eal US Army Corps of Engineers GS 450 THs” ho CERC: 90-3 TECHNICAL REPORT CERC-90-8 MIDSCALE PHYSICAL MODEL VALIDATION FOR SCOUR AT COASTAL STRUCTURES by Steven A. Hughes, Jimmy E. Fowler Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers 3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199 June 1990 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 31715 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. [DATA LIBRARY | ce aphic Institution | Woods Hole Oceanographic Institut 2 Saas a Unclassified SECURITY CLASSIFICATION OF THIS PAGE Fe rov REPORT DOCUMENTATION PAGE DISTRIBUTION / AVAILABILITY OF REPORT Approved for public release; distribution unlimited. 2b. DECLASSIFICATION/ DOWNGRADING SCHEDULE 4. PERFORMING ORGANIZATION REPORT NUMBER(S) Technical Report CERC-90-8 . MONITORING ORGANIZATION REPORT NUMBER(S) - NAME OF PERFORMING ORGANIZATION. USAEWES, Coastal Engineering Research Center 6c. ADDRESS (City, State, and ZIP Code) 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION (If applicable) 7b. ADDRESS (City, State, and ZIP Code) 3909 Halls Ferry Road Vicksburg, MS 39180-6199 . NAME OF FUNDING /SPONSORING ORGANIZATION Us Army Corps of Engineers ADDRESS (City, State, and ZIP Code) 8b. OFFICE SYMBOL (If applicable) 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 10. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK NO. NO. ELEMENT NO. Midscale Physical Model Validation for Scour at Coastal Structures 12. PERSONAL AUTHOR(S) Hughes, Steven A.; Fowler, Jimmy E. 13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) ||15. PAGE COUNT Final report rromAug 88 toDec 89 June 1990 298 16. SUPPLEMENTARY NOTATION Available from National Technical Information Service, 5285 Port Royal Road, Springfield, VAL 2216ih. WORK UNIT Washington, DC 20314-1000 ACCESSION NO. . TITLE (Include Security Classification) 17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD | GROUP | SUB-GROUP Beach profiles Erosion Scaling Coastal processes Movable-bed models Scour Coastal structures Physical models 19, ABSTRACT (Continue on reverse if necessary and identify by block number) Storm erosion A l-to-7.5 scale (midscale) movable-bed physical model was used to validate model scaling criteria selected as most appropriate for turbulence-dominated erosion of sediment by waves. Two-dimensional flume tests successfully reproduced profile evolution observed in prototype-scale wave flume tests conducted under both regular and irregular wave conditions. For the case of regular waves, a sloping concrete revetment was exposed, thus validating the scaling guidance for use in studying scour at coastal structures. Variations in experimental parameters were systemmatically examined. Comparisons between regular wave and irregular wave profile evolution indicated that best correspondence is achieved if the significant wave height equals the monochromatic wave height, although irregular wave profile evolution takes about twice as long. The impacts of a vertical seawall on profile change are briefly examined. 20. DISTRIBUTION / AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIED/UNLIMITED [J SAME AS RPT. (J DTIC USERS Unclassified 22a. NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) | 22c. OFFICE SYMBOL DD Form 1473, JUN 86 Previous editions are obsolete. SECURITY CLASSIFICATION OF THIS PAGE Unclassified 0030110001159 ED SECURITY CLASSIFICATION OF THIS PAGE ea SECURITY CLASSIFICATION OF THIS PAGE Preface This study was conducted by the Coastal Engineering Research Center (CERC), US Army Engineer Waterways Experiment Station (WES). The work described herein was authorized as a part of the Civil Works Research and Development Program by the Headquarters, US Army Corps of Engineers (HQUSACE), and was performed under the Scour at Coastal Structures Work Unit 31715, which is in the Coastal Shore Protection and Restoration Program, CERC. Messrs. John H. Lockhart, Jr.; James E. Crews; and John G. Housley are HQUSACE Technical Monitors. Dr. Charles L. Vincent is Program Manager for the Coastal Shore Protection and Restoration Program at CERC. This study was performed and the report prepared over the period 1 August 1988 through 30 Dec- ember 1989 by Dr. Steven A. Hughes, Research Hydraulic Engineer, Wave Dynamics Division (WDD), CERC, and Dr. Jimmy E. Fowler, Research Hydraulic Engineer, Wave Processes Branch, WDD, CERC. Dr. Fowler was Principal Investigator of the Scour at Coastal Structures work unit during this period. The research effort was under general administrative supervision of Dr. James R. Houston, Chief, CERGC, and Mr. Charles C. Calhoun, Jr., Assistant Chief, CERC. Mr. Gene Chatham, Chief, WDD, and Mr. Douglas Outlaw, Chief, Wave Processes Branch, provided direct supervision of Dr. Hughes and Dr. Fowler, respectively. The authors gratefully acknowledge the dedicated efforts of the following personnel who helped during the laboratory phases of the study. Mr. John E. Evans, CERC, was the laboratory technician overseeing the physical model; wave data reduction was performed by Mses. Robin Hoban and Christie Sanders, CERC; installation and maintenance of instrumentation and day-to-day operation of the wave machine and data acquisition systems were performed by Messrs. David Daily, Ricky Floyd, and Lonnie Friar, Instrument Services Division, WES. The report was edited by Ms. Lee Byrne, Information Technology Laboratory, WES. Special acknowledgment is given to Dr. Hans H. Dette, Technical University of Braunschweig, and Dr. Klemens Uliczka, University of Hannover in the Federal Republic of Germany, for making available their prototype-scale physical model results which formed the basis of comparison for the tests reported herein. Their cooperation throughout the course of the study contributed largely to the success of the research. COL Larry B. Fulton, EN, was Commander and Director of WES during preparation of the report. Dr. Robert W. Whalin was Technical Director. Contents Preface CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENTS PARTI INTRODUCTION Physical Models Movable-Bed Models Objectives and Purpose of Study Scope of Report PART Il SCALING GUIDANCE Movable-Bed Modeling Considerations Suggested Scaling Criteria Based on Fall Speed Parameter Selected Scaling Criteria Comparison to Xie’s Scaling Guidance Applicability of Selected Scaling Criteria PART III EXPERIMENT OVERVIEW Laboratory Facilities Prototype Condition Model Scale Selection Testing Procedure Model Experiments 24 26 26 28 31 32 33 PART IV VERIFICATION TESTS Regular Wave Validation Test Test with Increased Wave Height Experiment Repeatability Irregular Wave Validation Test Modeling Law Verification Conclusions PART V REGULAR WAVE PERTURBATION TESTS Increased Wave Height Decreased Wave Period Equal H/wT Parameters Sediment Grain Size Initial Profile Decreased Sediment Supply Absorbing Wave Board Summary of Perturbation Tests PART VI IRREGULAR WAVE TESTS Background Previous Efforts Irregular H,;3 Equal to Monochromatic Wave Height Irregular Wave Energy Equal to Monochromatic Wave Energy Discussion of Irregular Wave Tests Conclusions Regarding Irregular Waves 36 36 42 48 50 53 56 56 56 58 62 65 68 68 70 73 73 74 75 78 81 82 PART VII VERTICAL SEAWALL TESTS Background Impact of Seawall Regular Versus Irregular Wave Effects Vertical Seawall Summary and Conclusions PART VIII SUMMARY OF RESULTS Summary Conclusions REFERENCES APPENDIX A: DESCRIPTION OF WAVE ANALYSIS Data Acquisition and Analysis Time Series Analysis File (TSAF) Remarks About Wave Analysis Results APPENDIX B: WAVE ANALYSIS RESULTS FOR EXPERIMENTS APPENDIX C: TABLES OF EXPERIMENT PROFILES APPENDIX D: PLOTS OF EXPERIMENT PROFILES APPENDIX E: PLOTS OF PROFILE COMPARISONS APPENDIX F: NOTATION 84 84 85 89 92 94 94 96 97 Al Al Al A4 Bl C1 D1 El F1 List of Tables ao oOo fF WO WY Prototyperand yModelisedimentsbarametersmenres co a uel eeu tire) eer etc) ane eee 31 Prototype and Model Experiment Parameters ..... . A ciel ae ulti acri VAR ia tN ast Sly eta 32 Mescriptionsiotaboratoryplestsimen avai he cerry ty ee ena erent oe pees els ee cc oeeet a 35 Prototype and Model Values of Xie’s Parameter. ....................0000. 48 epeatabilityalestmRNISp Variations meme quer a sew nen me ee enn pet anne etna nee ee 50 WavesbertunbationgiuMSpVarlationsimeari en nee ation nackte nc it yoni ans aan ea Pier tr a 61 List of Figures oc moan rm oO FSF & WO a a wo wo - & Nomogram for estimating movable-bed model length scale ratio... .............. 25 Planjview of'6-ft flume and supporting facilities | 2 =... 4.46 se se 27 Prohleiview on6-tti fume (S\MWiGi—still=water level) i) -0 2.4) re letra) estes oe 2 ee ee 28 WaverceneratingscapabilitvloiG-ttiilunnelel siamo) ater ary eee Anes eae ab ewe pS an eeae 29 SchematicrotidataracquisitionssySternmencm sme iss) tiers eee en mre ee ern in ep anagn 30 Regularswavernitialiconditionyearas iis ie aie eevee) tele ute Ns AiMeo ites Aten ee ikea ania ewe 31 Brohlingsprocedurerdurineyexperimentsiie eae ease ee een emote eee 34 Prowilks clealojorancris Glimsayeirety INOS “sooo oo 0 Gb Go ep blo oe ae ob be eee 38 Average versus center-line profile at 1,650 waves, T03 ..................02.. 39 Prototype-model comparison for test T03 (RMS = root-mean-squared) ............ 40 Propilks loaltoyoyroverns Glruainys Wese INWY A a ool od 6 ob 5 6 6 o oo bles oe gue aleiploe oe Geos 43 Average versusicenter-linesprofilerat 1¢650) wavess M04s 55 icy ses) coeds) es 44 Erototype modelkcomparisonstonitesti il Ame sun omar el mene seh y ase wenn nile ei anes alee reine gral 46 RepeatabilityatestasOlMversus) MO 2m seid. veselsi sy Gre su nas tae Vier ae ena ecient Sepia) an Se oc 49 mrohlegdevelopmentad unin gates tym as mee eee reer i emer en ten eevee ar evn etl seen 52 Erofilesmodelkcomparisonprore:cestadlyl 4 gaunt etki psa ren * ee naseyare se env ate a a 54 WavesherghtsperturbationnlOAnversusilt Oona mre m aie ery yi culseeiuen Aileen ee seceeaiii yaen 57 Wiaverpenodtperturbation se hO/eversusmlO Saami eur crise Alseetnnirs isl mryie ese) teers notary aan 59 laomell Jey anh perenne, INOS were ILO, cvs oloke 46 6 ab G-b. cg 6 Blo do o> So 6 oo 8s 60 Schulzisi@l985)"experimentausing4088—mmarsan duet ae skeen yn ee 63 Sehulzgsn@l985)kexperimentiusing|0!35-mimysandaen aes kien peli alicia eunn yee ae wen 64 Prototype-model comparison, initial profile at 40 waves ..................... 66 23 24 25 26 27 28 29 30 31 32 33 34 Initialtprofilerat)40iwavess d0Giversusiel03e enemies) one ee 67 Reduced) sedimenticomparison,, h0ilversus) 203) 2 4.2. =: eee nen nen ne 69 AibsorbingawaveiboardytestawlOSiversusml03/ teas eae yeni tone ener wl Irregular wave comparison, H,/3 equals Hmono (Hmono = monochromatic wave height)... . 77 Irregular wave comparison, H/3 equals 141 percent Hmono .----+--++-+++-+----- 79 Irregularawave perturbation 0 9aversus/h0 85pm ie cnn nnn nena 80 Time-shifted irregular wave comparison, T09 versus T03 .................-.-... 83 Seawall impact under regular waves, T10 versus T03 .......-...----+-++-++--- 87 Seawall}impact:cross-tank variation» i1(0) versus) 203) 2)-,5,4) 5 4 oe eee 88 Seawall impact under irregular waves, T1l versus TO9 ..........--2.-.-..2.20..- 90 Seawalllirregular wave comparison, H)/3 equals) Hinono uss) 1 =e eee 91 Time-shifted seawall comparison with irregular waves. ............--.-.-.--+04. 93 CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENTS Non-SI units of measurements in this report can be converted to SI (metric) units as follows: Multiply By To Obtain cubic feet 0.02831685 cubic metres Fahrenheit degrees 5/9 Celsius degrees or kelvins* feet 0.3048 metres inches 2.54 centimetres *To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use the following formula: C = (5/9)(F — 32). To obtain kelvin (K) readings, use: K = (5/9)(F — 32) + 273.15. MIDSCALE PHYSICAL MODEL VALIDATION FOR SCOUR AT COASTAL STRUCTURES PARTI: INTRODUCTION 1. Scouring of noncohesive sediments in the coastal region has been a problem for engineers since the first coastal improvements were undertaken in ancient times. Modern coastal engineering recognizes the seriousness of scour at coastal structures, and measures are taken to reduce the scour potential, based largely on previous remedies that have shown some degree of success. There remains, however, a large gap between present knowledge of scour and the knowledge necessary to develop engineering tools for the prediction of scour evolution under specified environmental conditions. This gap in knowledge is not due to failure to recognize the benefits to be gained by understanding the causes of scour and developing the means for preventing it. On the contrary, much research has been directed at various aspects of the scour problem (Powell 1987). However, researchers are faced with the problem of understanding the immense complexity of the scouring mechanisms, such as waves and currents interacting with structures and resulting turbulent water motions suspending and transporting sediment away from the toe of the structure. Developing mathematical representations for this complex interaction is a formidable task indeed, and only limited progress has been made in this area. Physical Models 2. Physical models constructed and operated at reduced scale offer an alternative for examining coastal phenomena that are presently beyond analytical skills. Dalrymple (1985) points out two distinct advantages gained by using physical models to replicate nearshore processes: (a) the physical model integrates the appropriate equations (unknown to mortals) governing the processes without simplifying assumptions that have to be made for analytical or numerical models, and (b) the small size of the model permits easier data collection throughout the regime, whereas field data collection is much more expensive and difficult, and simultaneous field measurements are hard to achieve (Gourlay 1980). A third advantage of physical models is the degree of experimental control that allows simulation of varied environmental conditions at the convenience of the researcher. 3. Of course there are also disadvantages to using physical models, most notably: a. Scale effects occur in models that are smaller than the prototype if it is not possible to simulate all relevant variables in correct relationship to each other. b. Laboratory effects can influence the process being simulated to the extent that suitable approximation of the prototype is not possible. Typical laboratory effects arise from the inability to create realistic forcing conditions and the impact of model boundaries on the process being simulated. c. Sometimes all forcing functions and boundary conditions acting in nature are not included in the physical model. Nevertheless, a capability to model accurately the processes in the nearshore zone is essential to a wide range of problems (Dean 1985), and understanding physical model laboratory and scale effects will allow researchers to utilize these models to address problems that cannot wait until a complete, or at least sufficient, mathematical description of the process is available. 4. Two types of physical models can be employed to study nearshore coastal processes, fixed-bed and movable-bed. Fixed-bed models are used to study waves, currents, or similar hydrodynamic phenomena, and the scaling effects are reasonably well understood (Dalrymple 1985; Hudson et al. 1979). Less well understood are the scaling effects inherent in movable-bed physical models intended for use in studying sedimentary problems. Movable-Bed Models 5. A multitude of scaling relationships for modeling coastal sedimentary processes has been proposed over the years (see Hudson et al. 1979; Kamphuis 1982; Yalin 1971; Fan and Le Méhauté 1969 for overviews and lists of references). Hudson et al. (1979) give the basic philosophy for movable-bed scale modeling as fully understanding the physical processes involved and ensuring that the relative magnitudes of all dominant processes are the same in model and prototype. They also state, “This is an impossible task for movable-bed models ...” because of the complications of the fluid-sediment interactions, and thus “ it is necessary to attempt to reproduce the dominant process “... with the anticipation that other forces are small.” Similar views are held by Dean (1985), who lists two major requirements in proper physical modeling of sand transport processes: (a) knowledge of the character of the dominant forces and (b) an understanding of the dominant response mechanisms of the sediment. 6. In the absence of fundamental knowledge of the dominant processes and associated sediment response necessary to develop scale relationships, movable-bed scale models can be used to investigate the effects of certain parameters in systematic ways to establish general behavior patterns (Gourlay 1980). Alternately, the researcher can abandon the idea of reproducing the dominant physical processes and instead attempt to maintain similitude of important observed engineering characteristics such as beach profile shape or longshore transport rates (Hudson et al. 1979). 7. Regardless of the approach taken to develop scaling relationships for movable-bed models, the nearly unanimous opinion among researchers is that it is important to verify the scaling laws by reproducing prototype-scale events. Preferably, the scale model should be validated using field data, but often this is not practical, and large-scale laboratory results must suffice. Only after validation can credence be given to the model results, and then only for situations which seem to be governed by the same processes that were assumed dominant in the validation. That is to say, for example, a movable-bed model validated for surf zone sediment response is not necessarily valid for application outside the surf zone because different mechanisms may be governing the transport of sediment. This leads to the axiom that scale laws should be derived with a main requirement of invariability of the scale for the material transport over the entire area of the model concerned (Bijker 1967). Under such constraints, situations where sediment is transported by significantly different mechanisms in different regions usually cannot be modeled simultaneously except at the prototype scale. 