ood Nake ting. BeaCrv. lech. Nae NENR-Cig << ne / REPAIR, EVALUATION, MAINTENANCE, AND REHABILITATION RESEARCH PROGRAM US Army Corps of Engineers TECHNICAL REPORT REMR-CO-6 STABILITY OF DOLOS OVERLAYS FOR REHABILITATION OF TRIBAR-ARMORED RUBBLE-MOUND BREAKWATER AND JETTY TRUNKS SUBJECTED TO BREAKING WAVES by Robert D. Carver, Brenda J. Wright Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers PO Box 631, Vicksburg, Mississippi 39180-0631 August 1988 Final Report Approved For Public Release; Distribution Unlimited Prepared for DEPARTMENT OF THE ARMY US Army Corps of Engineers Washington, DC 20314-1000 Under Work Unit 32325 7 - The following two letters used as part of the number designating technical reports of research published under the Repatr, Evaluation, Maintenance, and Rehabilitation (REMR) Research Program identify the problem area under which the report was prepared: Problem Area Problem Area CS Concrete and Steel Structures EM Electrical and Mechanical GT Geotechnical El Environmental Impacts HY Hydraulics OM Operations Management CO Coastal Destroy this report when no longer needed. Do not return it to the originator. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. The 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. COVER PHOTOS: TOP — Field Research Facility, Duck, North Carolina. BOTTOM — Author delivers 42-ton dolos to Crescent City Harbor, California. SECURITY CLASSIFICATION OF THIS PAGE Form Approved REPORT DOCUMENTATION PAGE OMBINO10704-0188) Exp. Date Jun 30, 1986 Ja. REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS Unclassified 2a. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION / AVAILABILITY OF REPORT Approved for public release; distribution 2b. DECLASSIFICATION / DOWNGRADING SCHEDULE unlimited. 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S) Technical Report REMR-CO-6 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL | 7a. NAME OF MONITORING ORGANIZATION USAEWES, Coastal Engineering (If applicable) Research Center 6c. ADDRESS (City, State, and Z/P Code) 7b. ADDRESS (City, State, and ZIP Code) PO Box 631 Vicksburg, MS 39180-0631 8a. NAME OF FUNDING/ SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) US Army Corps of Engineers 8c. ADDRESS (City, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK WORK UNIT Washington, DC 20314-1000 ELEMENT NO NO NO es 11. TITLE (Include Security Classification) Stability of Dolos Overlays for Rehabilitation of Tribar-Armored Rubble-Mound Breakwater and Jetty Trunks Subjected to Breaking Waves 12. PERSONAL AUTHOR(S) Carver, Robert D.; Wright, Brenda J. 13a. TYPE OF REPORT 13b. TIME COVERED [14 DATE OF REPORT (Year, Month, Day) |15. PAGE COUNT Final report FROM TO August 1988 35 16. SUPPLEMENTARY NOTATION A report of the Coastal problem area of the Repair, Evaluation, Main- tenance, and vere (REMR) Research Program. Available from National Technical rma TOE GOES 18. SUBJECT TERMS (Continue on reverse if RECOSSaTy and identify by block number) SUBGROUP Armor units Jetties Breakwaters Rubble mound 19. ABSTRACT (Continue on reverse if necessary and identify by block number) An experimental model investigation was conducted to obtain design guidance for dolos overlays used to rehabilitate tribar-armored rubble-mound breakwater and jetty trunks subject to breaking waves. It was concluded that: a. The stability coefficient is independent of sea-side structure slope for slopes of 1V on 1.5H and 1V on 2H. Stability showed some dependency on both d/L and H/d with minimum stability occurring at the lower values of d/L and higher values of H/d , i.e. longer wave periods in shallower water. The minimum stability coefficient observed significantly exceeds that obtained for new construction. 