and was moored by chain lines. The test results from Byreswere obtained for monochromatic regular waves produced in a wave basin. Results fromNece and Skjelbreia were for ship-generated waves approaching at various angles ofincidence (from 0 to 36 degrees). Results from Nelson and Broderick were for the samebreakwater, but with wind-generated waves. Nelson and Broclenck used the average waveheight and period calculated from a spectral analysis of 8.5 minute records.The researchers cited above used the parameter, ka, as an indication of the breakwater’srelative size, where k is the wave number and a is the half width. In order to compare these33results to results for a circular-section, an effective diameter, D’, is defined for therectangular caisson. D’ is defined by equating the cross-sectional perimeter, P, of therectangular and circular sections:P = (for circular section)(5.1)=2w + 2d (for rectangular section)For a rectangular section with a width to depth ratio of 3:2:1 the conversion D’/L = O.266karesults. The comparison was based on equivalent perimeters since the magnitude of theperimeter is proportional to the amount of concrete needed to form the walls.Figure 5.11 compares the wave transmission characteristics observed for the circular cross-section floating breakwater to the transmission coefficients reported for a rectangular caissonbreakwater in the above studies. Figure 5.12 compares the motion response of the circularcross-section breakwater to motions observed by Byres for a rectangular caisson breakwater.Figure 5.11 shows that the circular and rectangular cross-sections perform similarly as thefrequency of forcing is increased. Both geometries are ineffective for values of D/L less thanabout 0.20 to 0.25. Because of the scatter in the data, no definitive conclusion can be drawnas to which cross-section performs better, although transmission coefficients for therectangular cross-section generally seem to be slightly lower.Figure 5.12 shows that heave and roll motions were nearly equivalent for both cross-sections.A resonance peak in the surge mode is present at D/L 0.27 for the rectangular caisson.This resonant peak was not observed for the circular cross-section and also surge motionswere considerably less for large values of D/L. These discrepancies could be due todifferences in mooring line properties between the two studies. As well, Byres reportedconcerns about the accuracy of some of his motion measurements.34CHAPTER 6: NUMERICAL MODELThe numerical model used is based on two component analyses: a hydrodynamic analysiswhich treats the problem of normal or oblique incident waves interacting with the breakwaterand is based on two-dimensional wave diffraction theory; and a mooring analysis, whichprovides the mooring line configurations, mooring line tensions and anchor forces. These aresummarized in Sec. 6.1 and Sec. 6.2, respectively. The hydrodynamic analysis for a 2-Dfloating body given in Sec. 6.1 is well documented by authors such as Chan and Hirt [5] andSarkaya and Isaacson [24]. The mooring analysis is that used by Isaacson [10] to quantifythe effect of nonlinear moorings on the floating body’s response.6.1 Hydrodynamic AnalysisThe flow about a long floating breakwater caused by incoming waves can be studied as thetwo-dimensional problem of a rigid floating body exposed to an incident wave train (see Fig2.1 for definition of variables). If certain conditions of linearity are met, it is possible torepresent irregular ocean waves as the superposition of linear regular waves of differentfrequencies. It can be shown that the resulting flow about the breakwater can be described asthe sum of the solutions to the simpler problem of linear waves incident on the breakwater.For simplicity, the problem will be stated only for waves approaching perpendicular to thebreakwater. However the theory can be extended to the three-dimensional problem ofoblique incident waves.In defining the problem in the above manner it is implicitly assumed that the fluid is inviscidand the flow is irrotational so that the velocity field can be described in terms of a velocitypotential, •. The horizontal and vertical velocities (u and w) are then given by:35(6.1) u= ; w=The continuity condition (conservation of mass) then reduces to Laplace’s equation:(6.2)The linearized boundary conditions for the problem are zero vertical velocity at the seabedwhich is assumed to be horizontal (Eqn. 6.3), the combined linear free surface condition(Eqn. 6.4), and the body-fluid interface condition requiring no flow through the rigid body(Eqn. 6.5).(6.3) atz=-d;t9zd2th dih(6.4)—f-=—g---- atz=O,wheretistime;dt dz(6.5) - = V on the surface of the cylinder;where V, is the velocity of the body normal to its surface and n is the direction normal tothe body surface. In addition to the boundary conditions, a radiation condition must beimposed to obtain a unique solution to the problem. The radiation condition requires that thedisturbed portion of the flow away from the body must represent waves with the same periodas the incident forcing traveling outward from the body.The method of solution adopted is to split the problem into: (i) a diffraction problem ofwaves incident upon a fixed body, and (ii) a radiation problem of forced oscillations of abody in calm water. The two problems are coupled by finding the forces acting on the fixedbody of the diffraction problem and applying these as the exciting forces in the radiationproblem. The total potential is expressed as the summation of an incident potential, a36scattered or diffracted potential, ,; and forced potentials; f3 caused by theheave, sway, and roll motions, respectively.