8. In spite of the problems associated with the use of movable-bed physical models, researchers must strive to improve their capabilities with these engineering tools. Dean (1985) summarizes the role of physical models by stating that they will continue to be important engineering tools for several decades because: a. They do not require mathematical quantification and representation of the physical processes as do numerical models. b. They can adequately deal with complex geometries. c. They offer advantages in measurement and visualization of the processes when dealing with small-scale versions of the system. 9. Bijker (1967) stated that “...a (physical) model can act as a means to guide the considerations of the engineer in charge of the design of the project”; but he also cautions, in reference to movable-bed models, “...the model is a rather dangerous tool in the hands of a not very cautious and conscientious investigator.” Objectives and Purpose of Study 10. The objectives of the study were to determine suitable scaling relationships appropriate for modeling turbulent wave-induced scour phenomena in small-scale movable-bed physical models, to validate 10 the selected relationships by laboratory reproduction of a prototype-scale scour event, and to examine the relative effect of the scaling parameters on the laboratory results. 11. The purpose of the study was to arrive at a validated set of modeling criteria and constraints so that future efforts can focus on systematic laboratory investigation of scour phenomena with the goal of developing engineering tools for the prediction of scour under a variety of environmental conditions. Scope of Report 12. Part II of this report provides the background and reasoning supporting the selection of the scaling criteria used in this study. Part III describes the experimental facilities and the testing procedure used in the laboratory tests. Part IV presents and discusses results from regular and irregular wave verification tests. Part V summarizes results from regular wave tests in which various parameters were changed to examine the effects of these perturbations on the resulting profiles. Part VI compares profiles from the base case condition (regular waves) with the results of similar tests carried out using irregular waves. Part VII briefly examines profile results obtained after a vertical seawall was added to the base condition. Finally, the testing program and key results are summarized in Part VIII. 13. Appendices to this report give a description of the wave record analysis, present tabulated wave statistics for each experiment, provide tabulated and plotted profiles for all experiments, and present complete plotted comparisons to supplement those shown in the main text of the report. 11 PART II: SCALING GUIDANCE 14. Water-related scour of noncohesive sediments in nature is caused by various environmental forces such as wave- and tide-induced currents and turbulence that act to mobilize and transport sediment grains. The interaction of the fluid with the solid boundaries of coastal structures increases the turbulence level, which is typically accompanied by increased local scour. 15. Scour can develop gradually over a long time span, such as the enlarging of a scour hole at the tip of a jetty, or rapidly during intense storms, such as at the toe of a seawall during severe wave conditions. It is reasonable to assume the dominant scour mechanisms associated with these two time scales are bed shear stress-induced sediment transport for the case of long-duration scour, and turbulence-induced sediment transport for the short-duration case. Although it is recognized that this generalization may not be strictly true, and in some situations a combination of these two mechanisms will govern, it is beneficial to have a broad framework with which to classify scour processes for the sake of developing scaling criteria. 16. This study focused on developing scaling guidance for modeling turbulence-dominated scour occurring over relatively short periods. Although the physics of this scour mechanism may be more difficult to express in terms of mathematical representations than the case of bed shear stress-related scour, favorable experience by others in the parameterization of beach erosion led to the belief that proper scaling criteria can ultimately be developed for this situation. Success in developing such a tool for studying storm-related scour has potential for great cost savings in scour prevention at coastal projects. Types of projects that could be examined with a valid movable-bed physical model include storm response of beach fills, scour at the toes of structures, and storm impacts to the fronting beach caused by seawalls. Movable-Bed Modeling Considerations 17. A limited number of studies have validated movable-bed modeling guidance for scour with prototype-scale data, and the observation has been made that although most guidance does well with the data used to establish the relationships, they do not fare as well with other data (Fowler and Smith 1986; Dette and Uliczka 1986; Lappo and Koshelnik 1988; Penchev, Sotkova, and Dragncheva 1986; Dean 1985). Consequently, no clear consensus presently exists regarding appropriate scaling relationships for small-scale movable-bed models of coastal scour, particularly in proximity to coastal structures. However, it can be stated that one set of universal scaling criteria covering all types and causes of coastal scour will never be developed; instead, there will be multiple sets of scaling criteria, each set specific to a particular genre of scour and the associated forcing functions, sediment characteristics, and boundary condtions. These 12 specific scaling relationships will make the physical model into a useful tool for studying scour, but care must be taken to assure that the entire regime being modeled behaves in a manner consistent with the assumptions of the modeling guidance. Careful thought must also be given to proper scaling of structural attributes, such as flow through rubble mounds, if scour might be influenced by such interactions. Scaling Requirements 18. Many investigators have expressed opinions regarding the important physical parameters and scaling requirements to be considered in formulating guidance for movable-bed models of coastal sedimentary processes. Rather than exhaustively reviewing the literature, only those parameters or requirements that appear to be predominant (to the authors) will be discussed. 19. Important sediment-related parameters are the mean (or median) grain size, immersed weight of the bed material, the sediment fall speed (settling speed of the grain’s centroid), and the Shield’s parameter (indicator of the fluid velocity necessary to initiate sediment movement). Additional modeling parameters are wave height, wave period, water depth, initial bottom configuration, and process duration. 20. The most common scaling problem arises when the prototype grain size is so small that geometric scaling of the sediment results in model bed material below the size considered the boundary between cohesive and noncohesive sediment (about 0.08 mm), thus altering the sediment transport mechanism in the physical model. Some researchers have developed dimensionless parameters by combining several of the sediment parameters listed above. Then, instead of decreasing grain size, similarity of the dimensionless parameter is maintained by using a bed material having, for example, a smaller specific weight than the bed material in the prototype. Unfortunately, lightweight materials introduce another set of problems, so that many investigators now recommend that the same type of sediment in the prototype be used in the model. 21. Distortion of the scale model, i.e., different vertical and horizontal length scales, has also been suggested as a means for overcoming the inability to geometrically reduce the sediment to model scale, and many scaling laws have been proposed that require model distortion; but this practice is still viewed with skepticism by some. Dean (1985) reviewed several studies and concluded that the state of knowledge on movable-bed models was largely based on empirical observations. Further, he argued against the use of dissimilar bed materials in scale models and also against distorting the model as required by many scaling relationships. This guidance essentially constrains the coastal processes movable-bed physical model to being geometrically undistorted using (most likely) fine-grained sand as the model sediment. 22. Perhaps the most relevant requirement for modeling coastal scour, as well as nearshore beach dynamics, is to attain similarity of the equilibrium beach profile between prototype and model, particularly in the surf zone. Parameters that appear to correspond to features of the equilibrium profile are similarity candidates for developing scaling criteria. 13 23. For physically modeling sediment transport processes predominantly driven by turbulence-induced fluid velocities, there is increasing evidence that a dimensionless number, commonly referred to as the fall velocity (or fall time) parameter, must to be kept similar in both prototype and model. This evidence is reviewed below. Dimensionless Fall Speed Parameter 24. Sediment grain size has often appeared in various dimensionless parameters intended for use in characterizing observed features of the beach profile. For example, Iwagaki and Noda (1963) investigated laboratory-formed beach profiles using the parameter H,/d', where H, is the deepwater wave height and d is the sediment mean grain size diameter. 25. More recently, increased attention has been given to a parameter referred to as the fall velocity parameter, which is defined as = (1) where H = wave height w = fall speed of the median sediment size T = wave period 26. Strictly, the term velocity represents a vector quantity and should be replaced with speed because the value of w is obtained as the fall distance divided by the fall time and hence represents an average scalar speed in the vertical direction.” For this reason the parameter given by Equation 1 will be referred to as the fall speed parameter in this report. 27. It appears that the use of the fall speed parameter was first proposed by Gourlay,? who suggested using the parameter for describing beach processes. Gourlay pointed out that H/w represented “... the time taken for a sand particle to fall a distance equal to the wave height.” If this time is large compared with the wave period, he reasoned the particle would remain in suspension and move as suspended load. Conversely, if the time is equal to or less than the wave period, then the sediment will move primarily as bed load. Gourlay also suggested that a fall speed parameter value around unity could be critical value in determining the different transport mechanisms leading to different profile types. 28. Around the same time, several other investigators also examined their results in terms of the dimensionless speed parameter. Nayak (1970, 1971) related beach slope with the parameter, and he noted 1For convenience, symbols and abbreviations are listed in the Notation (Appendix F). 2Philosophical lunchtime discussion with Dr. N. Kraus, CERC. 3M. R. Gourlay, 1968, “Beach and Dune Erosion Tests,” unpublished report, Delft Hydraulic Laboratory, The Netherlands. 14 that the parameter seemed to correlate with the beach reflection coefficient. 29. Noda (1971) investigated both prototype-scale and small-scale model results for profile similarity and found that a much closer similarity could be obtained if the H/wT parameter was conserved than if wave steepness, H,/L, (deepwater wave height divided by deepwater wave length), was held constant between model and prototype. He also offered an empirical relationship for the selection of model grain sizes and concluded that movable-bed coastal models could be distorted, but the validity still needed to be confirmed. 30. Dean (1973) popularized the fall speed parameter by incorporating it into an expression for distinguishing between swell and storm profiles. Dean used mostly small-scale movable-bed model results to establish an empirical coefficient for his expression. This coefficient was later revised by Kriebel, Dally, and Dean (1986b) by the addition of more prototype-scale data and reevaluation of the results. They concluded that Dean’s original results reflected significant scale effects. Kriebel, Dally, and Dean (1986b) extensively reviewed the literature on parameters pertaining to differentiating between swell and storm profiles. 31. Dalrymple and Thompson (1976) plotted foreshore beach slope as a function of the fall speed parameter using laboratory data available from both small- and large-scale experiments. Their plot indicated the importance of the parameter in governing beach slope, although considerable scatter appears about the trend. They reported that similar attempts to relate beach slope to other parameters exhibited greater scatter; hence the fall speed parameter performed best in their study. 32. Gourlay (1980) investigated equilibrium beach profiles in the laboratory using fine sand and coarse-grained crushed coal for bed materials. The results reaffirmed the contention that the fall speed parameter is an important parameter influencing both surf zone hydrodynamics and the resulting equilibrium profile. He also concluded that the initial profile impacts the final profile only when the initial slope is quite mild. Gourlay stated that the fall speed parameter is probably sufficient for defining similarity conditions for model beaches formed in relatively impermeable sand, but the parameter would not be sufficient for defining similarity conditions for model beaches in permeable conditions, such as crushed coal. For highly permeable beaches, Gourlay stated the ratio of flow speed within the deposited sediment to the sediment fall speed in still water is also important. 33. The fall speed parameter has also been used to characterize geometric profile features such as breakpoint bars and troughs, shoreline-to-bar-crest distance, etc. Hughes and Chiu (1981) based their profile parameterizations on small-scale movable-bed model experiments, and more recently Larson and Kraus (1989) used results from two prototype-scale wave tank experiments to characterize barred profiles and develop a cross-shore sediment transport numerical model. In both cases, the fall speed parameter figured prominently in the profile parameterizations. 15 Suggested Scaling Criteria Based on Fall Speed Parameter Previous Efforts 34. Dalrymple and Thompson (1976) were among the first to propose movable-bed modeling criteria that maintained similarity between prototype and model values of the fall speed parameter. Several sets of scaling criteria were developed by Dalrymple and Thompson, and some were tested in the laboratory. Among their more interesting findings were that the foreshore slope appeared to be independent of the initial profile and that the experimental results were repeatable. One of the developed model laws required an undistorted model with the waves scaled according to the Froude criterion and sand grain size selected to preserve the prototype value of the fall speed parameter. This law was not tested in the laboratory, but Dalrymple and Thompson stated that it appeared to be most practical because it also preserves the wave steepness parameter. Additionally, they recommended the model bed material be sand to avoid possible “alien” effects. 35. Kamphuis (1982) concluded that preservation of the fall speed parameter eliminates most of the scale effects associated with attempting to geometrically scale the grain size diameter of quartz sand. 36. Vellinga (1982) presented distorted movable-bed modeling guidance for dune erosion that incorporated sediment fall speed. Correct distortion in the model was determined through a scaling series involving 24 small-scale tests with various combinations of three length scales and four sediment sizes along with some prototype-scale laboratory experiments. Irregular wave trains were used during testing. These model results were used to determine empirical exponents in the scale relationships. In considering the undistorted version of Vellinga’s scaling relationship, the guidance is equivalent to preserving the fall speed parameter in an undistorted Froude model. 37. Hughes (1983) also proposed a distorted model law for movable-bed models of dune erosion that was derived specifically to preserve the fall speed parameter. Model distortion was achieved by modifying the time scale from the Froude requirement so that trajectories of falling particles remained in similitude. Although the scaling relationships differed with that of Vellinga (1982), the undistorted versions of both model laws were identical and conformed to that recommended by Dalrymple and Thompson (1976). Discussions of the distorted model law were presented by Sayao (1984) and Vellinga (1984). Hughes (1984) recommended the undistorted version of the model law be used when possible so that the wave steepness would also be in similitude. 