ales 8 Koa LETHE TP 76-11 3 Grain Shane and Size Distribution Effects in Coastal Models Jj. lan Collins and Charles B. Chesnutt TECHNICAL PAPER NO. 76-11 JULY 1976 “Approved for public release; ae distribution unlimited. ay Mai ' Prepared for . IS. ARMY, CORPS OF ENGINEERS yy STAL ENGINEERING 5 =ARCH CENTER _ Kingman Building 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: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 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 so designated by other authorized documents: HL I 0 0301 0089965 4 MBL/WHOI IMI UNCL IF SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO.) 3. RECIPIENT'S CATALOG NUMBER TP 76-11 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED GRAIN SHAPE AND SIZE DISTRIBUTION EFFECTS IN COASTAL MODELS Technical Paper 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER(e) 7. AUTHOR(s) J. Ian Collins Charles B. Chesnutt DACW72-72-C-0024 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS 9. PERFORMING ORGANIZATION NAME AND ADDRESS Tetra Tech, Incorporated 630 N. Rosemead Boulevard Pasadena, California 91107 11. CONTROLLING OFFICE NAME AND ADDRESS Department of the Army Coastal Engineering Research Center (CERRE-CP) Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) D31192 12. REPORT DATE July 1976 13. NUMBER OF PAGES 254 15. SECURITY CLASS. (of thie report) UNCLASSIFIED 15a, DECL ASSIFICATION/ DOWNGRADING SCHEDULE Approved for public release; distribution unlimited. 16. DISTRIBUTION STATEMENT (of this Report) . 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) Coastal models Sediment Grain shape Size distribution Profiles Longshore bars . ABSTRACT (Continue on reverse side if necesaary and identify by block number) Noda (1971, 1972) proposed a two-dimensional, coastal movable-bed, scale- model relationship with four basic scale ratios: (a) horizontal scale, (b) vertical scale, (c) sediment-size’ratio, and (d) relative specific weight ratio. The model law was derived by empirically matching the distance from the stillwater level (SWL) intercept to the toe of the foreshore. te This study was conducted to investigate the effects of the model sediment- size distribution and particle shape in movable-bed models and, if possible Dp ,7or", 14 EDITION OF 1 NOV 65 IS OBSOL S) oase aE SRE SO 2 Sl UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) further refine Noda's scale relationship. An experimental evaluation of the scale model relationship was also performed. The results showed that the effects of grain shape and size distribution are varied. In many cases there was little or no measurable effect; in others, particularly for smaller wave steepnesses, marked differences were apparent. These included multiple bars on profiles consisting of sediment with a bimodal sediment-size distribution and an unstable bar on profiles consisting of sediment with a very narrow unimodal size distribution or a spherical grain shape. Recommendations are made to avoid such sediments as possible model materials. The experiments showed that the initial profile slope influences the final stable profile shape. Under identical experimental conditions, the position of the longshore bar on the final stable profile varied between experiments, indicating that defining the "equilibrium profile" is not as straightforward as has been assumed. "Rocklite,'' a manufactured, lightweight ceramic sediment, was a potentially useful model material. The model evaluation tests were only partially successful. The slope of the foreshore was reproduced in scale, but the shape of the offshore and surf zones and the movement of the shoreline were not reproduced. The general results tend to confirm the difficulties of obtaining successful beach models in similitude. = UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report is published to provide coastal engineers with a further analysis and evaluation of the two-dimensional coastal movable-bed scale- model relationship proposed by Noda (1971, 1972). The work was carried out under the coastal processes program of the U.S. Army Coastal Engi- neering Research Center (CERC). The report was prepared by J. Ian Collins, Tetra Tech, Inc., Pasadena, California, under CERC Contract No. DACW72-72-C-0024, and by Charles B. Chesnutt, CERC. The work of Messrs. A. Yuen and C. Pettit, who conducted the experi- ments, and Mr. G. Smith, who handled the data reduction, is gratefully acknowledged. The authors express their appreciation to Drs. E. Noda, C. Sonu, and B. LeMehaute, who contributed much to this study through many useful discussions. Charles B. Chesnutt was the CERC contract monitor, under the general supervision of Dr. C.J. Galvin, Jr., Chief, Coastal Processes Branch, Research Division. 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. JOHN H. COUSINS Colonel, Corps of Engineers Commander and Director II IV VI APPENDIX A B C CONTENTS SYMBOLS AND DEFINITIONS ...... INTRODUCTION. . . REVIEW OF LITERATURE ON Ey cree PROFILES AND BEACH MODELING LAWS . 5 Ae old Shans: ae 1. Hydrodynamic Condakeione GROEN UCT oO ROG ne 2. Beach Profile Parameters. ... 3. Dimensional Analysis. 4. Empirical Modeling Law Based. on Beach Profile Similarity . 5. Comparison of Model Lame. EXPERIMENTAL DATA... . 