us, Arma Coast Cag Kes .Ae-TP 82-4 Wave Transmission and Mooring-Force Characteristics of Pipe-Tire WHOI — DOCUMENT COLLECTION , Floating Breakwaters by Volker W. Harms, Joannes J. Westerink, Robert M. Sorensen, and James E. McTamany TECHNICAL PAPER NO. 82-4 OCTOBER 1982 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING ep RESEARCH CENTER LW Kingman Building / Fort Belvoir, Va. 22060 Ay a) val Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: Nattonal Techntcal Information Service ATTN: Operations Diviston 5285 Port Royal Road Springfield, Virginia 22161 Contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. The findings in this report are not to be construed as an official Department of the Army position unless UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM ” REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER TP 82-4 - TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED WAVE TRANSMISSION AND MOORING-—FORCE Technical Paper CHARACTERISTICS OF PIPE-TIRE FLOATING SPD EEG aMING ONGEREBORTINUMNGER AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(e) Volker W. Harms, Joannes J. Westerink, Robert M. Sorensen, and James E. McTamany - PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-CS) D31679 Kingman Building, Fort Belvoir, VA 22060 . CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Re ea ty Coastal Engineering Research Center Kingman Building, Fort Belvoir, VA y 9 14. MONITORING AGENCY NAME & ADDRESS(/f different from Controlling Office) 15. SECURITY CLASS. (of thia report) UNCLASSIFIED 1Sa. DECL ASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) - SUPPLEMENTARY NOTES KEY WORDS (Continue on reverse side if necessary and identify by block number) Floating breakwaters Mooring loads Laboratory tests Tires Monochromatic waves Wave transmission ABSTRACT (Continue on reverse side if necessary and identify by block number) Wave transmission and mooring-load features were tested for a floating breakwater created from massive cylindrical members (steel or concrete pipes, telephone poles, etc.) in a matrix of scrap truck or automobile tires. The Pipe-Tire Breakwater (PT-Breakwater) was tested at prototype scale using regular waves ranging in height from 0.15 to 1.78 meters and period from 2.6 to 8.1 seconds; water depths ranged from 2.0 to 4.6 meters. Two designs were (continued) DD , Acta 1473 ~—s EDITION OF 1 NOV 651S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) tested--the PT-1 module, composed of steel-pipe buoyancy chambers and truck tires, and the PT-2 module, composed of telephone poles and car tires. Each design was 12.2 meters wide in the direction of wave propagation and was held together by conveyor-belt loops. Wave attenuation and mooring-force features were established based on data from 402 separate runs in which incident and transmitted wave heights were recorded, along with the tension in the seaward mooring line. Test results are compared with those of earlier experiments made on the Goodyear floating tire breakwater. The construction of these PT- Breakwater modules is outlined, along with the cost estimates for construction of components. A breakwater buoyancy test was made and the flotation require- ments calculated. The influence of stiffness on the mooring system was exper- imentally investigated and conveyor-belt material tested to the point of failure. Design curves for determining the proper anchor requirements and breakwater size are given. Apart from the incident wave height, the transmitted wave height and peak mooring force are shown to depend primarily on four dimensionless parameters: the relative wavelength, wave steepness, relative breakwater draft, and breakwater aspect ratio. The wave attenuation performance of PT-Breakwaters improves as either wavelength or water depth decreases, or the wave steepness increases. The shelter afforded by a particular PT-Breakwater is strongly dependent on the incident wavelength, L: substantial protection is provided from waves that are shorter than the width, B, of the breakwater but very little from waves longer than three times the width of the breakwater. The wave attenuation performance of PT-1 was found to be superior to that of PT-2 and the Goodyear breakwater: for L/B = 1 and deep water with H/L = 0.04; for example, the wave height transmission ratios are approximately 0.6, 0.4, and 0.2 for the Goodyear, PT-2, and PT-1 breakwaters, respectively. For the conditions investigated, the peak mooring force increases approxi- mately with the square of the wave height, more precisely: F « H" where n= 1.5, 2 and 2 for the PT-1, PT-2, and Goodyear breakwaters, respectively. 2 SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report is published to provide coastal engineers the results of a series of prototype-scale tests of a floating breakwater that incorporates massive cylindrical members (steel or concrete pipes, telephone poles, etc.) in a matrix of scrap truck or automobile tires. The breakwater, which was developed by the senior author while serving on the faculty of the State University of New York at Buffalo (SUNY), is referred to as the Pipe-Tire Breakwater (PT-Breakwater). Tests were conducted in the large wave tank at the U.S. Army Coastal Engineering Research Center (CERC) in a joint effort by CERC and SUNY personnel. The work was carried out under CERC's Design of Floating Breakwaters work unit, Coastal Structure Evaluation and Design Program, Coastal Engineering Area of Civil Works Research and Development. The report was prepared by Dr. Volker W. Harms, SUNY and University of California, Berkeley; Joannes J. Westerink, SUNY; Dr. Robert M. Sorensen, Chief, Coastal Processes and Structures Branch, CERC; and James E. McTamany, Coastal Oceanography Branch, CERC. The authors gratefuly acknowledge the assistance of SUNY technical spe- cilalist J. Sarvey and students T. Bender, P. Hughey, and P. Speranza, and the difficult crane operations and frequent wave generator stroke changes performed by CERC's research support personnel. This research was sponsored in part by the New York Sea Grant Institute under a grant from the Office of Sea Grant, National Oceanic and Atmospheric Administration (NOAA), U.S. Department of Commerce, through SUNY. It was also supported by the U.S. Department of Energy under Contract W-7405-ENG—48 to the Marine Sciences Group, Lawrence Berkeley Laboratory, University of California. Technical Director of CERC was Dr. Robert W. Whalin, P.E., upon publica-— tion of this report. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. Colonel, Corps of Engineers Commander and Director CONTENTS Page CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI)...ccccccccccecs 7 SYMBOLSMAND DE FAGNTsIlONSiereteveteieloreroteloterovetoretelieleloteioteierel cicielelistorciorsionsicichelels 8 IL LN TRODU GH ONepercucleketeloletoreteletetoxcloleiarclciciclclaiciolelekelsioleleicicicicleleletelelcielolslelclelele 9 IIE THE PIPE-TLIRE BREAKWALE Reveretereveveroleleicteketelelererclerolevetciohsielotelctonslorelciclehchorele 10 1. Breakwater Modules and ComponentS...cccccccscccccccccscccccee 12 Pe CONStELUCELON MELO CCAUBESisfeleleleleleleletelelelelolelelelclelelelcleleioioleleieleleleielele loin LO J BLeakwatermsbuUOV All Cyjelelelelolejekelololelaloiolele)clolsialolelelelololsiclovoleleketslelorelerel=) m2 O ih 6 Cost EsiGiimalze'Sereisicholeneloteleleicherclctetcreteicleiclclercioneieioiareroteleleleleteloietolclelele D3} ICICI EXPERIMEN TA SE LUP SAND pPROGED URE Steteveleeleloleielcleleleleleleleicleleleleleleielelelelelere) rch lulestbaciltityrandsslnstLumentatslOmers sleleielelehelofelerelsleletelelelolsteleyais)e: uar2e Die MOONS MOY SECMefeloketelolsieloieleielelorerereketoleKetelelelelerobeiotalelolelelelelolsicloleycls|<] onal O Beles erProceduremand ss Condit onStereretelclolelerelefeletolelelsleloleleleleloleleleleyelele) mall IV DATAMREDU GILONMANDMWANAILY SiltGleieleletoioleloleletelele| slolelcloleletoleiolelclclelciolcielslofalerelo) 0/2 io Wimamestomeail AmeulyestSgoagbadococc ob D0 NDO GODS OGDODDOOCOOOOOCGCS | 32 Qa Data-Reductlonweeroceduresriclelsieleioleleleleleleiolalelelcleieleloialeleloteleteielelsyele) St V EXPERIMENTAL RESUME Sis sietovovevereiene- crevensiclevetoreeierelelotelevelerslekeiorolelereroneevelere! wie 3i7/ euWaverehransmisSionmD at aletelovclolelel leleiohelolelolelokelolclolokeloleloleloleliclelolelelefelon tr S)i Ze MOOTAN T—KOLCCWDACAlelelolelelelolelo lolol lel olelelsvolol sie) lolol efololeleVoleleleloleloleiololel oi nn ct VI SUMMARYEVANDIMGCONGEUWSTHONSiareleicieiolorstelelolclolckclelchetelciclelehelicherelelctelereteletetolelereicle 50 LITERATURE GUILE D eeaievovetelo svevotorstcvonevovetonensterelevolocictetotoveieliohaiotcheieleloheicteiclcrera c 53 APPENDIX A TABULATED TEST RES UlesSioteretetetoietolaletotehetcioketeltetetoletekotelelclolelcdotevenolencreneleiel eters 5)5) B FORCE MEASUREMENT CORREEATION| @RsL--')) lie} elelolevolelelsls|olslelelsls)oleleleleielelels) efor OD) C DETAILED WAVE TRANSMISSION DIAGRAM. .ccccccccccccccccccccccccccce 14 TABLES 1 Cost estimates of PT—Breakwater cCOompOMeNtsS.cccceccccsccccccccccsccccsces 23 2 Compleancevore mooring Sy SteMmS\ejcjeicle)cleleloleleielelelelolololeieielelelelelslclelokelelelclolelelelelereloie Zo) 5) Summary jo test condtitTon's\eyeerelclelele|e/e)e cloleleleyele/oloteloleleleleyelololoiciclolelelelelololsyeleloreie: tS 4 Summary of mooring—force datac...ccccccccccsccccvccccesccccccccccccccss 46 FIGURES l' PT-Breakwater field installiatdon 7.5. 7. 16" STEEL PIPES (49 long, I2'apart ) 12 STRINGS, (10 tires each) TIRE RETAINER ne faa (405 dione 56 TIRES PER PIPE Lae ae Si sR ey Vane oe See lr 1 10 a Me 6 5 3 4 “| ( dA Vo De ve is UNG ee aD) SHORE WARD [+ -— = -—- - === | SEAWARD TE= TRAILING EDGE WIDTH B= 40' LE = LEADING EDGE Note :!£ Truck fires used, 40” diameter Figure 4. Schematic of PT-1 breakwater module. Figure 5. Definition sketch for PT-Breakwater. 13 Figure 6. Assembly of PT-1 (foreground) and PT-2 modules. —— PIPE RETAINER —— 4 SECTIONS OF 2" STEEL PIPE SCREWED INTO PIPE-CROSS AT CENTER 16" STEEL-PILE PIPE, 0.281" WALL ‘STEEL END PLATE, 5/16" FLOTATION CRAMBER ( foam filled ) Figure 7. Tire retainer at end of pipe. 14 The tire retainer used in the PT-1 module is shown in Figures 4 and 7. In the case of the PT-2 module, the retainer was a tire casing that was held in place by a 1.9-centimeter threaded steel rod extending through the telephone pole and casing. Standard marine steel-pile pipes were utilized as buoyancy chambers and stiffeners in the PT-1 module; they were 12.2 meters long and 41 centimeters in diameter, with a wall thickness of 0.71 centimeter. Scrap telephone poles were used for the PT-2 module; they were 12.2 meters long with a diameter of 33 centimeters at the butt end and 23 centimeters at the tip. Truck tires ranging in size from 9.00-18 to 10.00-20, with an average diameter of 102 centimeters were used for PT-l. Car tires with rim sizes ranging from 32 to 38 centimeters were used for PT-2; the average diameter was about 65 centimeters. A three-ply conveyor belt strip, 14 centimeters wide and 1.3 centimeters thick, was used as the binding material; this had a rated breaking strength of 7900 kilograms. A five-hole bolted connection (Figs. 8 and 9) was used to tie the belt into continuous loops. Figure 8. Breakwater and mooring-system components. 