38. Sayao and Guimaraes (1984) reviewed previous distortion relationships for movable-bed beach profile models and tested four similarity criteria in a two-dimensional (2-D) wave tank. Their results indicated an influence of the fall speed parameter relative to a critical value representing demarcation between onshore transport and offshore transport. They recommended that it was necessary for both 16 model and prototype values to be in the same range (either above or below the critical value), but did not require similarity of the fall speed parameter between prototype and model. However, they recommend that further tests using fine-grain sediment be undertaken to evaluate the influence of the fall speed parameter. Tests conducted using lightweight cellulose acetate were not successful, and they recommended avoiding these types of model sediments for beach profile modeling. 39. Dean (1985) reviewed previous movable-bed modeling criteria and considered the dominant physical mechanisms involved in surf zone sediment transport. He argued that the Shield’s criterion need not be met in the surf zone because turbulence, not bed shear, is the dominant cause of sediment mobilization; and therefore, bed shear is not an important consideration above Reynold’s numbers constituting the fully rough range. Dean made specific recommendations for successful modeling of surf zone processes: a. Undistorted model (equal horizontal and vertical length scales). b. Hydrodynamics scaled according to Froude similarity. c. Similarity of the fall speed parameter between prototype and model. d. Model is large enough to preclude significant viscous, surface tension, and cohesive sediment effects so that the character of the wave breaking is properly simulated. 40. Dean (1985) argued that, in an undistorted model, the fall trajectory of a suspended particle must be geometrically similar to the equivalent prototype trajectory and fall with a time proportional to the prototype fall time. This is accomplished by ensuring similarity of the fall speed parameter between the prototype and the undistorted model. Dean noted that similarity of sediment fall trajectory could also be achieved in distorted models, but he did not recommend distorting movable-bed models because of uncertainties involved if sediment fall speed is not scaled according to the Froude criterion. An additional concern is the possibility of dissimilar hydrodynamic surf zone conditions between prototype and model when distorted scaling is introduced. Dean evaluated his recommendations with intuitive reasoning and by examination of past results in light of the suggested criteria. He concluded by stating, “More extensive data are required to establish further the degree of validity of the proposed modeling criteria.” 41. Vellinga (1986) thoroughly detailed his own work and the work of others in the areas of dune erosion and movable-bed scale modeling. He examined many of the suggested parameters for characterizing surf zone processes, and he reviewed various methods for developing potential scaling guidelines. Large-scale model tests, with irregular waves having 2-m significant heights, were used to verify the previously developed (Vellinga 1982) scaling criteria. The distorted model scaling criteria were tested in a three-dimensional (3-D) situation having vertical scale of 60 and horizontal scale of 120 over straight depth contours. Results confirmed the 2-D development within acceptable limits (Vellinga 1986). Small-scale, 2-D undistorted tests with Froude scaling of the hydrodynamics compared very well with large-scale tests having the same value of fall speed parameter, showing geometrically similar profile development. Vellinga 17 concluded that Froude scaling of the hydrodynamics is necessary so that wave steepness is not distorted, the fall speed parameter should be constant between prototype and model, and wave heights should be as large as possible. These are precisely the criteria suggested by Dean (1985). 42. Kriebel, Dally, and Dean (1986a) adopted the criteria given by Dean (1985) to examine profile erosion and accretion characteristics in a 2-D movable-bed model. (Greater detail is given in Kriebel, Dally, and Dean 1986b.) They pointed out that the scaling criteria are not universally accepted; however, preservation of the fall speed parameter had been used successfully by others. They supported undistorted models by noting that in undistorted models ... ambiguous definitions of length and time scales are eliminated, unrealistic augmentation of gravity forces are avoided, and interpretation of all physical quantities is clarified. 43. Kriebel, Dally, and Dean (1986a) examined the validity of the proposed scaling guidance by attempting to reproduce the profile development observed by Saville (1957) in a prototype-size wave tank using uniform waves. The scale model bed material was quartz sand with a mean diameter of 0.15 mm. Application of the fall speed parameter criterion with undistorted hydrodynamic scaling gave a length scale of 9.6, corresponding to a prototype grain size diameter of 0.4-mm quartz sand. Reproduction of the selected erosive condition from Saville’s prototype-scale tests showed good overall profile development in the bar and trough and offshore geometry, lending credibility to the scaling guidance for the energetic erosive condition. Similar attempts to reproduce the selected accretive test case were not successful. Kriebel, Dally, and Dean (1986a) noted that the wave generator in their experiments was not sufficient to reproduce the scaled longer period waves, and reflections in the flume caused reflection bars that seemed to “lock up” sediment. Their detailed report (Kriebel, Dally, and Dean 1986b) indicates noticeable cross-tank profile variation due to the longer swell-type wave conditions. Trial tests with irregular wave trains were reported to reduce wave reflection, along with bottom ripples, and they suggested this should produce better results in accretive model tests. Erosive tests aimed at investigating the effect of the initial model profile found that the inner surf zone and beach face areas were not affected by different initial profiles, but the offshore region in the vicinity of the bar was different. This was attributed to different wave shoaling and breaking characteristics. They concluded that the scaling criteria performed well for the erosive conditions, but that realistic initial profiles must be used in physical modeling due to its effect on the incident wave characteristics. They do not recommend using movable-bed models to simulate beach recovery under regular (monochromatic) wave conditions. 44. Dette and Uliczka (1986) compared beach profile development observed in a prototype-scale wave tank with similar tests conducted at 1:10 scale. The objective of the comparison was to test validity of various scaling relationships and to examine the effects of the initial profile. The model used the same sand (grain size 0.33 mm) as was used in the prototype. Best comparisons between model and prototype were found when the model profiles were scaled to prototype using the distorted model guidance given by 18 Vellinga (1982); however, the good correspondence was found only in the surf zone. Offshore, the scaled-up model results were substantially too shallow. For this case, Froude time scale appeared to govern the transient response, i.e., similar profile development after same number of waves. Additional tests, documented in an extended version of Dette and Uliczka (1986)! utilized model bed material having grain size of 0.17 mm. Comparisons again indicated the distortion given by Vellinga’s guidance provided suitable replication in the surf zone, but not in the offshore portion. Comparisons were also made using the distortion required by Hughes’s (1983) scaling criteria, with similar conclusions; but the comparison is not strictly valid because the waves in the model were run according to the Froude criterion instead of the shorter wavelength dictated by Hughes’s distorted scaling of the hydrodynamics. Nonetheless, Dette and Uliczka’s results indicate that better similarity is achieved if the fall speed of the sediment is used in scaling model results to the prototype. They also found that the initial profile shape seems to influence the final bar configuration, but not the inshore portion of the profile. 45. Fowler and Smith (1986) conducted small-scale movable-bed model tests to evaluate the validity of five different sets of scaling criteria. The tests were aimed at reproducing both erosive and accretive profile response documented for Saville’s (1957) large-scale experiments. Different bed materials used in the 31 tests were sand (0.22 mm), crushed coal (1.2 mm), and glass beads (0.07 mm). Guidance suggested by Vellinga (1982) performed well for both accretive and erosive conditions, whereas tests scaled according to Hughes (1983) showed good correspondence only for erosive conditions. They questioned the distorting of the Froude scaling criterion as required by Hughes’s guidance. 46. Fowler and Smith (1987) conducted additional small-scale tests using three sizes of sand grain and scaling the models according to Vellinga’s guidance. They found that best reproduction of prototype observations were achieved with fine sand that allowed minimum model distortion. This is significant because Vellinga’s guidance approaches the guidelines spelled out by Dean (1985) when distortion is minimized. 47. Sayao and Nairn (1988) endorsed the scaling guidance outlined by Dean (1985) for beach profiles « by stating that the modeling requirements were “...necessary but not sufficient for dynamic similarity.” They suggested that, if possible, movable-bed model design should be geometrically undistorted with Froude-scaled hydrodynamics and similarity of fall speed parameter between model and prototype. However, it is necessary to quantify remaining scale effects due to dissimilar beach slopes and nongeometrically scaled sediment diameters using prototype-scale results. They developed a morphological time scale for onshore and longshore sediment transport rates by comparison of movable-bed model results to numerical simulations, but they concluded (based on the work of Kriebel, Dally, and Dean 1986a) that the time scale for erosive offshore transport was better represented by the Froude criterion. They noted that validity of their proposed relationships was awaiting the availability of an adequate field data set. 1Personal communication, 30 September 1988, Dr. Klemens Uliczka, University of Hannover, Federal Republic of Germany. 19 Summary and Conclusions About Previous Efforts 48. The previously cited studies tend to support the preservation of the fall speed parameter between prototype and model in undistorted movable-bed models with the hydrodynamics scaled according to the Froude criterion. As Dean (1985) discussed, the model law preserves similarity in wave form, sediment fall path, wave-induced velocities, break point, breaker type, and wave decay provided the model is large enough to preclude viscous and surface tension effects. He states further that bottom shear stress will not be correctly scaled using the fall speed parameter criteria because the bottom boundary layer and ripple formations are not reproduced. This will result in noticeable scale effects when wave breaking turbulence is not dominant in the domain being modeled. 49. The successes documented by Kriebel, Dally, and Dean (1986a, 1986b) and Vellinga (1986) when specifically testing the undistorted scaling criteria under erosive conditions lends further credibility to the guidance, and this is supported by the findings of Fowler and Smith (1987) that best results occur when Vellinga’s guidance is applied with minimum distortion. 50. There are definite limitations to the use of the fall speed parameter scaling criteria that restrict movable-bed modeling applications. Vellinga (1986) stated that the chance of developing universal scaling criteria applicable to both short- and long-term sediment process is slim because the short-term condition will usually require scaling of the H/wT parameter, and the long-term will probably be dominated by bed-load transport and require correct reproduction of the boundary layer shear stress. Kriebel, Dally, and Dean (1986a) noted the constraints the scaling relationships place on model facilities, stating that many’ prototype situations cannot be practically replicated at small scale with an undistorted model. Primarily this refers to prototype cases involving fine beach sands. The scaling guidance requires a large- to mid-scale physical model to avoid using model sediments with grain sizes approaching the transition point into cohesive sediment. 51. Opinion is divided on whether initial model profile shape significantly influences the equilibrium profile. The profile in the surf zone is well matched, but the bar region and the offshore portions appear to be impacted by initial model profile. Gourlay (1980) cites several other studies supporting both sides of the issue, but points out that the transient response is certainly affected by initial profile. 52. In conclusion, efforts aimed at reproducing surf zone profile response in small-scale movable-bed models during erosive conditions have converged on scaling criteria that preserves the parameter H/wT between prototype and geometrically undistorted model, with the hydrodynamics (waves primarily) being scaled by the Froude criterion. This scaling guidance was adopted for testing and verification in the study described by this report. Selected Scaling Criteria 53. The selected scaling guidance consists of simultaneously satisfying two scaling criteria in an undistorted movable-bed model. The first is the well-known Froude.criterion for the hydrodynamics that arises if the ratio of inertial forces to gravity forces is held constant between prototype and model. The Froude criterion results in the relationship N; =V Ne (2) where WN represents the prototype-to-model ratio of the subscribed parameter, ¢ is time, and £ is length. Note that scale ratios defined in this manner are usually greater than one and are always dimensionless. In deriving Equation 2, the gravity scale, N,, was set equal to unity. 54. The second criterion requires maintaining similarity of the fall speed parameter between prototype and model, i.e., ae = (3) WpLp IE where the subscripts p and m represent prototype and model, respectively. Rearranging Equation 3 yields Hy _ Wp Tp (4) LE etin lin Equation 4 can be written in terms of scale ratios as Ny = N. Nr (5) 55. Recognizing in an undistorted model that Ny = Ne and that the wave period will scale the same as the hydrodynamic time scale, the combination of Equations 2 and 5 results in the unique scaling relationships satisfying both criteria: Ni = Ny = VNe (6) Comparison to Xie’s Scaling Guidance 56. As mentioned, various parameters other than the fall speed parameter have been suggested for use in characterizing sediment transport processes. It is instructive to examine one of these parameters in more detail because it was found useful for analyzing some of the scale model results arising from this study. 57. Xie (1981, 1985) conducted numerous small-scale movable-bed model tests to examine the scouring of bed material adjacent to a vertical seawall subjected to nonbreaking waves. He observed two distinctly different responses in bed form that appeared to correspond to different mechanisms of sediment transport. 21 He classified Type I scour as fine bed material moving largely by suspension so that scouring occurs at the nodes of the regular standing waves and deposition occurs about the antinodes. Type II scour occurs when coarse-grained material moves as bed load, scouring sediment halfway between the nodes and the antinodes and depositing at the nodes of the standing wave pattern. After testing several parameters, including the fall speed parameter, Xie presented a criterion for distinguishing between the two scour patterns that depends on the grain size of the bed material and on the wave conditions. The criterion is based on the parameter Umaz al U. w (7) where Umax = horizontal component of the maximum orbital water particle velocity near the bed U, = critical velocity for incipient motion of the sediment w = sediment fall speed This parameter gives a relative comparison between the horizontal water particle speed beyond that necessary for incipient motion and the speed at which the sand grain settles. High values of the parameter imply movement by suspension (turbulence-dominated), and low values correspond to bed-load-dominant conditions. A similar parameter was proposed by Le Méhauté (1970), who stated that kinematic similarity was important for modeling beach profiles at small scale and suggested that the ratio of the horizontal component of the orbital water velocity to the sediment fall speed be maintained. 58. Xie (1981) suggested that similarity of the parameter given by Equation 7 should be maintained between prototype and model, but noted that this would be difficult at times because of the dependence of both U, and w on grain size. Barring complete similarity, he recommended that both prototype and model at least be in the same range for the type of scour being modeled, i.e., keep the value of the parameter above 17 for Type I scour of fine sediment and below 16 for Type II scour of relatively coarse sediments. A strong correspondence between the fall speed parameter and Xie’s parameter is evident and prompts further investigation. 