0 0 1. Experimental Apparatus “anal Procedures re Ze RES UMEES Wy Mca neiecaaisa Tuts) ey elo), , = Hey ilar Pia, 06> S, theo Vanes Ira. py R,, H,/D, i) 0 > (14) where, the equilibrium (assumed) beach profile is given by the curve y(x) H, = deepwater wave height for normal approach, P = period from wave breaking to top of uprush, S = a coefficient defining particle shape, og = skewness or other parameter defining the size distribution of the sediment, iG = an taalesVopesofuthe: beach, y' = submerged density of the sediment, F, = densimetric Froude number, R, = densimetric Reynolds number, D = characteristic diameter of the sediment, u = characteristic wave-induced velocity, and W = fall velocity of the sediment. At this stage, most investigators who use the dimensional analysis approach neglect some of the terms in equation (14) based on a number of physical arguments, e.g., (a) the ratio P/T will be a unique function of the wave characteristics and the equilibrium profile, and can be dropped; (b) R, is generally dropped because it cannot be modeled in similitude and it is further argued that the breaker zone is fully turbulent; hence, Reynolds number effects are not scale-dependent; (c) it is assumed that in has little effect on the final equilibrium profile; 20 (d) the effects of o, (skewness) and S (shape) are mostly dismissed but it is generally statéd that they should be the same in model and prototype; and (e) u/W is often neglected because it can be argued that W is already included in the sediment characteristics and u is included in the wave characteristics. The investigators generally concur with points (a) and (b). The initial slope, ig, is shown later in this report to be important if it is made too steep. A major part of this study has been devoted to the effects of og and S on equilibrium profiles. Paul, Kamphuis, and Brebner (1972) incorporated the effects of D509, og, and a by defining an equiva- lent sediment diameter which included these effects. It seems unlikely that such an assumption will always be valid. Monroe (1969) performed a series of tests comparing a rounded sand (oolite) and an angular quartz sand and found little difference in profile shapes. Although the applicable fall velocity is often considered as that obtained in still water, the phenomenon in the breaker zone is inherently turbulent in character; Murray (1970) showed that the true fall velocity of very lightweight material can be as much as 30 percent less when measured in a turbulent medium. Since the physical properties of the sediment are directly‘available, the fall velocity of a sediment particle in the breaker zone has not been reliably established and discretion is necessary in the use of relationships for this parameter obtained under very different flow conditions. In view of the disadvantages and use of questionable approximations which are inherent in the dimensional analysis approach, a purely empirical approach based on attempts to match gross beach profile measure- ments, was proposed by Noda (1972). 4. Empirical Modeling Law Based on Beach Profile Similarity. Noda (1971, 1972) developed a model law based on an empirical fitting of the beach discontinuity distance, 8 (see Fig. 1). The basic model requirement is to relate a model sediment density and grain size to the geometric-scale ratios. This is assumed in the form: ana MS sey (OVS) , (15) and (16) | ~ Ee My ae (OV 50) q! 2| After more than 130 experiments using 14 different materials and 22 different grain sizes, Noda found five model profiles with beach discon- tinuity distances which matched those on five profiles of Watts (1959). The five prototypes were all step-type profiles with sediment sizes of Dog > 0.46 millimeter. Noda derived the following relationships based on the five matching profiles: 1.85 0.55 Npn, = u 5 (i'7/)) and : -0.386 A = i Fa e > (18) which comprise the basic modeling law to be evaluated by further testing. A nomograph for use of equations (17) and (18) is presented in Figure 5. 5. Comparison of Model Laws. The theoretical and practical approaches to the development of model laws are considered as coming from two different philosophies. The first is from a desire to reproduce the dominant physical phenomena; the second is from a need to reproduce observed occurrences. Some of the theoretical conditions (eqs. 2 to 13) are satisfied even when practical laws such as given by equations (17) and (18) are used. A summary of the derived model laws based on the various theoretical similitude conditions and a compari- son with the empirical practical similitude condition of Noda (1972) are given in Table 1. III. EXPERIMENTAL DATA 1. Experimental Apparatus and Procedures. Experimental tests were performed in the wave flume shown in Figure 6. The flume is 105 feet long with a square cross section measuring approximately 4 by 4 feet. The wave generator is a plunger type and the prime power supply is through a silicon-controlled rectifier (SCR) to a 15-horsepower direct-current motor. The control system permits extremely accurate speed control over a wide range of load conditions. The motor is coupled through a 21:1 speed reducer. A range of wave periods from about 0.5 to 6 seconds can be generated. Longer periods are possible with a reduced duty cycle or by a change of speed reducer; however, the extended range was not needed for this study. To reduce the amount of test material and to obtain larger ampli- tude waves, a convergence was built to reduce the tank width by half. To further increase the rate of testing, a Plexiglas partition was also introduced parallel to the wave tank to test two materials simultaneously. This latter partition permitted comparisons of different materials under 22 re) 9 > t=) a 3 = se = = 5 > e f= Ore = 2 = e S 5 2 4 2 é 2 fe 28s She = = = aS Cc a=) a=) = = _ [3 WS S5e ¢ § Sob e a w mooTst @ N wo fo>) m9 ico} Be eR EC Bay es ae S WV ] {f/ / ALT 7 1/3 Ly 1/4 = : = | V J vam ve DE = ne Seo AMA ; ALLL =e ; = 1/20 VA S a 30 > 1/40 2 5 1/60 > 1/80 1/100 1/300 i 1/400 i 1/600 i 1/800 1/1000 o 0.040.06 | 0.2 0.30.4 0.60.81.0 A 3 a 6 B10 20 3040 6070 Np Material-Size Scale Figure 5. Graphical representation of model law (Noda, 1972). 