15 Conveyor belt (5% x V2, 3 ply) Auto tires Rear id eer lat Wire rope aa ; —_— 5— hole pattern for yo" bolts Af holes) @eoq Wee) = Oy = 15) = (Fe = ¥,) Using the following approximate values and estimates for the PT-1l module: 1 = 220 kilograms Fy = (60 kilograms per meter) (12 meters) = 720 kilograms Wey = 7 kilograms 19 = 17 kilograms (50 percent of value from buoyancy test) Fe = 34 kilograms (crown fully foamed, 34 liters) n = 176 tires to obtain F (17 71) + : ) (720 280) Z (34 7) = = a - +/{— = 1 eed 176 (=) m (3) ovaay @ US ae 17 (=) (estograns per tire) 22 The following examples demonstrate the increased load-carrying capacity when foam is added to the tires: ; (a) Example 1. If none of the tires are foamed, m = 0 and m/n = 0 in equation (3) so that F..qg = 13 kilograms per tire. Therefore, a weight increase of approximately 13 kilograms per tire can be accom- modated before the breakwater starts to submerge. (b) Example 2. If all the tires are foamed, m =n and m/n = 1 above so that F..q = 30 kilograms per tire. In this case, each tire can carry approximately 30 kilograms of additional load for a total reserve buoyancy of about 5300 kilograms per single-pipe module. 4. Cost Estimates. Major construction components for the PT-1 module and their respective costs as of mid-1980 are listed in Table 1. It should be noted that the steel pipe accounts for nearly 60 percent of the total cost. Therefore, substantial savings are possible if used pipe can be purchased, which was done for the floating breakwater at the Mamaroneck site where used dredge pipe was obtained at a fraction of the cost indicated in Table 1. As a precautionary measure, steel pipe should be filled with foam before the end caps are welded into place. The total component cost amounts to $19.60 per square meter of breakwater. Table 1. Cost estimates of PT-Breakwater components. Module dimensions: 3.7 by 12.2 m (B = 12.2 m) Materials: Truck tires (9.00-18 and 10.00-20) Steel pipe (4l-cm-diameter steel-pile pipe) Conveyor-belt material (three-ply, 14 by 1.3 cm) Nylon bolts, washers, and nuts (13 mm) Steel pipe 12.2 m $43.00 $524.60 $11.60 Polyurethane foam 2.4 m9 75.00 180.00 4.00 (pipe plus 20 percent of tires) Tying material 94m 1.15 108.10 2.40 (conveyor belt) Tires 176 0.25 44.00 1.00 (transportation cost) Nylon bolts, washers, and nuts 80 0.35 28.00 0.60 Cost of breakwater $19.60 (excluding mooring system and assembly) Assembly and launching procedures should be carefully considered and planned in advance so as to take full advantage of cost-saving site condi- tions. Since the anchoring system can be very costly, alternatives should be carefully investigated (e.g., the use of anchor piles may be less costly than concrete clump anchors or steel embedment anchors, depending on availability of pile-driving equipment and geotechnical conditions). III. EXPERIMENTAL SETUP AND PROCEDURES 1. Test Facility and Instrumentation. a. Wave Tank. Experiments were conducted in CERC's large wave tank which is 194 meters long, 4.6 meters wide, and 6.1 meters deep. The tank was oper- ated at two water depths, 2.0 and 4.7 meters, using regular waves ranging in period from 2.6 to 8.1 seconds and height from 0.15 to 1./8 meters. A sche- matic of the wave tank operating with a piston-type wave generator at one end and a relatively ineffective rock revetment wave energy dissipator at the other end is shown in Figure 18. The breakwater at high and low water is shown in Figures 19 to 23. b. Wave Gage. Two Marsh McBirney voltage-gradient water level gages (Model 100) were used to measure incident and transmitted waves. The waves were calibrated twice daily over a range of 2.0 meters by manually lowering and raising the wave staff. The output was recorded on a six-channel Brush oscillographic recorder. c. Force Gage. Loads on the seaward mooring line were measured by a single force gage located above the tank near the wave generator. The force gage consisted of a cantilevered steel plate with strain gages mounted near its base, as shown in Figure 24. The strain gages formed two arms of a full Wheatstone bridge that was driven at carrier frequencies. The sensitivity of the force gage could be varied over a broad range, not only electronically but also mechanically, by varying the mooring-cable attachment point on the can- tilever (Fig. 24). The force gage was generally calibrated before and after each test (one wave generator stroke setting) by applying a series of loads to the cantilever using a mechanical load tightener (come-along) and a 2270- kilogram dial force gage. The electrical output was displayed on the six- channel Brush oscillographic recorder; typical calibration curves are shown in Figure 25. Se Wave goge ee A ; k Vinee 1LOm_ Me eee Tee ae | —— mss i THY = = INOING/ x Ibs d=46m ond 20m fasim 30m ao 20 m——~ n 122m- ‘ +|- 19m—— oo 31m = 65m Tire mooring damper 12" pulley Saas st OD TEGO Ea 000d. ye re = 43m == a =>—___—_—_-—__]] Timah: -22oooo ' brie Ny 19m | | i 50m ~ ~ 50m SS -| Figure 18. Large wave tank at CERC with breakwater and MS-1 mooring system. 24 °(qJuolqzaAed YOO) yoreq PpieMol MeTtA °OZ ean3sty aB1eT) °(OuaD SyueQ eAeA iJoje19Uue3 sAeM P1IeMO META °61 aan3sta 25 Figure 21. Inserting PT-1 breakwater. Figure 22. Turbulence associated with wave damping. 26 Figure 23. Attachment of seaward mooring line (MS-1 mooring system). alae ji SIZ wee” Silas PUNE 3/4" BOLT SHACKLE 1/4" MOORING CABLE STRAIN GAGES STRAIN- GAGE - CANTILEVER STEEL BEAM ACROSS UNIT WAVE TANK — CANTILEVER FORCE GAGE —— Figure 24. Strain-gage-cantilever force gage. 27 50 40 s ae Chart Deflection (mm) 20 a a o Initial A Final 0 500 1000 1500 2000 Load (kg) Figure 25. Force gage calibration record and curve. 2. Mooring System. The basic mooring-line arrangement used throughout the test program is shown in Figure 18. The mooring lines were 6-millimeter-diameter wire rope, except for two removable segments 6 meters long that are labeled ttre mooring damper as shown in Figure 18 and in more detail in Figure 9. These sections were installed in order to determine whether a pliant mooring-line insert such as the six-tire mooring damper could significantly reduce peak mooring forces. Should a relatively “soft" mooring system be desirable, it may be achieved by installing a tire mooring damper. The shoreward mooring bridle was always attached directly to the steel pipes; no mooring-line inserts were used on this side of the breakwater. On the seaward side the mooring bridle was most often attached to the steel pipe with cables connected to shackles extending through the pipe wall. An exception to this is the third mooring system tested in which the mooring bridle was attached to the breakwater via conveyor-belt loops that were laced through two tires armoring the pipe. In this case the mooring-line forces are first transmitted to those two tires, then transmitted to the pipe itself after the tires have shifted some distance along the pipe and encountered the compressive resistance of the other tires restrained by the retainer at the end of the pipe (Fig. 7). The following mooring configurations were tested (major features are listed in Table 2): (1) Damper Pipe Connection (MS-1). In this module the tire mooring-force dampers are installed and the mooring bridle is con- nected directly to the pipes (soft line, hard connection) (see Figs. 18, 23, and 26). 28 Table 2. Compliance of mooring systems. Mooring system Type of mooring-line insert! Belting (hard) Type of breakwater connection Tires on pipe (soft) Mooring line stiffness (ranked) 2 linserts are 6 meters long; belting is in the form of a loop (used double strength) with elongation characteristics under load approximately equal to that of wire rope used. Figure 26. Mooring bridle used in field installation. (2) No-Damper Pipe Connection (MS-2). In this module the mooring bridle remained attached to the pipes but the mooring-force damper was removed and replaced with a conveyor-belt loop of equal length. The load elongation characteristics of the conveyor-belt loop are similar to those of the wire rope used (hard line, hard connection) (Fig. 27). (3) No-Damper Tire Connection (MS-3). In this module the conveyor- belt loop remained in place, but connection to the breakwater was made by guiding the belt around two tires located on each pipe. Im the PT-1 module, tires numbered 9 and 10 were used for this purpose; in the PT-2 module, tires numbered 15 and 16 were used (hard line, soft connection). 29 1000 500 TENSION T (kg) DEFLECTION X (cm) Figure 27. Load elongation curves for mooring-line inserts. A stress-strain diagram for the conveyor belt with a five-hole bolted connec- tion is shown in Figure 28. The strain values are influenced by the connec- tion itself (i.e., elongation of the boltholes is being measured along with any stretching of the belt). The belt failed at a load of 2270 kilograms, not at the five-hole bolted connection but at the transition, where the belt had to be reduced in width from 14.3 to 8.9 centimeters in order to fit into the testing machine. Force displacement relationships for MS-1 and MS-2 were obtained by ten- sioning the insert, using a large dump truck, and determining deflection and force, using a measuring tape and a dial force gage. The results are plotted in Figure 27. Corresponding relationships for MS-3 were not determined, but observations indicate that the elastic properties of MS-3 are between those of MS-2 and MS-1. A mooring bridle utilizing both truck and automobile tires is shown in Figure 26. This unit was not tested at CERC; however, it has been used in field installations. 3. Test Procedure and Conditions. This experimental program is limited to two designs, the PT-1 and PT-2 modules, and two water depths, 2.0 and 4.7 meters. The summary of the test conditions shown in Table 3 lists one other breakwater design--the PT-DB mod- ule; this design is simply a PT-] breakwater that has been lengthened in the 30 F/F,, x10 F=applied toad Fare (3150 Ib /in)(5.6in ) = 17,700 Ib (RATED BREAKING STRENGTH) Lo = 15-1 in 5.6 in 3-8 In a Figure 28. Stress-strain diagram for belt connection. Table 3. Summary of test conditions. Breakwater No. of Water Mooring Generator Wave height Wave period Type Beam runs depth system stroke (m)~ (m) (cm) (cm) (s) PT-1 12.2 101 2.0 MS-1 61 to 213 15 to 113 2.6 to 8.1 PT-1 12.2 92 4.7 MS-1 61 to 168 42 to 178 2.6 to 8.0 PT-1 12.2 62 4.7 MS-2 61 to 152 32 to 132 2.6 to 8.1 PT-1 12.2 SU 4.7 MS-3 61 to 122 30 to 130 2.6 to 8.1 PT-2 12.2 40 2.0 MS-3 61 to 122 18 to 110 2.6 to 8.1 PT-2 12.2 36 4.7 MS-3 61 to 122 30 to 150 2.6 to 8.1 PT-DB 25.9 34 2.0 MS-3 61 to 122 28 to 132 2.6 to 8.1 shoreward direction by flexibly attaching the PT-2 module by use of conveyor- belt loops. Data for the PT-DB configuration are listed in Appendix A. The PT-1 module was tested with three different mooring systems and was, in general, emphasized in the experimental program. Out of 402 runs tested, 290 were devoted to the PT-1 breakwater. Wave heights ranged from 0.15 to 1.78 meters, with wave periods ranging from 2.6 to 8.1 seconds; the wave generator stroke varied from 0.61 to 2.13 meters. With the breakwater floating in the wave tank and attached to the mooring system, test preparations were generally initiated each day by adjusting the water level, calibrating the wave and force gages, and checking the stroke 31 setting of the wave generator. The generator was adjusted to the desired frequency, started, and waves generated for about 5 minutes; this constituted a run. After shutdown of the wave generator, a necessary waiting period followed in order to regain quiescent conditions in the wave tank. When these conditions were attained, waves of another frequency were generated and this process was repeated until all the desired wave periods for that stroke setting were obtained; this process constituted a test. One, and sometimes two, tests were completed per day, and the generator stroke was changed in the afternoon so that a new