59. The scaling criterion derived from maintaining similarity of Xie’s parameter in an undistorted Froude model is developed as follows: oa uy 4 (Ge a, 6 where once again subscripts p and m represent prototype and model, respectively. Rearranging Equation 8 yields (ete) Gay _ . (i- pie.) (CR aie 22 60. Using the notation for scale ratios and noting that, in an undistorted Froude model, the scale for the water velocity will be the same as the time scale, Equation 9 becomes N, = Nw (10) (l=g25) or N,Nz = Nw (11) where NS (12) (eee) m 61. In essence, the scaling guidance given by Equation 10 is a more generalized version of the guidance determined with the fall speed parameter (Equation 6). The scaling guidance given by Equation 10 agrees with that given by Equation 6 if the scale ratio N, is equal to unity. 62. Examining Equation 12, there are two conditions by which N, could approach unity. The first is if Umar > U. in both the prototype and model. This would be representative of highly turbulent conditions, such as exist in the surf zone during energetic wave conditions; and in the limit it corresponds somewhat to the physical description given by Gourlay! and Dean (1973) for a suspended grain falling through the water column under the influence of horizontal currents. 63. The other conditions leading to unit value for N, is if the ratio U./Umazr is kept similar between prototype and model. Although there may be unique cases where this similarity could be maintained, in general the investigator will be unable to satisfy both the fall speed scale and the grain size scale necessary to meet this condition. Even if possible, the scaling would be valid for only one specific hydrodynamic condition because U,,a, depends on wave period and wave height, whereas U, is independent of wave height. This would hamper investigations using irregular waves, as well as studies in which numerous regular wave periods were of interest. The best achievable situation, if scaling according to the fall speed parameter guidance (Equation 6), is that where velocity ratios (Ux/Umaz) remain reasonably close in value for the prototype grain size and the derived model grain size. 64. The preceding discussion may help to explain why distorted model scaling guidance using bed materials similar in size to the prototype perform well in the surf zone, but suffer in the comparisons for the region seaward of breaking (Dette and Uliczka 1986, Fowler and Smith 1987). In the surf zone, Umaz is typically much larger than U,, and the scale ratio N, will be approximately unity. Seaward of the wave breaking zone, model sand grains having approximately the same mean diameter as the prototype sand will undergo transition to a bed-load dominant transport mode in the model sooner than the equivalent transition in the prototype, and the seaward migration of the sand will be less in the model than in the prototype (for the case of net offshore transport conditions). 1Gourlay, op. cit. 23 65. In undistorted Froude models where the model sand has been reduced in size from the prototype according to the fall speed ratio, deviations in the U./Umaz velocity ratio between prototype and model will also occur offshore of the breakpoint bar. However, these deviations will be less than in the case of a distorted model employing prototype-size sand. The consequences of this offshore effect will be examined further in Part IV using specific results from the present study. Applicability of Selected Scaling Criteria 66. The selected movable-bed scaling criteria given by Equation 6 are for undistorted Froude models where the sediment size is selected so that the fall speed parameter is held constant between prototype and model. Past experience with these and similar scaling criteria, coupled with the assumptions used in formulating the guidance, restricts application of this type of physical modeling to coastal sediment problems and processes that are chiefly erosional in nature, with the erosion occurring in an energetic, turbulence-dominated region such as the surf zone. Typically, the scaling is intended to replicate the short-term response of the sea bed to storm-induced waves. Examples of situations that may be candidates for modeling with the selected criteria include: beach and dune profile response to storm events, initial beach-fill adjustment to larger waves, beach-fill response to storm events, and storm-related short-term scour at the toes of structures. 67. Most experience with these scaling criteria, including the present study, has been with 2-D wave flumes; hence, applicability of the guidance to the 3-D situation is still in question, although Vellinga (1986) has performed related tests in a movable-bed basin with encouraging results. 68. An unfortunate aspect of the selected modeling criteria is that often a fairly large facility will be required to successfully model prototype situations having fine-grained sediments. For example, Figure 1 is a simple nomogram for estimating length scale ratio based on Equation 6. This estimate assumes a model median sediment size of 0.13 mm, prototype and model water temperatures of 60 °F!, and quartz sand. It is readily apparent that prototype sediment sizes representative of many beaches will require length scales on the order of 10 or less. 1A table of factors for converting non-SI units of measurement to SI (metric) units is found on page 7. 24 LENG SCALE Kel Le Fresh Water —\_.” oY Sele Wetrer gh pia Hes iS cS 4 ,45 SED IMENT see LN SIiLZe = Cini Figure 1. Nomogram for estimating movable-bed model length scale ratio 25 PART III: EXPERIMENT OVERVIEW 69. This section describes the laboratory movable-bed test facilities used to verify the selected scaling criteria, summarizes the prototype condition selected for reproduction in the scaled model, presents the model scaling as determined by the scaling criteria, provides a generalized description of the testing procedure, and lists the experiments conducted over the course of this investigation. Laboratory Facilities 70. The majority of tests described in this report were conducted in a 6-ft-wide wave tank at the Coastal Engineering Research Center (CERC), US Army Engineer Waterways Experiment Station (WES), during the period October 1988 — January 1989. The testing was preceded by a 2-month period of model preparation and wave machine calibration. Three additional tests were conducted in the 6-ft flume during September 1989. These tests were to confirm the results of one of the earlier tests and to verify the modeling guidance by reproduction of an irregular wave prototype-scale flume test. 71. The 6-ft flume is constructed of concrete and has glass viewing panels in the test section, which is located 75 m from the wave board. Figure 2 shows a plan view of the wave tank and supporting facilities, and a profile view of the flume is given on Figure 3. The flume has dimensions and capabilities as listed in the following tabulation: Length 100.0 m (328 ft) Width 1.83 m (6.0 ft) Depth 1.83 m (6.0 ft) Max. Water Depth 1922) 11420 ft) Max. Wave Board Stroke 0.66m (2.2 ft) Max. Wave Height 0.50m (1.6 ft) 72. The wave machine used in the 6-ft flume is hydraulically operated and is constructed such that it may be used in either the flapper or piston mode, and it can generate waves of 0.5 m at maximum operating conditions. For the reported tests, the wave machine was operated in the piston mode to generate both regular (monochromatic) and irregular waves. Figure 4 is a graphic representation of the maximum regular wave height generating capabilities of the wave generator as a function of wave period at the maximum water depth of 1.22 m. 73. Piston stroke and frequency for both regular and irregular waves are controlled using CERC software and a Micro-Vax I microcomputer. During operation of the wave generator, feedback from the 26 100 m >| — woreee eC“ S ox Wave gages WaVC BBECS OOOO, 12a 45 6 6-Ft Flume Hydraulic power supply oo XS J @ @ oo wn @ Q fod me 5 5 0: x? eee ee > ee BS % xs 2S DS & RS % BS BS Hydraulic power supply Wave Tanks Control Room Note: This drawing not to scale Figure 2. Plan view of 6-ft flume and supporting facilities piston motion and wave gages is actively monitored using a multichannel oscilloscope. 74. Water surface elevations were sensed using both resistance- and capacitance-type wave rods, which were constructed at WES. The wave data were recorded on the Micro-Vax I. An Automated Data Acquisition and Control System, designed and developed at WES (Turner and Durham 1984), was used to calibrate the wave rods and to ensure correct wave height. Figure 5 is a schematic of the data acquisition system used in the 6-ft-wide flume. Six wave rods were used in two groups of three (see Figure 3) to allow calculation of reflected wave energy in the deeper water near the wave board and in shallower water near the movable-bed portion of the tank. The wave rods were calibrated at the beginning of each test series to a tolerance of +0.002 ft in the model. 75. To generate regular waves, a wave period and amplitude were specified and a data file consisting of sinusoidally varying stroke as a function of time was generated and used as the input signal to drive the wave machine. For irregular wave generation, software developed at CERC! was used to generate a piston 1Long, C. E., 1985, “Laboratory Wave Generation and Analysis: An Instructional Report for Unidirectional Wave Generation and Analysis,” unpublished report, CERC, WES. Pail Initial sand layer, 1:4 slope Fixed structure, 1:4 slope k 80.8 m ———____5 Wave gages Wave gages 1 23 456 SWL o, SRR IKK 1.16 m Wave board > > > KO KO aailee bottom LQ “aa 0.67 Vs QL cP 4 o, OL 1 0.49 asa me S96" m— <23.5 m—> 1.46 m l« 3.75 | Note: This drawing not to scale Figure 3. Profile view of 6-ft flume (SWL = still-water level) stroke time-history record that produced a water surface elevation time series conforming to the input spectral representation and having significant height and peak period as specified. For regular waves, data were collected at a rate of 50 Hz whereas irregular wave data were collected at a 20-Hz rate. Wave data analysis was accomplished using a Vax 11-750 computer and software developed in-house!. Appendix A gives a summary of the analysis package used. Prototype Condition 76. The prototype data modeled in the tests described in this report were provided by Dr. H. Dette of Technical University of Braunschweig and Dr. K. Uliczka of the University of Hannover in the Federal Republic of Germany. These data resulted from prototype-scale tests conducted during 1985 in the large wave tank (Grofer Wellenkanal or GWK) facility at the University of Hannover. The GWK has dimensions of 324-m length, 5-m width, and 7-m depth and can generate regular and irregular waves at prototype scale. The laboratory procedures used and some test results were presented at the International 1Developed and modified by K. Turner, C. Long, and D. Ward, CERC, WES. 28 Maximum Monochromatic Wave Condition -- 6-ft Flume Water Depth = 4.0 ft 2.0 1.5 a Ss <= | 2 1.0 ay [s) es oO > us] = 0.50 0.0 0 2 4 6 8 10 12 Wave Period - T (sec) Figure 4. Wave generating capability of 6-ft flume Association of Hydraulic Research (IAHR) Conference in 1986 (Dette and Uliczka 1986), the Coastal Sediments Conference in 1987 (Dette and Uliczka 1987), and the 21st International Conference on Coastal Engineering (Uliczka and Dette 1988). The purposes of their prototype-scale tests were to investigate dune recession and beach erosion to aid in the development of numerical models and to determine appropriate time scales for these phenomena. 77. The sand in the prototype experiments had a median diameter of 0.33 mm and was representative of sand found on the North Sea coast of West Germany. Approximately 1,000 m? of this sand was placed in front of a concrete structure with a slope of 1 on 4. The sand was molded to the same initial slope as the concrete structure shown in Figure 6. For the regular wave tests, monochromatic waves with a height of 1.5 m and period of 6.0 sec in water depth of 5.0 m were used to erode the initial profile. As many as 80 waves were generated at a time; then the wave machine was stopped and profiles were measured. Stops were made whenever the wave height variation (due to reflections) reached +20 percent of the originally generated wave height. The experiment was continued until little or no change was observed in profile development, indicating the equilibrium profile had been obtained. 78. The regular wave prototype test is somewhat unique because of the exposure of the concrete revetment during profile adjustment. Not many prototype-scale movable-bed tests have been conducted, and this test represents one of the few cases where development of a movable bed adjacent to a hard 29 board he 100 m 7 Wave gages 4 5 6 Wave gages 12. Hydraulic 3 power supply 6-Ft Flume Wave gage input Command Feedback Control Room Oscilloscope Figure 5. Schematic of data acquisition system Signal Controller Note: This drawing not to scale structure has been documented and made available to the research community. 79. In addition, Uliczka and Dette conducted several prototype-scale flume tests using irregular waves and approximately three times more sand in the profile to avoid exposing the concrete revetment. One of the cases used the same grain size and initial slope as the regular wave case shown in Figure 6. The only difference was the sand berm width, which was three times as wide for the irregular wave test. This case was selected for reproduction during the irregular wave verification of the scale model relationships. In the prototype case, a JONSWAP spectral representation was used to simulate the irregular waves. Significant wave height, peak spectral period, and water depth were specified to be equal to the same wave values as used for the regular wave prototype condition. 30 PNOM| Vira SCALe Sand Berm 1:4 Concrete Revetment 20 30 40 50 RANGE - (m) Figure 6. Regular wave initial condition Model Scale Selection 80. The fall speed scaling relations previously discussed and summarized by Equation 6 were used to design the movable-bed model parameters. Fine quartz sand obtained from the Ottawa Sand Company in Ottawa, Illinois, having a median diameter of 0.13 mm and specific gravity of 2.65 was used to simulate the 0.33-mm median-diameter prototype sand. The Froude scaling criterion was used to determine model wave period and the time scale for morphological development. 81. An undistorted length scale ratio of 7.5 (prototype) to 1 (model) was determined using Equation 6 and the information given in Table 1. Table 1. Prototype and Model Sediment Parameters Parameter Prototype Sediment Median Diameter 0.33 mm 0.13 mm Mean Sediment Fall Speed | 4.47 cm/sec | 1.64 cm/sec 31 82. Prototype values in Table 1 were reported by Uliczka and Dette (1988). Model mean sediment fall speed was calculated using the formulation given by Hallermeier (1981) with 0.13 mm as the diameter of the quartz sediment and assuming a water temperature of 77 °F. 83. The scale ratio for the sediment fall speed was determined as 4.47 Ny = — = 2. oT Le @ This was then used to determine both the time scale ratio and the length scale ratio as given by Equation 6, i.e., and For convenience Ny = 7.5 was chosen as the length scale. Table 2 presents prototype and scaled model parameters used for the tests. Several of these parameters are illustrated on Figure 6. Table 2. Prototype and Model Experiment Parameters Wave Period Wave Height Water Depth Horizontal Berm Width Berm Thickness 84. Note that strict geometric scaling using the specified prototype and model grain sizes would have resulted in a length scale ratio of Ng = 0.33 mm/0.13 mm = 2.54. This illustrates the utility of the fall speed parameter scaling guidance in that larger length scale ratios are permitted, thus allowing modeling to be conducted in smaller facilities. An interesting experiment would be to attempt reproduction of the selected prototype event in a large-scale wave flume using geometric scaling of the sediment between prototype and model. Testing Procedure 85. The procedures used for all tests were intended to duplicate the procedures used by Dette and Uliczka (1986, 1987) for the GWK tests. The initial sand slope was smoothed to a 1-on-4 slope (as 32 illustrated in Figure 6) using a scrape and trowel, and initial profiles were taken. As previously stated, wave rods were calibrated to +0.002 ft tolerance prior to each test to ensure accuracy of recorded wave data. As was done in the prototype tests, regular waves were run in short bursts to minimize the effects of re-reflection off the wave board. Irregular waves were run for times equal to the scaled equivalent of the prototype wave runs. Time for water surface stilling was allowed between runs. Reflection coefficients measured during the tests at the gages nearest the wave board ranged from 0.06 to 0.2, but wave height variation never exceeded the +20 percent specified for the prototype tests. 86. Center-line profiles were taken during a test corresponding to similar profile measurements in the prototype after the same number of waves. Profiles were taken along each sidewall of the flume at the conclusion of each test to document observed cross-tank variations. A graduated rod with a 2-in.-diam circular foot pod was used to obtain all center-line profiles, as shown in Figure 7. Elevations were normally obtained along the profile at 0.5-ft intervals with additional elevations recorded as necessary to document profile irregularities, such as the erosion scrap. A benchmark elevation was taken at the beginning and end of every profile measurement to ensure that vertical elevations were consistent throughout the tests. Profiles measured along the flume side walls were obtained using a surveyor’s level and graduated rod. The same benchmark was used for both the center-line profiles and the wall profiles so that all profiles could be related to a common datum. Model Experiments 87. A total of 14 tests were conducted in the 6-ft flume at CERC during the two test series documented in this report. Test identification numbers, brief descriptions of each test, and reference to the section of the report that discusses test results are given in Table 3. 