23 SMET [apou P9q-aTqeaow [e3sB09 S22 ae PITA Jou st [epow B s[Tetiazew addjojoid Butsn 7 Pata y q is «4 " ec " uaym 3[Nsay uoTzTpuod pownssy AYTIOTOA $2403S Z uot ITpuog uoT3Tpuo) 3 * L Sedu jefrtzsit = “u Te oo apg 103985 MOTS uoTqoTIy quatnqiny ss qs du ‘ou ¢ v I ese) uo ya tpuoy uo }3}PUoD uoy3¢puoy | uoyatpuog | uozazpuog sean SUOJFPUOD OpNIT{TWTS “SMBT [@poll JO UOStIedwod pue euung “T OTeL 24 *(°our Syoey, eizZO]L) ApNysS Sty} UT posn Yue OAeM JO WeAdeTg °*9 9INIdTY 4} GO| 00+021S O0+193S 00+823S OO+0I13S MD erg [ana] Ja}OMIIINS SSD|9 410}D19UBH A@ADM uO0IJDAJASGO |O1Ja}0W yooag Jana] Ja}OM }1JO4d yoDag |O1)1U] (1 adojs ) SSv19 NOILWAYaSEO 25 identical wave conditions during the tests. Therefore, the test widths of the slopes reported in this study are approximately 1 foot wide. The wave height and profile elevations were measured in centimeters with a point gage mounted on an overhead trolley. Horizontal measure- ments were made in feet. The wave height was determined by searching for a maximum and minimum height ahead of the beach. These occur one-half wavelength apart. The incident wave is the mean of the measurements and the reflected wave is one-half of the difference. Profiles were taken initially and after reaching equilibrium (or close to equilibrium). Equilibrium was determined by periodically placing tape on the glass wall along the profile and continuing the runs until no further change occurred. Equilibrium was reached in most tests after 23 or 24 hours. Intermediate profile surveys were taken after 1 and 5 hours for most of the experiments. Water temperatures were monitored and recorded. It was difficult to isolate the effects of size distribution and particle shape with the practical materials available. The materials used in the experimental program were quartz sand, glass, polyvinyl chloride (PVC), pumice, and "rocklite." 2, Resuiles. The conditions for all the tests are given in Table 2. Table 3 summarizes the experiments by purpose. Tabulated data on all profiles are given in Appendix B; plots of the profiles are in Appendix C. IV. DISCUSSION OF RESULTS 1. Effects of Size Distribution. Comparative tests were made with materials having equal median diameters but different size distributions (Table 4). Tests 11B and 12B repeat the conditions of tests 5B and 6B, but with the materials crossed over between the two subdivided channels. The results of this comparison, as an indication of possible channel effects, are discussed later. Selected pairs from Table 4 are shown as Figures 7 to 14. Little difference was found in most profiles; however, profiles with sediment having the bimodal distributions show marked differences. Figures 7, 8, and 14 show that the size distribution does not play a major part in determining beach profiles. However, Figures 9 to 13 show profiles comparing equilibrium profiles obtained with a bimodal and a 26 Table 2. Summary log of test runs. Particle Water Wave Wave Sediment Bescrinricn diameter i depth | period steepness (Particle shape)? (cm) (s) (Ho/Lo) 1-Noda 65.0 2.67 1.58 4.300E-02 22.2 1.00 3.011E-02 | No. 12 sand, Dso = 1.58mm 2-Noda 65.0 2.67 0.560 4.300E-02 22.2 1.00 3.011E-02 1C sand, Dgg = 0.56mm 3-Noda 65.0 2.67 1.58 4.300E£-02 22.2 1.00 3.011E-02 | No. 12 sand, Dsg = 1.58mm 4-Noda 65.0 2.67 0.560 4.300£-02 22.2 1.00 3.011E-02 IC sand, Dso = 0.56mm 5-Noda 65.0 2.67 1.58 4.300£-02 22.2 1.00 3.011E-02 | No. 12 sand, Dsg = 1.58mm 6-Noda 65.0 2.67 0.560 3.900E-02 22.2 1.54 1.054E-02 1C sand, Dsg = 0.56mm 7-Noda 65.0 2.67 1.58 3.900E-02 22.2 1.54 1.054E-02 | No. 12 sand, Dso = 1.58mm 8-Noda 65.0 2.67 0.560 4.300£-02 22.2 1.00 3.011E-02 IC sand, Dsg = 0.56mm 9-Noda 65.0 2.67 0.500 4.300E-02 22.2 1.00 3.011E-02 | Uniform sand, 0.42 < Dsg < 0.59 10-Noda 65.0 2.67 0.500 4.300E-02 22.2 1.00 3.011E-02 | Uniform sand, 0.42 < Dsg < 0.59 11-Noda 65.0 2.67 0.560 4.300E-02 22.2 1.00 3.011E-02 | IC sand, Doo = 0.S6mm 12-Noda 65.0 2.67 0.500 4.300£-02 22.2 1.00 3.011E-02 | Uniform sand, 0.42 < Dsg < 0.59 13-Noda 65.0 2.67 0.500 3.900E£-02 22.2 1.54 1.054E-02 | Unifrom sand, 0.42 < Dsg < 0.59 14-Noda 65.0 2.67 0.560 3.900E-02 22.2 1.54 1.054E-02 IC sand, Dso = 0.56mm 15-Noda 65.0 2.67 0.260 4.300E-02 22.2 1.00 3.011E-02 | Uniform sand, 0.21 < Dso < 0.30 16-Noda 65.0 2.67 0.260 4.300E-02 22.2 1.00 3.011E-02 Fine sand, Dog = 0.26mm 17-Noda 65.0 2.67 0.260 3.900E-02 22.2 1.54 1.054E-02 | Uniform sand, 0.21 < Dsg < 0.30 18-Noda 65.0 2.67 0.260 3.900E-02 22.2 1.54 1.054E-02 Fine sand, Dso = 0.26mm 3A 24 63.5 2.42 0.500 4.300£-02 34.2 1.00 3.011E-02 | Glass beads 4A 24 63.5 2.42 0.600 4.300£-02 34.2 1.00 3.011E-02 | Ground medium glass SA 19 63.5 2.42 0.600 4.000£-02 34.2 1.54 1.162E-02 Ground medium glass 6A 19 63.5 2.42 0.500 4.000£-02 34.2 1.54 1.162E-02 | Glass beads 7A 1G, 61.0 2.42 0.600 5.600E-02 34.4 1.54 1.621E-02 | Ground medium glass 8A 15 61.0 2.42 - 0.500 5.600E-02 34.4 1.54 1.621E-02 | Glass beads 9A 26 61.0 2.42 0.600 7.300E-02 34.4 1.54 2.108E-02 | Ground medium glass 10A 26 61.0 2.42 0.500 7.300E-02 34.4 1.54 2.108E-02 | Glass beads 11A 5 62.0 2.42 0.300 1.000£-02 32.2 0.820 1.049E-02 | Glass beads 12A 3) 62.0 2.42 0.300 1.000E-02 32.2 0.820 1.049E-02 Ground small glass 13A 2 62.0 2.42 0.300 2.000E-02 32.2 0.820 2.002E-02 | Glass beads 14A 23 62.0 2.42 0.300 2.000E£-02 32.2 0.820 2.002E-02 | Ground small glass 15A 23 62.0 1.30 3.10 1.S00E-02 32.4 0.970 1.090E-02 | PVC cylinders 16A 23 62.0 1.30 2.90 1.S00E-02 32.4 0.970 1.090E-02 | Crushed PVC 17A 22 63.0 1.30 3.10 3.400E-02 32.3 0.970 2.520E-02 PVC cylinders 18A 22 63.0 1.30 2.90 3.400E-02 32.3 0.970 2.520E-02 | Crushed PVC 19A 29 63.0 1.30 3.10 4.200E-02 32.3 0.970 3.065E-02 | PVC cylinders 20A 29 63.0 1.30 2.90 4.200E-02 32.3 0.970 3.065E-02 | Crushed PVC 21A s 63.0 2.42 0.300 7.400E-02 31.2 1.54 2.108E-02 | Glass beads 22A 5 63.0 2.42 0.300 7.400E-02 31.2 1.54 2.108E-02 | Ground small glass 23A 23 68.0 1.30 1.20 5.600E-02 31.0 3.54 2.199E-03 | Rocklite 24A 23 68.0 1.60 0.800 5.600E-02 31.0 3.54 2.199E-03 | Pumice 25A 2: 68.0 1.30 1.20 3. 400E-02 32.5 2.58 2.888E-03 | Rocklite 26A 23 68.0 1.60 0.800 3.400E-02 32.5 2.58 2.888E-03-| Pumice 1B 15 65.0 2.42 0.620 4.100E-02 30.7 1.00 2.883E-02 | Two fine, one coarse, ground glass 2B 15 65.0 2.42 0.620 4.100E-02 30.7 1.00 2.883E-02 | Ground medium glass 3B 2 65.0 2.42 0.620 4.900E-02 30.7 1.54 1.405E-02 | Two fine, one coarse, ground giass 4B 24 65.0 2.42 0.620 4.900E-02 30.7 1.54 1.405E-02 | Ground medium glass SB 24 67.0 2.42 0.620 7.500E-02 30.8 1.54 2.135E-02 | Two fine, one coarse, ground glass 6B 24 67.0 2.42 0.620 7.S00E-02 30.8 1.54 2.135E-02 | Ground medium glass 7B 22 67.0 2.42 0.620 7.900E-02 30.8 1.00 5.509E-02'| Two fine, one coarse, ground glass 8B 23 67.0 2.42 0.620 7.900E-02 30.8 1.00 5.509E-02 | Ground medium glass 9B 24 67.0 2.42 0.620 7.100E-02 30.8 1.26 3.107E-02 | Two fine, one coarse, ground glass 10B 24 67.0 2.42 0.620 7 .A00E-02 30.8 1.26 3.107E-02 | Ground medium glass 11B 24 67.0 2.42 0.620 7.000E-02 30.8 1.54 1.999E-02 | Ground medium glass 12B 24 67.0 2.42 0.620 7.000E-02 30.8 1.54 