20. DISTRIBUTION / AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION CUUNCLASSIFIED/UNLIMITED EX). SAME aS RPT OC oric users Unclassified 22a. NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE (Include Area Code) | 22c. OFFICE SYMBOL DD FORM 1473, 84 MarR 83 APR edition may be used until exhausted SECURITY CLASSIFICATION OF THIS PAGE All other editions are obsolete Unclassified See aE Er-Terr™ BECURITY CLASSIFICATION OF THIS PAGE a —- SECURITY CLASSIFICATION OF THIS PAGE PREFACE Authority to carry out this investigation was granted the US Army Engi- neer Waterways Experiment Station's (WES's) Coastal Engineering Research Cen- ter (CERC) by the Office, Chief of Engineers (OCE) under the Repair, Evalua- tion, Maintenance, and Rehabilitation (REMR) Research Program Work Unit 32325, "Use of Dissimilar Armor for Repair and Rehabilitation of Rubble-Mound Coastal Structures." Tests of dolos overlays for existing tribar armor, which fulfill one milestone of this work unit, were conducted under the general direction of Mr. James E. Crews and Tony C. Liu, REMR Overview Committee, OCE; Mr. Jesse A. Pfeiffer, Jr., Directorate of Research and Development, OCE; members of the REMR Field Review Group; Mr. John H. Lockhart, Jr., Coastal Technical Monitor, OCE; Mr. William F. McCleese, REMR Program Manager, WES; and Mr. D. D. Davidson, REMR Coastal Program Area Leader, CERC. The study was conducted by personnel of CERC under the general direction of Dr. James R. Houston, Chief, CERC, and Mr. Charles C. Calhoun, Jr., Assis- tant Chief, CERC; and under direct supervision of Mr. C. E. Chatham, Chief, Wave Dynamics Division, and Mr. D. D. Davidson, Chief, Wave Research Branch. Tests were planned by Mr. Robert D. Carver, Principal Investigator, and Ms. Brenda J. Wright, Civil Engineering Technician. The model was operated by Ms. Wright, under the supervision of Mr. Carver. This report was prepared by Mr. Carver and Ms. Wright and edited by Ms. Shirley A. J. Hanshaw, Information Products Division, Information Technology Laboratory, WES. Director of WES during report publication was COL Dwayne G. Lee, CE. Technical Director was Dr. Robert W. Whalin. CONTENTS IPREPAGE faieiialcie, oieevsile re! cielieielerelctel/e\ sie] cies! ofe\elsiehelereletel'e).s:e evslie/felie sl sieie elelofeleieleise sje/elsleieia CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT... ccccccccccccccccecccesccesescesescesescecene PART I: INTRODUCTION..... 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TABLE 1 PHOTOS I-11 APPENDIX A: e@oeceeoeee eee ee oo eooeee eoceeeoe eee eoeceereeoeoerec ees ee eee eee ee oe Oo NOTATIONS. yore cic: otaye one ele! o elel eves el/elie) si «|c/.e! sl.evie ebeilere\eh.s\/e\ e! si(slie/ elie: clinisi ellen esels — DODD DN UNF LF W FF eS CoN W Al CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT Non-SI units of measurement used in this report can be converted to SI (metric) units as follows: Multiply feet inches pounds (mass) pounds (mass) per cubic foot square feet By 0.3048 254 0.4535924 16.01846 0.09290304 To Obtain metres millimetres kilograms kilograms per cubic metre square metres STABILITY OF DOLOS OVERLAYS FOR REHABILITATION OF TRIBAR-ARMORED RUBBLE-MOUND BREAKWATER AND JETTY TRUNKS SUBJECTED TO BREAKING WAVES PART I: INTRODUCTION Background 1. The experimental investigation described herein constitutes a por- tion of a research effort to provide engineering data for the effective and economical rehabilitation of rubble-mound breakwaters and jetties. In this study, a rubble-mound breakwater or jetty is defined as a protective structure constructed with a core of quarry-run stone, sand, or slag and protected from wave action by one or more stone underlayers and a cover layer composed of selected quarrystone or specially shaped concrete armor units. 2. Previous investigations, under Work Unit 31269, "Stability of Breakwaters,'"' have yielded a significant quantity of design information for new construction using quarrystone (Hudson 1958 and Carver 1980 and 1983), tetrapods, quadripods, tribars, modified cubes, hexapods, and modified tetra- hedrons (Jackson 1968), dolosse (Carver and Davidson 1977 and Carver 1983), and toskane (Carver 1978). Rehabilitation projects on several of the Corps' rubble-mound structures have revealed a total lack of design guidance or even information concerning the interfacing and stability response of armor units that are of dissimilar type and/or size. In the past, selection of new armor type, method of interfacing, and procedures for preparation of the existing section have been based on engineering judgment or, in more recent times, on site-specific model studies. The engineering judgment process can be expen- sive