(6.6) 0 0w3Ofl0f2’Pf3The governing equations and boundary conditions presented earlier must now be stated intenns of these potentials. The scattered and forced potentials represent the disturbed portionof the flow and as such must each satisfy the two-dimensional radiation condition whichrequires these potentials, denoted as , vary as:(6.7) oc e(jkW) as lxi —To further simplify the problem, the incident, scattered, and forced potentials aredecomposed using the knowledge that these potentials are oscillatory in time. As well, theincident and scattered potentials should be proportional to the amplitude of the incidentwaves, while the forced potentials will be proportional to the amplitudes of heave, sway, androll motions;,(3, respectively. Hence the following forms for the potentials can bederived:(6.8) • + = Re(A(q += forj = 1,2,3where the are complex amplitude coefficients for the harmonic motions of the three bodymotions. The partial potentials; ç), (p, i, q’j2, (f3, defined by the above equations arecomplex functions of position (x,y) that represent the magnitude and phase of the potentialswith respect to the incident flow. The boundary conditions, radiation condition, andLaplace’s equation stated earlier may now be expressed in terms of the partial potentials.376.1.1 Incident PotentialThe incident potential is defined as the flow existing in the absence of the breakwater. Forregular waves approaching perpendicular to the breakwater the incident potential is:irH(coshk(z-i-d)(6.9) = —I . isin(kx — cot)kT sinh(kd) )6.1.2 Scattered PotentialThe scattered potential is a result of the diffraction created by the presence of the body. It isindependent of the body motions and the boundary conditions are therefore defined with thebody fixed. The boundary condition on the corresponding fixed body surface is:(6.10) + =0 on the surface of the cylinderdn dnOther conditions on the scattered potential are the same as for the incident potential.Namely, no vertical velocity at the seabed, and the combined free surface condition at thestill water level must be satisfied for.In addition, the radiation condition (Eqn. 6.7) mustbe satisfied. Solution of the diffraction problem stated in this manner can be achieved usingvarious methods. The two most popular methods are a “wave source” method as outlined bySarpkaya and Isaacson [24] and a finite element method described by Newton [211.6.1.3 Forced Potentials and Body MotionsIn order for the total potential to satisfy Eqn. 6.5, the forced potentials must satisfy theboundary condition:(6.11) dlifl + df2 + = V, on the surface of the cylinder.38Eqn. 6.11 can be broken down into three separate equations with each forced potentialsatisfying the portion of the normal velocity due to motion in that mode. The forcedpotentials must also satisfy the other boundary conditions and Laplace’s equation. Byexpressing the problem in terms of partial potentials, the solution can be found using wavesource methods as in the case of the diffraction problem, except that the body boundarycondition is changed appropriately. Once this is accomplished the only remaining unknownsare the complex motion amplitudes, j’ s.Using the known partial potentials and carrying out suitable integrations, the unsteadyBernoulli equation may be used to develop an expression for the hydraulic force components.These can in turn be expressed in terms of; added mass components proportional to the bodyaccelerations, damping components proportional to body velocities, and exciting forcesassociated with the diffraction problem. Once the forces are split up in this manner, it ispossible to set up a complex matrix equation for the harmonic response of the floating bodybeing forced at an angular frequency, co.(6.12) (co2ImI+ [uj) — io4A,j + ([kj + [ki))() = (f(e) }where [4u] contains added mass coefficients, [] contains damping coefficients, and (f(e))is the vector of the exciting forces. Additional terms in the matrix equation are; the bodymass matrix, [m]; the linearized mooring stiffnesses, [k]; and the hydrodynamic stiffnesses,[k(h)]. A complex matrix inversion procedure can be used to solve Eqn. 6.12 for themagnitude and phase of the motions of the body. Once the solution is found the totalpotential can be found using Eqns. 6.6 and 6.8, and hence the problem is solved. As well,then quantities such as mooring line forces and the velocities and accelerations of the bodycan be calculated as needed.6.2 Mooring Analysis39The hydrodynamic analysis indicated above is carried out in conjunction with a mooringanalysis. For a specified three-dimensional mooring configuration and mooring lineproperties, the corresponding computer program first caries out a static analysis to obtain theequilibrium profiles of the moorings and the mooring line forces in the absence ofenvironmental loads due to wind, waves and currents. This mooring analysis is repeated fora set of unit displacements of the breakwater in order to provide the effective stiffnesscomponents of the breakwater for application to the hydrodynamic model. At this stage, thehydrodynamic analysis is carried out with these stiffnesses included in the equations ofmotion as indicated by Eqn. 6.12. This provides the breakwater motions and the wave driftforce in the presence of the moorings (assumed to behave with linear stiffnesses). Themooring analysis is then repeated with the steady environmental loads, including wind drag,current drag and the wave drift force, now assumed to be present, and this involves a balancebetween these forces and the mooring forces acting on the breakwater. This provides thesteady offset of the breakwater. Finally, the oscillatory breakwater motions which have beencalculated by the hydrodynamic analysis are now used to provide the extreme displacementsof the mooring line connection points, and the mooring analysis is carried out under theseconditions to obtain the maximum forces in the mooring line connections, the anchor forcesand mooring line tensions.6.3 Numerical ResultsThe numerical model has been applied to a series of conditions varying the dimensionlessparameters in a manner similar to the wave flume tests. Results plotted in Figs. 6.1 (chainmooring) and 6.2 (nylon mooring) correspond to the following base case:Breakwater geometry: D 3 mh = 2.25mWave climate: T = 3 - 6 s (varied)40H = up to 2 m (H/L constant)d = 15mMooring parameters: b = 5 m= 60mn= 1attachment point on bottom (as in Fig. 2.2)Mooring line parameters: chain nylonw’ (N/rn) = 140 20EA(N)= 2x108 2x106= 1.05 1.01In addition, the centres of gravity and buoyancy are taken to be 0.95 rn and 1.0 rn,respectively, below the water surface; and the roll radius of gyration is taken as 0.87 m. Theabove conditions correspond to the following dimensionless parameters:d/D =5Vd = 