1.999E-02 | Two fine, one coarse, ground glass 13B 24 67.0 2.42 0.620 7.000E-02 30.8 1.54 1.999E-02 | Ground medium glass 14B 24 67.0 2.42 0.620 7.000E-02 30.8 3.54 1.999E-02 | Two fine, one coarse, two medium, ground glass 15B 24 65.0 2.42 0.600 4.000E-02 30.8 1.00 2.819E-02 | Ground medium glass 16B 24 65.0 2.42 0.600 4.000E-02 30.8 1.00 2.819E-02 | Two fine, one coarse, two medium, ground glass 17B 24 65.0 2.42 0.450 7.000E-02 30.8 1.54 1.999E-02 | One fine, one medium, ground glass 18B 24 65.0 2.42 0.450 7.000E-02 30.8 1.54 1.999E-02 | One fine, one medium, ground glass 19B 24 65.0 2.42 0.450 4.300E-02 30.8 1.00 3.011E-02 | One fine, one medium, glass beads 20B 24 65.0 2.42, 0.450 4.300E-02 30.8 1.00 3.011E-02 | One fine, one medium, ground glass 218 24 65.0 2.42 0.450 4.300E-02 30.8 1.54 1.216E-02 | One fine, one medium, glass beads 22B 26 65.0 2.42 0.450 4.300E-02 30.8 1.54 1.216E-02 One fine, one medium, ground glass 23B 26 65.0 2.42 0.450 7.000E-02 30.8 1.00 4.869E-02 | One fine, one medium, glass beads 24B 26 65.0 2.42 0.450 7.000E-02 30.8 1.00 4.869E-02 | One fine, one medium, ground glass 25B 24 65.0 1.30 3.50 4.200E-02 30.8 1.00 2.947E-02 Green, one gray, PVC cubes 26B 24 65.0 1.30 2.45 4.200E-02 30.8 1.00 2.947E-02 | One black, one white, PVC cylinders 1c 24 65.0 1.30 1.20 0.116 27.0 4.30 3.084E-03 | Rocklite 2c 24 65.0 1.60 0.800 0.116 27.0 4.30 3.084E-03 Pumico 3c 28 65.0 1.30 1.20 0.121 30.4 3.03 6.978E-03 | Rocklite 4c 28 65.0 1.60 0.800 0.121 30.4 3.03 6.978E-03 | Pumice SC 24 65.0 1.30 1.20 7.000E-02 30.4 2.60 S.781E-03 | Rocklite 6C 24 65.0 1.60 0.800 7.000E-02 30.4 2.60 5.781E-03 Pumice 7C 26 65.0 1.30 1.20 0.100 30.4 27) 7.285E-03 | Rocklite 8C 26 65.0 1.60 0.800 0.100 30.4 2.75 7.285E-03 Pumice 9C 24 65.0 1.30 1.20 8.000E+02 30.5 2.46 - 7.622E-03 | Rocklite 10C 24 65.0 1.60 0.800 8.000E-02 30.5 2.46 7.622E-03 | Pumice 11¢ 24 68.0 1.30 1.20 8.200E-02 30.5 2.60 6.823E-03 | Rocklite 12C 24 65.0 1.60 0.800 8.200E-02 30.5 2.60 6.823E-03 | Pumice 13C 24 65.0 1.30 1.20 $.900E-02 30.5 2.20 7.280E-03 | Rocklite 14C 24 65.0 1.60 0.800 S.900E-02 30.5 2.20 7.280E-03 | Pumice 1SC 24 65.0 1.30 1.20 5.200E-02 32.7 4.28 1,294E-03 | Rocklite 16C 24 65.0 1.60 0.800 S.200E-02 32.7 4.28 1,.294E-03 | Pumice 17C 24 65.0 1.30 1.20 4.100E-02 24.8 3.70 1.404E103 | Rocklite 18C 24 65.0 1.60 0.800 4.100E-02 24.8 3.70 1.404E-03 |+ Pumice pSediment specific weight, 2Median grain size. adetails in Appendix A. “Tests performed by Noda in 1972-73. 27 (a) (b) (c) (d) (e) (£) (g) (h) (i) Table 2 notes. The first column indicates the run code number and the number of hours duration for that test, temperature is water temperature in °F, gamma is y,, the sediment specific weight, particle diameter is the median grain size in millimeters, wave height is in meters, water depth is in centimeters, wave period is in seconds, wave steepness is Ho/Lo (deep water), particle shapes describes the material, further details are given in Appendix A. 28 23A 17B 25B 1C Table 3. Summary of experiments. Preliminary experiments Size distribution Shape Shape and size distribution Shape Material evaluation Size distribution Shape Shape Verification 29 Material Quartz sand Quartz sand Glass PVC Glass Rocklite and pumice Glass Glass PVC Rocklite and pumice Table 4. Test pairs Effects of size distribution on profile shape: identification of comparative tests. @, 20, 12) 13 13B 15B and and and and and and and and and and and and and and and Remarks Natural sand; Ds59 = 0.56mm vs. nos. 30 to 40 sieve size. Natural sand; D590 = 0.26mm vs. nos. 50 to 70 sieve size. Crushed PVC well distributed vs. uniform PVC cylinders. Biomodal ground glass having same average diameter vs. unimodal ground glass. Repeat of 5B and 6B with materials reversed. Trimodal ground glass vs. unimodal. 30 89 *SUOTINGTIZSTp 9ZTS MozZeUu pue peper3s SuTAeY pues YIM pouTeigo seTTFord yoeoeq Fo uostseduo) (43) YOIDIS iL) 99 G9 v9 £9 Ae) (6 uny) WWEgGO>G >wWwW2pO —— (Q uNYy) UOIJNGI4}SIG AZIS |DIaUaD ——— puodS Z}J0NO GOO =scal/c ww 9G'O =9%q SOpel ‘ZL eins ty (W3) UOl}OAa|Z 3| 89 ANS) 99 (paysnid) 9Ad (S4saput}A9) Ad G9 v9 (4}) YOlsOIS £9 29 “SIOpuTTAD OAd pue DAd Peysnid sutsn sa[tzord yoeoq Jo uostiedwod oy Fo otduexse ,Teotdky, +g 8In3 Tj 19 09 6S 8G (0) Ol Oe, wy oO < Sl Jayoa1g f Bi = ) GZ00=°1/°H = WIPE =H O¢ 3 SJ60=1 Ov OS 32 89 *(y10°0 = O1/°H) TejoweTp ueTpow owes oy} SuTAeY uoTINqTI4STp JUdUTpas Tepowtq pue [TepowtuN YIM pouteiqo seTtzourd yseoq Jo uostizeduoy “6 o1n3TY (4}) UOollDIS 29 99 G9 v9 ats) 29 19 09 6S (ww 9'Q =9Sq) jopowiugn ——— (Www Z| JD | + WWEe'O }0 2) |JOPOWIg Jay0a1g t vlOO0=°1/°H WI6'b =H SpGl=1 O| oO N (oe) mM (wd) uoljoAa|zJ 33 "(1Z0°0 = O1/9H) 197OWeTp UeTPOW sues 94} BUTABY UOTINqTIISTp JUSWTpes [epoultq pue TepoWrTUN YIM pouteiqgo setTtzord yoeeq Fo uostzeduo) wWw9'Q =p ‘|jDpowig ——— WW 9°Q = Pp ‘|Dpowlun “OI emns ty Jayoosg { 120';0 =91/°H woG 2 =H SHE) sl 34 °(6Z0°O = O1/9H) sO.OWeTP ueTpou owes oY} SUTACY UOTINGTIASTp JUSWTpas [epowtq pue [Tepowtun YIM pouteygo settzord yoeoq Jo uostsieduoj “TT sInsTy wwo9O-=p‘'|opowiun ———— WW 9°Q = Pp ‘|Dpowlg Jayoaig f 6200 = °1/°H Ww |b =H SO) ell 35 89 “(1S0°0 = O1/°H) LoqoWeTp UeTpoU cules OY} BUTABY UOTINGTIISTp JUSUTpes [epoultq pue [epowtun YIM peutTeigo seTtzoid yoeeq Fo uostaeduo) (4}) vorDys 29 99 ¢9 v9 €9 29 (oe 209 (ww 9°90 =95q) jopowjun ——— (ww 2'| }0|+WWeE'?O IO Z) |Opowlg Jayoeig j 1€0°0 = °17°H wd}. =H SOG [3 dl "ZI ean3ty 6S 8G Ol 1S) N (wo) uoljoAalz (2) Mm Ov OS 36 89 °(¢$S50°0 LO = 07/OY) IoJOWeTp ueTpow owes oY} BUTABY UOTINGTIISTp JUOSUTPES [epoutq pue [Tepowtun yIIM pouteiqo seTTfZoad yoeeq Fo uostaedwoy “¢{ eindTy (44) woIs04S 99 G9 v9 €9 29 19 09 6S a. (ww 9'9 =9%q) jopowiun ——— (wwz | j0) + wwe go }02) |Opowlg 01 02 O¢ Jayoesg { Ov GGOIO=] 7 OH wo62 =H SO] sl OS (wo) uoljoAalz 37 89 "(0Z0°0 = CT/OH) L9}OWeTp UeTpoUl owes SY} SUTABY UOTINGTIISTp jUSUTpes [epowtrz pue [TepowWwruN YIM pouteiqgo seTtyoad yoeeq Fo uostzeduo) “pT sinsty (43) WOlOIS 29 D9 G9 v9 £9 79 19 09 6G (ww 99 -9%q) jopowiun ——— (ww 2) j0| + WW9C JO] + WWE'C JD Z) JOpowls Jayoaig } 0200=°1/°H wIQ2=H S7G'| Ol ‘e) O (eo) inp) Ov OS (wo) uoljDAa|J 38 unimodal (but narrow) sediment-size distribution. The