since experience is limited and there is not usually a solid basis for it. This process can lead to recurring failures that cost millions of dollars without a real solution being developed for the long-term problem. Site- specific model studies have provided good singular solutions, but site- specific data usually fail to meet the requirements of other projects (Carver, in preparation). It is anticipated that the problem will become more acute in future years as rehabilitation of major breakwaters and jetties becomes nec- essary to extend their project life or to meet greater design demands. Approach 3. Model breakwaters and armor units are being used to experimentally investigate the stability response of various armor combinations for selected structure geometries and wave conditions. It would be an extremely extensive task to comprehensively investigate all different types of existing armor units; therefore, this research effort will address only the three types (stone, dolos, and tribars) of armor most commonly used in the Corps. Selec- tion of these armor types should give test results the widest range of appli- cability possible. Tests will be conducted with breaking wave conditions on no-damage, no-overtopping breakwater trunk and head sections using sea-side slopes of 1V:1.5H and 1V:2H. Test results for dolos and tribar overlays of existing stone armor and dolos overlays of existing dolos have been reported (Carver and Wright 1987a and 1987b). Purpose of Study 4. The purpose of the present investigation was to obtain design guid- ance for dolos overlays used to rehabilitate tribar-armored rubble-mound breakwater and jetty trunks subjected to breaking waves. More specifically, it was desired to determine the minimum weight of individual armor units (with given specific weights) required for stability as a function of: a. Sea-side slope of the structure. b. Wave period. c. Wave height. d. Water depth. PART II: TESTS Stability Scale Effects 5. If the absolute sizes of experimental breakwater materials and wave dimensions become too small, flow around the armor units enters the laminar regime; and the induced drag forces become a direct function of the Reynolds number. Under these circumstances prototype phenomena are not properly simu- lated, and stability scale effects are induced. Hudson (1975) presents a detailed discussion of the design requirements necessary to ensure the preclu- sion of stability scale effects in small-scale breakwater tests and concludes that scale effects will be negligible if the Reynolds stability number (Ry) * gt ates, a are ae where g = acceleration due to gravity, Polaco H = wave height, ft he = characteristic length of armor unit, ft v = kinematic viscosity : 4 : é is equal to or greater than 3 x 10. For all tests reported herein, the sizes of experimental armor and wave dimensions were selected such that scale Ps aan. i 4 effects were insignificant (i.e., Ry was greater than 3 x 10°). Test Procedures Method of constructing test sections 6. All experimental breakwater sections were constructed to reproduce as closely as possible results of the usual methods of constructing full-scale breakwaters. The core material was dampened as it was dumped by bucket or shovel into the flume and was compacted with hand trowels to simulate natural consolidation resulting from wave action during construction of the prototype * For convenience, symbols and unusual abbreviations are listed and defined in the Notation (Appendix A). structure. Once the core material was in place, it was sprayed with a low- velocity water hose to ensure adequate compaction of the material. The under- layer stone then was added by shovel and smoothed to grade by hand or with trowels. No excessive pressure or compaction was applied during placement of the underlayer stone. Armor units used in the cover layers were placed ina random manner corresponding to work performed by a general coastal contractor, i.e., they were individually placed but were laid down without special orien- tation or fitting. After each test series the armor units were removed from the breakwater, all of the underlayer stones were replaced to the grade of the original test section, and the armor was