test could be started the following morning. Wave and force gages were calibrated both at the beginning and end of each day's testing (and sometimes more frequently). IV. DATA REDUCTION AND ANALYSIS 1. Dimensional Analysis. For a particular breakwater and mooring system, the transmitted wave height, H,, may be expressed as a function of the following variables: H, = f(H,L, B,D,G,A,m, k,e, d,y,v,g) where € = horizontal excursion of the breakwater from its equilibrium position k = measure of mooring-system stiffness (equivalent spring constant per unit length, i) m = mass of breakwater (per unit length, A) Y = specific weight of water v = kinematic viscosity of water g = gravitational acceleration The remaining terms are defined in the definition sketch (Fig. 5). Since this expression contains three dimensionally independent physical variables (length, mass, time), this relationship involving 14 physical variables may be replaced, according to Buckingham's t-Theorem, by one involving 11 dimension- less groups: = wave transmission ratio, Ce structure parameters oO} a wave steepness em u 32 ye = wave structure parameters 2 BD = fluid structure parameters d * mg (z)( DY gL a Reynold's number Delete the following parameters for the stated reasons: o|> ial5 ==} Ku) (ee) Only quasi-two-dimensional experiments will be considered (i.e., diffraction effects are absent when the breakwater extends across the full width of the tank). This is the ratio of mooring-system static restoring force to structure weight and is not changed during the experiment. Assumed to be a weak parameter that is of little importance for small values of e/H (i.e., for horizontal motions of the structure that are small compared to the wave height). This parameter relates the mass of fluid dis- placed by the breakwater to the mass of the breakwater itself. It would remain constant for geometrically similar breakwaters con- structed from the same materials. This Reynold's number is based on the tire diameter and a velocity that is related to the maximum wave-induced water particle velocity; it will be assumed large enough to insure Reynold's number independence. By eliminating the above dimensionless groups, the following is obtained L Cc. =f 3 ei als ol|lw Se 33 (4) This is the relationship on which the experimental program was based. Similarly, consider the mooring-force relationship to be ye £(H,H, >L, B,D,G,A,m, k,e, d,y,v,g) and, by similar reasoning, obtain F My al YD) B =—SSEl=pPoKose (5) L 2. Data-Reduction Procedures. Analog signals from the wave gages and force transducer were recorded on three channels of a six-channel Brush oscillographic recorder. Typical records of the seaward mooring-line force and the incident and transmitted waves are reproduced in Figures 29 to 32. Wave reflections from the steep, rock-armored beach at the end of the wave tank (Fig. 18) were an annoyance, particularly for the longer waves generated. The incident and transmitted wave heights were therefore generally obtained from the first 5 to 10 waves in the run (i.e., before wave reflections could substantially influence wave height measurements. Beach reflections were particularly bothersome when generating waves of low steepness and of periods larger than about 5 seconds. From the force gage records it can be seen that the seaward mooring load fluctuates with the passage of each wave between a maximum value, which varies i keep eet nage! Ha A Acces EEE BASSESUEESEREIT GE #96 vase ana ' Ee rf 1 aida ny cif pate aracyeat ti Hh : Oe ARS TESTE AIG fd re isia bie AAI uh AM ee A aR oe = ‘ TLE eH ; iets | | [| ei pa | | a Ei li | ipeaanenea ce: ALAA A A avai i f NENMENZINT Efces008 Pee | : q tnd a Soares aeene we Py 7] ea NATE A ae da he TET Eee Ke Gaal LE criti be goeuee ee ey He cH EEE PS WAVE Hy i + Figure 29. Wave and force record for long waves (d = 4.7 m, T = 8.0 s). 34 1 | v > i if | | A y T T | uty | AML WY B62) Do | | | Yl uJ T i AWM My I wail 40 cm T ho AU ATA) gem AN YAN LVAD i | t At 400 kg N\ Ad + ney! WEL Alt lA HT IA FORCE AAA | WAVE. H | | i ll ! es —=— = aa — i =i a —4 —— ——— al a | l] | l VAN A AANA AA A AIA ASATAV AVATAYAYA? AUB" AU WTA ATAUAGAUA M7 i tM : ii l | i H |] \ | ] A i J il | F ot ] ill ii HWY AAA TA A + il | MMC LAL AILA WAU Hy an Wave and force record for short waves (d = 4.7 m, T | | | | ayes ae SRE a i Hi | ut 1 Figure 31. Figure 30. Re eel ert lah TA | N SE it : L Falaat EEE 0 s) 4./ m, T = 3 35 Wave and force record for steep waves (d j 1 i Eon || Hl ed at i t ! Lh SIAL ry era | h A! 1h i wll IMs saieinitit TG MHL iil ey i AAA A TAA ni AU A A WAAL | ! TELE See mle iy ULL Hut WWWWWWWWW WWW CY | RY Kane) | eC EEA fF fete ete Hi a { Hage eee Ee ae) pe Se beOE EEE Se UL 40 cm ale aay T ST T Taal T T Tien] en Tom 7 TT T ici, Bee Pe eS Gy f aa eee ened | Hay Ie 0) espe vl i Biba fh EE ila hed g el | i Len A ARIAUNALR UML IV CNS 7 PO LE p "i GRECO Re ada Enh eae eae ra ! i tt tas cell i i Figure 32. Wave and force record for shallow-water waves (d = 2.0 nm, T= 5.5 8). throughout the run, and a minimum value, which remains essentially constant. The individual force peaks occur as the breakwater surges shoreward during the passage of each wave crest, but is prevented from moving too far in this direction by the mooring-line restraint. On the other hand, the seaward movement of the breakwater is not similarly opposed, since no force cantilever was installed on the leeward side of the breakwater. Instead, only a constant negative restoring force or preload of approximately 113 kilograms was exerted on the breakwater via the shoreward mooring line and pulley-weight arrangement shown in Figure 18. The zero-force referen¢e position recorded at the begin- ning of each run always corresponds to this static preloaded condition of the cantilever force gage. Negative force values up to the magnitude of this preload can consequently be obtained as the breakwater surges seaward; these constitute the stable lower limit of the force records. A time-series analysis of the force data was not performed because the experiments were limited to regular waves and because the level of effort required did not make it feasible. For practical purposes, each force record is therefore characterized by a single force value that is considered most useful for design purposes—the peak force, F, occurring during the length of record (excluding wave generator start-and-stop transients, which have no counterpart in nature). Typically, this implies that the first 5 to 10 waves were not included in the analysis, nor were those last waves propagating down the tank after shutdown of the wave generator. Each run consists of at least 50 waves. In addition to the peak mooring force, F, an approximation to the drift force, F, is also obtained, as is the significant peak force, F The drift force F is the net, time-averaged force acting on the seaward mooring line; it was determined “by eye” as show in Figure 33 and is there- fore subject to larger errors. The significant force, Fz. represents the average of the largest one-third of the force peaks, again excluding stop-and- start transients; it is obtained manually, directly from the data trace. If stop-and-start transients are included in the determination of the peak mooring force, as has been done by other investigators (Giles and Sorensen, 36 O O LL REGION 1 START BEST DATA REFLECTIONS STOP TRANSIENT TRAN. F = PEAK FORCE F = DRIFT FORCE, WHERE F = 1/215 aA ) FROM REGION 1 LA = AVERAGE OF HIGHEST 1/3 PEAKS on “ AVERAGE OF LOWEST 1/3 EXTREMES mul i) HIGHEST PEAK FORCE VALUE FOR LENGTH OF RECORD Figure 33. Definition sketch for force analysis. 1978), the difference between F and this peak force is frequently small, but on the other hand can be quite large as shown in Appendix B. In that appendix the peak mooring force, F, is also compared to the significant peak force, F,, for a large number of the tests. The cantilever force gage is calibrated at least once at the beginning and ending of each day's testing; if zero drifts are observed, it is calibrated more frequently. Calibration is accomplished manually via a separate cable with mechanical load tightener and 2270-kilogram dial force gage in series, attached close to the cantilever. A typical calibration record is shown in Figure 25. The force values are always referenced to the static no-load condition (i.e., with pully preload but no waves). V. EXPERIMENTAL RESULTS 1. Wave Transmission Data. For each breakwater configuration and water depth, the transmitted wave height depends primarily on the width of the structure and the incident wave- length (or period) and wave height. Dimensional analysis and physical insight were invoked in Section IV to arrive at dimensionless parameters that would describe the problem more succinctly and clearly and would also guide the experimental effort and analysis of the results. This evolved in the presen- tation of the data in the format shown in Figure 34. The wave height trans-— mission ratio, C, = H,/H, is presented as a function of relative wavelength L/B, with different symbols designating ranges of wave steepness H/L. These are the primary parameters. The secondary parameters are listed in the insert of each figure. These parameters specify the water depth (relative depth, 37 CERC.1979. PT-1 BREAKWATER WITH MOORING TYPES 1.2,3; DEPTH=4 6M T T cae Ear lar T W T 1.20 1.00 80 3 5 B oy i Gct B BB B+ 0 @ a rc] e 0.60 cc) e\i3 \ iC] ) got ci 2. S af x (H/L)I0" ——D/d B/D G/D (o>) x f + 06-19 0.22 12.0 3.3 we m 2.0-60 ° a) 2 vA x 6.1 IL6 WAVE HEIGHT TRANSMISSIGN RATIO CT x ¥ — 40 %.00 0.50 1-00 oO oO 1.50 2'.00 2.50 3.00 RELATIVE WAVELENGTH!!! L/B Figure 34. Wave transmission data for PT-1 breakwater (d = 4.7 m). D/d) and breakwater geometry (aspect ratio, B/D, and pipe spacing, G/D). For design purposes, the transmission characteristics of each breakwater are summarized in the form of a single wave height transmission curve. This curve corresponds to a wave steepness of H/L = 0.04 (a moderate value frequently encountered in practice) and different values of D/d. Although much data have been obtained at wave steepness other than 0.04, indicating that the transmission ratio, Ces generally decreases with increasing wave steepness, the available data are not adequate for defining transmission curves for wave steepness other than 0.04. Nevertheless, the influence of wave steepness has been preserved to a large extent by grouping the data according to steepness categories; in Appendix C the value of H/L is actually listed next to each data point. Appendix C should be particularly useful for design cases with wave steepness near the extremes encountered in nature, either high or low (e.g-, H/L larger than 0.08 or less than 0.02), since deviations from the 4- percent design curve may then become significant. The wave transmission data in Appendix C have also been segregated with respect to the type of mooring system installed, but it was found that this had no discernible influence on wave transmission characteristics. It is therefore permissible to combine the data for all of the mooring systems as has been done in Figure 34. a. PT-1 Breakwater. Wave transmission data for the PT-]1 module (truck tires, steel pipe) are show in Figures 34 and 35 for two water depths, D/d = 0.22 and 0.51. In both cases the transmission ratio, C., increases mono- tonically with relative wavelength L/B. The breakwater is very effective 38 Wave Height Transmission Ratio (C,) LEGEND (H/L) 10° 0.4 to 1.9 2.0) {0 G0 6.1 to 10.1 x 40 0.51 = 12.0 > 3.3 0) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Relative Wavelength (L/B) Figure 35. Wave transmission data for PT-1 breakwater (d = 2.0 m). in filtering out waves that are shorter than the width of the structure, but becomes increasingly less effective as the wavelength increases. breakwater is significantly more effective at the lower depth, particularly for longer waves. The influence of water depth, or relative draft D/d, becomes particularly apparent in Figure 36 where the transmission dent that the curves are compared. Figure H/L2=Q04 0/d =0.51 Wave Height Transmission Ratio (Cy) @/D GD Dim 122.0 33 102 () 05 1.0 15 20 25 30 35 4.0 Relative Wavelength (L/B) 36. Wave transmission design curves for PT-1 breakwater. 