88. Representative results are presented in the following report sections to illustrate observed profile development. Complete results are given in the report appendices. Wave analysis results for each experiment are given in Appendix B, the experiment profile data are tabulated in Appendix C, the experiment profile plots are in Appendix D, and comparison of profiles from different cases (model versus model and model versus prototype) are shown in Appendix E. 33 Figure 7. Profiling procedure during experiments 34 Table 3. Description of Laboratory Tests Description of Test Rpt. Section Reproduction of prototype experiment using Part IV 10-m-horizontal-width berm Repeat of T01 to demonstrate repeatability Part IV Reproduction of prototype experiment using Part IV 11-m-horizontal-width berm (same as prototype) Repeat of T03 with wave height increased by Parts IV & 10 percent to examine impact of height variations V Repeat of T03 using absorbing wave paddle Part V Repeat of T03 starting with the prototype profile Part V at 40 waves molded in the flume Repeat of T03 with wave period decreased Part V 10 percent to examine impact of period variations Repeat of T03 using irregular waves having Hy 3 Part VI equal to 140 percent of monochromatic wave height Repeat of T03 using irregular waves having H,/3 Part VI equal to the monochromatic wave height Repeat of T03 using regular waves with a Part VII vertical seawall on the revetment Repeat of T10 using irregular waves with H,/3 Part VII equal to the monochromatic wave height Undocumented repeat test of T08 Aborted irregular wave test Reproduction of prototype irregular wave test 35 PART IV: VERIFICATION TESTS 89. Verification of the selected movable-bed scaling criteria by reasonable reproduction of prototype test. profiles was the primary purpose in conducting the experiments discussed in this report. No clear quantitative guidance has been given for determining what constitutes successful reproduction in the model, although Dean (1985) lists reproduction of the correct beach slope and type of profile (barred or nonbarred) as good indicators of the relative success of the attempt. Generally, a visual comparison between prototype and model profiles, supplemented by some type of parameter describing the variations between profiles, forms the basis for a subjective opinion as to whether or not the experiment has been successful. Regular Wave Validation Test 90. The first two tests performed (T01 and T02 in Table 3) were conducted with a sand berm having a scaled horizontal width equivalent to 10 m in the prototype (see Figure 6). After completing these two tests, plotted results indicated a discrepancy in volumes of sand between model and prototype. It was subsequently discovered! that the prototype berm was actually 11 m in the horizontal dimension, slightly greater than the nominal horizontal width given as 10 m. Hence, the tests T01 and T02 represented a berm having approximately 10 percent less sand than the actual prototype berm. These tests will be discussed later in relation to experimental repeatability and impacts of reduced or inadequate sediment supply. Test T03 Results 91. Test T03 represents the best attempt to reproduce every aspect of the prototype experiment in accordance with the selected scaling criteria. Summary wave statistics resulting from analysis of water level fluctuations recorded at the two gaging locations are given for Test T03 on Table B3 in Appendix B. (A description of the wave analyses procedures is given in Appendix A.) Time series wave statistics in Table B3 refer to the average of the results obtained from the three gages comprising the array at each location. Spectral values (Hm.,T7,, where H»,. = zeroth-moment wave height and 7, = period of spectral peak) represent the incident wave condition after removal of reflected wave components. 1Personal communication with Dr. Klemems Uliczka confirming horizontal berm width used in prototype case, 28 Decem- ber 1988. 36 92. Figure 8 shows the developmental response of the center-line profile in the model. The solid line is the model profile measured after the specified number of waves, and the dashed line is a model profile measured at an earlier point in the experiment. The purpose of Figure 8 is to illustrate the relative change of the center-line profile as it approached equilibrium. A complete set of profiles for test T03 is given in Figure D3 in Appendix D, and the profile measurements are given in Table C3 in Appendix C. 93. For regular waves, the profile reached a quasi-equilibrium condition somewhere between 1,200 and 1,400 waves with very little change occurring thereafter. The most noticeable change occurring after 1,400 waves was an observable cross-tank variation in the profile. This variation is shown in Appendix D (Figure D3) by the plots comparing profiles at 1,650 waves. In these plots, the suffix P represents the center-line profile (dashed) while G and C represent profiles along the glass sidewall and the concrete sidewall, respectively. Figure 9 plots the average of all three profiles after 1,650 waves as compared with the center-line profile (dashed). 94. This cross-tank variation is thought to have been caused by a small misalignment of the revetment in the flume which in turn caused nonuniform reflection of waves from the exposed concrete revetment. Similar cross-tank variation was not present in the prototype-scale tests of Dette and Uliczka!. It was noted that the cross-tank variation in the model did not materialize until after the profile was close to an equilibrium condition, even though the revetment was exposed somewhat earlier. This may indicate that the profile is more susceptible to cross-tank perturbations when the profile has reached a quasi-equilibrium state. If the profile is not close to equilibrium, the onshore/offshore movement of sand seems to overwhelm any cross-tank-induced sediment transport, indicating that storm-induced profile adjustment exhibits a strong onshore/offshore trend? Comparison with Prototype 95. Representative profile comparisons between prototype and model after equal numbers of waves (Froude scale for morphological development) are given in Figure 10. In these plots the model results have been scaled up to prototype dimensions using the length scale ratio of 7.5. A complete set of profile comparisons is given in Figure E2 in Appendix E (Test T03 versus Prototype). 96. The comparison after 40 waves (Figure 10) shows that profile development in the model did not match the development in the prototype for the underwater portion of the profile. The form of the prototype profile suggests that massive slumping may have occurred in the prototype, although this has 1Personal Communication, Dr. Klemens Uliczka, 28 December 1988 2This trend was also observed in the field during the DUCK85 experiment (Howd and Birkemeier 1987). A prestorm breakpoint bar that exhibited nonuniform alongshore variation became quite linear and moved offshore during the storm. Near the end of the storm, when presumably a near-equilibrium had been reached, alongshore variation in the bar began to reappear. 37 40 Waves - Solid 370 Waves - Solid 170 Waves - Dashed 1650 Waves - Solid 1450 Waves - Dashed 4 G RANGE - (ff) Figure 8. Profile development during test T03 38 ELEV. - (ff) Average Profile - Solid Centerline Profile 4 6 RANGE - (ff) Figure 9. Average versus center-line profile at 1,650 waves, T03 39 - Dashed Model - Solid 40 WAVES Proto - Dashed RMS Diff = 0.698 m Model - Solid 370 WAVES Protomembashec RMS Diff = 0.484 m Model - Solid 1650 WAVES Proto - Dashed RMS Diff = 0,444 m 20 RANGE - (m) Figure 10. Prototype-model comparison for test T03 (RMS = root-mean-squared) 40 not been confirmed. The model, as scaled, cannot correctly simulate this type of geotechnical failure, if indeed this was the cause of the prototype profile shape after 40 waves. 97. An RMS variation between profiles was calculated for the vertical variations between prototype eee 2 RMS Variation = — do (hp hm) (13) where hp and hy, are the prototype and model profile elevations at equivalent horizontal positions. The and model using the formulation: RMS variation for the comparison after 40 waves was 0.70 m, which implies a reproduction accuracy of +0.35 m. 98. The profile comparison after 370 waves (Figure 10) is somewhat better, having an RMS variation of 0.49 m. The berm in the model was not eroded as much as in the prototype, and not as much sediment was moved to the region seaward of the breakpoint bar. The profile comparison in the surf zone and in the vicinity of the bar is quite good. 99. The center-line profile after 1,650 waves (Figure 10) represents the equilibrium condition for this test. The RMS variation for the 1,650 wave comparison was 0.44 m when the model center-line profile was used. This RMS variation was slightly reduced to 0.40 m when the average profile (Figure 9) was used in the comparison. The model did not succeed in eroding the final portion of the berm on the upper portion of the revetment. There are two possible explanations for this. First, the concrete revetment in the model had a rough finish that, when scaled to prototype, would be much rougher than the concrete revetment used in the prototype tests. This may have limited the extent of wave runup in the model due to frictional effects. Wave runup may also have been influenced by the difference between prototype and model in the offshore portion of the profile which could have affected wave characteristics. 100. Another difference between model and prototype is that the model did not succeed in moving enough sediment to seaward of the breakpoint bar, and consequently the scouring in the surf zone was not as severe as evidenced in the prototype. 101. The observed difference between prototype and model in the region offshore of the bar is most likely a result of the scaling relationship selected. This scaling relationship works best for regions dominated by turbulence-induced sediment transport. Because the model sand grains are not scaled according to the geometric length scale, they undergo a transition from suspended mode to bed-load mode of transport before this transition occurs in the equivalent prototype flow regime. With the selected scaling criteria, the bed-load mode of transport is not properly scaled in the model; consequently the model sand grains are at rest under scaled conditions that still result in offshore sediment transport in the prototype. This concept is further examined in the next subsection. 102. The observed difference between prototype and model in the surf zone may be related to the aforementioned differences in the offshore portion of the profile. If the offshore bar has a sediment storage capacity under a given wave condition, and sediment to meet this capacity must come primarily from the 41 nearshore region, then it may be that the surplus of sand observed in the model surf zone was a result of the offshore sediment requirement having been met. If this is true, it follows that exact reproduction in the model will require correct development of the bar feature and sediment volume in the bar. Several of the additional tests in this model series were designed to investigate this possibility, and they are discussed in later sections of this report. 103. A second contributing factor to the nearshore model results may have been the aforementioned difference in maximum runup between model and prototype. Greater wave runup should contribute to the corresponding downwash on the face of the revetment, which in turn influences the amount of scouring that occurs at the interface of the structure and sediment. However, this factor is thought to be less important than the equilibrium state of the offshore bar. Test with Increased Wave Height 104. Test T04 was the first of several tests conducted to investigate the relative influences of selected model parameters on the model scaling. In test T04, the wave height in the model was increased by approximately 10 percent over the scaled equivalent of the prototype wave height that was used in test T03. Test T04 Results 105. Test T04 was also conducted in the same manner as the prototype-scale regular wave test. Figure 11 illustrates the temporal development of the profile in the model. Comparisons in Figure 11 are to earlier profiles in this same model test. Wave data and statistics for this test are given in Table B4 (Appendix B), profile data are given in Table C4 (Appendix C), and a complete set of profiles for this test is given in Figure D4 in Appendix D. 106. Similar to test T03, test T04 also exhibited a cross-tank profile variation as the test approached equilibrium as shown by the profiles in Appendix D (Figure D4). Increased wave heights apparently made the cross-tank variation a little more severe than observed in test T03. Figure 12 shows the average model profile at 1,650 waves compared with the center-line profile. 42 40 Waves - Solid 370 Waves - Solid 170 Waves - Dashed 1650 Waves - Solid 1450 Waves - Dashed 4 6 RANGE - (ff) Figure 11. Profile development during test T04 43 ELEV. - (ft) Average Profile - Solid Centerline Profile - Dashed 4 6 10 12 14 RANGE - (ff) Figure 12. Average versus center-line profile at 1,650 waves, T04 44 Comparison with Prototype 107. Representative profile comparisons between prototype and model after equal numbers of waves are given in prototype dimensions on Figure 13. A complete set of profile comparisons is given in Figure E3 in Appendix E (Test T04 versus Prototype). 108. The net effect of increased wave height after 40 waves is slightly more erosion of the berm and more transport of sediment into the deeper portion of the profile. Calculated RMS variation between prototype and model after 40 waves was 0.64 m (compared with 0.70 m for test T03). 109. The model comparison to prototype after 370 waves is judged as being very good with an RMS variation of 0.38 m (compared with 0.49 m for test T03). At this point, more of the berm had been eroded than in test T03 (see Figure 10), and a good correspondence is also seen in the surf zone and in the offshore region. 110. The center-line profile after 1,650 waves, when near-equilibrium had been achieved, showed a very favorable reproduction of the prototype profile development. The RMS variation calculated for this comparison was 0.30 m (compared with 0.44 m for test T03), whereas comparison with the model average profile at 1,650 waves (Figure 12) produced an RMS variation of 0.36 m (0.40 m for test T03). 111. Test T04, with the wave height increased 10 percent over what should represent the equivalent scaled model wave height, produced better comparisons to the prototype case. The increased wave-induced water velocities in the offshore region appear to have transported sediment in the model to a greater offshore depth that more closely corresponds to the prototype. This increased sediment demand was met by the removal of more sand in the nearshore region; consequently, better profile reproduction, both in the final equilibrium and in the developmental stages, was achieved. Experiment Serendipity 112. The fortunate discovery that a 10-percent increase in model wave height provided better reproduction of prototype behavior merited further examination. The possibility that reported prototype wave conditions were 10 percent less than actually generated was immediately discounted given the care with which the prototype experiments were conducted. Instead, the differences between the prototype and model in the region offshore of the breakpoint bar were examined. 113. It was shown in Part II that the fall speed parameter scaling criterion represented a special case of the criterion developed from maintaining similarity of Xie’s (1981, 1985) parameter (see Equation 8). Ideally, the scaling criterion given by Equation 10 should be preferred over the selected criterion used in this study. However, as was pointed out, this criterion is impossible to satisfy throughout the modeled regime. To examine the variation in Xie’s parameter between the prototype and model, idealized 45 40 WAVES Ei une Wel fo RMS Diff = 0.6339 m Model - Solid 370 WAVES Proton Dashed RMS Diff = 0.380 m Model - Solid 1650 WAVES Proto - Dashed RMS Diff = 0.304 m 20 RANGE - (m) Figure 13. Prototype—model comparison for test T04 46 calculations of the parameter were made at different water depths in the offshore region. These calculated values, along with ratios of Xie’s parameter between prototype and model for tests T03 and T04, are shown in Table 4. The maximum bottom velocity, Umarz, was determined from the linear theory relationship nH(1+K;) 14 T sinh (222) (14) Umar = where H = wave height K, = reflection coefficient T = wave period h = water depth L = local wave length 114. Reflection coefficients were measured in the model experiment to be about 0.5 at the nearshore gage position, and it was assumed that prototype reflection coefficients were similar. Critical velocity for sediment motion, U,, was calculated using the relationship of Hallermeier (1980) given by ms 0.35(ds0)"/*(y1g)°/4 Qn Tt U. (15) where ds = median grain size y! = immersed specific weight of sediment (about 1.65 for sand) g = gravitational acceleration Sediment fall speed of the prototype and model sediment are given in Table 1. 