4H/L=0.035h/D = 0.75DIL = upto0.4chain nylonw7pgD = 890 x 10 130 x 10-6E’/pgD2= 4000 401.05 1.01The results obtained can therefore be applied to a range of alternative prototype conditionswith similar dimensionless parameters.41Figures 6.1 and 6.2 show the transmission coefficient, motion amplitudes and mooring lineforces (in N) as functions of D/L for the base case with chain mooring lines and with nylonmooring lines, respectively. The differences in the wave transmission and motion amplitudesbetween the two sets of data is very minor, suggesting that mooring properties play only aminor role in the breakwater’s response. Both figures show that the breakwater experiencesresonance in the heave mode at approximately D/L = 0.15. The resonant peak occurs at alower D/L (as compared to D/L = 0.22 from experiments) because of the higher relative draftwhich effectively reduces the buoyancy force. The wave transmission predicted for bothbase cases is between 75 and 100% for all values of D/L except for DIL = 0.15 where it isvery low.The maximum mooring line tensions predicted by the numerical model for the chainmoorings are much higher than for the nylon lines. This corresponds with the physicalreality. By virtue of the nylon moorings being in constant tension, the momentum of thebreakwater is absorbed throughout the cycle. As opposed to the chain moorings, which tendto experience high snapping forces over a short fraction of the cycle.The influence of breakwater draft, wave steepness, mooring line slackness, and mooring lineattachment points are further examined by altering the following parameters individually insubsequent sets of numerical tests, as shown below:h/D = 0.67, 0.75, 1.0 (chain mooring base case, see Fig. 6.3)H/L = 0.0175, 0.035, 0.070 (chain mooring base case, see Fig. 6.4)s/s0 = 1.05, 1.10 (chain mooring base case, see Fig. 6.5)attachment points : bottom, crossed, uncrossed (chain mooring, see Fig. 6.6)Figures 6.3(a)-(f) show the transmission coefficient, motion amplitudes and mooring lineforces as functions of D/L predicted for three values of relative draft, h/D. From the figures,we can see that the natural frequency predicted in heave increases (higher D/L) as the relative42draft decreases, as expected. For h/D = 0.67, the resonant condition is at DIL of about 0.19,and for a h/D = 0.75 at D/L = 0.15. For h/D = 1.0, no resonant peak is evident which agreeswith theory since the breakwater has no positive buoyancy.Figures 6.4(a)-(b) show the upwave and downwave mooring line forces as functions of D/Lfor three values of wave steepness H/L. The non-dimensionalized wave transmission andmotion amplitudes predicted by the numerical model were independent of H/L and so are notshown.Figures 6.5(a)-(b) show the upwave and downwave mooring line forces as functions of D/Lfor two values of line slackness, s/s0 for the base case with chain mooring lines. The figureindicates that mooring line forces increase dramatically as the line slackness is decreased.Figures 6.6(a)-(b) plot the mooring line forces as functions of D/L, showing the influence ofattachment points for the base case with chain mooring lines. The numerical model does notpredict any variance in forces due to changing the attachment points.6.4 Comparison of Numerical and Experimental ResultsFigure 6.7(a)-(d) shows the numerical results compared to experimental findings for waveflume test conditions 1.1 to 1.8 (chain mooring lines, s/s0=1.06). Figure 6.8(a)-(d) are asimilar set of graphs comparing numerical and experimental results for flume test conditions2.1 to 2.8 (nylon mooring lines).In general, there is good agreement between the numerical model and experimental data.The two sets of data indicate the same trends at approximately the same values of D/L. Thenumerical model tends to overestimate the wave transmission for D/L values greater than0.15. This effect may be due to an underestimation of damping effects caused by viscousaction which becomes more important at higher frequencies As well, the numerical model43tends to underestimate surge response, most likely due to an overestimation of the mooringline stiffness.44CHAPTER 7: EVALUATION OF PERFORMANCE7.1 General ConclusionsAs a result of the physical and numerical testing of a circular-section floating breakwater, abetter understanding of the role of the governing variables was gained. Some of the mostimportant points are summarized here:(i) The relative size of the floating breakwater, D/L, is a dominant parameter indetermining the efficiency of the breakwater. As DJL increases, wavetransmission decreases. To be effective, a circular floating breakwater shouldhave a diameter of at least one quarter of the wavelength of the design waves(D/L 0.25).(ii) The relative draft, h/D, is directly related to the natural frequency in heave. AshID h/D approaches 1, the natural frequency in heave approaches zero.Ideally the breakwater should be operated at a D/L value which correspondsto a forcing frequency greater than the natural frequency so that response willbe out-of-phase from the forcing. A local minimum in the wave transmissioncurve was observed when DIL was equal to the natural frequency of thebreakwater in heave.(iii) The breakwater motions decrease as h/D increases (due to increased inertia)but overtopping may occur resulting in higher transmission coefficients. Ah/D value of 0.6 - 0.7 performed best in testing (optimum h/D would dependon the D/L and H1/L values present in the wave climate of the location).(iv) Wave steepness, H/L, did not greatly effect the non-dimensionalized results.45(v) An increase in the slack in the mooring lines will tend to result in somewhatincreased breakwater motions and wave transmission but greatly reducedmooring line forces. It was found to be very difficult to maintain linepretension in nylon lines. The choice of mooring line does not appear tosignificantly affect the overall performance of the breakwater. Thisconclusion is supported by Cox [6].(vi) Positioning the mooring lines in an uncrossed arrangement seemed to reduceroll motion and result in slightly better wave transmission.