39 It is evi- The influence of wave steepness is most readily detectable for longer waves (e.g-, L/B larger than 2) and may be important at low water depths. For L/B = 2.9 and D/d = 0.51 (Fig. 35), the value of C, decreases dramati- cally from 0.9 to 0.4 as H/L increases from 0.007 to 0.028 (refer also to Fig. C-7 in App. C). The data in Figures 34 and 36 apply to the PT-1 module, which has a pipe spacing of G/D = 3.3, aspect ratio of B/D = 12, and beam B = 12.2 meters. These conditions may not be altered greatly without also influencing the wave transmission characteristics. For example, the design curves of Figure 36 may not apply to a structure with a much larger beam, e.g-, B = 24 meters (i.e., or B/D = 24). Until further data on the importance of B/D are obtained, it is suggested that the PT-l1 wave transmission design curves of Figure 36 be limited to beam dimensions in the range from 9 to 15 meters. Such information has been recently provided in Harms, Bishop, and Westerink, 1981. Existing data from small-scale experiments (Harms, 1979) indicate that the transmission curve for D/d = 0.22 does not change signifi- cantly as the water depth increases. For deepwater applications with D/d less than 0.2, it is therefore suggested that the D/d = 0.22 curve be used for design purposes, at least until further data become available. In addition, curves should not be extrapolated beyond the range of data shown (i.e., L/B > 4.5 and 3.0). b. PT-2 Breakwater. Wave transmission data for the PT-2 module (con- structed of automobile tires and telephone poles) are shown in Figures 37 and 38, with design curves given in Figure 39. The behavior of the PTI-2 module is very similar to that of the PT-1 module, although a decrease in wave attenua- tion performance is indicated, at least at the larger water depths considered in Figure 40. It was observed that the influence of wave steepness H/L is again particularly apparent at the lower water depth (D/d = 0.33, Fig. 38) and large values of L/B. The actual H/L values associated with each data point are given in the appendixes. Again, curves should not be extrapolated beyond the range of the data shown (i.e., L/B > 4.5 and 3.0). al T lee a eal | a Sa aE | Sesame a Res RE Vesa D/d=0.14 es + © 1.00 ~~ g i x + x fe} + 2 ‘ce, o re 3 S 8 wo ee E a LEGENO = 2 2 (H/L) 10 S + 0.6 to 1.9 r= © 2,010 6.0 an a X 6.0 to ll2 aw oT: g > oO = PT-2, MS-3 O i | ee N pee () 0.50 1.00 1.50 2.00 2.50 3,00 350 4.00 4.50 Relative Wavelength (L/B) Figure 37. Wave transmission data for PT-2 breakwater (d = 4.7 Mm) 40 1.20 D/d = 0.33 wal OO + 2 + ec a rs) < 080 ‘ " Cc 2 + _ 2 ° ; e) cz mith E ° + a oe aP Bee LEGEND eS o <<, (H/L) 10° - {o) fo) fo) ag & ° + 0.5to 19 reap Ro © 2,010 6.0 ® X 6:0 to 9.2 a : | > io) r = O 0.50 1,00 1,50 2.00 2:50 3.00 3.50 4.00 4,50 Relative Wavelength (L/B) Figure 38. Wave transmission data for PT-2 breakwater (d = 2.0 m). H/L =0.04 D/d=0.14 G/D D(cm) 5.5 66 6) 0.50 1,00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 Relative Wavelength (L/B) Figure 39. Wave transmission design curves for PT-2 breakwater. 41 1.20 T H/L= 004 +) G 5 fo) PT-2 at D/d=0.14 PT-1 at D/d=0.22 iS} @ [e) 9 fon) [e) io) Ss (e) Wave Height Transmission Ratio ( S) ine) fo) ! JL | | | | | 00 150 2.00 2.50 3,00 3150 4.00 ~ 4,50 Relative Wavelength (L/B) | 0.50 Figure 40. Comparison of PT-1 and PT-2 wave attenuation (d = 4.7 m). c. Goodyear Breakwater. Giles and Sorensen (1978) obtained prototype- scale wave transmission data for the Goodyear floating tire breakwater using the large wave tank at CERC. Data for the 6-module-wide Goodyear breakwater are plotted in Figures 41 and 42, along with the wave transmission curve for the PT-2 module. Both breakwaters are constructed from automobile tires and have a beam of 12.2 meters which is equivalent to B/D = 18.5. For the lower water depth case considered in Figure 42, it is evident that the PT-2 break- water is substantially more effective than a Goodyear breakwater of equal size. At the larger water depth considered in Figure 41, the PT-2 breakwater is still superior but not as much so as at the lower water depth. From extensive small-scale experiments by Harms (1979a, 1979b), the influence of water depth is found not to be of practical importance for the Goodyear breakwater, at least for values of D/d less than 0.4, although C clearly decreases as D/d increases. How significant the influence of pid is for the full-scale Goodyear breakwater (Figs. 41 and 42) is shown in Figure 43 where the data for D/d = 0.16 and 0.33 may be compared while keep- ing L/B, H/L, and B/d constant; the difference in C, is typically less than 0.1 (the C, values near L/B = 2 are probably false). Small-scale and prototype-scale data are therefore in agreement and the single Goodyear wave transmission curve of Figure 44 (Harms, 1979a) may be used for most practical applications as long as D/d does not exceed 0.4; near D/d = 0.4 the design curve will be somewhat more conservative than at lower values of D/d. The performance of the PT-1 module is compared to that of a Goodyear breakwater of equal size in Figure 44. It is apparent that the PT-Breakwater provides substantially more wave protection than the Goodyear breakwater. It 42 =} 1,00 oO S) =) log 0.80 5 x a o E 0.60 2 LEGEND = (H/L) 10? = ~ + 0.6 to 1,9 ‘& 0.40 © 2.0 to 6.0 @ xX 6.0 tc 98 I= © D/d B/D Dicm) G/D = 0:20 PT-BW 014 185 64 55 + 0 X GOODYEARO.I6 18.5 64 0 | aah NL l l if Nl L o) 0.50 1.00 1.50 2.00 2.50 3,00 350 4.00 4.50 Relative Wavelength (L/B) Figure 4]. Comparison of Goodyear and PT-2 wave attenuation (d = 4.7 m). Goodyear data a LEGEND (H/L) 10° Ve ae + 06 to 119 o 2.0t0 6.0 X 6,0 to 89 D/d B/D D(cm) G/pD 0,33 18.5 64 55 enlees 0.50 1,00 1,50 2.00 2.50 3.00 3.50 4.00 4.50 Relative Wavelength (L/B) Wave Height Transmission Ratio (Cy) fo) iS} 9° ° = = N 7s (on) @ (e) nN ° iS) iS) ) fs) } iS) a ae a ae rl oom % xCOD = if x00aD lo eee) @wo+ 0 | ocodgD COD +4#+ O+FOF+ + + + Figure 42. Comparison of Goodyear and PT-2 wave attenuation (d = 2.0 m). 43 H/L In % Wave Height Transmission Ratio (Cy) 0.0 1.0 2.0 3.0 Relative Wavelength (L/B) Figure 43. Influence of D/d on Goodyear wave attenuation. 1.2 H/L = 0.04 ° = @ le) Wave Height Transmission Ratio (Cy) oO oa 0.2 B/D G/D D (cm) PT- BW 12.0 3.3 102 —-—-— Goodyear 7- 42 815, 64 (0) 0) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Relative Wavelength (L/B) Figure 44. Wave transmission design curves for Goodyear and PT-Breakwater. 44 should be noted that the Goodyear design curve in Figure 44 is independent of B/D, having been tested over a broad range of B/D during experiments at the Canada Centre for Inland Waters (CCIW) (Harms, 1979a, 1979b). A similar series of experiments for the PT-Breakwater was scheduled at CCIW in September 1980 (see Harms, Bishop, and Westerink, 1981 for results). 2. Mooring-Force Data. a. PT-l1 Breakwater. This breakwater was tested most extensively in the MS-1 mooring configuration (i.e., with a six-tire mooring-force damper installed). It was also tested with the MS-2 and MS-3 mooring systems at the deepest water depth of 4./ meters. As is explained in Section III, the MS-2 mooring configuration is the “stiffest” system tested and the MS-1 is the most elastic or “softest” system tested with the elastic properties of the MS-3 system lying somewhere between them. The peak mooring force is plotted in Figures 45 and 46 as a function of wave height for the case of MS-1 and two water levels, D/d = 0.51 and 0.22. An exponential relationship between the mooring force and the wave height can be detected in the data, even though this information is masked at times by the relatively large scatter of data (even at fixed L/B) that is common in this type of measurement. The best “by eye” fit has been drawn and indicates that at both water levels F is proportional to H3/2. For a given wave height and wavelength, the peak mooring forces are clearly higher at the lower water level. This is shown in Table 4 where the value of the force coeffi- cient K is listed and defined. The influence of L/B is difficult to quan- tify from the data: an increase of F with L/B appears to be indicated, particularly at D/d = 0.51, but additional tests would have to be made to define this relationship. 450 375 300 LEGEND 225 L/B 2.%) 1.7 \_3 150 4 in 1.0 Peakload (kg/m ) 75 (0) .25 50 nthe) 1,00 125 150 1.75 200 Incident Wave Height H (m) Figure 45. PT-1 peak mooring-force data (MS-1, d = 2.0 m). 45 450 Sh) 300 € g BS LEGEND § L/B oO 2.4 to @ Pe 1.7 150 13 }.@) m5 (0) (0) 28) .50 we 1.00 25 150 175 Incident Wave Height H (m) Figure 46. PT-1 peak mooring-force data (MS-1, d = 4.7 m). Table 4. Summary of mooring-force data.! Mooring Force coefficient, K system Goodyear lFor design purposes, suggest that F be increased by 100 kilograms per meter. 2Estimated values. 3Data not available. 46 200 How the mooring-system elasticity affects the peak mooring force is shown in Figures 46, 47, and 48. In each case the water level is fixed and only the mooring-line flexibility is changed. A substantial increase in F is noted when the six-tire mooring-force damper is removed and replaced with a rela- tively inflexible section of conveyor belt (i.e., switching from the MS-1 to the MS-2 system). This is apparent in Figure 47 where the MS-2 data are shown with relation to the MS-1 curve from Figure 46; all the data are above the MS-1 curve with much of the data far above it. The MS-3 data and curve- through data are shown in Figure 48. This system results in forces that are somewhat higher than those for the MS-l1 system but lower than those for the MS-2 system. The corresponding values of K are provided in Table 4. b. PI-2 Breakwater. The PT-2 module was tested only in the MS-3 mooring configuration; test results are shown in Figures 49 and 50. Again as for PT- 1, the force is proportional to He. but for PT-2 the appropriate exponent is 2, not 3/2 as it is for PT-1. The curves for n = 2, fitted by eye, are shown in Figures 49 and 50; the corresponding values of K are listed in Table 4. Although PT-2 was tested with the MS-3, and not the preferred MS-1 mooring system, the effect of a change from MS-3 to MS-1 may be estimated by assuming that the ratio of the respective forces is the same as for the PT-1 module (for which such data exist and are conveniently summarized in Table 4). For PT-1 it is noted K(MS-1) _ 280 _ KQis=3)) 370 7 7 Assuming that this ratio holds for the PT-2 module as well, the estimated MS-1 values, shown in Table 4, are obtained. Although the peak mooring forces for the PT-1 module are higher than those for the PT-2 module for the same wave height and water depth, it should be noted that the transmitted wave is also smaller in the case of the PT-1 module. eS NN en Oa eye a ae Ae geeaey an] re O/d = 0.22 Peakload fF (kg/m) LEGEND L/B AaB) wey et TO Be (es Vou ( EORSsto= | fe) FS) 50 7S 100 (25 150 75 200 Incident Wave Height -{ (m) Figure 47. Effect of mooring-system compliance on F (MS-1 and MS-2, d = 4.7 m). 