115. The model values of Xie’s parameter in Table 4 were calculated using the model depth equivalent to the prototype depth listed in the table. Columns 5 and 6 in Table 4 present the ratio of Xie’s parameter in the prototype to that of the model. For test T03, this ratio is always greater than one, approaching unity as the depth decreases. However, the ratio for test T04 is nearer to unity over the range of offshore depths, and quite by accident, appears to be a reasonable compromise over the extent of the offshore portion of the profile. 116. The better comparison to prototype shown by test T04 suggests a modification to the selected modeling criteria that includes a procedure for adjusting the scaled model wave height in such a manner as to achieve better similarity of Xie’s parameter in the offshore regions of the modeled regime. This adjustment is dependent upon the wave period and should probably be limited to the more dynamically active portion of the offshore profile rather than being extended to full depth of closure. 47 Table 4. Prototype and Model Values of Xie’s Parameter Prototype (Umar — U.)/w Ratio of Xie’s Parameter Depth (m) | Proto. 410% | WUmez=U=)/w]prote | [(Umez—U~)/w] proto Umar—Us)/W)base Umar —Us)/w) 410% 117. It is also noted that this experimental result pertains to regular waves, whereas the natural variability in wave height and period existing in irregular wave trains may help to compensate for the differences in Xie’s parameter without augmentation of the significant wave height in the model. This possibility is investigated further in the section of this chapter discussing movable-bed model law verification employing irregular waves. Experiment Repeatability 118. As previously discussed, tests T01 and T02 were conducted with a smaller sand berm width than was actually required. However, these tests were conducted in an identical manner to assess the repeatability of the movable-bed model experiments. Figure 14 presents three profile comparisons between model tests T01 and T02 plotted in model units. A complete set of comparisons is given in Figure E8 in Appendix E (Repeatability Test), and profile and wave data are given in the appropriate appendices. Visual inspection of the profile comparisons indicates that the movable-bed model is very capable of producing repeatable results. In fact, examination of the comparisons at the two sidewalls after 1,650 waves reveals that the observed cross-tank variation was also reproduced to a sufficient degree of accuracy. Calculated RMS variations between the two experiments are given in Table 5. For reference, the values are given in both model units (inches) and equivalent prototype units (metres) as determined using the 7.5 length scale employed in these experiments. 48 40 Waves T01 - Solid 40 Waves T02 - Dashed 4 6 12 14 16 RANGE - (ff) 370 Waves T01 - Solid 370 Waves T0e2 - Dashed 1650-P Waves T01 - Solid 1650-P Waves T02 - Dashed 4 6 10 12 14 16 RANGE - (ft) Figure 14. Repeatability test, TO1 versus T02 49 Table 5. Repeatability Test RMS Variations Model RMS | Prototype Equivalent Variation RMS Variation in. Irregular Wave Validation Test Experiment Setup 119. Following completion of all regular wave testing in the 6-ft flume, the authors requested and received from Drs. Uliczka and Dette prototype-scale test data stemming from irregular wave tests conducted in the GWK. The prototype tests requested were conducted using the same sand (0.33 mm) as was used in the regular prototype-scale wave tests discussed earlier in this report. The primary difference between the two cases was that approximately three times as much sand was used in the irregular wave tests. This sand was a sufficient amount to prevent exposure of the sloping concrete revetment during testing as occurred during the regular wave tests. Consequently, the irregular wave tests took significantly more time to approach equilibrium, and in fact, had not reached equilibrium after nearly 7,000 waves (compare with equilibrium being reached after 1,600 waves when the revetment was exposed in the regular wave tests). 120. The irregular waves used in the prototype test series were a time series realization of a JONSWAP spectrum having an H,,,. equal to 1.5 m and a spectral peak period of 6.0 sec. As in the regular wave tests, water depth was 5.0 m. These waves were scaled to model size using the same scaling determined for the regular wave tests. An irregular wave train was generated using CERC software that reproduced the prototype spectral parameters of significant wave height and peak period. The spectral width parameter, 7, in the JONSWAP spectrum was set equal to 3.3. Fine adjustment to the time series amplitude was made prior to testing to assure accurate reproduction of the scaled waves. 121. Examination of the extent of profile erosion documented in the prototype test indicated that doubling the volume of sand used in the previous regular wave tests would be sufficient to prevent exposure of the revetment and still provide adequate sand cover of the sloping revetment. Therefore, rather than increasing the sediment in the flume by a factor of three, it was increased by only a factor of two (the 50 advantage of a priori knowledge of the ultimate outcome of the experiment). 122. In the prototype-scale experiments, irregular waves were run in bursts for durations up to 12 min. The same duration sequence as was used in the prototype tests was scaled and followed in the model tests. As in the regular wave tests, time was allowed between wave bursts for the tank seiching to subside. 123. Two irregular wave tests were conducted as described above. The first (test T13) began with an erroneous command sending long period (10 sec) waves onto the initially plane-sloping beach. This error contaminated the experiment; however, the test was continued to gain experience and to assure that sufficient. quantities of sand had been placed to avoid exposure of the concrete revetment. Profile data and wave data were obtained, but only a few wave records were analyzed, and none of the profile or wave data are reported herein. The second test (T14) was conducted as designed and is reported below. T14 Results 124. Test T14 reproduced most aspects of the prototype irregular wave experiment in accordance with the selected scaling criteria. Summary wave statistics resulting from analysis of water level fluctuations recorded at the two gaging locations are given for test T14 on Table B14 in Appendix B. (Note that the addition of sand required movement of the nearshore wave gages to maintain the same distance between gage and beach as existed for the regular wave experiments). 125. Figure 15 shows the developmental response of the center-line profile in the model. The solid line is the model profile measured after the specified number of waves, and the dashed line is a model profile measured at an earlier point in the experiment. Figure 15 illustrates the relative change of the center-line profile as it evolved. A complete set of profiles for test T14 is given in Figure D12 in Appendix D, and the profile measurements are given in Table C14 in Appendix C. 126. Unlike the regular wave tests (where the revetment was exposed), the profile under irregular waves continued to evolve throughout the duration of the test. Toward the end of the test, the flatter portion of the profile within the surf zone maintained a constant depth; and the only profile changes were due to relocation of sediment from the berm to a region offshore of the slight bar feature. Bar formation was virtually absent with only a slight crest-trough feature appearing near the end of the test series. No significant cross-tank variations were evident throughout the test. This can be attributed to the irregularity of the wave train and to the fact that the revetment was never exposed. No sidewall profiles were recorded to document this observation. (However, previous irregular wave tests had exhibited similar cross-tank profile uniformity, and sidewall profiles were recorded to document the fact. These tests are discussed in Part VI of this report.) 51 720 Waves - Solid 80 Waves - Dashed 4 6 12 14 16 RANGE - (ff) 2770 Waves - Solid 720 Waves - Dashed 6810 Waves - Solid 2770 Waves - Dashed 4 6 12 14 16 RANGE - (ff) Figure 15. Profile development during test T14 52 Comparison with Prototype 127. Representative profile comparisons between prototype and model after equal numbers of waves (Froude scale for morphological development) are given in Figure 16. In these plots, the model results are presented in prototype dimensions using the length scale ratio of 7.5. A complete set of profile comparisons is given in Figure E7 in Appendix E (Irregular Test T14 versus Prototype). 128. The comparison after 720 waves (Figure 16) shows that profile development in the model (solid line) closely resembled that of the prototype (dashed line) with the exception of the amount of berm recession. The calculated RMS variation between the profiles (as calculated by Equation 13) was 0.263 m. After 2,770 waves, the model continued to match the prototype response to an uncanny degree (Figure 16) with an RMS variation between profiles of 0.141 m. By the end of the test, the model profile showed some variation from the equivalent prototype profile, but the reproduction was still considered to be very good. The RMS variation between the profiles after 6,810 waves was 0.222 m. As seen in Figure 16, the model did not erode quite as deeply in the foreshore area above the still-water line, a little more sediment was carried offshore of the bar feature, and a slight bar-trough development occurred in the model that was not present in the prototype profiles. 129. The attempt to reproduce the irregular-wave prototype-scale flume experiment was considered to be very successful. This further validates the selected movable-bed modeling guidance as being appropriate for energetic regimes of sediment transport. It is significant that close reproduction was obtained over the entire extent of the profile using properly scaled irregular waves. Recall from previously presented results that the regular wave tests suggested augmentation of the model wave height to provide a better correspondence of the Xie parameter between model and prototype. Because this was not required for the case of irregular waves, it is tentatively concluded that the natural variations within the irregular wave field were sufficient to assure correct redistribution of sediment over the entire extent of the modeled profile. However, further validation of this conclusion would be desirable. Modeling Law Verification Conclusions 130. Visual comparisons of prototype and model profile development due to regular waves indicate that the movable-bed scaling criteria given by Equation 6 did a reasonable job of reproducing the prototype-scale profile evolution in the physical model at reduced scale (test T03). However, the model did not move as much sediment from the nearshore to the offshore region as was documented in the prototype experiment. This appears to be caused by sediment coming to rest in the offshore portion of the model under scaled conditions that would still promote bed-load transport in the prototype. 53 Model - Solid Proto - Dashed RMS Diff = 0,263 m Model - Solid Proto - Dashed RMS Diff = 0.141 m Model - Solid Proto - Dashed ~S Js i Bee ee eS -10 0 10 20 30 40 RANGE - (m) Figure 16. Profile-model comparison for test T14 54 131. When regular wave conditions in the model were increased 10 percent, better profile reproduction was observed with increased movement of nearshore sediment to the offshore region of the model. An explanation for this behavior was found by examining the ratio of the Xie parameter between prototype and model. Model test T04, with wave height increased 10 percent, showed better similarity of Xie’s parameter in the offshore region than did test T03, as shown in Table 4. This supports the contention that the offshore bar has a sediment capacity for a given regular wave condition, and it suggests that the scaled wave height determined by application of the movable-bed modeling criteria given by Equation 6 should be augmented for uniform regular waves so that closer similarity between prototype and model values of Xie’s parameter is achieved. 132. Verification of the scaling guidance under irregular wave conditions was highly successful (test T14). Profile development in the model closely followed that of the prototype-scale experiment and did not require altering the model significant wave height to provide closer correspondence to the Xie parameter. Based on these results, it appears that the irregularity of the wave train extends the region of sediment transport dominated by turbulence and hence moves the sediment farther offshore before transitioning into a bed-load-dominated mode. 133. Experimental repeatability was shown to be quite satisfactory at midscale under regular wave conditions, and overall, the verification of movable-bed scaling guidance based on undistorted Froude models preserving the sediment fall speed parameter has been achieved for the specific case of turbulence-induced profile development of regions characterized by noncohesive sediments. However, bear in mind that these results are encouraging to the extent that prototype-scale wave tanks can reproduce natural beach response without adverse laboratory effects. 55 PART V: REGULAR WAVE PERTURBATION TESTS Increased Wave Height 134. The effect of a 10-percent increase in wave height in the movable-bed physical model was previously discussed in Part IV in conjunction with the observed improvement in the prototype-to-model comparison for regular waves. This observation resulted in a suggested adjustment to the previously presented scaling criteria when regular waves are used in the model. 135. Representative model-to-model comparisons, where the only difference between the compared tests was increased wave height, are shown on Figure 17 at equivalent stages of profile development. Comparisons are plotted in model units and have not been scaled to prototype dimensions. In these plots, the baseline case (profiles shown dashed) is test T03, and test T04 (profiles shown solid) is the case where the monochromatic wave height was increased by 10 percent. Wave height statistics and profile listings are given in Appendices B and C, respectively. Complete profile comparisons are presented in Figure E9 in Appendix E. 136. Increasing the wave height by 10 percent resulted in a 10-percent increase in wave steepness, H/L, at the position of the nearshore wave gage. The 10-percent factor may have varied as the wave underwent additional shoaling, but the wave steepness remained greater for test T04 up to the point of wave breaking. The increased wave height in the physical model resulted in an increased offshore movement of sediment due to the greater bottom water velocities under the steeper waves. A corresponding adjustment in the nearshore region was also observed as sediment was transported seaward. The larger regular wave heights also resulted in greater wave runup and more scouring of the berm after an equivalent number of waves. It is not known if the observed difference in the surf zone after 1,650 waves was due to the different sediment demand of the offshore bar or to the sediment deficit in the nearshore region resulting from the presence of the revetment. Decreased Wave Period 137. Test TO7 was designed to be the same as the base test T03 except that the regular wave period was decreased by 10 percent from the wave period used in test T03. This decreased wave period resulted in shorter wavelength, which in turn increased the wave steepness, H/L, in test TO7 over that of test T03. In the shallow-water limit, where wavelength is proportional to wave period, a 10-percent decrease in wave 56 80 Waves T04 - Solid 80 Waves TO03 - Dashed 370 Waves T04 - Solid 370 Waves T03 - Dashed 1650 -P Waves T04 - Solid 1650 -P Waves T03 - Dashed 4 6 RANGE - (ff) Figure 17. Wave height perturbation, T04 versus T03 57 period gives nearly the same wave steepness as a 10-percent increase in wave height. However, at the depth of the nearshore wave gage, the water depth is transitional, and the corresponding increase in wave steepness was calculated (linear theory) to be about 14 percent. 138. Representative model-to-model comparisons between tests T03 and T07 are shown on Figure 18 in model dimensions, and a complete set of profile comparisons is given in Figure E10 in Appendix E. Other results are given in the appropriate appendices. Differences between the base case (dashed line) and the test with decreased wave period (solid line) are not very apparent in the plots for 80 waves and 370 waves. There was slightly more scouring of the berm along with evidence of greater offshore transport, but not as much as in the case of increased wave heights. It was not until later in the experiment that differences became more evident (see Figure 18 at 1,650 waves). 139. As the test approached the equilibrium condition, case T07 exhibited greater movement of sediment offshore and substantially more scouring in the bar-trough region. This was due primarily to a change in the breaking wave dynamics brought about by the decreased wave period. It is also possible that backwash from the wave runup on the impermeable slope influenced the wave breaking kinematics. Generally, the differences in model profiles are similar to that observed for the perturbation of wave height. This is not unexpected in light of the induced increase in wave steepness, and the similarities are examined further in the following section. Equal H/w7T Parameters 140. The perturbation tests of wave height and wave period were designed so that test T04 (wave heights increased 10 percent) and test TO7 (wave period reduced 10 percent) had nearly equal values of the fall speed parameter. The purpose in doing so was to compare the resulting profile evolution and to assess the relative importance of the fall speed parameter and the Froude scaling of the hydrodynamics. In essence, this comparison represents the situation where the fall speed parameter was held constant in an undistorted model, and the hydrodynamics were distorted from one case to the other to maintain H/wT similarity. 