figures are arranged in ascending order of wave steepness. The smallest steepness tested (Hp/Lo = 0.014) shows a tendency for a bar formation in tests with bimodal and unimodal distributions (Fig. 9); however, in tests with a bimodal distribution, the bar is formed farther offshore. The slope of the beach face is also different. For a steeper wave with the same period, Figure 10 shows the bar formations even farther apart than those shown in Figure 9. However, Figure 11 shows similar profiles for a wave steepness (sb 0.029) lying between that of Figure 10 (Ho/Lo = 0.021) and Figure 12 (Hp/Lo = 0.031). This apparent contradiction can only be explained by the difference in wave height (4 centimeters versus 7 or 8 centimeters). For waves of very large steepness (Hj/Lo > 0.05), the differences between bimodal and unimodal distributions diminish (Fig. 13). Finally, it was found that the trimodal grain-size distributions tested always produced profiles similar to those of unimodal distributions (Fig. 14). An apparent consistent difference between a uniform-sized sand and a sand with broader size distribution is that the uniform sand tends to form more ripples. Another phenomenon was noticed for some wave conditions, where the uniform sand size produced an unstable equilibrium profile which oscillated between two extreme profiles: one with a bar -and one without. This phenomenon appeared again in tests which compare the effect of grain shape. 2. Effects of Grain Shape. Pairs of tests performed to determine the effects of grain shape are summarized in Table 5. Examples of beach profiles using selected pairs of runs are shown in Figures 15 to 18 (profiles have been shifted hori- zontally to superpose the SWL intercepts; see Appendix B for actual positions). In most tests the effect of shape was represented more by Figures 16 and 18 than Figures 15 and 17. The different PVC shapes, the smallest glass sizes (Ds5g = 0.3 millimeter), and most of the graded mixes seemed to produce similar profiles independent of grain shape. However, some exceptions occurred as shown in Figures 15 and 17. Other pairs (not shown in the figures) which illustrated similar phenomena only occurred with the larger glass sizes (Dsg =0.6 millimeter) and mixtures having larger glass sizes, and then only for relatively small-wave steepnesses. The profile differences appear to be related to some instability associated with the formation of a bar. This phenomenon, shown in Figure 9, has also been observed for sand having a very uniform grain size. The phenomenon appears to follow the sequence: (a) Waves breaking on the beach slope (Fig. 19, a) causes scour just inshore of the breaker and the scoured material is deposited on the beach face and the bar (Fig. 19, b); (b) the bar continues to build (Fig. 19, c) until of sufficient size to move the breaker point offshore of the bar (4 to 5 hours in this particular test); 39 Table 5. Test pairs 3A and 4A SA and 6A 7A and 8A 9A and 10A 11A and 12A 13A and 14A 21A and 22A 15A and 16A 17A and 18A 19A and 20A 17B and 18B 19B and 20B 21B and 22B 23B and 24B ‘25B and 26B Effects of particle shape on profile shape: identification of comparative tests. Remarks Glass beads vs. ground glass; Dsg = 0.6mn. Glass beads vs. ground glass; Ds5g = 0.2mm. Crushed PVC vs. PVC cylinder; Dsg = 2.9mm. Glass bead mixture vs. ground glass mixture. PVC cubes vs. PVC cylinders. 40 -(910°0 = 1/°H) sseT3 punozs pure speed sse[3 roy odeys uters Jo I9FFO Sutmoys seTtzord yoeveq FO uostzedwoj “ST eansty (43) VQ ‘uol;DIS 89 29 99 G9 v9 £9 GE) 19 09 6S 8S (ww 9°09 =9%q) sspj9 puno1g9 ——— (ww9o =°%q ) sppag sso —— ai [e) N oO Mm 910°0=°91/°H Ob wo9'G=H S7.Guleeall OG (wo) uoljDAe|3 4 89 -(0¢0°0 = O1/9H) sse1s punozs pue speoq sse[3 zoyz odeys utesr3s Fo JOOFZO BuTMOYS setTtzord yoeeq Fo uostzeduoj) “OT eins ty (43) WE ‘uorsD4S ES 99 G9 79 a) Ge) 19 09 6S 8S (ww 99 =9%q) ssoj9 puno1g ——— ( ww 99 =-°%q) spoag sso} —— Ol ©) N (wo) uolyDAa|J fo) ne) ‘7 -075/70 OSOOs -1/ hl Op WIE Pp =H SEOn ese OS 42 89 *(Z10°0 = °1/°H) Sezts pextu Loz eduelezFtp odeys uters Aq poouen,jJut se sattyord yoeeq Jo uostszedwoy “fT ozn3Ty (43) Gl? ‘uoND}S 19 99 G9 9 €9 29 (ww ¢'O JD] + WW9'C JD]) SSD] punos9 jopowig ——— (WwW ¢'O JD | + WW9'C JD|) Spoag $sD/9 jDpPOWIgG —— I in eV IhI 19 09 6S gC 0 0! Oz o¢ Jayoasg f ZAlOOs 97724 Ov WIE'y =H SpGl =1 OS (wo) uoljonalz 43 89 “(2070 = °1/CH) sezts poxru cox souetleFFtp odeys uteszs Aq paouentzur se sottzord yoeveq JO uostaeduoy) (13) B21 ‘uoNDIS 29 99 G9 79 €9 29 19 09 (WWE'O 1D} + WW9'O JD] ) SSD] punos9 jopowig ——— (ww e'O JD | + WW9'C JD] ) SpDag ssD|9 jopowig ——— °8I oun3Tty 6S Jayoaig { 200 =97/7°H woQ'. =H SHG) si 0! fe) N fe) mM Ov OS (wd) uoljpAalz 44 Breakpoint IOA- 18h (a) I0A- 20h (b) val Sil IOA- 22h (c) le ieee ay olds: F ee Breakpoint Bhetiol melee IOA- 23.5h (d) Y~ ; oe pee "Essay NEEL 7 a areUae ND a Pe ahi gawm't VW | ee Figure 19. Sequence of profiles illustrating instability. 45 (c) after the wave breaks offshore of the bar, the bar is quickly scoured (Fig. 19, d) and the beach profile subsequently returns to that of Figures 19, b or 19, e and the breaker location returns closer to shore (about 1 hour and then the cycle repeats). The apparent instability occurs with beach profiles developed using uniform (periodic) waves, a uniform grain size, or smooth, spherical grain shapes. The appearance of this phenomenon when only the grain shape is different occurs less frequently. 