replaced. Selection of critically breaking waves 7. For a given wave period and water depth, the most detrimental break- ing wave (i.e. the most damaging wave) was determined by increasing the stroke adjustment on the wave generator in small increments and observing which wave produced the most severe breaking wave condition on the experimental struc- tures. Wave heights of lower amplitude did not form the critical breaking wave, and wave heights of larger amplitude would break seaward of the test structures and dissipate their energy so that they were less damaging than the critically tuned wave. 8. A typical stability test series consisted of subjecting the test sections to attack by waves of given heights and periods until all damage had abated or the structures failed. Test sections were subjected to wave attack in approximately 30-sec intervals between which the wave generator was stopped and the waves allowed to decay to zero height. This procedure was necessary to prevent the structures from being subjected to an undefined wave system created by reflections from the experimental breakwater and wave generator. Newly built test sections were subjected to a short duration (five or six 30-sec intervals) of shakedown using a wave equal in height to about one-half of the design wave. This procedure provided a means of allowing consolidation and armor unit seating simulating that which would normally occur during pro- totype construction. Method of determining damage 9. To evaluate and compare breakwater stability test results, it is necessary to quantify the changes that have taken place in a given structure during attack by waves of specified characteristics. The US Army Engineer Waterways Experiment Station (WES) developed a method of measuring the percentage of damage incurred by a test section during the early L950Usearhas method has proven satisfactory and was used as a means for analyzing and com- paring the stability tests delineated herein. 10. The WES damage-measurement technique requires that the cross- sectional area occupied by armor units be determined for each stability test section. Armor unit area is computed from elevations (soundings) taken at closely spaced grid-point locations before the armor is placed on the under- layer, after the armor has been placed but before the section has been sub- jected to wave attack, and finally after wave attack. Elevations are obtained with a sounding rod equipped with a circular spirit level for plumbing, a scale graduated in thousandths of a foot, and a ball-and-socket foot for adjustment to the irregular surface of the breakwater slope. The diameter in inches of the circular foot of the sounding rod was related to the size of the material being sounded by the following equation: where C = coefficient We = weight of an armor unit, 1b Vinee specific weight of armor unit, pcf C = 6.8 for tribars and stone and 13.7 for dolosse. A series of sounding tests in which both the weight of the armor and the diameter of the sounding foot were varied indicated that the above relation would give a measured thickness which visually appeared to represent an acceptable two-layer thickness. 11. Sounding data for each test section were obtained as follows: after the underlayer was in place, soundings were taken on the slopes of the structure along rows beginning at and parallel to the longitudinal center line of the structure and extending in 0.25-ft* horizontal increments until the edge of the armor was reached. On each parallel row, sounding points, spaced * A table of factors for converting non-SI units of measurement to SI metric units is presented on page 3. at 0.25-ft increments, were measured. The 0.5 ft of structure next to each wall was not considered because of the possibility of discontinuity effects between armor units and the flume walls. Soundings were taken at the same points once the armor was in place and again after the structure had been sub- jected to wave attack. 