47 Peakload F (kg/m) 300 |- mae Ooh ay aie o ot ° ° a ° 150}- Oo ° LEGEND _ ©) AN °o° 2.5 to 43 BS tov 1 20 eh Otes {t) 066 tl ObetOmalee. a TE Oe Se | O 2B 50 75 100 125 150 175 200 Incident Wave Height H (m) Figure 48. PT-1l peak mooring-force data (MS-3, d= 400i/ me D/d =O.14 Peakload F (kg/m) LEGEND 2.5 to 4.3 1.7 to 2.4 I3 to V6 10 to 1.2 fe) .25 50 as) 00 l25 150 7S 200 Incident Wave Height H (m) Figure 49. PT-2 peak mooring-force data (MS-3, d = 4.7 m). 48 525 > O/d = 0.33 450 uw NI e,) —E ° ~ = % 300 al a=) o : | = + cs Ses LEGEND sob L/B + © 25 to 2.9 4 #61.7 to 24 75 e 13 to 1.6 | op Ikey tts ThA ee la Gk che est le neh OP i a | 0) 25 50 75 Koyo) 125 I) 175 200 Incident Wave Height H (m) Figure 50. PT-2 peak mooring-force data (MS-3, d = 2.0 m). c. Goodyear Breakwater. The Goodyear module tests by Giles and Sorensen (1978) also included an evaluation of the breakwater mooring loads. Data from those experiments are plotted in Figures 51 and 52 for the case corresponding most nearly to the conditions in the present study (i.e., for the six-module- beam Goodyear breakwater that is also 12.2 meters wide). The curves shown in Figures 51 and 52 indicate that F is proportional to H%; the correspond- ing force coefficient K is listed in Table 4. The hyperbolic relationship between F and H adequately describes the data. pe Goodyeur 0.11 QO. 2 Peakload (kg/m) me) 20 40 _ 60 .80 _ 1,00 120 140 160 Incident Wave Height H (m) Figure 51. Goodyear peak mooring-force data (Giles and Sorensen, 1978; d = 2.0 m). 49 180 Goodyear 150 LEGEND mn, L/B to 120 ze = 1.3 to & 1.0 to o = 0.8 bo} 90 =) & = ) a 2 60 30 fe) fo) 20 40 60 8 Incident Wave Height Figure 52. O/d 0.16 B/D 12.0 D (m ) 0.65 1,00 120 140 H (m) \60 Goodyear peak mooring-force data (Giles and Sorensen, 1978; d = 4.0 m). For a given wave height and length, the mooring forces on the Goodyear breakwater are clearly much lower than those for a PT-Breakwater of equal size. importance of which cannot be quantified at this time: This finding is attributed principally to three factors, the relative (1) The transmitted -wave for the PT-Breakwater is smaller than that for the Goodyear breakwater; 2lL6Qa 6 different levels of energy dissipation occur on each structure (wave breaking and impact, etc.). (2) Different mooring systems were utilized. The importance of this has already been demonstrated with regard to the PT-1 breakwater (see Table 4). (3) The Goodyear breakwater design stretches extensively under load, being very pliable throughout. This influences or perhaps even dominates the mooring dynamics and load transmission characteristics. VI. SUMMARY AND CONCLUSIONS Two prototype-scale PT-Breakwaters were tested in CERC's large wave tank using regular waves: the PT-1 module, constructed of truck tires and steel pipes in waves up to 1.8 meters high, and the smaller PT-2 module, constructed from automobile tires and telephone poles in waves up to 1.5 meters high. Wave data were transmission and mooring-load characteristics were established based on from 402 separate runs in which incident and transmitted wave heights recorded, along with tension in the seaward mooring line. In the course of the investigation, it became increasingly evident (during construction, crane operations, and early experiments) that the PT-] break- water was more rugged and could potentially function and survive under more 50 severe wave conditions than those normally considered acceptable for floating tire breakwaters. For this reason, the PT-]1 module was emphasized in the test program. Although structural failures were not experienced on either the PT-1 or the PT-2 breakwaters throughout the many weeks of testing, and posttest inspections did not reveal areas of imminent failure or excessive wear, it became clear that the PT-2 module was inherently more pliable than the PT-1 module because it was composed of automobile tires, not truck tires. Conse- quently, as waves broke over the structure, greater compression and displace- ment of leading-edge tires occurred on the PT-2 module than was true for the PT-1 module under the same conditions. Although PT-Breakwaters were designed to be pliable, with relative motion between individual components, under severe wave-induced loads, the observed compression of leading-edge tires on the PT-2 module is felt to be excessive for continuous operation. It is therefore suggested that the PT-2 breakwater be limited to sites with signifi- cant wave heights of less than 0.9 meter; this condition is considered to be equally appropriate for Goodyear or Wave-Maze floating tire breakwaters that are composed of automobile tires as well. The value of 0.9 meter was chosen by the researchers as representing the best, though inherently somewhat sub- jective, estimate for the maximum acceptable significant wave height; it is based on extensive laboratory observations and experience with a variety of field installations. The above rule is considered to be of practical importance because it reminds the designer that the environment is hostile and that PT-Breakwaters constructed from automobile tires are inherently less rugged than those composed of truck tires; both have survival limitations. The wave attenuation performance of PT-Breakwaters improves as either wavelength or water depth decreases, or the wave steepness increases (i.e., C, increases with L/B and decreases with D/d or H/L). The shelter afforded by a particular PT-Breakwater is strongly dependent on the incident wavelength: substantial protection is provided from waves that are shorter than the width of the breakwater (i.e, L< B), but very little from waves longer than three B. As the water depth decreases, the wave attenuation performance improves; a breakwater that provides inadequate shelter at high tide may therefore be satisfactory at low tide. Wave attenuation generally improves with increasing wave steepness, especially for relatively long waves in shallow water (e.g., L > 3B and d < 3D). This behavior is attributed principally to the inherent instability of waves, which increases with wave steepness and, for waves near the breaking limit, is so great that only a small perturbation is required to “trigger” the breaking process. For steep waves, breaking was observed to start just seaward of the breakwater with large amounts of energy being dissipated as the wave rolled and surged over the breakwater. The wave attenuation performance of the PT-1 module was found to be superior to that of the PT-2 module and the Goodyear breakwater. For L/B = 1 (and deep water with d > 3D and H/L = 0.04), for example, the wave height transmission ratio was approximately C, = 0.6, 0.4 and 0.2 for the Goodyear, PT-2, and PT-] breakwaters, respectively. Wave transmission curves given in this report should not be used to design breakwaters that are less than 9 meters wide or more than 15 meters wide (see Harms, Bishop, and Westerink, 1981 for further data). For a given breakwater, the peak mooring force, F (on the seaward moor- ing line, per unit length of breakwater) was found to depend primarily on the wave height, H, and water depth, d, with wavelength, L, apparently only of secondary importance. For the conditions investigated, F increases 51 approximately with the square of the wave height; more specifically, F« Ho where n = 1.5, 2 and 2 for the PT-1, PT-2, and Goodyear breakwaters, respec- tively. For design purposes, and until the results from ongoing experiments become available, it is suggested that the following formula be used to cal- culate anchor requirements for breakwaters that range in width from 9 to 15 meters: F = 100(1 + 10 KH”) (6) where H = wave height (meters) F = restraining force (kilograms per meter) to be provided by the anchor system for each meter of breakwater length n = 3/2 for the PT-1 breakwater or 2 for the PT-2 and Goodyear breakwaters K = force coefficient from Table 4. The available small-scale and prototype-scale data have recently been synthesized into detailed design curves (Harms, Bishop, and Westerink, 1981). In order to be conservative, mooring loads should be determined from these design curves as well as equation (6), and the larger value chosen for design purposes. 52 LITERATURE CITED CANDLE, R.D., “Scrap Tire Shore Protection Structures,” Engineering Research Department, Goodyear Tire and Rubber Company, Akron, Ohio, 1976. DAVIS, A.P., Jr-, “Evaluation of Tying Materials for Floating Tire Break- waters,” Marine Technical Report No. 54, University of Rhode Island, Kingston, R.I., Apr. 1977. GILES, M.L., and SORENSEN, R.M., “Prototype Scale Mooring Load and Transmis-— sion Tests for a Floating Tire Breakwater,” TP 78-3, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Apr. 1978. HARMS, V.W., “Design Criteria for Floating Tire Breakwaters,” Journal of the Waterway, Port, Coastal and Ocean Divtston, Vol. 105, No. WW2, pp. 149-170, Mar. 1979a. HARMS, V.W., “Data and Procedures for the Design of Floating Tire Break-— waters,” Water Resources and Environmental Engineering Report No. 79-1, Department of Civil Engineering, State University of New York, Buffalo, N.Y, Mar. 1979b. HARMS, V.W., and BENDER, T.J., “Preliminary Report on the Application of Floating Tire Breakwater Design Data,” Water Resources and Environmental Engineering Report No. 78-1, Department of Civil Engineering, State University of New York, Buffalo, N.Y., Apr. 1978. HARMS, V.W., BISHOP, C.T., and WESTERINK, J.J., “Floating Breakwater Design Criteria from Model and Prototype-Scale Experiments,” Proceedings of the Second Conference on Floating Breakwaters, 1981. KAMEL, A.M., and DAVIDSON, D.D., “Hydraulic Characteristics of Mobile Break- waters Composed of Tires or Spheres,” Technical Report No. H-68-2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1968. KOWALSKI, T., “Scrap Tire Floating Breakwaters,” Floating Breakwater Con- ference Papers, Marine Technical Report Series No. 24, University of Rhode Island, Kingston, R.I., Apr. 1974, pp. 233-246. STITT, R.L., “Wave-Maze Floating Breakwater,” Brochure No. 10732, Temple City, Calif., 1963 (revised 1977). 