3. Effects of Channel (Test Repeatability). Laboratory effects are the undesired differences between laboratory and prototype conditions caused by physical conditions unique to the laboratory, and would include such conditions as wave paddle to beach face distance, left- or right-hand channel, effect of channel side and bottom convergence, and the effect of finite water depth at the toe of the beach. Initially, the hydrodynamics of the surf zone in the presence of a movable bed were thought to be unique; hence, the equilibrium beach obtained would be independent of the initial beach profile. However, the profile shape ahead of the point at which sediment moves was found to affect the wave, the breaker characteristics, and the resultant profile (Fig. 20). An indication of laboratory effects can be derived from a cross- comparison of several runs. Test repeatability was checked at intervals since a "control" sediment was used in several of the shape and distribu- tion tests. Comparisons of such tests are shown in Figures 21, 22, and 23. Some apparent differences are present but the general beach profiles show some repeatable characteristics, e.g., in all profiles the beach face has the same slope. Some laboratory effects are believed to be present, but the profile differences due to other phenomena (see Figs. 7 to 18) are not masked by the laboratory effects. The position of the bar varied considerably under nearly identical wave conditions (Figs. 21 and 22). Noda's (1971, 1972) model law was based upon the horizontal distance from the SWL intercept to certain profile features, e.g., the bar. Modeling that distance (if not repeatable) is not easily achieved. Noda's law and most other profile modeling laws are based upon reproducing an equilibrium profile. If the shape of the stable (unchanging) profile which developed for a test series with identical wave conditions is not repeatable, then the concept of equilibrium must be qualified, and all modeling laws based upon the usual equilibrium assumptions are open to question. These few tests are not sufficient to prove or disprove the concept of profile equilibrium. However, the lack of repeatability suggests that the concept of equilibrium should be reevaluated. 46 89 “(wm 99°09 = OSq ‘pues) sodo[s JeIIIUT JusreFFTP YZIM pouTedie so[tzord wntaqtrttnbe Fo uostzeduo) (44) woos 29 99 G9 79 €9 Go) 19 "OZ osn3Ty 09 6S 8S 0! (eo) N je) np) Ov OS (wo) uolyona]3 47 89 “(uu 9°9 29 OSq) sse[s punozs 10% settzord yuopuedeput znoz jo uostaeduo) ; (44) @9 ‘U01}DIS 99 G9 v9 €9 29 19 09 "IZ eansty 6S O| Oo N (e) De) Ov (wd) uoljyonalyz OG - 48 89 "(um 9°90 a) 0Sq) sse{8 punois toy soTtyord jyuspusdeput sory. Jo uostxeduoy (43) YOILDIS 29 G9 v9 £9 c9 19 09 "72 emns Ty 6S O| fo) N oO Mm Ov OS (wd) uoljoAa|Z 49 89 (uur 9° 0 19 0Sq) sse[s punozs 1LoF sottzord juspuedeput om} Fo (43) Gp ‘UOI}DIS 99 G9 09 €9 Z9 uostizeduo) KS 09 % Z eins ty 6S 8c O| (2) (aN) (e) Mm Ov OS (wo) UOlyOAD]3 50 4. Experimental Evaluation of Proposed Model Law of Noda. The last part of this study was modeling beach profiles obtained independently by CERC and not available to Tetra Tech, Incorporated, at the time of testing. A summary of test conditions for the CERC unpub- lished profiles is given in Table 6. An investigation of the implications of Noda's model law (eqs. 17 and 18) indicated a requirement for a modeling material having a submerged specific weight in the range y' = 0.3 to 0.8 with a size in the range of Deg = 0-6 to 1.5 millimeters for the most useful modeling scale in the available wave flume. In practice, this particular submerged specific weight range was awkward. The materials available were "loaded" PVC (y' = 0.3 to 0.4), rocklite (a patented ceramic sand, y' = 0.3), pumice (y' = 0.6 to 1.2), coal (y' = 0.3), anthracite (y' = 0.3 to 0.5) and various miscellaneous substances like ground walnut shells and ground apricot shells. Materials chosen for this study were pumice, PVC, and rocklite. Unfortunately, each of these materials presents some problems. PVC is used commercially in "granular" form, normally a size of 2 to 4 millimeters. Several hundred pounds were special-ordered in "pulverized" form with a median diameter of 0.6 millimeter after washing out the dust. However, at such sizes the surface-tension problem was insurmountable. After several weeks of soaking and treatment with detergent the material formed a beach, but even the slightest wave action would "float" the material in large masses. Pumice appeared to offer many advantages after the dust was well washed out and its behavior in water created no problem other than a slight milky cloudiness. However, pumice abraded under handling and its density was difficult to determine. The dry specific weight of pumice is about 1.6; different qualities are available with higher specific weights of 1.8 to slightly over 2. The grains definitely soak up water and prob- ably behave as if they have a higher effective specific weight, but this effect is unknown. Rocklite appeared to have several practical advantages. It is rela- tively cheap, and does not dirty the water too badly. Grain sizes larger than 2 to 3 millimeters may include air pockets, but this was not a prob- lem during tests which used a "rocklite sand" having a median diameter of 1.2 millimeters. Rocklite and pumice were used for the model evaluation tests. In practice, the rocklite was the most suitable material for modeling the 0.22-millimeter sand; pumice was the most suitable for modeling the 0.46- millimeter sand. A summary of the model scale-ratio computations for rocklite, PVC, and pumice versus sand of 0.22- and 0.46-millimeter diameter, and a set of scale ratios for ground glass of 0.3 millimeter versus 0.6 millimeter 5| ‘powxoztod ON, *poyst tT qndun, “Peystrqnd, 2 PF 2 44 4 2 Se Ay 2a 2a 2 2 = a apoo QdUdLOF OY aZTS pues Tetatu] “(LS6T ‘98TTTAeS) SUOoTZTpuod 359} DYyD Azeuumsg “9 OTGeL OZ (scales were confirmed by tests made for this condition) are presented in “Table 7. Runs 13A and 14A are models of runs 9A and 10A. Conditions for the model evaluation tests are given in Table 8; results are shown in Figures 24 to 27. These tests failed to verify the model law. The slope (but not position) of the foreshore zone was reproduced fairly well in three of the four tests. The offshore and surf zone profiles were not reproduced. Moreover, the model predicted that the shorelines would prograde signi- cantly; however, the prototype shoreline retreated or prograded only slightly. The model law was based upon modeling the slope of the foreshore, and the good agreement between the model and prototype in this region is encouraging for two reasons: (a) Noda's model law is useful in simulating the shape of the foreshore; and (b) the “empirical approach" may be use- ful in establishing scale relationships for distances between particular beach features at other limited