(vii) The efficiency of the breakwater increases dramatically for incoming wavesapproaching obliquely (8 00). As well, mooring line forces and breakwatermotions were reduced. This conclusion contradicts Nece and Skjelbreia [17]who concluded that the angle of incidence did not affect wave transmission.However, the results obtained clearly show that wave transmission is reducedfor 800.(viii) Horizontal and vertical bending moments induced in the breakwater walls willbe an order of magnitude larger than any torsional moments.(ix) The wave transmission past the circular cross-section breakwater for aparticular wave period was comparable to that of a rectangular breakwater ofequivalent size. The amplitudes of the surge, heave, and roll motions of thecircular and rectangular sections were also very similar.7.2 Performance of Numerical ModelThe numerical model based on linear potential theory and linearized mooring stiffnessesprovided results which corresponded approximately with the physical results for most of the46conditions examined. The numerical model does not properly model the extremely nonlinearmooring forces. As well, the model does not truly reflect the viscous behaviour of the fluid.These two pitfalls (particularly the nonlinear moorings) prevent the numerical model fromproviding more accurate results, particularly concerning the prediction of peak mooring lineforces. However, as a whole the numerical model provides a good approximation of theresponse of the breakwater.7.3 Potential for Improvement and Further StudyFrom a study of related literature on similar floating breakwater designs, it becomes apparentthat there are several modifications to the design proposed which may improve the overallperformance of the breakwater. However most of these modifications would complicate thefabrication of the breakwater and it is difficult to determine without further study whetherthese modifications would be economically efficient.During the tests, it was noted that the breakwater’s surge motion was basically unconstrictedfor small displacements. A way of introducing pretension in to the mooring lines would behelpful in reducing surge motions. One method of achieving this goal is to include hangingweights on the mooring lines, as has been done for the breakwater at West Point, Washington[17]. The use of nylon cables in pretension is a good solution theoretically, but may beproblematic because of the tendency of the cables to undergo plastic elongation over time.Vertical barriers extending from the bottom of the breakwater (skirts) as shown in Fig. 1.8 ona rectangular caisson would certainly reduce wave transmission by decreasing wavetransmission underneath the breakwater, increasing added mass in roll and surge, andintroducing considerable turbulence. However they would also most likely introduceconsiderable internal stresses and increase mooring line forces. Horizontal barriers47extending from the sides of the breakwater may also be beneficial by virtue of increasing theadded mass in heave and roll and increasing turbulent dissipation.Results from the wave basin (3-D tests) suggest the possibility of a breakwater designed suchthat incident waves are always oblique to the breakwater’s axis. One method of achievingthis would be to arrange short lengths of breakwater connected in a zig-zag pattern. Theobvious disadvantages of this type of system would be the increased lengths of breakwaterrequired to protect an equivalent length of harbor and the difficulty of designing theconnections between breakwater units.Finally, it should be noted that the breakwater was only tested with regular periodic waves,not with random waves. On the basis of linear potential theory, superposition of thebreakwater’s response in regular waves can be used to predict response to a specified wavespectrum. However, linear potential theory does not account for effects such asnonlinearities associated with the moorings or with turbulent dissipation. Therefore, it wouldbe useful to test the breakwater in irregular wave conditions to determine its effectivenessand compare results with predictions based on a superposition of regular wave test results orthe numerical model.48BIBLIOGRAPHY[1] ASCE Ports and Harbors Task Committee, 1992. Progress Report on Small CraftHarbors, Proc. Ports ‘92 , ASCE, Seattle WA, Vol. 2.[2] Bai, K. J. and R. Yeung, 1974. Numerical Solutions to Free Surface Problems. 10thSymposium on Naval Hydrodynamics, Cambridge MA, pp. 609-647.[3] Blumberg, G. P. and R. I. Cox, 1988. Floating Breakwater Physical Model Testingfor Marina Applications, Bulletin of the Permanent International Association ofNavigational Congresses, No. 63, pp. 5-13.[4] Byres, R. D., 1988. Floating Breakwaters in British Columbia. M.A.Sc. Thesis,Dept. of Civil Engineering, University of British Columbia, Vancouver BC.[5] Chan, R. K. and Hirt, C. W. 1974. Two Dimensional Calculations of the Motion ofFloating Bodies. 10th Symposium on Naval Hydrodynamics, Cambridge MA, pp. 667-683.[6] Cox, J. C., 1989. Design of a Floating Breakwater for Charleston Harbor, SouthCarolina, Proc. Ports ‘89 , ASCE, Boston MA, pp. 411-420.[7] Giles, M. L. and R. M. Sorenson, 1979. Determination of Mooring Loads and WaveTransmission for a Floating Tire Breakwater, Proc. Coastal Structures ‘79, AS CE,Alexandria VA, Vol. 2, pp. 1069-1086.[8] Greenhow, M. and Y. Li, 1987. Added masses for circular cylinders near orpenetrating fluid boundaries - review, extension and application to water-entry - exit andslamming, Ocean Engineering, Vol. 14, No. 4, pp. 325-348.[9] Isaacson, M., 1993. Hydrodynamic Coefficients of Floating Breakwaters, Proc.1993 Annual Conference of the Canadian Society for Civil Engineering, Fredericton NB,Vol. 1, pp. 485-494.[10] Isaacson, M., 1993. Wave Effects on Floating Breakwaters, Proc. 1993 CanadianCoastal Conference, CC-SEA, Vancouver BC, Vol. 1, pp. 53-65.49[11] lsaacson, M. and 0. Nwogu, 1987. Directional Wave Effects on Long Structures,Journal of Offshore Mechanics and Arctic Engineering, ASME, Vol. 109, No. 2, pp. 126-132.[12] Jones, D. B., 1971. Transportable Breakwaters- A Survey of Concepts, TechnicalReport R-727, Naval Civil Engineering Laboratory, U. S. Navy.[13] Kim, C. H., 1969. Hydrodynamic Forces and Moments on Heaving, Swaying, andRolling Cylinders on Water of Finite Depth. Journal of Ship Research, Vol. 13, pp. 137-154.