53 ae (ER) oy ay La APPENDIX A TABULATED TEST RESULTS DS) GH H/DT (DT) (OT) L/B H/L PT-1 breakwater with MS-1 (d = 4.7 m). Table A-l. 4.650 (m) = 101.600 (cm) 3.350 (m) 12.200 (m) 0.218 12.008 3.297 Hl 3sDT 3B : BLOG :DT/D :B/DT :BLOG/DT = (8) D (m) Relative draft Tire diameter Breakwater beam Log spacing B/DT Water depth BLOG/ DT (cm) O srt HORM WF VDNRORAONAMDNDNMHADMMOPEDAMHHDOLFNOMWAMANMHAI WADOOMo ANNAN HAA AA AHA HRAAAANNANMYMNNMMMMOANNNN ARAN eA AA AHAAAMONNNN AGA eo ereceoeo eee eoFFFee2FeoeooeFFCseveveese2eeoereF 22220077 H9 F288 Oo MATE OMT MED DWMMANM HOON COW GT ONDWIOM CID GOR Mr ADP NOP (Ce 4rd war OTDOCDVE-EENMMMNNE FMONNANNDDMAADODOCOWGDUOWT Ed TINNDONDAODWO eeeeoeeveeeeeFeereeeeeeeeeeeeoeereeeeeoeeeteteeeeeeeeeeeserteeeeereee a rAd vrnot A Ht Calc) Gok) DAEOWM AMO AMM UNVWDOMOANHM TOA DMNOCVNOrOWTWMIAMOFGOMFNOMWNANOM MWEIHMADOVIWIMMNMMN FS FT ODHDMAYODWENVAMANHONMOWE ANNO DOONMNFTHOMWDGHOT AAANMPCNWDOVGDODDDOQWOSCHAAANNUNMMONWM SH OAD GMDYUHDOWOOMM Ww MP or oeeGee eo ®eeeeeteteeereeeeeeeetr-eeoaeeeeeeevetrt*seeveeee Geet F Feee rao eetes UADAUNVNDHUNV AVNAUNDDOHPQVODDHUMMNNADNNHD tT ACHMNOT™ OFTEN EDWDOONST DDNHANNT THDOATT FRrOOCVDDODDHNAANNMN SG DOF ORMMFEEDHAONOANT OF OMMEFO eer8®eereto®eeerFP82eFeFGeere2ereereneF 2 ovpvevevceeeveeF 8 Fe 2788 0 @ AAA AAA ANNAN EDD PD AAA AAA AANANAAOAINMMMM AA ARAN NNN PUNDIT DOWF- AWM DYDD DWANM DOWD HANDMNMNMANEODEFMHDODPMVNQVOATHAVMHHOO eocevoeeeeeoer eee SG Geee ete Feeeeteeeoreeereerteeerseeeeet eee 8 FG 8B eo eo ADAMDAVNMOMWM PMMA AAOCMOM ODE AN STONUNANSA HoH AAADOANWMAAIMI OC Adda LN ODM O MONA ALN TUN tt OWN AAP DWOOMMNMOCDNAA-ONMMNH + NOrNneacoMOOMD eoeoeaoeveeeeeeeereet®eeeteeeeee PG eeerF Geeeereeeerte teeFeeeee eee e PAN TFMAMDDAUNVNT DOM K-NVWDUAIMMNOMN NDS OFA DUDHOMOMMOODK-MFMMOKFOAWHDDMW AAA MAAAACINN COIN MMM ST AAR HAAN A AIN CIPRO rt HNN NCR e2CeeoeeoG Foe HeeeePGe eet FGgotree7Hpedsgteeoeosoeee7e7%087070987 8087890 © & OW FH TFORMMONAMMNOMASCE-OUOF THHON OF COPGAHT OM OMVDHVOrHOSGTHAN DVNWUF FOINANEDVOQDDND AT NN ARE ODNVON FAAP LNMMFAGOOMTOVUNAWE NNO delist ddd ae ANNNMMNAMQNMNNAN A ste ANAM NANNderiet eoceeeeoeeeooe eee Gees FS Goo®HeeFoFee2KFoFeFFFeeFFe2LFH72 HHH Oe O NOADANONOVTHOMDANDMTEKOPgADAITHGST SVD ON FT OHV HMVHHOO-MAWOSHWM OANMOPMK-DE™ NV AOHACHMAVWAME Sqr IEMPrDOMN OHO MMNAM ST VOMDDNAHMO NANNN ASAHI HANA NMMM MMM MANAN NAN AAAI AMMMNNNSeeiedt eco eo 8o9 e208 608 GH FHS BH EHF oe wo Mrg 9509 F009 9 00-9 OF 02 HoH Oe 9-9 GSVMDMO- AU VOAAAMAARMNCUHRTFTONMNOMNFKANDOFMEKEMNFOFVDOAVROMDINADONM AAHCEH VME FMOANNMHAANDVID AHODDDMNUAUMDOM-NUNIMMMMMMHAMOanas4AIN rte AAANNAdddnnt Neat ee®eoee®FeeoeeteeeeFeeteeeeeeveeoFeeFetFeoetFetFeereoaeFeHeHHeBeet oes DW ANDNVDNDDO FT AOCMDAMOM--E ONADAAHnT THOVMODNS COVAMVUAHHORANSOHW BARASKE CGEUNAC HH OCAMDVQOMMOR FT MPF DAMDHOCKr EF wWIMNAMTWMMOCMNNVNOHMA ANNAN ANd detest Ht HNNNMMMMMMMNANN HAN AHHH MMNNNAs it eece®eoot®eeteeeteeeeereeetFeeeBeFoOpaet®FeBeeteoetFeFFet FBS GFF FF & O FOSOFVONNNODNOVI TTI FAVIOGCDNUVNWONUAOT NOWNDVQDOODTTFOWNDFWONTITON AAANMMIDSTMMNMNT FHI SITMAAANNANMs STMT NHUUMNMNTHNIFFITTMNDOOVOM e@ceeeaeeeeeeeeeeeteoeeGeeeseeveaeeteeeoeeevet?Geeoeee8F FG eee e @ OVVANS DIDOOV AE TINATAANTNNDVOT DUNST FT OOCODTANDUOI SG TOMDTNATIOO ag NETS ISOC OSTREAM ASIST NT RIND FS LEE ISIENE IDE ddd AHH mM 6 an cic ot A2L PONOMWIM NOGCOUNNAOOMBAACNVUONMNDGOCOMNIOMWMrPNWDEMAMOMMMMmW WDDOHDBNM NE OMYOCKOMOCHANYVDQDOOCHNMMNE DOSY, NYUOAUNDAVNODOONNDAStHHNO -9 © .0°9 ©.0 0-9-0° 0.6 © O4O-9.G © O.0°O-R 6 .0.9-0.8.0 O~9 © 9-8 0.2 &©- 9.9 @ O.H.P~o O09 9 B.9-o p-9 © ANAM MMM Mt FIO MNINNDOE ANNAN ANMNOMM MMP Mt tI TITOWWODOVEMMMMts9 tINwW emer Seer S) Gh Ohne oko Olen ee er a alred enrol Enrol tenalaltalralela olrelalalay eran elton ay Mellel en ger el el en ita y a) WVDODOUDW WV CVOUVUVVUNNDVDODOVUOOVYVVUVYYDVDVVOVU DOVOVUVVYYWVOUVUVNVNUVUNWUWNU eeeeeeteereeeeeFeet®oeeteegeeoeeeeeseeeeeer eee nese GG geo & 6 g.6 @ ataatsesese deter tarrgeett¢dgesdd ged eget IssesIses¢s¢ds¢gggsestgss oeeeteee@eeeoaeeree®eesoeeseeeteeseeeeseeeeeereeseeeeeeeseeee SG eevoe seeee @ Aes AAA ATAOUMW DOU WY VVYVNUUVYOUNY NUOVO QOUUDV AHN nAAAtddtHHied WM DOWDOW OD O.0OWDDDMWORE ERE REPRE PEE Ee EEE NHHHOHHHHMH 56 y) (DT) (DT) H/ DT CT L/B PT-1 breakwater with MS-1 (d = 4.7 m).--Continued 4.650 (m) = 101.600 (cm) 3.350 (m) 12.200 (m) 0.218 12.008 3.297 Table A-l. BLOG BLOG/ DT :DT/D B/DT sDT B ° ° ° ° ° ° ° ° Water depth Tire diameter Breakwater beam Log spacing Relative draft B/DT (m) BLOG/DT WIW NDWND ed DMM AMWDNAMNONAAAM WI WNODWWEIMOO AAMNNNNAN A AAA HAMMNNAAAN TMM PTONNANSMMNM NMI eoe@oeoteteeeeeeeeeeeseeeeet®eaeeetet®Feeset eeee @ TMV TFVAODDNMNGDNHAAVGWOHDNMN ANNIE DOVE MOOwWOUF HO OW ANOIDOD™ WOW DAOMODREIKR THrtANVNODOWIMOMNAHAA eoeoeeeeeteeeoeefeoaeeeeveeeeeeeeeteteeeet® eee & Ain adn AMAA Addn a QBYIDANBODNVMDOSTAUMDNDPSOVIWMGEWOF DOW MWA) OE RE 2YQIAIMNMrNVNVOOSCSTTFOOMeCGNarrra NDM AMOR ANNI AO NAW) QDWWM~OWDHYDHNEWOM—M DO ONNHN OWwwW Dd a9 uN) WU WF arc OVUr 0.0 eoeeeteo et be FF Gee FF 228278 FF FF 2&8 © eo eo 6 eo bent a OMTWONTOMINMNTDONM sMNVWOHKWREKMMMNA gs OR IMs ANOW TANTO OME DANDE OMT DAN WE OMME KR DANDOMRDA ANwOWw eooeeesee eee 2278207802828 F226 & 82 © © 0 © © © 6 POE A AHO COND PD OD 8 OND DD AIO OI CY O09 PD PALO CUCU PD 6D MWMMAMOADADNMWDONANNOM ONAN NM OWANG Vet aNAw eeoeoeeeeae eo eee eee P 2222 GC eere2eeeve eee eee AD OW TMI NA AAS FP TANA AOU MOI MMM HOY SHINO! OSHAAVUDDWDMDNCMNDAVMVDFIHDNWDIANAHDMM~— 4s OD TOMMHAWNH ow eoeoereeertteeeeF eet Fees eeFetFeqaeteeeteteoeeege DOP HAPFOMN ODN E AODMNDANT ANDKCMMMwOA + NAMWMASs POD ANA CUOMO ST AANA MST INNA OMIM ST ANNO t a + DOOD OF 990000109000 0'0909 005.00 00 01600 00600 DAS TI WPIOAINVVANMMWA NW EAP HMM DING Ht ~HOonN OO He 4ONE Oyu ACU PITMODOANAOWOKWMAYSY MWLIPWMCO SFM HW) A PON ete tet RIN ANd AMONCAMAKtIA hon US Do RGIS Ce att aNy @oeG Ge FHF H8HHLHHHHHHH KH EHH HHFT HH OHH OHHH Oe QUO T~ OK DOWVO™ NKR Fh DONA ST ANAMADOANHH OOH VODOPMMITHSOKDKE OND ONMAN AVNAMVUDOADUNINMOW ANAM FMA AAAAHOIMNNARANTMOM S FSMNANANTOMN MOND v0 9.@ 000 0-008 OG FT OH EHH 4-9 He 8HKHH EHD O.O OOO WONAANTOTSAMDHHDONIMNDNMON gc OMANAORDS ONDE NAME FONNAMDDNDUMM s ODHODONAWN TNE OME OMUOh reir Co] aaa ee a «4 e@eeeeneeveeoeteoeveeegeeGeoeteeeeeeevetekRO0ee8 00 6 NQNOAKDM~ OF DOD OM FANE ONDOHD ST ANMINHDHODHDHD SOON WODMAMMOIHMONDAUTNONAMHIM ANAMVNOVDOFMHuMWNNMoOND AAMMNANN ARIAT AMMNN ARAN ISM FGMNN MNT MN MN IM eoeoeeeFee eG eG eFeeFetGebKeoeteetoeFeoe2ee0e2 60 CNONSONNDG DOO FOUVOTNOFGOO SG ODNWDODDDONDOMMOW NONMEOPR ODD DO OF ADEE KANAKRQOQNHKEDOGDOWODN a a Cal 4H A ei dart «A @ooeoeeeeeee®G2@ee® 22 ee 02009 08S © © oo eo e@ DIVNODOSCTFWOVO DTA NWOT NDINVDANDVDFIOMNOVOUNN WN ANMOU DRE ODWHOTHEELK THAGNOMNWDOAMMMUOHMe Adri Cs hn hel AMAA Asie a CMNOAVSCCOMAMMAANOTAO rg OHAVNAQWMHONTDANIOMOANSs NDNDAIFTRMNAONDONE”HMDADOHIONH NN DADO THD NoOnuDoo “2 Bree OG OF 0 :0.9-0-9°9 0-9-9 +9 020,860 -G-O © OWP 0.9100 Oh 0:.0-9-9 0-8 WIMM Ts TNNOOR STs FNNVUURK ss 4¢ THNMOUr +g HNO ORE L120 1) 6 0 I WD Wn LO a iin NINN nw uw) WOWDDNNOW DODVWVNDDUVY QVUDDDNDVNHNDVDUWDUNHONONUW eFC F eet SG GeeFFGHFHROFT HB BHHF HLTH HHOC HE OBS EO teostarsgetser¢etdaergtcs¢ssagrgd¢t¢agdgsgyer4ess¢sss @eeoeeoeeeeeeoeeeseeeeeevaetreeegpeeseeeteeee® eee @ ah Ph EERE NANA AER RE RERRR AIOINNAIAO DHROOCO OAS HOO ONAN AN CIN POND 9 0 $9 F900 In En ITN inwn AAAs Adee HHA I IM tet ied 57 (y) (DT) (DT) CT H/ DT H/L L/B (m) PT-1 breakwater with MS-1 (d = 2.0 m). Table A-2. 3.350 (m) 2.000 (m) = 101.600 (cm) 12.200 (m) 0.508 12.008 3.297 D DT B BLOG DT/D B/DT BLOG/ DT (8) Relative draft (m) B/DT Breakwater beam Water depth Tire diameter Log spacing BLOG/ DT (cm) RANA 0 OO OD OST TNF AITMNANAMNDVSOrMADVONUNFOMNUWVOPPraTNus HALOS 090000 OO pata NAAAHOOANNNN at AAAAON NNN et ted IN CORR HHSOKBLOFTHTHHHFEHCHHHTHLOHEHH BHF OSS EES HOEK EO EHH HEE HE OS NOMNGNOMTHATODrT FADAUNNHDOHUHN ST UHKHKDnVNAHADVOH SG -THso PANNONNADE EONS FSMMMMNOR DTT NNWMN TOME OWOUNETNTMAHRE CROAT HSH HOHE TEHHHDHOHLHCHHH KOSH FSH FGHLHOFL OSCE HCOTHOEHEHH OS o37 AO OMEONCOFrSCOMDDAMDOUVTMNNNOrNMNTM?s QDNONDOWNCOrONUTNAWD HMVOMNOVADDOMMEMM DMA THVHOONONDM OF- NE NDO NNW NAOMNNRAMMNN SANANNNG TEE VDEFDOnRNAANMS VOVOR AHA AHAHRMM FON OE AAANNT NTN ArAN OO ee D ee eee eee ee Re eae ay ONT ere SBS poo FMM DH ANON ONOAMNM- MAND DHOAMNKHANDHO AM FVD ONMMANH ee gee egeoeoteeooege Hoot o FGF eeg tHe eeet neo 02 F FF FH He Ann nN AANAS AHA AARAANNN MAAANAANNN BAHAR ANNNRIeH TFONCATHAVAAND YT HOVUIMORMNM sO gh OTOP OMF DNHUNOTMIHUNNNOWDST@ @eoeGGeoeseseeeeeaeveeeaeetMeH gee BeQgeeoeeeeeoeaeHeeaeteeeoeeteoeeeeeee PON TMNNA AA SrUNtANAtAAR FEFOVWMMNAAH ODO IMNNNA AOS a TIN FNDNO HE AY Ts FNOMNODNOVO ANF SNOT F OM MIN AM FO AGT AMMO ©0090 02 C'G0F9 HCHO AHHH HEH HEBHOHMHCHHHHFOSLCHHS OHO HE HHL HEHOHTHOH HOH HES DOANS VOOMMNOMHHOANT DDSMNQNHSGANTVD OM NAO HANMUMDOMNONMA. AAARAAANNNNMMNM AAA ANNNMNM FAIA MAA AANNNMNM dete oF CPeCHFHO FOB SCHOHFBHOHRLCH FOOSE HL ETO HOHE SOT OHHH OHS OS ee e090 0:90 099 QHMTFNINSIMADWSSATADGODs FOr DAVINA HDOSOELMANYMODMAOAMAadrs DADO DODMVDDOVMEMS NOHDOOMDADMNAMODSMr IFOVOUNHEMDS ONAL Mr a ‘ Adddddeet AANA adda ANNAN tRNA Co POC SCH HOH OHHH HHEHTECHHHEHHLHHOHHHOHEHHHH EHH OHH L OH OHHH HOKE AHOAIMOMNS SF TROHDNTODATATHAVQAVDTONHNAVNOOSIVnSTNOWNH TODO TANSNAD ANAL DD OR FUHUUE TNE ANSFNANNNMDEFODMNADYDOODOMNDOWNNWUSOTratMKs Ane AaAddtaAnddeicdialt ANNANNAANAA ANNAN Str NM 40029 682 &2G 7 OH SMe OPe boo F.4d 0-2 OHV HHH HES NVDADOWONMNWs DOr ANAHMNMAMF DDO MONNSTTO WUNMMNMNAMA ODAMAEOCFNUNNM SenNCOrmrnnnnse Ade aadae aad @oeereeveo®eeosct®®G0eFeepG®Fee FF FHeeFFHHOFFHFFLHEHSF HOF HKH OHA eS AOATFMOMSTIFDDTOATAP AVA FOUNDNAVNOCOKHVEUONHTOVSANOMAH ANE OADMor-h VHUNST FN APTMANNANMHVZGOOMANVGCNONFOUMWOOUOArOTMEs ann Adds ANNNANRAINA SAH NANA AAI Ne CoP HGP oF GH EHHSHHHTHHHHSHGEHOHTHHHEHOHEHRHFTHTFLHO EASE HE HOHE HEHHHEHHOS NDOOMN CNMND DOSMMDOVQOMNMOMMWIAMBDOSOMOOWNNNWN NT OMBoNNMNMMMNa AHARARAANNAT FHAAHHNNANNN ATAAANANNANN BHA ANNAINNNA IS e@oeregeoteoageeG eee Fe eoFFGFeteGFeeeeeF®FFGe22220246 80 8% Ge SMSO CDMNNMAMNSNNMNADODNNMSMNASCDODONMMTDHOMMNEoMmMCMooNnanNnMNa TNOVUNST TMOMANAMNANADEOVTIMMIMNNF-ADOrWOMMHTsITMr OCH OVUMMNSMOEOOr NOINNN ODMOVOMNDHDOAHOSNNDONODADNSIONNG ANDE OSNMNAGCNAVWOOMMMG UDONWM CMNHWNNESHS YVDAONMNATHMOKOCODQVDWNNS eHIHDOOENNVTHMOCOWrO @ 0,2:0r6 0.0 © 0.6 0.0 © © o,0 029 0.9 0H 9 OSH HHH HFG FOOT HS e228 OF CD NANMMMN FST MNMNOFFONNMMMNM dT FOU ONNMMMsS +IOMF AM MTT IMNOFOMMY Vitel altel an pital elvarratt Sen Ol Pref el ty a elrolteltol onal py oitel elrel al al armel ei ai laltel ait On Ol ot PIR eked —Lak mt —) 9H900 OHO 0c. YVOOVGOQSOCHAVO OOOSOSNGDOOOOSAL VOOGAH AH OHDH DH AAVOS ooo eoeGeoeeeeantGeeooaoereeeeetPteeoeoetgeeteeoeneeeeeee @2 Goes @ & @ NANAN NANA NANIN NAAN NINA NANA AINNAIN A tA AONNNN eae OFee tee eF Gee GF FF2HReePFHaeateeeeetet®eeoeeeoeoees Bo Addn OV OOO OU Vetted PEEP REE NNY WWD VUNY WO VOD VUOVUR EE ETE TET EK Kr HNXONADHNAHTHHHDHCOHACOSOE NOON AN 7 Madd ddtdtdddddetet 58 (y) (DT) (DT) CT H/ DT L/B H/L PT-1 breakwater with MS-1 (d = 2.0 m).--Continued 3.350 (m) 0.508 12.008 12.200 (m) 3.297 2.000 (m) = 101.600 (cm) Table A-2. BLOG DT/D B/DT :BLOG/DT B 3D :DT T Relative draft D Water depth Tire diameter Breakwater beam Log spacing B/DT BLOG/ DT AMOAKNDWADATMNNUMNMIDW EG gENWVO NAT AODMACDNONME VDMNOAH GNM TOWTO DED FD OGD OY ON OI ON 0h FD FFD OD 0 FD 0D OD OND PDO 9 OO CPD 9 0D PO —NM MN ND Coeeeeeaeeaete ep Fea Foe Goeeeeeeoeoge0288 0282000 000808700 88 0060 FHNAM AAD DOTS THD ANT FWOWHOVATHOHNV GE FSH AAMHDTOANDIHDIHDVMS SD SSO Fe UU AD SSO UD ALT 9 foc 60 oO cD Fe DBO Ot et, c0. a9 60 GO = be 0N C9 GO OS OSS? OC DUIS es COHCHCHLREHOOCFC HEC CHOHOHLHHHHE HOHE LC OHHHHO HH HH HKHHHHHHH HHH HE Oe “A «i «4 4 NAOH NDONODINNM ODMDT FMEKADHD TMNT AOA MPCMNNDVNAG AON gs Hi-OMOMrwW MVNA ST E-WMNS ONNADOKHDHVOS ATDTONWVO TG VMAVOMDINOMS FHODOWD NMMMN MMT TIFT ITSTORAMAANANMMS THTNVUMMT se HT TEMNNTMsrTaet dg GTNWNwWMM CHOHOKOHTH HOARE HG LCHOHLHOHFLHOHHSHROG HH OH HLTH XH HHH FOXHT HOH HF FOG ANDNHOCGOCANNOCODD DVS AONODNAOHNDVOHVNACSCHOVWVNMONVUG ST FFGPMAt eth Me SEK KRDDHAATT ONMT NOEL NANT OOK HDAMMNVOOR OHH A AMINO D DW a COLORS GC LOPE HOC HOHOHHELCHHHEHHH OHHH H HOCH HHH HHH OIF HHH HF Oe AAA AAA ANN ANN AAA NNNN ANANSI ON NKNOFT MN OW DUN ADHANANWMN-NADSTER TNA MENVNOV EE DOOHN NE DMM OMaD CoHCCCHE RO CHET OHOLECHEOHOHLHOHHTHLCHHEHOHHH HE HHHHO HHH LETH HOH HAO OC 1M FSMMMANNANN ARAL MNMN STONMMMANAHST FMMNNNNRW S SMPTMOMMNANNSAM A ANARERIng ¢MUMMND TMHAMDONPFOATR ARDS OAM NVNQMOHAINNAOMMN VOM eoOeCeoeoeoeeveerexeteB2 OG geese Geene?®FKHe®FeeF2e0807F 80H 020% 0 WDVDOOSMMMNMNOCFTNOE DHOAMN DON TOAMNDONTORNMM OVA HAMNMNANS AAAAN NAAN ANN AA ARAN NAMM ANNA AMMMAN CIN GIN AS MhMm mr mn eC eFCC CLO CELT LH LHF HHHHHH EHO HOS PQ 0209009002000 F008 TO ALK DINTDH:0 VF MOV ADDN AUOMHAUNDVNE VEMVBODDONATOUISGMNT Mes PEEK OF DMONNDONDNVNAADAHOADODCUFE NEM FHONHRADMONE AAO CM AUINAAIN HAAN AN ANIM NAMA NMA NAM NAAM AMMMAN CM NIM M Mag 19 et eecececovoee ere eee F Geet PFeveeeeeoHeat?eeot®ee7e270070048 F080 AT DDH WNDU nt TOWN OTFMHDADNS DAMS UME OMMVUO APN DO HMIW FH NF OADTNUDALW MON ADE FNOWUDODADATOIFVNANTMOMMOF FNCAD TODS OF OD FO MMO UM UAN NNN FOS MMMTMNMNMOMNT MMMM NON AMMMMMMMMMMMAO st mM 0.9 020d 0 0:00 Go o-oo CO 0.9 9-6 8 6.00 HF OHO OB ©0260000.606890 6% © @ 0.9 ED SMTWOHAVUNUANNDOAI SF OOANNE AND ADANNEST NOMNDDHAACNNDONME 1c NANOCNOWTIDOS wh + VOM ¢ COOWOSL HBHMNHD Ary OCAWVANNAOCONVNDNAARE STN Addicted 4 AAdAciried et hen oH Ae added cite met eoceoeoeoe etc eoovoevee Geee7eaeee2eoaee eae eoeveeeeevnev7e77e820289%F GO FFG EH Ge ATVDH VUANDOHATFMNMNVDTFNDHONS OM NO OMMO00 AMrDODHMMNH t ur ow NF ORNC NODATMOMMN ACR FMNOVVOHRN HOES VNHOKMMM FMAHAHDT ODF OrOwW MMM NMA INNA TP NIN TONMONUMMNEMOMMA NM AMM MM MMMMMMMNAS MH eCOCHTHT LO LCHG HOF LHTHOHHLOTHHOHHLHHFFBOHLH FHT FLL E EHH OHO OO OO SHOMWIN DOWDESEQNN CHM NNNNEMMOMIOSAMMANMOMMSSCACONODDMNADON ANANSI MANA ANAAAN NM MMMM MMAMMMPMMMrMme taeTaeTSIPMMMPMIMMMY eeoeokKeoeoe®FereeGeooet®ooFe7HFF F227 248 FHF F027 FF2H6F82 FO 688 O Oe WOCMNAIMMOADBDNNM AG CMOWNABCMAHOMNOVDODNMNMM aM NN QWSOMOM OMNOMNW ORE OWOMOU Ws VAD CORE EEO WWADO OF —KWMAMWOHMWOCHMaAOrOOC a aA et ac p Cm) CHAM N WE NUS et FOO UNM COBANBAF COOMOCANMADSONOOSOMIMAnoo OI TFOHDMMNWMEOCOC GBOAgGe—AG7MOMPS MEHAMOMWGSWOKHANWISOOCMOOMCOMNO © © © © © ©. 