ranges of depth. The particle Froude and Reynolds numbers under waves vary with depth and time, and, as a result, the mechanics of sediment suspension and transport cannot be reproduced at all depths simultaneously. At most, a model law can only be correct over a limited depth range; for this model law it is the foreshore zone. The lack of repeatability in the position of the bar suggests that the equilibrium profile should not be used as a basis for modeling. V. COMPARISON WITH OTHER PROFILES Several investigators (discussed previously) have proposed relation- ships for the value of certain physical characteristics of beach profiles, and Sitarz (1963) and Nicholson (1968) are the most prominent. The experimental data gathered in this study can be compared with some of their relationships. Sitarz (1963) proposed two principal relationships: wae Mn ean? pee yi: (19) and ee Mr Gye Die wo: (20) where, X_ = distance offshore measured from the beach crest to the origin of a parabola defining the offshore profile. This distance is close to the breaker to beach crest distance (in meters) ; 3) Table 7. Summary of scale ratios for various materials. Material Prototype ny! Nh r material Rocklite Sand, Dsg = 0.22 Os2 5.45 Glass Glass 1.0 0.5 0.284 Ds = 0.3mm Dso = 0.6mm S) || OO | OC ]]| © ]| © S) OV NO Table 8. Test conditions for attempted model law verification. Model/CERC Rocklite/7 (0.22) 0.0028 Rocklite/3 (0.22) 0.0078 Rocklite/6 (0.22) 0.00099 Pumice/4 (0.46) 0.035 54 “O4YTTyoor sutsn (pues ZoJOWTTTW-7Z°0) ZL Lequnu UNI DYAD LOF 359} UOTIBITFTIOA peqdueiiy ‘pz eansty (19POW) 44 ‘SUOIZO}S 69 89 rR) 99 G9 v9 €9 Ge) 19 09 6S 8 (ayljyooy) wwoz'| = Sp (Zj10nO) ww 2z'0 “0Sp 6S0'0 = X 80200 = 7 8200'0 =°1/°H a . c= —"~ (adhyojord) 44 “Suo1y04S 09- Ob- O2-— Ov 09 08 }j ‘UOlDAa]J IdAJOJOJY |OIJIUI adAjOjO1q pug Za ze Se ga A= |apow jour Olt . Jaypaig Gt (J@POW) wo ‘uolyDAa] 3 55 Ol (pues Zo OWTTTIW-7z°0) ¢ LEquNU UNI DYqD) OF 3$03 uoTIedTFILeA pozdwoziy (1apow ) 69 89 29 adAjojOsg jOUl4 9 9 G- G ©) }} ‘uolj0Aa]3 ) me) 4 (o) — fo) — =< ao) @ — *OqTTyoor sutsn GZ ans ty Jy ‘Su01}D4S 79 ¢9 29 19 09 6S adkyojO1d |DI}IU| }} ‘Su0l}O4S 08 (exo) (ay1y90y) wwOZ"| = Sp (Zj0np) ww zz'o = Sp 6S0'0 = YX 80200 = 7/ 8200'0 = 97/°H Jayoesg (|apow ) wo ‘uolyDAa|3 56 249 *O4yTTyooL sursn (pues IoJoWTTTTw-zz°0) 9 ZequMU UNI DYqD TOF 3809 uoTIeOTFT40A poqdueziy “97 eANdTY 99 G9 v9 \j ‘uolyDAa}J 0 a [o) = (oe) = = Ve) Oo £9 Jayoaig (}9POW) Ge) 19 6) Z Pd Ba p 9 }} ‘SUOI}OIS 6G 8S LS 9S Ss adhyojosdg [D1 1U] (adA4j0j01d) 09 08 J} ‘SUOI}OIS 001 (aypy20y) wwoz| = Sp (Zj40NO) ww z22'0 - 1085 6S0'0 = X 8O20i0r= am 66000'0 = °1/°H ( |@POW) wo ‘uolyDAa|3 57 *ootund sursn (pues IoJOWTTTTW-9p°0) p Loqumu un DYq) TOF 180} UOTIedTFIIEA poqdweqqy “LZ 9aindTYy 89 39 = zy ° =< ° = < aS) © ae —~ (12POW) 44 ‘SUO1}DIS v9 29 09 8G 9G vS Ae} *UOl}DAa|J adAjoyOsg |OUl4 44 7. (aolwng) wwog'o= Sp (zj20n9) ww gp'0 = “Sp 2900 = Y Go600 = 7 GEOiO= c/cH jaypesg (adAjyojO1g) 44 “SUO!}DIS Ov 08 Od! 091 002 IMS adhj0jJO4q PUD japoW |O!4IUI (19pOW) wd ‘uoIjoAa] 3 58 Dy = median diameter of the beach sediment in the breaking zone (in millimeters) ; H = wave height in the wave flume (in meters) ; y' = submerged unit weight; Aj = a constant (=43.5) for a wave flume but varies for wave basins and shorelines; and m = slope of the beach face. Figures 28 and 29 compare the results obtained in this study with the relationships of Sitarz (1963). In judging this data, the following should be considered: (a) The observed X, was taken as the distance from the stillwater line to the breaker; and (b) the beach face slope was taken as the ratio of the elevation change from the breaker point to the stillwater line to X). The results from these experiments do not agree well with the relationship of Sitarz. Although the observed values used for Xp and m do not satisfy the definitions of Sitarz exactly, some relationship might be expected, e.g., the relationships of Sitarz (1963) imply Av u 1.5 for the same material in model and prototype. Nicholson (1968) derived a relationship between Y,/H, and H,/L, for sand beaches; where Me was defined as the vertical distance between the crest of the bar and the crest of the beach for a "barred" profile, and was defined as the vertical distance between the top of the step and the crest of the beach for a "stepped" profile (see Fig. 4). Figure 30 presents the results obtained in these tests and shows no agreement between the data collected and the relationship of Nicholson. In the case of very shallow water; U ~ 0.5 H gl? a2 P (il) b max where, U = maximum orbital velocity at the bed; b max H = local wave height; = gravity constant; and d = local water depth. 59 OFS Figure 28. * Y = 1.42, Ds5q = 0.60 mm o Y = 0.30, Ds = 1.20 mm o Y = 0.60, Dso = 0.80 mm ey i 1.42, Deo = 0.45 mm 1.0 1.5 2.0 2.5 3.0 43.5 H3/2 /(Y'D) '/2 Comparison of shoreline to breaker distance with relationship of Sitarz (1963). 60 8). 0.30 50.25 = wn 2 ® sS 0.20 2 a o ey 7m [oo ( DEMS I lal ond 2 Pea i wthbe owe APPENDIX A MATERIALS USED IN TESTS The materials referenced in Table 2 are shown in Figures Rol. Kap and A-3. Sieve analyses are summarized in Figures A-4 and A-5. 69 cv If i) XK 4 a € *poqyseq STetTszo}ew FO $o10Ud wu ¢°g = 95q speeq punoisy wu 9°9 = 95q *sse[3s punoly "[-V ean3ty me gop =e OFa ,A £ssezT3 punory wu ¢°Q = 0Sq ,A *sseqTs punory 70 "po se} spTetiojew FO sojOUq “*Z-V 9ANsTY Wi = OSq Win = OSqg 6°90 = ,A *punoz3 9d €°0 = A “SsteputTAD DAd wu ¢ = OSq wu 9°9 = O5q iA “saqnd dd 7O°T = ,A “speeq sseTs i} 3 0) 7 6 *peqseq sTeTreqzew FO so.OUd 0 = 0Sq a2 TTYOOY "¢-V ernst SO = o& mn og = Oa ‘(poztaeatnd) Ad OS eo a Usa ,A faotund Arq 72 Size (mm) 10 Figure A-4. Test material Blue PVC Sand No. I2 Dsq = e-9imm Deo = 1.58 mm Rocklite Pumice Deg = 0.84 mm Fine Sand Dsq = 0.26 mm 30 50 70 90 98 Percent Finer sieve analysis data. Ue Size (mm) fo) oO S nm Coarse Ground Glass Dsg = |.2 mm Medium Ground Glass Deg = 0.62 mm Glass Beads Ds = 0.52 mm Glass Beads Ds9 = 0.60 mm Small Glass Beads Ds = 0.52 mm Fine Ground Glass Deg = 0.3 mm 10 30 50 70 90 98 Percent Finer Figure A-5. Test material sieve analysis data. 74 APPENDIX B TABULATED ORIGINAL DATA Tables in Appendix B are identified by a number (sometimes followed by a letter) followed by a hyphen with either the letter I (for initial) or another number. The last number indicates the number of hours of running time. 