[14] McCartney, B. L., 1985. Floating Breakwater Design, Journal of Waterway, Port,Coastal, and Ocean Engineering, Vol. 111, No. 2, pp. 304-317.[15] McLaren, W. L., 1981. Preparation of Floating Breakwater Manual, Proc. 2ndConference on Floating Breakwaters, University of Washington, Seattle WA, pp. 22-47.[16] Muschell, J. E. and J. H. Schiak, 1989. Floating Breakwater for Small RecreationalHarbors, Proc. Ports ‘89, ASCE, Boston MA, pp. 44-53.[17] Nece, R. E. and N. K. Skjelbreia, 1984. Ship wave attenuation tests of a prototypefloating breakwater. Proc. Coastal Engineering 1984, pp. 2514-2529.[18] Nelson, E. E. and L. L. Broderick, 1984. Floating breakwater prototype testprogram. Proc. 41st Meeting of the Coastal Engineering Research Board, U.S. ArmyCoastal Engineering Research Center.[19] Newman, J. N. 1977. Marine Hydrodynamics. M.I.T. Press, Mass., pp. 285-311.[20] Newman, 3. N. 1962. The Exciting Forces on Fixed Bodies in Waves. Journal ofShip Research, Vol. 6, pp. 10-17.[21] Newton, R. E. 1975. Finite Element Analysis of Two Dimensional Added Mass andDamping. Finite Elements in Fluids - Vol. 1, editors. R. H. Gallagher, J. T. Oden, C.Taylor, and 0. C. Zieniewicz, John Wiley, New York NY, pp. 2 19-232.50[22] Ofuya, A. 0., 1968. On Floating Breakwaters, Queen’s University, CivilEngineering Report No. 60.[23] Rao, S. S., 1990. Mechanical Vibrations, 2nd ed., Addison-Wesley Publishing,Reading, MA.[24] Sarpkaya, T. and M. Isaacson, 1981. Mechanics of Wave Forces on OffshoreStructures , Van Nostrand Reinhold, New York NY.[25] Van Damme, L. V., D. J. Vandenbossche and G. Gyselynck, 1985. The ZeebruggeBreakwaters, Developments in Breakwaters: Proc. Breakwaters ‘85, ICE, London, England,pp. 285-286.[26] Vugts, 3. H., 1968. The Hydrodynamic Coefficients for Swaying, Heaving andRolling Cylinders in a Free Surface, International Shipbuilding Progress, Vol. 15, pp. 251-276.[27] Werner, G., 1988. Experiences with Floating Breakwaters, a literature review,Bulletin of the Permanent International Association of Navigational Congresses, No. 63,pp. 23-30.5100000______-0000000b•0o:t)00000(_) 0_____-iI.-000C0 0C00000._._._____________0__0peGUi•obàoooj:’0e000————eq CD CDpp0000 eq0000000 CD 0- 0 0——ppe_CDbooo-eqppppp00000_-———00%O—0%Table 3.1 Experimental Program for wave flume testsBreakwater Specifications Wave CharacteristicsTEST Draft Mooring Connection Slackness PeriodNCX (hit)) Material Pt. s/so T (s) D/L Hi (m)1.1 0.579 Chain Bottom 1.060 0.79 0.329 0.0601.2 0.579 Chain Bottom 1.060 0.95 0.230 0.0871.3 0.579 Chain Bottom 1.060 1.11 0.174 0.1221.4 0.579 Chain Bottom 1.060 1.27 0.139 0.1231.5 0.579 Chain Bottom 1.060 1.42 0.116 0.1211.6 0.579 Chain Bottom 1.060 1.58 0.100 0.1291.7 0.579 Chain Bottom 1.060 1.74 0.088 0.1191.8 0.579 Chain Bottom 1.060 1.90 0.079 0.1372.1 0.579 Nylon Bottom 1.000 0.79 0.329 0.0602.2 0.579 Nylon Bottom 1.000 0.95 0.230 0.0982.3 0.579 Nylon Bottom 1.000 1.11 0.174 0.1322.4 0.579 Nylon Bottom 1.000 1.27 0.139 0.1362.5 0.579 Nylon Bottom 1.000 1.42 0.116 0.1312.6 0.579 Nylon Bottom 1.000 1.58 0.100 0.1292.7 0.579 Nylon Bottom 1.000 1.74 0.088 0.1192.8 0.579 Nylon Bottom 1.000 1.90 0.079 0.1373.1 0.579 Nylon Bottom 1.000 1.11 0.174 0.0633.2 0.579 Nylon Bottom 1.000 1.11 0.174 0.0843.3 0.579 Nylon Bottom 1.000 1.11 0.174 0.1063.4 0.579 Nylon Bottom 1.000 1.11 0.174 0.1323.5 0.579 Nylon Bottom 1.000 1.42 0.116 0.0623.6 0.579 Nylon Bottom 1.000 1.42 0.116 0.0813.7 0.579 Nylon Bottom 1.000 1.42 0.116 0.1023.8 0.579 Nylon Bottom 1.000 1.42 0.116 0.1324.1 0.579 Nylon Bottom 1.000 0.95 0.230 0.0984.2 0.579 Nylon Bottom 1.000 1.11 0.174 0.1324.3 0.579 Nylon Bottom 1.000 1.27 0.139 0.1364.4 0.579 Nylon Bottom 1.000 1.42 0.116 0.1314.5 0.657 Nylon Bottom 1.000 0.95 0.230 0.0984.6 0.657 Nylon Bottom 1.000 1.11 0.174 0.1324.7 0.657 Nylon Bottom 1.000 1.27 0.139 0.1364.8 0.657 Nylon Bottom 1.000 1.42 0.116 0.1314.9 0.738 Nylon Bottom 1.000 0.95 0.230 0.0984.10 0.738 Nylon Bottom 1.000 1.11 0.174 0.1324.11 0.738 Nylon Bottom 1.000 1.27 0.139 0.1364.12 0.738 Nylon Bottom 1.000 1.42 0.116 0.1314.13 0.832 Nylon Bottom 1.000 0.95 0.230 0.0984.14 0.832 Nylon Bottom 1.000 1.11 0.174 0.1324.15 0.832 Nylon Bottom 1.000 1.27 0.139 0.1364.16 0.832 Nylon Bottom 1.000 1.42 0.116 0.1315.1 0.579 Nylon Bottom 1.000 1.11 0.174 0.1325.2 0.579 Nylon Bottom 1.000 1.42 0.116 0.1315.3 0.579 Nylon Crossed 1.000 1.11 0.174 0.1325.4 0.579 Nylon Crossed 1.000 1.42 0.116 0.1315.5 0.579 Nylon Uncrossed 1.000 1.11 0.174 0.1325.6 0.579 Nylon Uncrossed 1.000 1.42 0.116 0.13153Table 3.1 Experimental Program for wave flume tests (cont.)Breakwater Specifications Wave CharacteristicsTEST Draft Mooring Connection Slackness PerIodNC (hJD) Material Pt. s/so T (s) D/L Hi (m) HilL6.1 0.579 Chain Bottom 1.060 1.11 0.174 0.122 0.0666.2 0.579 Chain Bottom 1.060 1.42 0.116 0.121 0.0446.3 0.579 Chain Bottom 1.020 1.11 0.174 0.132 0.0716.4 0.579 Chain Bottom 1.020 1.42 0.116 0.131 0.0476.5 0.579 Chain Bottom 1.000 1.11 0.174 0.132 0.0716.6 0.579 Chain Bottom 1.000 1.42 0.116 0.131 0.0476.7 0.579 Chain Bottom 1.041 1.11 0.174 0.132 0.0716.8 0.579 Chain Bottom 1.041 1.42 0.116 0.131 0.0477.1 0.579 Chain Bottom 1.046 0.63 0.518 0.051 0.0817.2 0.579 Chain Bottom 1.046 0.71 0.408 0.056 0.0727.3 0.579 Chain Bottom 1.046 0.79 0.330 0.065 0.0677.4 0.579 Chain Bottom 1.046 0.95 0.230 0.099 0.0717.5 0.579 Chain Bottom 1.046 1.11 0.173 0.130 0.0708.1 0.579 Nylon Bottom 1.000 0.63 0.518 0.051 0.0818.2 0.579 Nylon Bottom 1.000 0.71 0.408 0.056 0.0728.3 0.579 Nylon Bottom 1.000 0.79 0.330 0.065 0.0678.4 0.579 Nylon Bottom 1.000 0.95 0.230 0.099 0.0718.5 0.579 Nylon Bottom 1.000 1.11 0.173 0.130 0.0709.1 0.579 Chain Uncrossed 1.047 0.63 0.518 0.051 0.0819.2 0.579 Chain Uncrossed 1.047 0.79 0.330 0.065 0.0679.3 0.579 Chain Uncrossed 1.047 0.95 0.230 0.099 0.0719.4 0.579 Chain Crossed 1.046 0.63 0.518 0.051 0.0819.5 0.579 Chain Crossed 1.046 0.79 0.330 0.065 0.0679.6 0.579 Chain Crossed 1.046 0.95 0.230 0.099 0.07154Table 4.1 Experimental program and results for wave basin testsAngle Wave Characteristics Mooring Breakwater Wall ForcesTEST of Incidence Tp D/L Hi Kt Forces -Ioriz. Bendin; Vert. Bending TorsionNO. (deg) (s) (m) (%) Cf Cm Cm Cm1.1 0 0.411 0.573 0.0129 28.10% 