141. Representative comparisons between tests T04 and T07 are shown in Figure 19 with complete comparisons given in Figure £11 in Appendix E. Visually, a good correspondence is seen between the profiles on Figure 19, and it appears that a better match was obtained than in the two cases where the fall speed parameter was increased by 10 percent and compared with the base-case profiles (see comparisons in Figures 17 and 18). Table 6 presents the RMS variation between profiles as calculated by Equation 13. The top half of Table 6 lists the results in model dimensions, and the bottom half gives the same results scaled to equivalent prototype dimensions. 58 80 Waves T07 - Solid 80 Waves T03 - Dashed 370 Waves TO? - Solid 370 Waves T03 - Dashed 1650-P Waves T0? - Solid 1650-P Waves T03 - Dashed 4 6 RANGE - (ff) Figure 18. Wave period perturbation, T07 versus T03 59 80 Waves T04 - Solid 80 Waves T07 - Dashed 370 Waves T04 - Solid 370 Waves TO? - Dashed 1650-P Waves T04 - Solid 16S0-P Waves TO? - Dashed 4 6 10 12 14 16 RANGE - (ft) Figure 19. Equal H/wT parameters, T04 versus T07 60 142. Notice that the RMS variations calculated for the equal H/wT comparisons are in the same range as those values obtained for experimental repeatability (Table 5), whereas in the two cases when there was a 10-percent variation in fall speed parameters, the RMS variations are nearly twice are large. 143. Clearly, the tests with equal values of H/wT exhibit good agreement and support the importance of maintaining similar values of the fall speed parameter for this type of movable-bed modeling. However, this correspondence was demonstrated only for small perturbations in the wave parameters used to express the fall speed parameter. At some point, larger variations of the wave parameters to achieve similarity of fall speed parameter will undoubtedly affect the hydrodynamics to the extent that satisfactory similitude of profile evolution will not be achieved. As previously mentioned, tests T04 and T07 had similar values of H/L, and it should be expected that similar profile response would be observed. Table 6. Wave Perturbation RMS Variations Model Dimensions (feet) Case 370 Waves | 1650 Waves Increased Wave Height (T03 vs T04) Decreased Wave Period (T03 vs T07) Equal H/wT Parameters (T04 vs T07) Increased Wave Height (T03 vs T04) Decreased Wave Period (T03 vs T07) Equal H/wT' Parameters (T04 vs T07) 144. The Froude criterion for scaling hydrodynamics is apparently still the best approach; however, the results (Table 6) suggest that the experimenter may have some latitude in applying the Froude scaling guidance and still achieve reasonable modeling results. 61 Sediment Grain Size 145. All tests conducted as part of this test series used the same sand for the model movable-bed sediment; therefore, no direct tests involving perturbation of the sediment fall speed value were performed. However, it is possible to qualify the impact of different grain sizes in the model by examining similar model experiments conducted by Schulz (1985). 146. Schulz (1985) conducted movable-bed model simulations aimed at reproducing the same GWK prototype regular wave experiment as described in Part III of this report. Schulz’s experiments were conducted at an undistorted length scale of 1:10 with hydrodynamics scaled according to the Froude criterion. Tests were conducted using three different grain sizes (0.18, 0.35, and 0.70 mm) to simulate the prototype grain size of 0.33 mm. 147. Figures 20 and 21 give intermediate and equilibrium comparisons of Schultz’s 0.18-mm and 0.35-mm sand tests with the prototype condition. In both figures, the solid line is the model result scaled to prototype dimensions, and the dashed line is the prototype. For intermediate comparisons, the number of waves is different because profiling was performed at times different from in the prototype; hence, the closest profiles in terms of number of waves were chosen for comparison. The bottom plot on each figure represents the equilibrium condition, which occurred much later in the scaled model than in the prototype. 148. Neither the 0.18-mm nor the 0.35-mm grain size achieved a good match for the prototype profile evolution. The test compared in Figure 21 represents the use of model sediment nearly the same size as the prototype, which would be much coarser than what would be recommended using the scaling guidance presented in this report. The test compared in Figure 20 used a finer sediment than the prototype, but one that was still coarser than the scaling guidance would recommend. 149. At the 1:10 scale used by Schulz, the fall speed parameter scaling guidance (Equation 6) gives Ni, = 3.16 and would require a model sediment fall speed of 1.4 cm/sec to correspond to the prototype sediment (see Table 1). Model sand having a median diameter of about 0.12 mm would be required to adhere to the fall speed parameter scaling criteria with length scale equal to 1:10. Sand finer than the 0.18 mm used in Schulz’s experiment (Figure 20) would be mobilized easier and could move toward the offshore region under the generated wave conditions. 150. Qualitatively, it can be concluded that large perturbations in the model sediment fall speed parameter due to grain size can greatly influence the movable-bed response. Similar conclusions cannot be made regarding the effects of small perturbations in grain size. It may be that perturbations in the sediment fall speed resulting from variations in water temperature or mean grain size may also contribute to the overall experimental error (see Part IV). 62 ELEV. - (m) ELEV. - (m) ELEV. - (m) Model - Solid 80 WAVES PROTO Proto - Dashed 100 WAVES MODEL 10 20 30 40 =o RANGE - (m) Model - Solid 1650 WAVES PROTO Proto - Dashed 2000 WAVES MODEL RANGE - (m) Model - Solid 1650 WAVES PROTO Proto - Dashed 40000 WAVES MODEL RANGE - (m) Figure 20. Schulz’s (1985) experiment using 0.18mm sand 63 ELEV. - (m) ELEV. - (m) ELEV. - (m) Model - Solid 80 WAVES PROTO Proto - Dashed 100 WAVES MODEL -10 0 10 20 30 40 RANGE - (m) 50 7 Model - Solid 1650 WAVES PROTO Proton Dashed 2000 WAVES MODEL RANGE - (m) = So) 1G! 1650 WAVES PROTO - Dashed 40000 WAVES MODEL RANGE - (m) Figure 21. Schulz’s (1985) experiment using 0.35-mm sand 64 Initial Profile 151. Test T06 was conducted to examine the importance of initial profile on the equilibrium profile and the attempt to reproduce the prototype event. During the base test, T03, a substantial erosional difference was noted between the prototype and model profiles after 40 eres (see Figure 10). Because the difference in profiles is quite significant after a relatively short time into the test, it was thought that part of the prototype profile possibly had evolved as a result of massive slumping during the early portion of the experiment. If this was the case, this type of behavior would not be in similitude in the scaled model because it occurs in a regime controlled more by pore pressure than the fall speed parameter. 152. The prototype profile measured after 40 waves was molded into the wave tank to serve as the initial profile for test T06. The test was then conducted in the same manner as test T03. Figure 22 presents representative prototype-to-model comparisons of the temporal profile development. A complete set of profile comparisons is given in Figure E5 in Appendix E. Other relevant data pertaining to test T06 can be found in the appropriate appendices. 153. After 170 waves (the test was initiated at the 40-wave point) the prototype-to-model comparison seems to be quite good; however, after 370 waves, not as much sediment was being deposited in the offshore region as was observed in the prototype. This is more apparent after 1,650 waves, where a distinct difference is seen between the model and prototype profiles. 154. Figure 23 shows comparisons between tests T03 and T06 at selected surveying stops. Appendix E (Figure E12) contains the complete set of comparisons. Initially, the two profiles are quite dissimilar due to the different starting condition at 40 waves. Note in particular the difference in berm erosion. However, the two profiles soon started to match more closely as equilibrium was approached, and at the 1,650-wave profile, very little difference was observed. 155. Placing the 40-wave prototype profile in the wave tank as the initial profile improved the model-to-prototype comparisons for the short-term profile development (several hundred waves), but the resulting profile at the near equilibrium condition was very similar to that of test T03, indicating that this variation had little effect on the ultimate outcome of the experiment. 156. Uliczka and Dette (1988) discuss prototype-scale movable-bed tests where the only difference was a significantly different initial profile. Comparisons between tests indicated substantial differences in profile development due to the different profile slopes. Gourlay (1980) discusses the differences arising from varying the initial profile and also provides several references that give differing opinions. 157. In designing movable-bed models, it is wise to approximate the initial condition profile, particularly in the offshore portions, which may affect wave shoaling. However, the results from this test indicate that a certain degree of profile variation in the nearshore portion of the initial profile is permissible without unduly impacting the final outcome of the experiment. 65 170 WAVES 20 RANGE - (m) 370 WAVES 20 RANGE - (m) 1650 WAVES 20 RANGE - (m) Figure 22. Prototype-model comparison, initial profile at 40 waves, T06 66 Model - Solid Proto - Dashed 30 40 Model - Solid Proto - Dashed 30 40 Model - Solid Proto - Dashed 40 50 50 SO 80 Waves T06 - Solid 80 Waves T03 - Dashed 370 Waves TO6 - Solid 370 Waves T03 - Dashed 1650-P Waves T06 - Solid 16S0-P Waves T03 - Dashed 4 6 RANGE - (ff) Figure 23. Initial profile at 40 waves, T06 versus T03 67 Decreased Sediment Supply 158. The impact of decreased sediment supply available to the profile can be examined by comparing tests T01 and T03. As previously mentioned, tests T01 and T02 were conducted with approximately 10-percent less sediment in the berm than the equivalent prototype conditions. Therefore, test T01 represents the case where there was less sediment available for redistribution across the equilibrium profile. 159. Figure 24 shows representative comparisons between tests T01 and T03, while the complete set of comparison plots is given in Figure £13 in Appendix E. The solid line is the test with 10-percent less sediment, and the dashed line is the base test T03. There was not much difference between the two tests other than the reduced sediment profiles appear to be slightly lower because less sediment was available for depositing over the profile. 160. If the offshore bar indeed has a sediment demand under given wave conditions, then it would be expected that the comparisons would show the same offshore bar configuration with the nearshore profile being scoured more deeply for the reduced sediment case. The comparisons shown in Figure 24 are inconclusive in this respect because the observed variation in the offshore profile was not significant enough to disprove this hypothesis. Other tests where sediment was withheld from the profile by placement of a vertical seawall are discussed in Part VII of this report. Absorbing Wave Board 161. Waves reflected from the beach and sloping revetment in the movable-bed experiments necessitated stopping the wave machine after about 80 waves so that re-reflected waves from the wave board did not adversely affect the experiment. This was the same procedure followed in the German GWK prototype tests. Test T05 was conducted with a wave-absorbing capability activated on the wave board in the 6-ft wave tank. This was the first time this feature had been used in laboratory tests since installation. 162. The absorbing board has three wave gages spaced across on the face of the board that sense and average the water level. This averaged value is compared with the specified value of water level that should be present without any reflected wave energy, and any difference is compensated by the appropriate increase or decrease of board stroke. Present equipment limitations require that a lower frequency cutoff be employed to avoid damage to the hydraulic components. This means that reflected waves with frequencies below the cutoff frequency cannot be absorbed. 163. Figure 25 compares test T06 (solid line), where waves ran continuously between profiling stops, with base test T03, where stops occurred after 80 waves to allow the reflections to settle. As evidenced by 68 4 g RANGE - (ff) 80 Waves T01 - Solid 80 Waves T03 - Dashed 370 Waves T01 - Solid 370 Waves T03 - Dashed 16S0-P Waves T01 - Solid 1650-P Waves T03 - Dashed Figure 24. Reduced sediment comparison, T01 versus T03 69 the figure, the absorbing wave board produced a significantly different response from the standard method of stopping wave generation more frequently. The profiles formed by the absorbing wave board exhibit smoother features and substantially more movement of sediment to the deeper portions of the profile. In addition, berm erosion was more pronounced during the intermediate stages of profile development when wave absorption was being performed. 164. Examination of the wave records from the absorbing board test reveals that the system correctly removed the reflected waves at the incident frequency, but the procedure produced a spurious long wave at a frequency below the cutoff frequency. Thus, the incident waves attacked the profile while the short-term mean water level was oscillating up and down. When the water level was elevated, more of the berm was susceptible to erosion, and when the water level was depressed, the waves moved more sediment into deeper water. During the test, it was observed that the break bar feature was migrating back and forth due to the low-frequency oscillation in the flume. 165. This first test of the absorbing wave board indicated that it will probably be necessary to use this capability in conjunction with spurious long wave suppression techniques when attempting to generate monochromatic waves with active absorption. Summary of Perturbation Tests 166. Movable-bed physical model tests designed to examine the effects of parameters thought to be important in reproducing prototype-scale behavior were conducted in the 6-ft wave tank. Increasing the height of the regular waves promoted further offshore movement of sediment and a corresponding adjustment of the surf zone profile. Similar behavior was observed when the wave period was decreased by 10 percent. This similarity is probably related to both perturbations resulting in similar increased values of wave steepness. 167. The importance of preserving the fall speed parameter was confirmed by comparing tests where the hydrodynamics were varied from the Froude criterion in order to maintain equal values of H/wT between experiments. Although good results were obtained in this instance, it is still recommended that the Froude criterion be adhered to, as well as maintaining the same value of fall speed parameter. 168. Grain size perturbation was examined using previous results of Schulz (1985). Qualitatively, the behavior was consistent with the established scaling criteria, at least for the case of the undistorted scale model. 169. Differences in initial profile did not substantially affect the ultimate outcome at near-equilibrium; however, short-term differences were expected and were observed. For reproducing prototype-scale events, it was concluded that accurate reproduction of the offshore profile is desirable, whereas accurate details of 70 80 Waves TOS - Solid 80 Waves T03 - Dashed 370 Waves TOS - Solid 370 Waves T03 - Dashed 1650 -P Waves TOS - Solid 1650 -P Waves T03 - Dashed 4 6 RANGE - (ff) Figure 25. Absorbing wave board test, T05 versus T03 71 the initial surf zone profile are of secondary importance. 170. Comparisons between tests with differing amounts of available sediment were inconclusive because the observed differences were of similar magnitude to differences arising from experiment repeatability. 72 PART VI: IRREGULAR WAVE TESTS 171. This section of the report examines profile evolution caused by irregular waves and compares the results with corresponding regular wave cases. All of the irregular wave tests were conducted with the sloping revetment as illustrated in Figure 6. Background 172. Much of the established design guidance for sediment transport has been derived in part from laboratory tests conducted with movable-bed models using uniform, regular wave trains. For engineering design based on this guidance, the irregular wave condition which exists in nature is commonly represented by a single statistical wave height parameter that is taken as being equivalent to the regular wave height in the design formulae. 173. With the advent of irregular wave-generating capabilities in the laboratory, the means are available to systematically examine differences between regular and irregular waves and their effects on the process being modeled. The objective of such studies is to determine which irregular wave parameter best matches the regular wave parameter used to establish the design guidance. This is most important for projects that are constrained to using design criteria developed from regular-wave tests. Eventually, older design criteria will be superseded by new criteria developed from field data and/or laboratory tests incorporating irregular waves. 