12. Sounding data from each stability test were reduced in the follow- ing manner. The individual sounding points obtained on each parallel row were averaged to yield an average elevation at the bottom of the armor layer before the armor was placed and then at the top of the armor layer before and after testing. From these values, the cross-sectional armor area before testing and the area from which armor units were displaced (either downslope or off the section) were calculated. Damage then was determined from the following relation: 2) Percent damage = — (100) il where Ay = area before testing, fea Ay = area from which armor units have been displaced, ft The percentage given by the WES sounding technique is, therefore, a measure- ment of an end area which converts to an average volume of armor material that has been moved from its original location (either downslope or off structure). Test Equipment 13. All tests were conducted in a 5-ft-wide, 4-ft-deep, 119-ft-long concrete wave flume with test sections installed about 90 ft from a vertical displacement wave generator. A thin divider was installed in the center of the test section area, thus yielding two 2.5-ft-wide sections. The first 10-ft length of flume bottom, immediately seaward of the test sections, was molded on a 1V-on-10H slope, while the remaining 80-ft length was flat. The generator is capable of producing sinusodial waves of various periods and heights. For all tests, waves of the required characteristics were generated by varying the frequency and amplitude of the plunger motion. Changes in water surface elevation as a function of time (wave heights) were measured by electrical wave height gages in the vicinity of where the toe of the test sections was to be placed (without the structure in place) and recorded on chart paper by an electrically operated oscillograph. The electrical output of the wave gages was directly proportional to their submergence depth. Selection of Test Conditions 14. Breaking wave tests were conducted using dolos overlays. A review of past site-specific stability projects and hydrographic data showed that typical prototype sea-bottom slopes could range from almost flat to as steep as 1V-on 10H. Realizing that wave deformation and severity of breaking action increases as bottom slope increases, and since time constraints would allow testing of only one slope, it was decided to use a 1V-on-10H slope, thus ensuring severe depth-limited breaking wave action (plunging breakers). When breaking directly on the structure, this type of wave normally causes the most damage to rubble-mound structures. 15. By nondimensionalizing design conditions from site-specific pro- jects, it was found that a relative depth (d/L) range of 0.4 to 0.14 should include most prototype conditions encountered in breaking wave stability designs. A review of capabilities of the available flume and wave generator showed that this range of d/L values could be achieved for a reasonable range of testing depths. 16. The wave flume was calibrated for depths from 0.40 to 1.00 ft in 0.05-ft increments at d/L values of 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14. This range of depths, and consequently breaking wave heights, proved to be compatible with the selected armor weights and sea-side breakwater slopes. 17, All stability tests were conducted on sections of the type shown in Figure 1 and Photos 1-4. Sea-side slopes of 1V on 1.5H and 1V on 2H were in- vestigated, while the beach-side slope was held constant at 1V on 1.5H. Heights of the simulated existing structures (prior to placement of the dolos overlays) varied from 1.0 to 1.2 ft. The height necessary to prevent wave overtopping of the existing structure was determined from the slopes, water depths, and wave heights investigated in determining stability coefficients for the dissimilar armor overlays. 