0.0079 0.131 0.155 0.0201.2 0 0.516 0.364 0.0419 60.13% 0.0053 0.067 0.063 0.0101.3 0 0.652 0.228 0.0452 84.34% 0.0290 0.112 0.113 0.0091.4 0 0.780 0.160 0.0442 78.86% 0.0465 0.105 0.094 0.0101.5 0 0.863 0.132 0.0437 86.05% 0.0750 0.111 0.113 0.0121.6 0 1.068 0.092 0.0524 86.55% 0.0674 0.072 0.072 0.0462.1 15 0.413 0.567 0.0251 9.04% 0.0024 0.040 0.097 0.0172.2 15 0.520 0.358 0.0380 19.87% 0.0024 0.109 0.159 0.0182.3 15 0.655 0.226 0.0511 42.09% 0.0071 0.141 0.177 0.0142.4 15 0.751 0.172 0.0521 70.46% 0.0104 0.126 0.130 0.0112.5 15 0.872 0.130 0.0475 62.48% 0.0210 0.112 0.120 0.0092.6 15 1.085 0.089 0.0609 67.89% 0.0866 0.091 0.082 0.0463.1 30 0.414 0.563 0.0205 18.31% 0.0037 0.043 0.075 0.0193.2 30 0.521 0.356 0.0460 31.18% 0.0017 0.062 0.101 0.0143.3 30 0.653 0.227 0.0522 27.14% 0.0036 0.100 0.123 0.0113.4 30 0.749 0.173 0.0416 56.19% 0.0096 0.238 0.253 0.0163.5 30 0.864 0.132 0.0454 55.46% 0.0174 0.236 0.271 0.0123.6 30 1.085 0.089 0.0637 71.73% 0.0291 0.131 0.140 0.0114.1 45 0.412 0.570 0.0249 20.85% 0.0021 0.022 0.038 0.0084.2 45 0.520 0.358 0.0459 14.59% 0.0023 0.040 0.035 0.0124.3 45 0.651 0.228 0.0507 32.29% 0.0024 0.062 0.056 0.0134.4 45 0.759 0.169 0.0580 21.95% 0.0034 0.128 0.121 0.0104.5 45 0.868 0.130 0.0630 48.13% 0.0026 0.196 0.204 0.0114.6 45 1.079 0.089 0.0529 86.48% 0.0088 0.207 0.236 0.016Parameters Draft, hJD=0.735 Attachment point spacing;held constant: Diameter, 0=0.151 m n=2, b=0.66mSlackness, s/so=1.02 Mass, m 28.88 kgWater Depth, d=0.44 m55Table 5.1 Summary of experimental results from wave flume testsMooring Forces Non-Dimensional Breakwater MotionsTEST Kt Cf Surge RAO Heave RAO Roll RAONC D/L (%) Upstream )ownstrear Offset/(H12) Amp/(H12) AmpI(H12) rads*D/H1.1 0.329 69.7% n/a n/a 1.16 0.17 0.57 0.981.2 0.230 67.0% n/a n/a 0.73 0.71 1.69 1.131.3 0.174 92.3% n/a n/a 0.11 0.90 1.46 0.591.4 0.139 104.8% n/a n/a 0.13 1.11 1.26 0.701.5 0.116 101.1% n/a n/a 0.09 1.03 1.16 0.481.6 0.100 105.3% n/a n/a 0.07 1.15 1.07 0.351.7 0.088 102.7% n/a n/a 0.05 1.38 1.27 0.321.8 0.079 94.4% n/a n/a 0.05 1.36 1.01 0.212.1 0.329 47.9% 0.36 0.46 0.03 0.47 0.90 0.502.2 0.230 49.2% 0.45 0.38 0.04 0.50 1.32 0.702.3 0.174 81.6% 0.38 0.39 -0.10 0.77 1.08 0.792.4 0.139 80.4% 0.37 0.44 -0.05 0.90 1.02 0.862.5 0.116 90.4% 0.40 0.41 -0.13 1.15 1.03 1.282.6 0.100 81.8% 0.43 0.58 -0.16 1.49 1.09 1.592.7 0.088 114.0% 0.73 0.85 -0.21 1.88 1.28 1.842.8 0.079 99.5% 0.65 0.70 -0.15 1.71 1.27 1.903.1 0.174 83.8% 0.34 0.38 -0.06 0.74 1.07 0.743.2 0.174 8 1.3% 0.34 0.39 -0.01 0.72 1.09 0.763.3 0.174 79.9% 0.34 0.38 -0.01 0.68 1.08 0.783.4 0.174 81.3% 0.37 0.38 0.00 0.70 1.14 0.803.5 0.116 86.5% 0.29 0.49 -0.03 1.17 1.02 1.253.6 0.116 86.3% 0.31 0.51 -0.04 1.14 1.06 1.283.7 0.116 89.1% 0.31 0.49 -0.05 1.13 1.05 1.393.8 0.116 94.2% 0.33 0.49 -0.06 1.25 1.18 1.384.1 0.230 51.3% 0.45 0.38 0.04 0.50 1.32 0.704.2 0.174 77.7% 0.38 0.39 -0.10 0.77 1.08 0.794.3 0.139 77.3% 0.37 0.44 -0.05 0.90 1.02 0.864.4 0.116 94.8% 0.40 0.41 -0.13 1.15 1.03 1.284.5 0.230 70.9% 0.48 0.22 0.09 0.60 0.83 0.624.6 0.174 73.8% 0.52 0.36 0.02 0.77 1.31 1.004.7 0.139 81.5% 0.36 0.52 -0.01 0.82 1.21 0.814.8 0.116 93.5% 0.34 0.51 -0.07 1.02 1.20 1.124.9 0.230 90.0% 0.23 0.21 -0.03 0.53 0.28 0.594.10 0.174 81.8% 0.29 0.27 -0.02 0.61 0.56 0.714.11 0.139 86.9% 0.50 0.46 -0.03 0.79 1.43 0.864.12 0.116 92.0% 0.45 0.48 -0.08 0.87 1.23 1.024.13 0.230 91.5% 0.19 0.28 0.01 0.54 0.14 0.604.14 0.174 92.2% 0.23 0.31 -0.01 0.64 0.26 0.604.15 0.139 95.1% 0.32 0.36 -0.01 0.79 0.33 0.744.16 0.116 89.7% 0.39 0.34 0.01 0.92 0.58 0.815.1 0.174 82.3% 0.41 0.36 0.00 0.72 1.20 0.825.2 0.116 91.8% 0.30 0.59 -0.03 1.20 1.09 0.985.3 0.174 84.4% 0.34 0.24 0.06 0.73 1.13 0.755.4 0.116 95.8% 0.24 0.32 0.00 1.14 1.04 1.115.5 0.174 78.3% 0.69 0.57 -0.05 0.83 0.83 1.095.6 0.116 82.8% 0.75 0.75 -0.13 1.35 1.05 1.2956Table 5.1 Summary of experimental results from wave flume tests (cont.)Mooring Forces Non-Dimensional Breakwater MotionsTEST Kt Cf Surge RAO Heave RAO Roll RAONC D/L (%) Upstream Downstrean Offset/(H12) Amp/(H12) Amp/(Hf2) rads*D/H6.1 0.174 92.3% nJa n/a 0.11 0.90 1.46 0.596.2 0.116 101.1% n/a n/a 0.09 1.03 1.16 0.486.3 0.174 72.0% 1.57 1.65 0.05 0.48 1.18 0.776.4 0.116 87.6% 0.79 2.28 0.04 1.11 1.10 1.036.5 0.174 89.4% 1.32 1.46 0.00 0.69 0.78 0.826.6 0.116 95.2% 1.85 1.80 -0.02 0.99 0.76 1.276.7 0.174 81.6% 1.22 0.64 0.09 0.71 1.36 0.696.8 0.116 90.5% 0.96 1.41 0.03 1.03 1.08 0.667.1 0.518 30.7% 0.00 0.00 0.66 0.06 0.10 0.297.2 0.408 61.9% 0.00 0.00 0.43 0.14 0.32 0.647.3 0.330 61.4% 0.00 0.00 0.47 0.21 0.55 0.897.4 0.230 38.9% 0.60 0.06 0.50 0.38 1.46 1.077.5 0.173 76.8% 1.36 0.90 0.09 0.63 1.28 0.618.1 0.518 34.3% 0.00 0.11 -0.01 0.14 0.08 0.328.2 0.408 55.0% 0.05 0.15 -0.02 0.35 0.39 0.418.3 0.330 47.0% 0.20 0.21 0.01 0.47 0.74 0.518.4 0.230 52.7% 0.42 0.28 0.19 0.54 1.35 0.708.5 0.173 84.0% 0.42 0.36 0.00 0.69 1.11 0.799.1 0.518 36.6% 0.00 0.00 0.51 0.08 0.08 0.279.2 0.330 59.6% 0.00 0.00 0.67 0.29 0.57 0.919.3 0.230 46.0% 1.45 0.06 -0.09 0.95 1.43 1.299.4 0.518 32.5% 0.00 0.00 0.50 0.30 0.24 0.329.5 0.330 58.7% 0.00 0.00 0.47 0.26 0.55 0.799.6 0.230 39.3% 0.22 0.04 0.63 0.35 1.39 0.9557(n 00—I.*(t B )— Cc, I-t 0I-.\D0ooCD nj0 C I CD CD I—. Iopoopooooo0C.D0000-.1-Q’LALAUi0Ui0cLAC00000LA00cQc. 0 z0000000000..0000D -‘oppoppppppg0O\O00-—0LALA)00040LA00.000C0>.000000000020CLAALAJi)b)LALA00(A00.‘.00’t’30-000*.-+000000000-i--6’bbo’.ob0‘.0400LA‘.0LA0.C00000000000II00’i‘.0i-’LALA—00&-J4—00QLALAOz00000000.i_..i_.0-LA0C)0i-’i-004.i—iLAi-’‘.t’.)‘.0j..0LALAC’0’.00Q0-LAi—.i-.S0----——---————-0—.0000LA..4.LA•0LA‘.0000‘4t’34‘.0(AOOOLA00LA-J SD:.Ui-rj (iq C-) :!‘. CD 1 CD CD -i cuF1in0 I‘I 0: 6M mF1 [Iifn___/_-__-( :__80 Co of a,00,00CO‘:‘:::u‘k”i’irritypcal 18-fke adaI.‘9I1I’ ‘f.,’Uooinq IM6 eok af Wdrn CW)Fig. 1.2 Floating tire breakwater, [7]./Fig. 1.3 Equiport breakwater, [27].60cQ 0 CD 0H(19 -t CD CD -4m C) -4 0 zr1C.) -4 0 I0 -4 r ft (.4 0 0 •d.,.rz000- fl44 c—I 1-4’. z 3 ‘.4 I-a’ 0 C-, CD CDC,CD oC))z ag•CD0o cli.Cl) CDg)C) .-I0 8 CD CD C’)0•irJQ (I) CDI CD0 0 I______—iL S.‘•r.0 0.8 0.6OILas(3a.0‘pz0U,a,z4(a) floating tire breakwaters(b) floating rectangular caisson breakwatersFig. 1.7 Comparison of transmissability of rectangular caissonand tire breakwaters, [12].C,0C,1171I4I1.6 1.4 1.2— — 1 2.0 • IV 14a7fl CT St. 1.0 0/4 •—— 8. 