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Multiple- time sequences are shifted vertically for separation purposes. The SWL intercept is the reference datum. 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— 30eI}U0D) OSTY (11092 ‘ou $ 1ejU~AaD yoreeseay BZutiseuz3uq Teqseop — zeded Teotuyoel) “TTT : *d cz "9/6, ‘1eqUeD YOIReSey BuyiseuTsug Te Jseog "S'n : “eA S2TOATegG JIOq — *JANUSeYD *g SeTAeYD puUe SUTTTOD ueT ‘fC Aq / STepow Tejseod ut sjDejjJe uoTInqTAISTp ezts pue edeys utery uel “¢ fsut{TqTo9 d3igcn* £29 bbcteyg =the d3.gcn* £0201 °77Z00-0-EL-ZLMOVA FORPAJUOD = *19RUa0 yoreesey ButzsvouT3ugq Teqseog *S*N : SefzaS "AI “[1[-92 *ou azoded Teofuypey, ‘tejueg yoreesey duf~teeutsug Teqyseop *s*n : sefzesg “LIT *zoygne jutof ‘*g satTzey9 *349nUSeYD “II “eTITL ‘1 “sjyuewtTpes “yh “spoaq eTqeAoW *¢€ “UOFINGTAISTp ezTs sToTAIeg *Z “seTTJOId “1 *pequesead st dtysuoftjeter Tepow sTeos ay} jo uofjenTteas TeJueutTiedxs uy ‘sTepow peq-etTqeAow uf edeys eToz,z1ed pue uotjng -T1ISTp eZTS-JUeWTpes Tepow Jo sjOeszZa ay sajedtqsaaut Apnjs stu *£9-99 ‘dd : Aydersotrqta (7Z00-0-€L-ZLMOVa + 203UaD yoreesey ZutivoutT3uq Teqjseop — toeded [TeotTuyoer) “TTF : “d 4¢z "9/6, ‘2e}UeD YoTeaSey Zutiseuf-suq Te seoD *s*n : *BA SAfOATEgG 3204 — *]9NUSeYD *g SeTAeYD pue sUTTTOD ueT ‘LC kq / s[Tepow Te}seoo UT sjJdeFjJe uot INqTAISTp ezTs pue edeys uperap ueyT "¢ ‘surTToOD dqigcn* 129 LL-92 ‘ou d3,gcn* €0Z0L “7700-0-€2-Z2ZLMOVE ORARZU0D = * Te3UeD yoieesoy BuTivseuTZuq Teqseop *S*n : Setzeg “AI “{1-9/ *ou azaded yTeopTuysey, “tajuaQ yoLeesey ButTreeuTZuq Teqseop *S*n : setaAes “III *zoyjne jutol ‘*g seTzeyp ‘74nUSeyD “II ‘“eTITL ‘I “squewTpes “hy “speq eTqeaAoy] “€ “UOTINGTIASTp 9ZTS eToOTIAeg *Z “SeTFJOAd “1 *poqueseid st dtysuotjejTeit Tepow aeteos ay} jo uot Jen TeAs Tequeutiedxe uy ‘“sTepow peq-eTqeAow ut adeys eToTIa1ed pue uot Ing -TIISTP eZTS-JUSWTpes Toepow Jo szDezTJe ay. sazestzseaut Apnjs sTyL "19-99 ‘dd : AydeasotTqTg (7Z00-0-EL=ZLMOVa + 19}UaD yoreesey ZuTisveuTsuq TeIseoD — 30e13U0D) OSTY (LL09Z “OU $ 1e3RUED yoreesoy Su~AeeuTZugq Teqseog — 1zeded Teotuyoez) “TTF : “d oz "9/6, *‘19]UeD YOAeVSey BuTreeuTZug Te seo) "N 3 ‘eA fATOATOgG J40q — *}]NUSeYD *g SeTABYD pue SUTTTOD UPI “LC / STepow Tejseod ut sjoesze UOT INGTAISTp ezTs pue edeys uTery uel “f ‘suTT TOD mS) &q d3igcn* L279 LL-92 "ou d3igcn° €07OL "7Z00-O0-E€L-ZLMOVA 20R1IU0D =*1a3UaD yoivessy Buptiveut3uq Teqseop *S'n : SeTIaS “AI “[1-9f “ou rzaded TeoTuyoe, “1eqUeD yOTeasey BuTIssuT3uq TejseoD °S*N : SeTIIS “TIT *zoyjne jutof ‘*g saTiey) *33nuseyD “II “eTITL “I = ‘SsqUeWTpes ‘yh *speq eTqeAOW *€ “UOTINGTAISTp ezTS eToTAAed *Z ‘*SeTTjJOId *| *pequeseid sft dtysuotjeTer Tepow aTeos ayQ jo uoTJenTeArs [ejueutiedxe uy ‘sTepow peqe-etTqeaow uyt edeys aeTot zazed pue uotjng -TAIISTP eZTS-JuUsWTpes Tepow jo sjIezFe |y. sazestyseauT Apnys stu "19-99 ‘dd : AyderzorTqtg (¥Z00-0-E€L-ZLMOV $ 1293uUe0 yoreesey BuTiseut3suq TeIseop — WOePTWUOD) OSTY (1109 “ou § zaquUAaD yoreesey Supiseutsuq Tejseog — reded TeoTuyseL) “T{TT : *d Gz "Q/6| ‘teqJUeD YOIeasey BuTIseUuTZuy_ [Te IseoD *S'n : ‘BA SATOATEgG 310g — *R4NUSDYD *g SeTAeYD puUe sUTTTOD URI *¢ &q / s[Tepow Te seod ut sjOezjJe uoTANqTIASTp ezTs pue edeys uteayg uel *f ‘sutT—To9 d31gsn° £79 eye oe d31gcn* €020L “7700-0-EL-7L MOVE 79F13U0D §=*1e3UaD yoreesoy SuTiseutsuq [Te 3seoD *S*N : SeTzeS “AI “11-97 ‘ou azaded TeofFuyoeL *1ajueD yOAPesey BuTiseuTSuy TeqyseoD *s*n : SatzeS “III ‘zoyane qufof ‘*q saTieyo ‘34nuseyD “II “eTITL ‘I “*squewptpes *y “speq eTqeaow *€ “UOT INGTAISTp ezTS eTOTIAeg *Z ‘“SeTTjJorg *| *pejueseid st dtysuotjeTel Tepow eTeos oy} jo uot JenTead Tejueufiedxe uy ‘*sTepow peqeeTqeaow ut adeys eTotqaed pue uotjnq -TAISFP OZTS-jJUeWTpes Tepow jo sjzIeTje ay, saejzeBTIseauT Apnqs stTyy "49-99 ‘dd : Aydes80tT qQTg (7Z00-0-€L-7LMOVA § 193uUaD yoreesey Sutlseuzsuq TeJseoy — 30e1}U0D) OSTY (11092 ‘ou { 2eQUAaD yoreesey Sutiseuzsug Teqseon — aeded TeoTuysey) “TTT : *d 4Gz “9/6, ‘2e}UeD YDreVssSey But~iseuTsuq Te seo) "S*N : “eA fATOATEG 3404 — *34NUSeYD *g SeTAeYDQ puUe sUTTTOD ue] ‘fC &q / STepow Te seod UT s}zDeTJS UOTINGTAISTp ezts pue odeys uqtesy uel *f¢ SsutTqTo9 d3igcn° L729 Biiso ZOU d3.gcn* £0201 “9700-0-€L-ZZMOVA 30BAZU0D «6° 19380 yoieesey BuysvouTsuq TeIseog *S*N : SeFIIS “AT “{{[-9/ “ou azaded TeoTuyse] “tajueD yoIeesey BuTiesuT3uq Teqseod *s*n : SetiIeS “IIT *zoyajne jutof **gq setTazeyO *34nUSeYyD “II “eTIFL *1 “sjJuewtTpas “yh “speq eTqeAom *E “UOTINGTAASTp VZ2FS sToOFAAeg *Z “seTFJOAd “| *pequesead st dtysuotjzeTet Tepow apteos ay} jo uotzentead TeJUueuTiedxe uy ‘“sTeapow paq-eTqeAow uz edeys s~tozqzied pue uoytq4ng -T4I3STp ezTSs-jUeUTpes Tepow jo sjzOazjZe ay} saqedtqyseaut Apnqs stu °19-99 ‘dd : AydearsotTqtg (7Z00-0-€L-ZLMOVa § 193Ua0 yoivesey SuTiseuTsugq Teqseog — 30eP12U0D) OSTY (L109L “ou $ reqUAD yoreesoy SutieeautTsug Teqseop — aeded [Teotuyoey) “TTF : *d 4¢z “9/6, ‘2e}UeD YOTeesSoy BuTAvsuTsugq TeqIseOD "S*n : ‘BA SatoATeg J10q — *]3NuUSeYD “gq seTAeYD pue sUTTTOD ueT “fC 4q / S[Tepouw Te seod ut sjdezje uoTINqTIISTp aezts pue edeys upesg uel ‘¢ ‘suzT—o9 d3igcn° £29 iceye Moe d3igcn* £02OL "7700-0-€L-7LMOVG 39PA}U0D §6* 1983UeD yoivesey BuTreeuTsuq TeIseoD *S* : SeTIeS “AI “|1-9/ ‘ou aaded Teotuyse, “1eqUeD YyoIeesey BJu~teeuTsuq Teqseog *Ss*g : SetseS “III *zoyqne qutof *°g seTzeyp *34nUSeYD “II “eTITL "I “SsquewTpas *y “SP2q eTqeAoy] “Eg “uoTINGTTISTp eZTS sTITAAegG *Z “SETTFOAd “| *pequeseid st dtysuotjeyTe1 Tepou etTeos ey} Jo uoTIenTens Tejueutiedxe uy ‘sTepow peq-eTqeAow ut adeys etotzaed pue uoytqng -TI]STp eZTS-jUsUTpes Tepow fo sJoazFjJo 9yR saqestqseaut Apnys stu "49-99 ‘dd : AydeazotTqta (7Z00-0-€£-Z/MOVa $+ 1283UeD yoreesoy BuTreeuTsuq Te seoD — 3De13U0D) OSTY (11094 ‘OU £ AzeqUAaD yoievesoy BZutieeuTsug Te;seog — tzeded Teotuyoey) “TTT : *d 4¢Z "9/6, ‘1e]qUaD YOAeeSey BuTAseUuT3Uq TeJseOD "S°n = *eA fATOATeg 310q — *3]9NUSeYD *g SeTAeYD pue SUTTTOD uel °C &q / s[Tepow Teiseood ut sjoeFjJa uoTINGTAISTp ozts pue sdeys utTead uel *f ‘sutT{oo