18, It was assumed that the overlaying dolos armor could be slightly to significantly smaller than the existing tribars. A review of existing model 10 6850 crv 0 4z9'0 g1 ‘LHOISM Ad!IS HOVAd uoT}IeS SSOID AeeMyYeeI1q [TeoTdA] AWV1845A0 SO100 AV1Y3A0 SO10d0 SYVdINL ONILSIX3 AdAl YONYV AV144dNO SOTOd YOWEY YVE/YL ONILSIXI YFIAVTIYIGNN *I ean3ty ‘3d01S WO1LLOS HOL-NO-AL V Ad Q3SLNOHW4 SNOILOAS LS3L :3LON SAIYVA aqdIs Vas Hat materials was made in concert with this assumption, and 0.627-1b tribars were selected to simulate existing conditions. Tribars were randomly placed in two layers. Overlaying dolos weights of 0.442 and 0.589 1b were used. 12 PART III: TEST RESULTS 19. Various combinations of wave height and period and water depth were investigated for the selected armor weights and structure slopes. Some of these conditions proved to be too severe, i.e., they produced excessive damage as measured by the sounding method. Conversely, some conditions proved to be conservative. Results of those tests which yielded stable design conditions are summarized in Table 1. Presented therein are experimentally determined design wave heights and calculated stability coefficients K's as functions of relative depth d/L and relative wave heights H/d. The stability coef- ficient Ky is determined from the Hudson formula, i.e., where K, = stability coefficient = specific gravity of armor unit a@ = reciprocal of breakwater slope Armor units were placed randomly in two layers, and the number of armor units per given surface area was equal to that presently recommended for new con- struction in EM 1110-2-2904 (Headquarters, Department of the Army 1986). Photos 5-11 show typical after-testing conditions of the structures. 20. Figures 2 and 3 present Ky as a function of d/L , H/d 3 ‘and sea-side structure slope. These data show the stability coefficient to be independent of sea-side structure slope; however, a slight dependency on both d/L and H/d is observed with minimum stability occurring at the lower values of d/L and higher values of H/d , i.e. longer wave periods in shal- lower water. 21. The minimum stability coefficient (20) observed in the present in- vestigation is very significant. Previous tests of dolos overlays for exist- ing stone armor (Carver and Wright 1988a) and existing dolosse (Carver and Wright 1988b) yielded minimum stability coefficients of 12 and 15. Thus, the obtained value of 20 significantly exceeds that observed for other dissimilar armor combinations and present recommendations for new construction (Kp = 15). 13 30 1V-ON-1.5H STRUCTURE SLOPE 0.04 0.06 0.08 0.10 0.12 0.14 d/L 30 1V-ON-2H STRUCTURE SLOPE 0.04 0.06 0.08 0.10 0.12 0.14 d/L Figure 2. Stability coefficient (Ky) versus relative depth (d/L) 14 30 1V-ON-1.5H STRUCTURE SLOPE H/d an 1V-ON-2H STRUCTURE SLOPE e e@ @ ®@ 20 er2%® e (a) MS 10 NOTE: NUMBERS BESIDE DATA POINTS INDICATE THAT THE NUMBER OF DATA POINTS EXCEEDS ONE. H/d Figure 3. Stability coefficient (Ky) versus relative wave height (H/d) 15 Therefore, due to superior stability, a tribar dolos combination might be con- sidered for new construction. 16 PART IV: CONCLUSIONS 22. Based on tests and results described herein in which dolos armor is used to overlay existing tribars on breakwater trunks subjected to breaking waves with a direction of approach of 90 deg, it is concluded that: The stability coefficient is independent of sea-side structure slope for slopes of IV on 1.5H and 1V on 2H. Stability showed some dependency on both d/L and H/d with minimum stability occurring at the lower values of d/L and higher values of H/d , i.e. longer wave periods in shallower water. The minimum stability coefficient observed significantly exceeds that obtained for new construction. 197: REFERENCES Carver, R. D. 1978 (Jun). "Hydraulic Model Tests of Toskane Armor Units," ETL 1110-2-233, US Army Engineer Waterways Experiment Station, Vicksburg, MS. . 1980 (Jan). "Effects of First Underlayer Weight on the Stability of Stone-Armored Rubble-Mound Breakwater Trunks Subjected to Nonbreaking Waves with No Overtopping; Hydraulic Model Investigation," Technical Report HL-80-1, US Army Engineer Waterways Experiment Station, Vicksburg, MS. . 1983 (Dec). "Stability of Stone- and Dolos-Armored, Rubble-Mound Breakwater Trunks Subjected to Breaking Waves with No Overtopping," Technical Report CERC-83-5, US Army Engineer Waterways Experiment Station, Vicksburg, MS. . In preparation. "Prototype Experience with the Use of Dissimilar Armor for Repair and Rehabilitation of Rubble-Mound Coastal Structures," Tech- nical Report REMR-CO-2, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Carver, R. D., and Davidson, D. D. 1977 (Nov). "Dolos Armor Units Used on Rubble-Mound Breakwater Trunks Subjected to Nonbreaking Waves with No Over- topping," Technical