0. IV *SUU$ (T*p..p*0 •a.o—— I • LI IT USIUS C? *L,IQ WI • 0.1*0.4 02I.c.S II.‘?0.e——— - —. —--——-—- - ...——3—I.. II. IIS•.......,•1’(3-: —i:--; :—- -01.5.4.2 1.0 0.8— O/La • .. — •—— I • 0$ IV 8(22 I I’C11t? ‘8—— I 7.11 — ST 071I75.I$IS— I • 1.10 — IT UCUC. 11710.6 0.4 063I 4.I..I—_I 5 Double withSingle 2 m intermediate-,-‘“ç I i1rskirtI2 Double I4s. I6 Double with__________4 m intermediate LI 72________3 Triple 4Skirt 4__ __ _ __I “ I4 Double with I I 7 Catamaran ‘“ç.1 m intermediate . /Nç, .‘-4 1skirt1.01—._•...•.5___. — II0.8 —#1 7——I-.— 3zIII zg 0.6 /I’U- //Z__.1__ 4 3V0.4 1•—•U,0.270 I I I ItO 1.5 2.0 2.5 3.0 3.5 4.0WAVE PERIOD Cs)Fig. 1.8 Comparison of transmissability of various caissonbreakwater types, [3].64zLbottom unciossedFig. 2.2 Mooriflg line attachment point arrangements.K6420Fig. 2.3 Importance of inertial and viscous effects, [24].dFig. 2.1 Definition of design parameters for proposedbreakwater system.crossed0 0.1 0.2 0.3 0O/t.65WavePaddlewidth =0.60mdepth = 0.60 mFig. 3.1 Experimental set-up used in wave flume tests.20 m 2.6mModel(D=0.32 m)7mHoldingTank66______BreakwaterMotionsFig. 3.2 Schematic layout of wave generation and data collection hardware.WaveHeights_Mooring LineForcesbLL’IFig. 3.3 Photgraph of wave probes.67Fig. 3.5 Photograph of model brealcwater used in wave flume tests.68Fig. 3.4 Photograph of a load cell.69Fig. 4.1 Photograph of wave basin.Wave Paddle Ji]Strain gagetest section5m13.7m 8.8m - — -___6rnBeacIi1 8mN N 4 NN INFig. 4.2 Experimental set-up used in wave basin tests.70Fig. 4.3 Arrangement of strain gages.Fig. 4.4 Photograph of model breakwater used in wave basin tests.71z,2.001.6zFig. 5.1 Defmition sketch for six degrees of freedom.Fig. 5.2 Response of a SDOF system to periodic forcing, [231.72y, sway= 0.0yawrollpitch x, surge0 0.4 0.8 1 1.2 1.6 2.0 2.4 2.8 3.01.0Frequency ratio: r == 0.01.5 2.0 2.5Frequency ratio:r =I I I= I (a)- o000 s/s0 = 1.0460 00.8 -.00K 0.6-t0.4.0.2-0- I I I0 0.1 0.2 0.3 0.4 0.5 0.6D/LI I I(b)+ Surge (Amp/(Ht2))• Heave (Amp/(H/2))1.5- 0 Roll (rads*D/H)••S.+S .Ce._1— + S.bO\ +/•SS_q. S.9 s.., +S *S. S.S.0.5- 5.... 5V.V V.5+ •5..•1.d•.-* 1—0 I I I I0 0.1 0.2 0.3 0.4 0.5 0.6D/LFig. 5.3 Wave flume test results for base case with chain. (a) transmission coefficient,(b) motion amplitudes.73+ Surge (Amp/(H12))Heave (Amp/(Ht2))0 Roll (rads*D/H)1.2-(a)1- 000.8- ° 0Kt 0.6-0 0o0.4 -00.20- I I I I0 0.1 0.2 0.3 0.4 0.5 0.6D/L2- I I I I(b)1*1.5-_____________llb.RAO 1-B0.5-I I I I I0 0.1 0.2 0.3 0.4 0.5 0.6D/LFig. 5.4 Wave flume test results for base case with nylon moorings. (a) transmissioncoefficient, (b) motion amplitudes.74____________ID Upstream Mooring Forces4’ Downstream Mooring ForcesI I I I0.0 0.1 0.2 0.3 0.4 0.5 0.6Fig. 5.4 Wave flume test results for base case with nylon moorings (cont.).(c) mooring line forces.4’04’0(c)Cf1.00.80.60.4-8.2-0.00 4’ H4’CD/L751.2 I I I1.5-RAO 1.0-0.02 0.04 0.06Hi/L—a———— D/L=. 116 I (a)---.-..o—... D/L=.1730.08 0.10Fig. 5.5 Wave flume test results showing the influence of wave steepness H/L for thecase of nylon mooring lines. (a) transmission coefficient for D/L = 0.116 and0.173, (b) motion amplitudes for D/L = 0.116.•.0—-1.00.8-K 0.6t0.4-0.2-. I I I I0.00 0.02 0.04 0.06 0.08 0.102.0HLI I I I—+--•• Surge (Amp/(H12))—0——— Heave (AmpI(H/2))----0---- Roll (rads*D/H)(b)•00-+... .0.5 -0.0- —0.00762.0 I I I ISurge (Ainp/(H/2)) (c)—0——-— Heave (Amp/(Ht2))1.5 O”- Roll (rads*D/H)RAO 1.0-0.5 -0.0- I I0.00 0.02 0.04 0.06 0.08 0.10HL1.0 I I I ——— DIL=0.173, Upstream(d)—0-— • Downstream0.8 D/L=0.116, Upstream0, Downstream0.6-Cf0.4- 0— —— —a0•0.20.0 I I I I0.00 0.02 0.04 0.06 0.08 0.10Hi/LFig. 5.5 Wave flume test results showing the influence of wave steepness HJL for thecase of nylon mooring lines (cont.). (c) motion amplitudes for D/L = 0.173,(d) mooring line forces forD/L = 0.116 and 0.173.771.2— I I I I I(a)K 0.6..________—a--— h/I) = 0.579—+-— h/I) = 0.657O.2 h/D=O.738-—*--— h/I) = 0.8320.0- I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.:DIL1.50 I I I(b)0.00 0.05 0.10 0.15 0.20 0.25 0.30D/LFig. 5.6 Wave flume test results showing the influence of relative draft h/D for the caseof nylon mooring lines. (a) transmission coefficient, (b) surge RAO.781.50- I—U——— hID = 0.579——. h/D = 0.657----0---- h/D = 0.738----*---- h/D = 0.8320.00-— I I0.00 0.05 0.10 0.15 0.20I I I I I0.00- I I I I I -0.00 0.05 0.10 0.15 0.20 0.25 0.30D/LFig. 5.6 Wave flume test results showing the influence of relative draft h/D for the caseof nylon mooring lines (cont.). (c) heave RAO, (d) roll RAO.1.25-1.00-Heave 0.75-RAO0.50-0.25 -(c)D/L0.25 0.301.50-1.25-1.00-RollRAO 0.75-0.50-0.25(d)791.20- 1 I I(a)1.00- a0.80K 0.60-t0.40-a s/s0 = 1.00• s/s0 = 1.020.20- 0 s/s0= 1.04a = 1.060.00-0.00 0.05 0.10 0.15 0.20 0.25 0.30D/L1.50- I I I I —(b)1.251.00- 8aSurgeRAO a0.50•0.25-0.00-0.00 0.05 0.10 0.15 0.20 0.25 0.30D/LFig. 5.7 Wave flume test results showing the influence of line slackness, s/so for thecase of chain mooring lines. (a) transmission coefficient, (b) surge RAO.1.50- I I I: (c)1.25ae1.00-HeaveRAO 0.75 - a0.50-O s/s =1.00• s/so = 1.020.25 - 0 s/s0 = 1.04A S/SO = 1.0600.00- I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.D/L1.50— I I I I I(d)1.25 a1.00-aRoll 0.75-RAO o0.50-0.25 -0.00- I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30D/LFig. 5.7 Wave flume test results showing the influence of line slackness, s/so for thecase of chain mooring lines (cont.). (c) heave RAO, (d) roll RAO.811.20- I I Io c000 0(a)00.0C.9I• I — I0.0 0.1 0.2 0.3 0.4 0.5 0.6DILI I I I I1.00-0.80 -K 0.60t0.400.200.00 -______1.201.00-0.80K 0.60t0.40 -0.20 -0.00-D)LFig. 5.8 Wave flume test results showing the influence of mooring line attachment pointson transmission coefficient. (a) chain mooring lines, (b) nylon mooring lines..000 @ Bottom• @Sides (Crossed)0 @Sides (Uncrossed)0(b)I I I I I0.0 0.1 0.2 0.3 0.4 0.5 0.6821.2- I I I0 0 degrees (a)10- l5dcgreesO- 3Odegrees0.:(b)O.080.06-CF0.02-..-0 010203 0.4 5O.6Fig. 5.9 Wave basin test results showing the influence of the angle of wave incidence.