2 © © © e.e % © © © O06. O © 0,%,0,0 © ©,0 © © 6.0,0,0 0 Oo Po @.0.8 00-00 6.0 e © SITITZNOWNVOORF OMS 7 gS TMNMNVOVFE DONO hOs sc NNMMWVOrrrwvwara IO 9 © 9 PD OE OPEN PDN MIM MLE VOKOLEOVOYTC UND VGQOOVDESCO COON BOD9OCBODIOSOOS 2000 SOV OGOHANAAMAA AANA ADH COCHFe FPO SFeGe8RHOTFTFeESFTHHTHHSHSC HG PCHKRHFHe eC eCHHF BOF EF LC HCH 22GB FEES NUNN OCIA AICI NI OIAIOIA NAN QAI NEY AINA NOI OIAN QUAN ANNAN O CCCP FC COT eFHe BFP LCHeCHLHHFSeEOBeCHeEA2LeTTHF OS HHTOSFT HC HHE EHH EEE EO NAN AINNNN ANNE EERE EEE ER UN NN NCO DODNDDDDONOOMDMDaMM CEQA EL I OU AL QIU QIAO! CUP ED 69 9 ODPD PD PDD FF FOUN (HW WIN IND ONOWOWODOWWOeted AAAS HIS IAAI ee I ed I ted et I it NO 59 PT-1 breakwater with MS-2 (d = 4.7 m). Table A-3. 4.640 (m) = 101.600 (cm) Water depth Tire diameter DT 3B 12.200 (m) Breakwater beam Log spacing 3.350 (m) 0.219 12.008 3.297 BLOG DT/D Relative draft B/DT B/DT BLOG/ DT BLOG/ DT CT H/DT L/B HT (y) (DT) (DT) (m) (s) (cm) (cm) AO NAD De D THOM ADEE OS NMMONON TAM TOM TADNMNMOMUVONNANTOMSTTONT NSO RN NN WNN UNS ttt SRO MN UNS NIN TOM NMOS SIMMS ATANMT MOMENT ET TSOTIMMI TEMS ef eoee CFS CCC OFSCHCF FC FEHBSH SEES FOHESFSOHFEEEEFT OES SH HOHHOSH SHOES E OBOE BEE Oe MORK SR NM aN saaDoo RAMON KDOMMRN RBA MMsT NEMO MUOENOUEE MANN TOOVTANMN se aMmWRK OADODDRPNTTMMMMDOM VGN gs THMMDO-NNWTTOHNDOS OW THOT HUE NMNUNDADOOURAADOM woe ee coc FooeSFFED OFS OFLC ESCO SE HZEOSHO HE OS OCHO L SCE ESS OTE EET OOF LEO oj “_ -_ —— Cele to lal TOMS WSR WTNH OOH ANMANUEMIBSS VONOHDSOrSCHMOONTOSOPDOTHIMNEFOVUFOMATRR ehh SORT MRANSAO THD OMONNLMOUNMONM IUD VO RBOOF DE MOODV OM OF Sa MUODNUVSE MNS ANNO ASAAMD NDDHNHAAD OHTIVDODAHNKHODOLEELOSOCODN Or DOOHHOS ODHAAKAHA™ CEE HOAAAHRHD ann eooese eee eee eo FSeF LF SCHOF ESB EOS FE EFS FEHB TSC SHEESH HO SES HOKE EOF OBESE OHS OREO -_ -_ A -_ - -_ LOMR © OWORMMNW UD TCHMVOMMTONADVOMMcVN sc VOMMTOOMOMTDOUME Re CHUA STIOROM ODA TROMFOMUINNTROMEOMUNDNNE SGMROMURANOMESMONAMEOMUNNEMNNOAMUNMMETN eco ot ree tc eo ee FFCee eo eFe2e eee eee eo CLO ECE BC HO POEMS OOH FEL OES HOES CoeEeL OOS BRAIN ANIM TSN NAMM PMT SUNN MMM TANNA MMM ST ANMMMMINNANAMMMMT MMMM Ss MOT NNWNN ST AND VOND MH TSTHODDSMMNMOMVNODNMMDODVIVNARVAID-NVOMRBDVOITNDTSMOOW eee eco ee ee ee ee F2e2e eo eee Fee hee ee eee reese eee FF oee eT Foe Feo ee ee Oooo ee DOOWTMNases WSN NS ete OMNNG ese MONS OMAN eS TITMONNN SANNA - COR NA CAAQM CHROME CCH AMODUNINO BAM DEVE SOND EE MDONSDENIONSIDRU NDE FTOHNOMO eo eoFeees ere o eee FF eo Gere ee HO eo CooL eo oF HO CEO TLE EHH CE EE ESCO ETHOS CHO SEES OOO SCNUMNDAN ROR STD ALAM DML STO RARNODMPKOTHMRHNAMVSTOAHDMRSCTODANDOMRDOTHOSC CoM SSSR NN ON SFT TORN NM TTS NNO M STF ONAMMTITTONMMT TIE NNMMMMsTIT NST TSeTW ceo cta ee eee oe CPO eS eo oP CoE OF Coe E SoC ESE LCoS CHO CET COB EO COEF OSC HOES EEO ONS DD WSS GUIR ODL HRA D RDN ON AMDUO UME NR eI BOUT RRR Oh AD FENNCDWOOSHWOTS DWMOM AD AN ADAN NANT RT TODDS T TAO RMWIMNDNO DGS TONDO VWI TOO VEDAS ANNAN NR Sete NGM RN ttt TONS RNS NSE NMA SOT MMMANNM TAM SNS ee ee ee DNA Bese TOSS TF TOIFN DOM AOTNTOND ROW TDM AD THVNONAD We OGD 9 DOT D Oe tO Nt NEL IMMMON BANDON CADPR DT SOTSHODS SVC SR Ma TAERMMODMAMNTOTNNWOTMNDOMM CUES CUCC ROU DD RISE MIN SSN TTT OINTMENT NST TIMI N STS ef ee o.n ce 0 oe Coe O00 wooo oo De eo oe ooo oo LC oe RD Eo CEE oOo LOE Loe OO e-8 ee Oo C-e POE Os et GAO OG TM eR Da BOON SRT ID OR RST TIER CRD TU IM ORR NS ORG SOON CY AL SOE MN ANNM NANI ODE NT IN TOMO RST DUNNO OW NNR OCT SE ORTON MOF Cone Ne} aot Ae ca aa aa A -- = Nea ada = ecco rece ec eee Dee eee eee Fe ee Feet eo Pere re et eee eZro eee ee ee oe eee oeo COS DAVNAD A SAOFT VOS TE OIPVADE AOS NTONCAOQUWNTNDANADOOAD OVNSDND RANDHAMSHDOAM AUN NEL AMM D WAN DSO SPODNREDTOFRAVOO TAM RD WAS RNREORDMNMM TT TOT MIMANDOOM ONO OC Ot et) OPIN ON SIN RS NT TON TSO MINT AINMTMOMI NST re TSIM TITIM INS cece we eee oer ee ec oe reece ee eoeereeeceer esc eeo ee se ere ee ee eset ooeeestoecosece OVTCg FTOT DIAN VNGSTNT ODNOVIT NEC BOTVOOMNDMOMsWe TANTO IT TIOVOT UMS Secor Sr Dar OS MAN e FITTOMMMMMAOT OES TSMORP USOC NUTTER RCS CNTGAIE EP CUNDADNHOOCLOEMYDIDeErPr eoceece see care eee ere eS FeO SeF FF LFE CHEF EEL ED oC Ce EE EL OOOO EEL CoO oo OOO DODDUNVTVDNVINNOVSE ONAUWOONT FT CONNa Ss cOUOT TOT TONOTOOUNDOUNSTOUNGC US DNODO-NNTTMMOMMNO- DOWNS TSEFCMCOrOUNNTTON ODVOVN ST SeOR LEE OAUMANADNAROCEOAM or — “a ~“_ < a— Set NOAA ONISOMM OT KON FSONNNVNON TOO NCNM MTSOCNFCUTONMEENTWNMM eRe DOMSNIM DROANN SCTRN SMS MS WLOTHWMOM OMSSTHANGMOMS FHRNOMSMHOHDLOVIONOTHasNMonNeownanoe NS 0-0-0. 2 0 0-0-0. 0.0 0.8 2 0.0 0.0 018-8 0.9 0-0. 6.0~0. 0.09 010-2 0X8 x2 © o~0~0-0.0-0.0.0-0 0-0 0.2 00-0-2 © ovo 0-8 NAMM eT TO COR POM TT TOOUOESMS TIT IMOCCP REC TSTUOCR EP OTE OMR POST TO OWOEEr COCR Ee DOIN OID AW TW OW WL WNW OW GDL MMM MMMMMMMM MMM MMMMMMMUMMMMG WCO DD DOD DDDD DW QOD SDODDDDDODODDDDODO YO HODOK HON EUKO COU DOO OUOWN eeeecoceeeeeoes ef eee ae ee ese ee eee sce ee eases eee oer FOZ Fee2e2Fe Fe 2e SFE oe Oo vaesoresvrorogrrrssesqredgesesssosIisegertetcercessesetcgssssegser¢see¢seresgrcrsr2 eeeerece sce eee oe Pe ee ese cee e Cree snes eseccere rere ers e tere eerccrerecececece NE et tet ot emg tt mt F010 GD OO D0 0 ttt tte PER REE RINNE RE RRR RRR NAAN WCOLIGOOWG0D DER EEE ERR ERR O OO DDE NED © SOTHO KOLO CN GEOL RT RT rR I I Et et de Nd et et ed es eed tt gett ted et tt tnt 60 (y) (DT) (DT) CT H/DT L/B B/L PT-1 breakwater with MS-3 (d = 4.7 m). Table A-4. 4.640 (m) = 101.600 (cm) 3.350 (m) 0.219 12.008 12.200 (m) 3.297 BLOG BLOG/ DT DT/D B/DT B Relative draft (m) Tire diameter Breakwater beam Log spacing B/DT Water depth BLOG/ DT (cm) SOS CO SUM AT MHAICIM SG TUONAANONMNSTHONe cCRoOcSs NNN et tet St IO SEMI NON NNN NS NS SMM Nee eeecoteeeoeeFteee@ePeteeeveee eee ees eaeciecancecec ASSAD KREEH ORK MNASCOD FON ME ANME NYVUOOQM amma DNDRLL LE TNFTMMMMM UNARNDOOFNMMNSs cmH CORR ON ecrcee®egaoeeeeeP2teevneeeteee®e2eeeeateteeegeve00 = Sas qa aA DOTMOMOMNDVOHYMTFOSrRnDOODRDaIM eT OFonorcnernoo ST TOPE AOOSFMNTTHOHRVTOODNMNMVNSLDMOUONE HCO SN NE FEE DSNHAHOUMTNNVEEAHRHDKHRHR DOLL AARHRON e@eeetetoeoeveeeeeeeeeeeeeeeeeeeteaeetongeoe & « = - VRMEDD OUR CNVELE SMO DURTMOMVEVOFUN seonrvue DRAENEI TE OME OM IORVNANTVOEFOMMFOMcCANVNOMPFaoMmungd @eeerteeeeoe2reeteeoeeaeeeesG®ee2re ee eeeeo8t28e000 ett St SII NICU PD SF Sm SOON 0 ON CY OD DD PD FeMNNSTPFOURDMODVNODEUM ST SHE TONMVSTAUSHRFEAMMOKMA e@eeeeeeeteeoee ee de? €¢080068 fF S&F @& 882 OSHSoee EB Bown sr gM KRODOCWNMMNNaSaHqSs STOMUNANee « WSO Mss CantFNOrPfPeQNsPOsaNMoocmMonarrtgrcr eeaoet®@eteeeoeetoaeeeeeeeoeeeeeeeqgaerteoeeeoeeweeeeaee @ SNM DD ANDO SATO aeMN COSC DRM Reo QunnnMrorcrte Set SISSON NNMO MOD ST PSM ANNNNNMOMT ST CONN Mere eceeteeeet® oot 2 ©Cegqeoe e227 eeFe2t®e® FL eetFFHe000 NOVDVD UNM aMAVOKNDOTM FVUSNSSTITDOAMEAURKHHNKDH SHDMHDEVHOMOSM—ASSOTSVNEMONHAEUNS@VWOT Nest SS ASSIS SAIS MMO MNNG 4 SSNS StS IMUM NA ai e@ceoteteeeaeet@eet?t®eteeteet®eeeeteseseoee eget eeeee oe STUNNASDVMOKNDAVNTOS SDADeOQMUOMD ATOR AN CNW StS SS AMM STAT CIFMMOAVUFUVNSUCAUDNMAHROHDONHRSHDND NEON OS ON et et ct wt tt tt St PO ON NI IN SI MNO @erpertieag@2eeae%F FG qgoe8GG8FH9HEFHFHFHFEFHE OH DAO ® SKNNescooOncocoooeoscesesorosescoc9ooSsscoeSsess cS ano be) va = ®Coeceevre®eoe® SP eer®eo2eFe2 022% e2e2 220200 BDOVDNUNUAHRVOIMANM SSN VARKROHMDKR HMI ao QuNnaN Qua «+ ASSO BUMS TSAO M ST TUOVN SHUN MMTHADMNOWKAHSWM NANA RRM SS. SMO MO NM NQUANN RUSS MOMM NAMA D@ eee eeaoaoF®FeeFeee2 ee FF Fee BGG F820 Oe ScOoummer¢ reer sT SOOO CNOWNOCANSe CT OTONS ST ODOOSS FSV AMMSTN Tes MMMMMTNCOUDUUNNYNSTsVoOcroNuWNM @eeseeeeoeretoeese? ©e-82O0:928SGCeSkCABPHCeHee THF SHSE FE SE NUNNSOcoWGeOVIUNSDOOVOlrTVuTcCeVUsTOVUCNotNT TO ANDKDWOETVCMMMMMNVUMMHAUNDOOr CONT tensor wow = Son en hem hee hon) eet SSNUMSTOMUNAUMNEAMNNMSMOM NGOS VOFOMLYNAMFOWM WOHONNNATN NSMNSMBONN DS TAHNMSM SHaTANOMOMA © FSH LF FO CO KL O-LO © 0~O. ROS 9-0-0 0 09 99% 0-0 0 Oo HO UWNMMM Me TeNVUUE KH GoMMmMMs ts STM OR ROTTS OURS errsrrrrrrrrrercrrrrss error rrgsersrsrsrscsr WucsUVDOVUOUOUVWVNOVUSKUOUUUOUY DUVUUUNOUWUYW @eeeeoeeereeeceeaeteeeweeereecet PF eceeeneseeeeoese Perr P Perf cere Pr Terrr ts Terr ree Terres rTse @eotceeevrereeseerecreereceeserseecoeree2eacee See eS tI SIS St SH St SS Set St tet SII UNO WV UY VOVVVVUVWUDVAARAKRAHHRMAMHARARKHVAAANNAA Aaa esate 61 PT-2 breakwater with MS-3 (d = 4.7 m). Table A-5. 4.700 (m) 66-000 (cm) Water depth Tire diameter DT :B 12.200 (m) Breakwater beam Log spacing 3.660 (m) 0.140 18.485 : BLOG DT/D Relative draft B/DT B/DT ° : 5-545 BLOG/DT = BLOG/ DT L/B CT H/DT H/L Ihe HT (y) (DT) (DT) (m) (cm) RSE NOMSSMGOMNVDOMCMNUTAN TOTNUVIOM DARN ST ONE TITTITTIMNVNGC ROBO OCON DOM LITMAN RDODDLLE HO MMoN @e@eooeot®eeeeeeeeeeeveeteeteevoeeeeeteeee te ee @ a ANMOOCNY AEM Sas CMY AMHR SBODMITOURDOANGH FOOMTIHVDGRVOMNN SNORT UMOADAHROE KWH CF LTMNAON e@eceoeeo®teoeeveevpeeeetr?geeeeoeeeeeet?eaeeeeeteeee et © Gg @ BNNs NAS Ssae NN Nast See DAMDVAFOCUMCOTAFCOTMNWHOMLOMLEONECMHSCMOoM AHOADN FINM ACSTODIVVaMNMNKDDMMRVNARVAVADNSREM MAUMN FIND EAHONHDDRNOLK DEE DANDHAHLDECOKKAKHRHAH eeeeot®eaeeseeeet®egeeeeeeeeeseeete@ eeeteee © @ @ @ Cy PODMVONVD STUDEVOEVDER SPP EOE HRVUAT TIP EN DRKNAN SCPOMEFSMIRANTVUEOMPFOMUR NUE OME SMunn eeeettegevee2e2eSFeeoett2e2e Fes FF ee FeSO e 8 DAURVRKMOHKNON FT ARASDPVUPDVVTNOAPOMARMOTanMoren @-6 08 2 @ 6608 F82F SHS SCE O89 FFF SFG SFO. fe OS ES BROVIVNAUNaAas REYSIMNAeSeeae PVUNENANSSs an WSSO FORN SAPARD SAR PHRHMOVNASPVBOONTOLTVDNaTaOoas e@eec®t®®eqgqeoe®eoest®?eeoeeeeeeetee geeoeteteqeteeereeeae @& SAUNMN DRO ROE OTORNFCANMKAMKSTDAaASaNNMrclran SSS SS ANNAN ST TN AVRANNNMMS STNOANNAM Mee ee eeeteseseWen#teoeee@eeeeeeeeeeset? @eeeete Geeee see BVMOKRODVNSRR Re tT NVAaATH NE TT STOUQVORPMNEDAVAD OE BEN MNSVaTUNSN SAD HNN PODSSRITNNANTUM OAS Ansa AMMA A FONSRN a @eeteeeeoteoeet*?eoteoeteeeeeeee PF eeee® &ege eee & ONMFADRDADNE NER TUM N eae TO TT RUAIMOMPFMCAS SOMMA HREM TNNON VA VNOSNED TI OUTMO NM Past rTrmMmnN NNNN Sew TNHIMNSeas SIMO MOM aaa dD @2@e 0g 8020202 © & @ o-F FOF 0&2 0.08 FFG 07 FH8 98888 WUMMVDOEDBOCSCSOCSSSCSOVUSSCS CHOSOCSCOSCSeS Fo2S900So co Oo ann N e@eoeoeteseeet®eSFeeveeeeeeeenet?e2teeateeo® 2 & @ o & ONTOE STSOSNANITNE EST OM NE DR ~TOTOQUM NONE VAARAOS SOKNSDEMSNT RMON TMND TT OUND Tar rNmmn NN AN Sates FOTN FOMMMasAI- @eeeeeteeteeoeeeteeegeeeeeeteetesteeeeteoeet® © Fe & @ SSOANMANDUONAVTONATVSSOSTOVNATND TOC NNANS Mtr rNONMNeSTeTTSMMMARCOCTH cOoOuUNTsasSoNTDProNM Oe be oe} eoeoeoeeee @PGeoqoeeeGgeeeseeeeeegeae®F SCtHEeetGeet &€FEeSe FINVTOSINVSSOVUSTOCOUTWUVOANTONDTNGDAONYVOCUSTUSo HMOMADKNHROUNS TIM NMMNMMaHNoderQouwMsseMnmaDorcrwow as aA =< Se hee hae NASR MAM sOOnVIOGaNroOMMOooonrnmaoconMmMIcSoNnaT WVFTCOVNMOSTANSNMSCMOENNDOTHR HMOnecnooaernvowoswnese © @ & Oo 2 0-0. Bp 0-8 O-2. ee 8 -O O.4 O-O @ @ eC @ege®eee? O08 8 AQNNMM MS SSN OOEESCMMMS eT NOUR aOMter WN OCR ODO AMNSFRDO MM MNAURAHKHKAKHKRAHAMK HAHAHAHAHA AHA HAHXHAKAHKRG WVVVVOVUDWVUU CODON UCDUSDUVNOUUVEWUNOUNUUNY