H-77-19, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Carver, R. D., and Wright, B. J. 1988a (Feb). "Stability of Dolos and Tribar Overlays for Rehabilitation of Stone-Armored, Rubber-Mound Breakwater and Jetty Trunks Subjected to Breaking Waves," Technical Report REMR-CO-4, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Carver, R. D., and Wright, B. J. 1988b (Jun). "Stability of Dolos Overlays for Rehabilitation of Dolos-Armored, Rubble-Mound Breakwater and Jetty Trunks Subjected to Breaking Waves," Technical Report REMR-CO-5, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Hudson, R. Y. 1958 (Jul). "Design of Quarry-Stone Cover Layers for Rubble- Mound Breakwaters; Hydraulic Laboratory Investigation," Research Report No. 2-2, US Army Engineer Waterways Experiment Station, Vicksburg, MS. . 1975 (Jun). "Reliability of Rubble-Mound Breakwater Stability Models; Hydraulic Model Investigation," Miscellaneous Paper H-75-5, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Jackson, R. A. 1968 (Jun). "Design of Cover Layers for Rubble-Mound Break- waters Subjected to Nonbreaking Waves; Hydraulic Laboratory Investigation," Research Report No. 2-11, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Headquarters, US Army Corps of Engineers. 1986 (Aug). "Engineering and Design; Design of Breakwaters and Jetties," EM 1110-2-1904, Washington, DC. 18 Table 1 Vailuestote wee. odie. mH dw «cand KH for Dolos Overlays of Existing Tribar Armor Subjected to Breaking Waves tee mp Gly SEE T, sec fegtat: d/L H/d 1V-on-1.5H Structure Slope 0.442 0.60 Zi oe 0.58 0.06 0.97 21.0 0.442 0.95 IS) 0.61 0.14 0.64 THESES) 0.589 0.70 bsSy7/ 0.63 0.10 0.90 19:59 0.589 0.70 TZ 0.63 0.08 0.90 1a) 0.589 0.90 We Sy2 0.64 0.12 0.71 20.8 1V-on-2H Structure Slope 0.442 0.65 2.42 0.63 0.06 0297 202 0.442 0.70 Weeyy 0.63 0.10 0.90 2052 0.442 0.70 We O2 0.63 0.08 0.90 2 Orer2: 0.442 0.90 Tea 5i2 0.64 0.12 OS 7All DMG? 0.589 0.75 1399 0.70 0.08 0.93 20.5 0.589 0.85 Mas) Onl 0.10 0.84 21.4 0.589 0.95 SEIS) 0.72 OR 0.76 2233 0.589 1.00 1.40 0.72 0.14 0.72 22153 qI Z77°0 = a $ado[s einjoniq4s epts—ees HG* [-uo-AT eB 3e yor}}e BAPM 2IOJeq UOTIDeS 4Sa} [TeOTdAQ e& FO MATA puy *] O04 aGiS HOVAag e = 6] 1401s qI 7Z77°0 = a $edo[S ainjoniqs aepts—-eas yCg°][-uo-Aj] eB 3e Yee VACM 91OJeq UOTIIeS Seq [eoTdA, B JO MaTA apTs-eeag °Z OOUg aqais vas qI 68S°0 = a $edo[s eanjoniqs epts—-ees HZ-u0-A] e 2e@ yor 2e AAPM aAOJOq UOTIDeS 3Seq [TePOTdA, e& JO MaTA pug “E 02I0Ud 912-9209 —gais vas SI} 8 0°2:1 FdO1S -ONILSAL ANOdTE qI 68S°0 = PM Sedo[Ts ainjonaqs epts-—ees qZ-uUo0-A] yoe19e VARM VsTOJeq UOTIIEeS 4Sseq TeoTdAR & JO META apTs—-es9g °y OJOYg O'%:] 3do01S ONILSAL JuOAIG ado[Ts e1njzoni4s HSG*{[-UO-AT “41 7Z77°0 = an Galas G6°0 = P $saaem 135-19°O Sdaes-/€°]T Jo youqqIe a9 Fe MoTA pu °G OF0Ud = -ONILSGL UdLdV adoTs 91njonaqs yG*{[-UO-AT *qT 68S°0 = “4 gala 02-0 = P $SOACM 35-€9°0O SJeS-/G°T Jo yore A9VFe MITA OpTs—e9sS °Q O20Ug sibs ast ceeatnnnas ances cantons semen cane) ado[Ts a1njonajs HG*[-UO-AT $41 68S°0 = ny $43 06°0 = P {Seaem 35-79°Q S2eS-ZG°] JO YoRIIe AajJe MoTA pug “/ 010Ud 10e¢-9de) 996 291 <1 Li 060 -4 Q*I:] adOTS ONILSAL Ya lav ado[Ts 91n}90n14s HZ-UO-AT {qT Zy7°O = a £33 69°0 = P {seaeM 3J-€9°Q ‘90S-Zy¥°Z JO YoRIIe ATeqJe MaTA pug °g OJOUg e ado[s 91nqoni3s WZ-UO-AT ‘41 7Z77°O0 = M $33 06°0 = P {seaem 33-79°Q 69e8-ZG°] JO Yo!e!IIWe Ae je META epTs—eeS *6 OI0Ud ddis vas ado[sS ainjoni4s WZ-UO-AT {qT 68G¢°0 = M $13 G8°0 = P fsSeaem AJ-12°Q ‘90S-E/°] JO yoe!IIe AeqzFe MaTA ePTs-ees “QT O10UNg ado[s 2anjoni3s HZ-UO-AT *4T 68S°0 sa SsaaeM 4J-Zl°0 £929S-9G°T JO youaqe TejJe META pUy “TT 070Ud ONUSGL waldVv APPENDIX A: NOTATION Surface area, fe5 Coefficient Water depth, ft Relative depth Acceleration due to gravity, Pefaeee Wave height, ft Relative wave height Stability coefficient Characteristic length of armor unit, ft Reynolds stability number = alg alone Wave period sec, time Weight of an armor unit, 1b Reciprocal of breakwater slope Specific weight of an armor unit, pcf Kinematic viscosity Al ns Mayen st, Leta oa a ce Hee ay vais aor PRUE hey 1M A Ky ri be Yh Tone pea Mt , : 4 DOR NE Ln ; y and Auk) Ni Navan , ST eh Dire we i v A 1 ‘i Y ce hi Noe a eer tote as : My (rad AIOE a iy ay 1 Me Pie beer =f 2 cu i. “e ORS Giese eS “