(a) transmission coefficient, (b) mooring line forces.83025- 0 0 degrees(c)5“O 15 degrees0.20 - ---0---- 30 degrees/ \ 45 degreesCMh 0.15 - ; \ \.....0 204006: \ .CMVo.:(e)0.250.20C 0.15-Mt0.10-0.05 -0.00 I I I I I0 0.1 0.2 0.3 0.4 0.5 0.6D/LFig. 5.9 Wave flume test results showing the influence of the angle of waveincidence (cont.). (c) horizontal bending moment, (d) vertical bendingmoment, (e) torsion.84(a)5040-30-F(N)2010-0-—ILJ —0 2 4 6 8 10Time (s)60I I I____ __(b)40-Time (s)Fig. 5.10 Record of mooring line forces for wave flume test 2.5. (a) forces in upwaveline, (b) forces in downwave line.85I I IDJLFig. 5.11 Comparison of transmission coefficients betweenrectangular and circular caisson breakwaters.1.2T7 n. a.a 0 Byres[4]1 Nece and Skjelbreia [17]• Nelson and Broderick [18]0.8 0 Measured (Chain Moorings) -• Measured (Nylon Moorings)0‘.t-C,B.:. • a B BBu.4•IH aaB0.2-a0aA-I I I I0 0.2 0.4 0.6 0.8865C Rectangular Caisson (Byres)0 Circular Caisson (Chain Moorings)I I I I I - I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.81.8-1.61.41.2Heave 1RAO0.60.40.2-RollRAO1.41.210.8•0.60.40.2I I I I I — I — I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.81I I I I I — I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7D/LFig. 5.12 Comparison of observed breakwater motions.(a) surge, (b) heave, and Cc) roll.0.8ElSurgeRAO4-3.2-1—(a)ElogC0El ElC)ElLI (b)0CEl 0._09Eb0El0(C)0Ua0ElC0ElI-I871.2 I2.5.2.0RAO 1.5.1.0.0.5-0.0-0.I I I I0.05 0.10 0.15 0.20 0.25 0.30 0.35D/L10000.0-________________8000.0-6000.0-4000.0-2000.0-0.0- I0.00 0.05 0.10Fig. 6.1 Numerical results for base case with chain mooring lines. (a) transmissioncoefficient, (b) motion amplitudes, (c) mooring line forces.1.0-0.8-Kt 0.6-0.4.0.2-0.0 -0.3.0.(a))0I I I I I I I0.40-----i---- surge (b)I I I I i -r0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LI I I III—0---— Upwave................ DownwaveI I0.15 0.20 0.25 0.30 0.35 0.40D/L881.2- —1.0-0.8-Kt 0.6-0.4 -0.2 -0.0-—0.00 0.05 0.10 0.15 0.20 0.25 0.30--- -+--- - surge• heave-.- •0---• rolli_[__L_ I I—0— Upwave (C)0 Downwavee -0...,0.....Fig. 6.2 Numerical results for base case with nylon mooring lines. (a) transmissioncoefficient, (b) motion amplitudes, (c) mooring line forces.I I I I I I(a)4.0D/L0.35 0.403.0RAO 2.0.0.00.00(b)1.0-I I0.05 0.10I I0.15 0.20 0.25 0.30D/L0.35 0.405000.0- —4000.0-C’,E 3000.0-2000.0-1000.0-0.0- —0.00I I I0.05 0.10 0.15 0.20 0.25 0.30 0.35D/L0.40891.2- I I I I I(a)“VJ —4—— h/D=O.670.2 4WD=1.OO0.0-0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40Fig. 6.3 Numerical results showing the influence of relative draft, hID, for the case ofchain mooring lines. (a) transmission coefficient.goI I)0 0.05 0.10I I I0.05 0.10 0.15I I I I I0.15 0.20 0.25 0.30 0.35 0.40I I I -0.20 0.25 0.30 0.35 0.40D/LI I I I I I II I I I I I I0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.3 Numerical results showing the influence of relative draft, h/D, for the case ofchain mooring lines (cont.). (b) surge RAO, (c) heave RAO, (d) roll RAO.I I I I I I•—O—• h/D = 0.67•--••---- h/D=0.75—0-—— h/D = 1.00(b)D/LI I I I I I I2.0-1.5-surgeRAO 1.0-0.50.0-OJ3.0-2.5heave 2.0.RAO 1.51.0-0.5-0.0- —0.004.0- —3.0-roll 20RA01.0-0.0- —0.00(c)I ‘/t-(d)*9].10000. I I I I I IhfD=0.67 (e)8000- ..•..- “ h/D = 0.75bj) hfD=1.000%..“—‘. I••6000 -4OOOE2 2000.I I I I I I I(0.00) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/L10000 I I I. 8000-60004000 e..74.j_.____.e::-::.I_..2000•0— I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.3 Numerical results showing the influence of relative draft, h/D, for the case ofchain mooring lines (cont.). (e) upwave mooring line force, (f) downwavemooring line force.921rn_ I I I I I I I8000 -6000•4000.2000-0-0.00 0.05I-I-- I0.10 0.15 0.20 0.25 0.30 0.35D/L0.40UJI I I I I I I0 I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35D/LFig. 6.4 Numerical results showing the influence of wave steepness, H/L, for the caseof chain mooring lines. (a) upwave mooring line force, (b) downwavemooring line force.zIU.Cl)E2H/L=0.017----a---- H/L=0.0350—0-—— H/D = 0.0700?..1.t.1.7.T.100008000-6000-4000-2000(b)oZ0.409-310000 I I I I I I I\ —0-—— s/so = 1.05 (a)8000- \ \ ,/\ ••••-•o- 1.106000-4OOO- ‘./ \z \2000-0 I I I I I I0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/L10000- I I I I I I I_(b)8000-60000.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.5 Numerical results showing the influence of wave steepness, H/L, for the caseof chain mooring lines. (a) upwave mooring line force, (b) downwavemooring line force.941 I I I I I I0000bottom (a)8000__4000.• 2000-0-0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40DíL10000• I I I I I I Ig (b)8000.2000I I I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.6 Numerical results showing the influence of mooring line attachment point forthe case of chain mooring lines. (a) upwave mooring line force,(b) downwave mooring line force.95I I I I I I Inj-. .Kt(a)1.2• —1.0•0.8 -0.6-0.4-0.20.0- —0.00I —o-——— numericalexperimentI I I I 1---—-——--- -0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.7 Wave flume test results compared with numerical results for base case withchain. (a) transmission coefficient.962.0 -.(c)I I I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LI I I I I II T I I I0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.7 Wave flume test results compared with numerical results for base case withchain (cont.). (b) surge RAO, (c) heave RAO, (d) roll (rads).I I I I I I I1.51.00.50-c0.00______—0—-—— numerical.jexen0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LSurgeRAOHeaveRAORoll(rads)5.0- —4.0-3.0 -2.0-1.0 -0.0- —0.00(d)••.971.2- I I I I_____(a)—°-——— numencalKt0. O.b5 0.10 0.15 0.0 0.25 0.30 0.35 0.40D/LFig. 6.8 Wave flume test results compared with numerical results for base case withnylon. (a) transmission coefficient.9:80.0- -0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LFig. 6.8 Wave flume test results compared with numerical results for base case withnylon (cont.). (b) surge RAO, (c) heave RAO, (d) roll (rads).4_..- I—I I I I I ISurgeRAOHeaveRAO.‘(b)• I —°—— numerical I1.5- • I II • experimental1.0-0.5-0.0— I I I I I I0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40DJL2.0. I I I I I I(C)1.5- •1.00.5 -0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40D/LI I I I I I I5.0-4.0 -3.0.Roll(rads) 2.0.1.0.•(d)••••99

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