eeeoefteereeeeeeresesesetoeeegeeveoesneeeg ot © & & weerrrrrrerrrrrsrrsrr ret ter rr rer reer rsrrerS e@eceetmoooeceeeteceeerereeceszcoececeoece ae SC eeoe & MARS AA RN ted tt et at St RN III INN WDD WODODVDUVUY GQUNTDAAARKRAAADRAAQAAANAN AANA SS east SIS SS 62 cr W/DT TyTN) T) L/B PT-2 breakwater with MS-3 (d = 2.0 m). (kg/m) (kg/m) Table A-6. (kg/m) 3.660 (m) 2.000 (m) 66.000 (cm) 12.200 (m) 0.330 18.485 5-545 :D :DT 2B : BLOG :DT/D :B/DT :BLOG/DT = T Water depth Tire diameter Breakwater beam Log spacing Relative draft B/DT BLOG/ DT RODD WOAM SO MIRCMRORDRROMATROUTR aM MUOMURETRWo NANA Nat Ne COR ROM TIL CO MN SNR NO LONDON eNMINM CCPC ee HOC OC RO Ce Coe C CCC CCC CCC CCDC CD DCO eC I SMMMODNUNVADSOSLHAAHONSTHANERONMARRORONMRAD SSF FEET OTMMMNSNOSCONDEDNDVDWUNN OM WDORDRMAHONnOR ° DOD BOOT OF O50 OF OIO OO OOO OO OOOO OM O OO OUD OG UOmlIG = ey Sanaa FASS Seid TOTEDVONSTOITNOSTMRITNTOTEMVBMVETNNOCDNADOWOMON TMOWVAW TORMAIDAMVDOOSTMAYTOTFODNMMNAMNDVANADMoCDANOUM]E NMS TTF OP OR COMM M eT ITs TTONNNOORF ss smMNCIrNNNOY W900 00020 OT O OOK OOOO OOO OOOO OOOODOCODOGODOOU - ETO ONT AAMAS AOOSTMNSNON RAST NUNROOUMNMNROACWDORX F ONS AVM DAMN EDD HORBUMNKRDAMNRMNOAMNUMSEHNANSTVO eeoneeeteeereee et eoece reece eee e eee eee oe ee eo een © Rete IAI QCUN CUCU AAAS ANNANN Sates See UCC NIEND FUNSCM TAN QUONDOLATNNAVENOMNANCMANocearin @ e028 F862 FF LE SHHS BEL ELC OCC HCL ELEC OL OS ELE Oe SOC = QNM MMM Aaa FOUTS IEMANNA ARREST MMMANKNRA FMSNASN FERNAND MSIHMONINCHMLNATNOMNAREMODMRO eceeesteeeeeeet eet eeeeseteenoetFeeeeet geet eenece KNOAMVNTMNVDOMNDSAVNOANMNUYDOMTS®IANAMNWOMEMINnKounN hd rt at CO ON Dt tt ad SE OO OO DD et St et SO CDOT PTD erxreeteeteseree ee ee ®Feceeee® eceoeecsre2e2recrevne et eeece NOSODM—HSAUNDVONVOTMVUENNONMMEMOVeMenaoroOnOsosr SRASDVOVDNSINVGNASTHEDVQODOKR OTONADACTRONCNHOMND Saeet aSSsSsqges SOOM VAN eet e@eeeteete®eeteteeete® tee ®eereeteex2eereeeaeeeee KHOMMONOHR-NM-ODUNDN VM VUE VOM MN aNMOanr NR BUNTRINNA SANNA OFOMNMNTNNVSTASeNATMOFOFOUOVOaeNMmMNAmMeENW Aneaa ANNAN Sas SS MOST SENMNNANS @ STF HHH AaS OST HFC LEO MEZA DP EOFOHEO TA KFLSC OT CBE OF OROECE TRO OOOSCSSSSCC SO BDOCOOCO OOO CDOS OCOOCOCOO DOS OOS curW e@eeetrteetetet® Gee eeeneetFeeeeeeeseeeeeevtesee®&e eee DOMMONS ON DVND LOMO NOW MNANHNNSEH RONEN RAN NA OF SwWMNneg NNGERTNRTMOR OFOSCMUVORAMNaMSeNWN esas = ANNNNN See FS NMS TSVNMONNNe eefeeeeetee ee eS eFeeette et FFeFFe2eFetFoeFeeeFeeeteo SNNSNNTNSCOCOSCDR Ee TUNNNOSTNOUDUVUEOWNNNT NOT USN NANNY AN UN NNNONN BAND IMMMMMMMANNNNT Se Tee TSEMPMIMY Pees ®eeeteoeeoeeweeeeoeet ©GeePeeeet®F GCeeKeeeeeteeeeeeete®ee aOOSDONVOATOWSCONNSTNINOEONNOSTSOTSTOSOCOTWONVASCSNH WDOTSTWOUMANMAN NNR OCH OF CDOWWNS SOM GoOasAr OSE OWN - Co Lon hen! NDR NSN SOCDP-MVODMOT VRTNROMNUMOLT OS MCOOAM Se CONN OSSTHANGCHSNMNSK CNY HDSTHNMOMWGCMONMODSCsDWCceCMo © 0.6 © 0:82 ©. 0 © © © © & © © c.e © © © & ©-8 © © &-8-@€ 60 0 & © © Oe BO 2 eo RAMOS STU SCOP EDOM STO CURE OMMMT Ss SMOORE WOES EEO LIE LI RP RR LOU Le IS SGOOc ec OOSCCCOLOE COCSCOCLOOCSIMDOOGCCEC ADE eCOCCee CSe-u e@oxv tesveer Feoet ete ete eoFeeeee7ee ee eee eeeee ee NOUN AINE NOS CS CEOIN NINO NAO OS OI IOI CUCU ONIN NOON IOLA CL eoececererea ere eoeotF Fe eee eee eee eeevoete te eoees eae te 8 eoe I tt Sh st et St tt I INO NOUN UN OCI DON WOW SD OWDOOW LWADONAOHOSMAMDMOARHAANOS ANNAN AOe: Sh tt tt et ot 63 PT-DB breakwater with MS-3 (d = 4.7 m). Table A-7. 4.650 (m) = 101.600 (cm) Water depth DT B Tire diameter 25.900 (m) Breakwater beam Log spacing 3.350 “m) 0.218 25-492 3.297 BLOG DT/D Relative draft B/DT B/DT BLOG/ DT BLOG/ DT L/B CT H/DT H/L HT (cm) (y) (DT) (DT) (kg/m) (m) (8) (cm) (cm) ANOS TMOEMOMW NAD OROSHNIWE THCNUMQAGOGNOS SO tt at tt ah tt St EON ON OO CU OVO OOOOOOVIOOGCOOCOOD OOOO DO ODDO OG GOD POM gar AK PEEK a COOF OME OVnnMnstsTON OK ems BMOPGOFDNON TMOMOMMNUMSCOFFNNMMN ST Tee OtDnrrww eeceneve7e0ee2eeetoeeseeee?eet®eeeee eeog 0 o = aS aAa4 PWD OMVSEAN NEN NODDNHRSOW EL AMMSOM ai ereans Ss NEATFDMOQMNODIDRANAUED GE MMOnDnNVEONQVM ANIONS SOCRANTMRUPEFNDAHRAMS CORNDDRN ODOWVGHDD DOD @ceeeeteee et ese eeeee ee eee see eed eee HUM SONTHRMHDMODMTRHNSHMSOTOVMVARMSORnMNDMR TINGE LODHANTORrADDDRAMSTO-DHANMMSMrao @eetoeetdeeeteegeeeeeeeeteteeeeoeeeee gee Saas AAAS AS SAAS ata MOS SAMOQRASTON GE NSTMOEMVTMHSONOLNSTHHRWOSN @eeeoereeeateot®eeetenvneeee2f®eegeeteeeoave DAVCSTMMONNSS OIF MNNSASS FOMNNS ae = WSR UNsOANS HOOF OMAMUNDOWQUNAUAHrOaVS e@eeeeoceeeetetaeoeeeteeoeaeeteeeeet eeee e @ SAM NDSSCKDM ERASE ANMNAME SLTOaNaMQrastcacn AAS AANA ND IS SEFTON SST NNMMMMST eT edeoereereeeeoeone 22 eee eee eee eee eee oO INS ert DO NSS TOON NNO VNV SDD ANEOMW SADR aS TOSTCMOMSTONITMN CMD ODWOMNN ID OPO NN SSS S334 SOO NANANN aNAMaVNaemaC @eeoeeee2ee 0229 208228 e000 60.0008 © © Coe AD-OOBMSONADNMNSVDOABFCOCOUVUVSOUFN TOMA rovw NNO ADU OMWMaAcCOCAASCMGRCAE NOTE MSF HSS TOIN NI ttt te tt SS IT FPN IOP St CP PP) -@ @5© © O~2 © @.0-o © 0-8-0-2 @ 0 @ 9-@ &-e © © © & © © © 8-2 o-0-6 SOTO OCSCSBOSCSSSOSSCsSeosoeocoee ceocoqoceoeo e@eceeeteeeget®eteaeveeeretFeeeeeteetee 8 82 eee & AD STaVTOOMANNMDOSCOCSSVORHE ON sEMaOornOortw NNO SCHON MMNAOO GaAs COCuDrsmONuVMrrutannce NCVNS RSS eet ST TMONN RR NUM ANIM MAM ANM ARO eteeoerteoec ee eoser ere cet aoe es 2 et oF eee oc e AUST TSTNUDOVIOT ST OUSOWOTUTSOOVNUSONNNG eros MANO TOM MOC MMANMNNNMWNON TSH eee ouwM eeeteeeeoereeeeaeeeeceeeeeeeeteeeteese @ TOUNDITUNDACDWANCAUANDS CWVVUOUVVDA VVANDS BAOE-CHM TMOMNHMAMoGOenonworewaeSGomrrwvwd =a asain ee oN acm - NDOT EMOMM ANDER EMD ME Maar SCmMUNTtDUNEOn MFSNNDSOqC$H NSM HSTIVSOAIMNSMNSVUSAHRVNDOMNSVS ~O7 0.9. @ S2040, 0g, 0-920°8- oO. B29 Hi Ge so 2 G.0 .@-8 © o @ e-ere UNMM MO Meee NUORRoe seo NCORRocnoNnuUcnrs HOODINNM WI OWI MN HWW NUINGYV QDYUNDVODWUUMWMNWHMNMWMWY WOWVW GDYUDVGDVOVODUWO OVO VOY COVODVUUUONS @eeotoeraeereresneee®% geet Fe 2 & O59 FA e eo > werrr tree rrr rr ese errr er trrrre rts Seer eeSeeetoere ste 2e2 ce 6 F007 eS e 0 0 © Seas SS ett St Set St te RSI SI NINN SUNOS OWRD WN IW OUVF FARA RAAHAKRA UVUQny aan cn et Retest St a 64 APPENDIX B FORCE MEASUREMENT CORRELATION (PT-1) 65 (KG/M } 300.00 PEAKLGAD F 225 -00 150.00 450 -00 525 -00 375-00 75 -00 -00 CERC.JUNE.1979.PT-1 BREAKWATER MOORING TYPE L, .00 75.00 150.00 225.00 300.00 375.00 MaAWLOR Fe Uwe) DEPTH = 2.0M. 450 .00 525 .00 Figure B-]. Correlation of F and F, (MS=1, d = 2.0 m). 66 F PEAKLGAD 150.00 375.00 450-00 625 .00 225.00 75-00 CERC.JUNE.1979,PT-L BREAKWATER.MOGRING TYPE 1. DEPTH = 4-65h. -00 75 .00 150.00 225.00 300-00 375.00 450.00 525.00 REAKEORDI RA yeCKhEAn) Figure B-2. Correlation of F and F (MS-1, d = 4.7 m). 67 (KG/M } 300.00 Peis — |F 225.00 150.00 450.00 525 -00 375 -00 75 -00 CERC.JULY.1979.PT-1 BREAKWATER.MGORING TYPE 2. DEPTH = 4-6H.- -00 75.00 150.00 225 .00 300.00 375 .00 450.00 525 .00 FeARMMLORIO Fez CW) Figure B-3. Correlation of F and F, (MS-2, d = 4.7 m). 68 (KG/M } 300.00 PERISLORIO IF 225.00 150.00 450.00 525 .00 375 -00 75 .00 CERC.JULY.1979.PT-L BREAKWATER MOORING TYPE 3. DEPTH = 4.6H. 00 75 .00 150.00 225 -00 300.00 375 -00 450.00 525 -00 PEAKLOGAD F2 (KG/M) Figure B-4. Correlation of F and 13s (MS-3, d = 4.7 m). 69 (KG/M J 300.00 PERICLOED lr 225.00 150.00 450.00 625.00 375 -00 75.00 p-00 == -00 75 -00 150.00 225 .00 300.00 375.00 CERC.JUNE.1979.PT-1 BREAKWATER.MOORING TYPE L. DEPTH x 2.0M. 450.00 525.00 SIGNIFICANT PEAKLGAD FS (KG/M) Figure B-5. Correlation of F and 19 (MS-1, d = 2.0 m). 70 (KG/M) 300.00 F PEAKLOAD 450.00 525.00 375.00 75 -00 150.00 225 -00 0.00 0.00 CERC .JUNE.1979.PT-1 BREAKWATER MGGRING TYPE 1. 75 .00 150-00 225.00 300.00 375.00 STGNIFICANT PEAKLGAD FS (KG/M) DEPTH = 4.65H. 450.00 525 .00 Figure B-6. Correlation of F and 13 (MS-1, d = 4.7 m). 7 (KG/M } 300.00 F PEAKLGAD 150.00 450 .00 625.00 375.00 225.00 75 -00 p00 CERC.JULY.1979.PT-L BREAKWATER MOORING TYPE 2. .00 75 .00 150.00 225.00 300.00 375.00 SIGNIFICANT PEAKLGAD FS (KG/M) DEPTH = 4-6H. 450.00 525 -00 Figure B-7. Correlation of F and F, (MS-2, d = 4.7 m). 72 (KG/M } 300.00 AD F 225 .00 PEAKLO 160.00 450.00 525.00 375.00 76 -00 ele) .0. 0. CERC.JULY.1979.PT-1 BREAKWATER niJORTNG TYPE 3, DEPFH = 4-6. See Wi) SE Serena ee 00 150.00 225.00 300.00 375.00 SIGNIFICANT PEAKLOAD FS (KG/M} Figure B-8. Correlation of F and F, (MS-3, d = 4.7 m). 73 Says ce 450 .00 $28. APPENDIX C DETAILED WAVE TRANSMISSION DIAGRAM 74 Wove Height Transmission Ratio (C,) Wove Height Transmission Ratio (C, ) LEGEND (H/L) 10° + O.7 (oy Le) ° 2.0 to 6.0 x 6.1 to 1t.6 x 40 D/a = 0.22 (0) 0.5 1.0 1.5 2.0 2.5 3.0 315 4.0 Relative Wavelength (L/B) Figure C-1. PT-1 wave transmission data for MS-l. LEGEND (H/L) 10° O37 TO 12) 2.0 to 60 6.1 to 11.6 O/a = 0.22 10) (0) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Relative Wavelength (L/B) Figure C-2. PT-l wave transmission data for MS-1 (discrete H/L). 75 Wave Height Transmission Ratio ( Cy) 1.20 r T a earls T Sarre lee D/d=0.22 ae % 4 1,00 ‘ ? a u | Wy £ i t 6 + (0) 0.80 2 xv ‘ 8 ® @ 6 (e) ro) oO 0.60 - ) x (2) Oo 0.40} LEGEND _ ro) (H/L) 10 , + 0.6 to 1.9 x © 2.0 to 6.0 0.20 X 6.1 to 10.0 x x 0 = 1! hee es aes fee aay a O 0.50 1.00 1,50 2.00 2.50 3,00 3.50 4.00 Relative Wavelength (L/B) Figure C-3. PT-1 wave transmission data for MS-2. eo a T iamecern ale ar Sananiealine: = D/d=0.22 1.6 AS = 1.00 edz E18 412 YG 99 © a L4+ 234.09 tg +10. 7.45 = + 269 W822 g:1:7 28 Roe ° sq 1Ot 9 : 2 = GO AG Ml 6 eyo) = 22 Sho UNO. Gj C8 S ° ites a 0.80 GED) al Pe 3,38 t 5 339 A ‘02.3% 3.8 ry 03.3 945 —E 02.8 @ 060 Bets o 045 x6 = 05.0 04.9 r= 2 0,40 __LEGEND _ r 57 (H/L) 10° @ + 0.6 to 1.9 3 mes © 2.0 to 6.0 = 0.20 X 6.1 to 10.0 x x 10,0 8.3 (0) 1 See 0) 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 Figure C-4. Relative Wavelength (L/B) PT-1 wave transmission data for MS—-2 (discrete H/L). 76 Wave Height Transmission Ratio Cy Wave Height Transmission Ratio Cy 1.20 T T T =n T Tr T T D/d=O.22 a 1,00 ref in A oo Oa: as tas h 0.80 Oo 0.60 acre oi (H/L) 10 + 0.6 to 19 © 2.0 to 6.0 0.20 xX 6.1 to 10.1 O ot ij. Ey oO 0.50 1.00 1,50 2.00 2.50 3.00 3.50 4.00 4.50 Relative Wavelength L/B Figure C-5. PT-1l wave transmission data for MS-3. 1.20 in Seal! = sal 7 — T T D/d =0.22 + 1.0 |,00}- 1.4 +1.3+06 1.6 4.0.9 0.8 b Ito LOT 2,3 ! hie SOR t 5 +0,0 0.80 pig 923 3.8 03,3 si 8 219 3,4 az 3.0 0.60}- 6 af 0.40 LEGEND (H/L) 10 + 0.6 to 19 © 2.0 to 6.0 0.20 X 6.1 to 10.1 O Se eee 1 1 oO 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 Relative Wavelength L/B Figure C-6. PT-l wave transmission data for MS-3 (discrete H/L). 77 LEGEND (H/L) 10? OL i) Tee) 2.0 to 61 6.1 to 10.1 D/d = 0.51 Wove Height Transmission Ratio (C;) 32029 B35, {@) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Relative Wavelength (L/B) Figure C-7. PTI-l wave transmission data for MS-3 (d = 2.0 m, discrete H/L). 1.20 D/d =0.14 1,00 0.80 Wave Height Transmission Ratio (C+) 6 a0:88 LEGEND (H/L) 10° + 0.6 to 1.9 0.40 ° 2.0 to 6.0 X 6.0 tolh2 0:20 O 0) 0.50 1.00 1150 2.00 2.50 3,00 3:50 4.00 4.50 Relative Wavelength (L/B) Figure C-8. PTI-2 wave transmission data for MS-3 (discrete H/L). 78 Wave Height Transmission Ratio Cy 1.20 ° } 0.80 0.60 0.40 0.20 PT-2 D/d= 0.22 1.3 im 3.1 + +12 @25 1.4 02-0 + tetis +14 41.6 e2.1 o2. 043 250 939 O37 02-4 LEGEND (H/L) 107 + 06to0 1.9 9 2.0to 6.0 x 6-!1 te 10.0 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 Relative Wavelength L/B Figure C-9. PT-2 wave transmission data for MS-3 (d = 2.0 m, discrete H/L). 79 Le9 7=C8" OU da1gcn° €07COL *y-78 “ou £((°S*N) aequa9 yoreesey Butiseutsuq Teqjseoj) tedeq Teo~uyse, :setseg *A °(°S°n) Joque) yoleessy ButiseuTsuq TeqIseopD “AI °W Jleqoy ‘uasuaer0s “TTI °f souueor ‘yUTIAISEM “TI "aTATL “I *uotqesedoad aaem °C “SOIT, °y “SuTIoom *€ “*SaAeM °Z “*SiaqzeMyPeAq BuTIeOCTY “I *230 ‘satod suoydeteq ‘sadtd ajaa19u0. 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