174. Shallow-water, irregular waves typically can be represented either by a statistical wave height parameter or by an energy-based parameter. Statistical wave height parameters are averages of the time series of waves taken over time whereas the wave process is assumed stationary. Typical parameters include mean wave height (average of all waves), Hyms (RMS square wave height), and H,/3 (average of highest 1/3 waves). The primary energy-based wave height is H,,., which is directly related to the energy contained in the wave spectrum and approximately equal to H,,/3 under the narrow-banded Gaussian assumption. 175. Although H,,, and H;3 are approximately equivalent in deep water, the two parameters can be distinctly different as the waves shoal (Thompson and Vincent 1984, 1985; Hughes and Borgman 1987). Therefore, in selecting an irregular wave parameter to provide equivalence to regular waves, it will be necessary to determine whether a statistical parameter or an energy-based parameter is more appropriate. 73 Previous Efforts 176. Only recently have researchers begun using laboratory facilities to examine differences between regular and irregular waves on beach profile development. Consequently, studies documenting the differences are limited. 177. Mimura, Otsuka, and Watanabe (1986) conducted a series of small-scale, movable-bed model tests using irregular waves. The test flume was partitioned down the center line, and a fine-grained sand (0.18 mm) was used on one side while a coarse-grained sand (0.75 mm) was used on the other side. Initial beach slopes of 1:10 and 1:20 were tested, and irregular wave tests were conducted to cover the range of previous tests performed using regular waves. 178. Mimura, Otsuka, and Watanabe examined several different aspects of sediment transport to determine the most appropriate irregular wave parameter for each case. As a result of their tests, they concluded that the mean wave height of irregular waves gave best correspondence to regular waves when used to predict whether the profiles were either eroding or accreting. The prediction technique they used was formulated with a coefficient based on regular wave tests. They further concluded that use of Hy/3 in the formula required modification of the coefficient. 179. Threshold of sediment movement under irregular waves was found by Mimura, Otsuka, and Watanabe to be better represented in existing prediction expressions by H/3 than by the mean wave height. They based their conclusion on experimental determination of critical depth for motion under irregular waves compared with a formulation previously determined for regular wave tests. They stated that this finding is logical because the sand grains are more responsive to the larger waves in the wave field. 180. Profile evolution in the Mimura, Otsuka, and Watanabe tests was observed to be much slower for the irregular wave case, and this was thought to be the result of both erosive and accretive wave conditions being present in the irregular wave train. A representative wave parameter could not be specified for sediment transport rate because both the mean wave and the significant wave height (H,/3) produced similar results. 181. Recently, success has been reported in efforts to numerically simulate profile response due to cross-shore sediment transport (Larson 1988, Larson and Kraus 1989). The numerical model of Larson and Kraus (1989) incorporates several empirical formulations obtained from analysis of prototype-scale wave tank experiments conducted with regular waves. Application of the model to field situations requires specification of representative statistical wave heights. In simulations of documented field erosional events, they found that the numerical model produced better results when the energy-based H,. was used as the equivalent wave height. Use of the average wave height as the irregular wave parameter did not perform as well because an insufficient quantity of sediment was moved during the simulation. Their simulations of field events provide a link between the proper representative irregular wave statistic and the equivalent 74 regular wave height used to develop the empirical basis of the numerical model. 182. Larson and Kraus (1989) also developed a predictor for delineating erosive and accretive conditions by assembling both prototype-scale and small-scale regular-wave laboratory data. In application of the criterion to a collection of field observations, they found that the mean wave height of the field data provided best correspondence to the regular-wave laboratory results.- This further supports the conclusions of Mimura, Otsuka, and Watanabe (1986). 183. Uliczka and Dette (1987) compared profiles from regular and irregular wave tests in the prototype-scale GWK wave tank. Each test began with a plane beach installed on a 1:4 slope with median grain size of 0.33 mm. Regular wave heights of 1.5 m at periods of 6 sec were run intermittently in bursts of up to 80 waves until an equilibrium was established. The irregular waves were generated with significant height (H/3) equal to 1.5 m and peak spectral period of 6 sec; these conditions were run for intervals totaling nearly 12 min until little change occurred between subsequent profiles. 184. Uliczka and Dette (1987) reported the regular wave case reached an equilibrium state much faster than the irregular wave case (4,000 waves as opposed to about 7,000 waves), and the total eroded volume of sediment was approximately 20 percent greater for the regular wave case. They also observed that sediment was not transported as far offshore in the irregular wave case, and the profile was smoother and did not produce a breakpoint bar under irregular wave action. The lack of a bar feature was attributed to the range of depths over which the irregular waves were breaking. Although the irregular wave condition eroded approximately 20-percent less sediment, note that the irregular waves contained approximately 30-percent less total energy than did the regular wave case. 185. The remainder of this section discusses the results obtained from tests conducted as part of the present study. Irregular H,;; Equal to Monochromatic Wave Height 186. Prior to placing the sand in the 6-ft wave tank, the wave machine was calibrated to produce an irregular significant wave height at the nearshore gage location equal to the regular wave height of the base case T03. Test T09 was conducted using this calibrated condition. The water depth at the nearshore gage was sufficiently deep so that the measured statistical significant wave height was approximately equal to the energy-based parameter Ho. 187. Subsequent analysis of water surface elevation data collected at the nearshore wave gages showed values of the irregular wave statistic, H,,3, slightly higher than the target height of 0.66 ft (see Table B9 in Appendix B). The increase over the nearshore gage values measured during low-reflection calibration tests is attributed to wave reflection that increased the nonlinear aspects of the wave forms. 75 188. Beginning with the usual plane-sloping beach, irregular waves were run in the physical model for approximately the same time spans as the regular wave experiments, with stops in between to allow water motions in the tank to settle and to survey the intermediate profiles. At the stopping points of the experiment, long-period seiching motions, with largest amplitudes estimated visually to be about 5 to 7 cm, were present in the wave tank. Suppression of spurious long-wave motions in the wave tank was not implemented at the time of the test; therefore, it is not possible to determine how much of the long-wave energy was associated with spurious long waves and how much could be attributed to reflection of the naturally occurring bound long wave of the irregular wave train. Nevertheless, long-period motions were allowed to subside before continuation of the test. 189. Figure 26 compares representative profiles from irregular test TO9 with the corresponding profiles from the base test T03 after approximately the same number of waves (equal elapsed time of wave action). The complete set of comparisons is given in Figure E15 in Appendix E, profiles showing the evolution of test T09 profile are given in Figure D9 in Appendix D, and wave analysis results and profile soundings are in Appendices B and C (Tables B9 and C9), respectively. 190. Generally, the irregular wave condition (solid line) produced similar erosional history as the regular wave case (dashed line), but at a slower rate. The initial adjustment of the plane-sloping berm occurred over about the same time span in both cases (regular and irregular waves). After the initial adjustment, evolution of the profile under irregular wave action was less than in the regular wave case, with the most noticeable region of difference being the berm recession. This observation follows the same trend as reported by Mimura, Otsuka, and Watanabe (1986) and Uliczka and Dette (1987). The irregular wave-induced profile reached a near-equilibrium state at the 1,650 wave-profiling stop (see comparative profiles in Figure D9 in Appendix D), which corresponds to the same response of the profile under regular wave action. 191. Comparison of the regular and irregular wave profiles after 1,650 waves shows a close correspondence between profiles, indicating that the regular wave condition was well matched by the irregular wave condition where H/3 equals the monochromatic wave height. Cross-tank variation in the profile after 1,850 waves was minimal compared with that observed in the regular wave case. (See center-line profile 1850-P versus sidewall profiles 1850-G and 1850-C for test T09 in Appendix D.) It is presumed that the irregularity of the wave field helped to subdue whatever mechanism was responsible for the cross-tank variations in the regular wave tests. 76 80 Waves TO09 - Solid 80 Waves T03 - Dashed 370 Waves T09 - Solid 370 Waves T03 - Dashed 4 6 12 14 16, RANGE - (ff) 16S50-P Waves T0939 - Solid 1650-P Waves T03 - Dashed -4 -2 0 4 6 RANGE - (ft) Figure 26. Irregular wave comparison, H,/3 equals Hmono (Hmono = monochromatic wave height) 77 Irregular Wave Energy Equal to Monochromatic Wave Energy 192. Test T08 was conducted with an irregular significant wave height of H,/3 equal to 1.4 times the monochromatic wave height used in base case T03. This provided approximately the same spectral wave energy to the profile as present in the regular wave case, and under the Rayleigh assumption for wave height distribution, corresponded to H,m; of the irregular waves being equal to the monochromatic wave height. The purpose of this test was to examine whether equivalent energy levels are necessary to obtain similar profile development between model regular and irregular wave physical model tests. 193. It was originally thought the target significant wave height of 1.4 times the monochromatic wave height had not been achieved in the flume. This condition had not been previously calibrated, and analysis of the nearshore wave gage array (see Table B8 in Appendix B) made it appear as if the measured significant wave height was too low. To further clarify the situation, the wave machine was calibrated during the September 1989 series to produce the correct wave condition, and test T12 was run to duplicate test T08. Wave measurement analyses and profile response were nearly identical for both T08 and T12. This confirmed that test T08 represented the desired 41-percent increase in significant wave height, but that reflected waves acted in some manner to decrease the nearshore wave heights as when compared with the nonreflective calibration condition. Even so, the important aspect to remember is that the total wave energy in the flume had been increased by 41 percent. 194. Results from T12 are not documented in this report because they were essentially the same as test T08. Test T12, however, did provide another example of experimental repeatability, and the comparison is included as Figure E18. 195. Comparisons between the irregular wave test T08 and the base regular wave case T03 revealed a substantially different profile response to the increased wave energy. Figure 27 compares irregular wave test T08 (solid line) with regular wave test T03 (dashed line) at various profiling stops. Additional comparisons are given in Figure E16 in Appendix E. 196. The increase in wave energy resulted in greater erosion of the berm area and also resulted in movement of the sediment farther offshore than in the regular wave case. The comparison after 1,650 waves also reveals a significantly different profile in the region of wave breaking and seaward of breaking. Visual comparison between the results shown on Figures 26 and 27 clearly indicates that better correspondence between regular and irregular wave tests was achieved if the significant wave height was made equal to the monochromatic wave height. The relative differences between the two irregular wave tests are illustrated on Figure 28 where the more energetic case is shown by the dashed line. (Also see full comparisons in Figure E17 in Appendix E.) 78 80 Waves T08 - Solid 80 Waves T03 - Dashed ELEV. - (ff) 370 Waves T08 - Solid 370 Waves T03 - Dashed ELEV. - (ff) 4 6 RANGE - (ff) Aan eve Raees ae rae 1650-P Waves T08 - Solid 1650-P Waves T03 - Dashed ELEV. - (ft) 10 ie 14 16 4 6 RANGE - (ff) Figure 27. Irregular wave comparison, H1/3 equals 141 percent Hono 79 80 Waves TO09 - Solid 80 Waves T08 - Dashed 4 6 10 12 14 16 RANGE - (ff) 370 Waves TOS - Solid 370 Waves T08 - Dashed 4 6 10 12 14 16 RANGE - (ft) 1650-P Waves T09 - Solid 1650-P Waves T08 - Dashed 10 le 14 16 4 6 RANGE - (ff) Figure 28. Irregular wave perturbation, T09 versus T08 80 Discussion of Irregular Wave Tests 197. Movable-bed model tests using irregular wave conditions showed better success at reproducing regular wave results when the significant wave height (H,,3) of the irregular waves had nearly the same value as the monochromatic wave height. This was well demonstrated by the comparison shown in Figure 26. Increasing the energy level of the irregular waves by 41 percent resulted in excessive erosion relative to the base case T03 (Figure 27). 198. Although irregular waves with significant wave height equal to the regular wave height contain approximately 30-percent less total energy than their regular wave counterpart, the two conditions are similar in terms of the waves that move the sediment. In the irregular wave case, the waves in the distribution larger than the significant wave height are expected to move more sediment than what would be moved by waves in the monochromatic case, whereas waves in the distribution less than the significant height should move less sediment than in the monochromatic case. Irregular waves much smaller than the regular wave height might be expected to have minor effects on the sediment transport. 199. The fact that significant wave height emerged as a good parameter for reproducing observed regular-wave tests indicates that the higher 1/3 waves in the distribution are the most important for sediment transport. Experiments conducted with equivalent energy levels (73 is 1.4 times greater than Hmono) contain a proportionally higher number of waves greater than the monochromatic wave height and, thus, should cause significantly more erosion of the nearshore profile. Therefore, it is believed that maintaining equivalent energy levels between regular and irregular waves is not proper guidance for the situation of beach profile development due to cross-shore sediment transport. 200. For purposes of analysis, assume for the moment that the only waves in the irregular wave height distribution that contribute to net sediment transport are confined to the highest 1/3 waves; waves with lower heights are present, but have no appreciable effect. Under this assumption, it might be expected that profile development in the irregular wave case should take approximately three times as long as the regular wave counterpart. Three times as many irregular waves would need to impinge on the beach to produce the number of irregular waves in the highest-1/3 category equal to the number of regular waves required for the same profile development. However, it is quite unreasonable to assume that all waves smaller than the highest 1/3 waves make no contribution whatsoever to sediment transport. It is more likely that profile development under regular waves is somewhere between one to three times more rapid than the irregular wave case with some smaller waves actually having an accretionary effect as discussed by Mimura, Otsuka, and Watanabe (1986). 201. Figure 29 shows time-shifted comparisons between the irregular wave test T09 and its regular wave equivalent, test T03. In Figure 29, regular wave profiles (dashed) are compared with profiles that took approximately twice as long to develop in the irregular wave test (solid). Generally, a slightly better 81 correspondence is seen for 370, 750, and 1,450 waves (irregular waves) than is seen when the two conditions were compared after equal numbers of waves (see Figure 26 and other comparisons in Appendix BE). However, the improved correspondence obtained by time-shifting the profiles is evident only after the first 300 waves. Prior to that point, profile comparisons are better when the morphological time scales were equal. 202. The observed trend for irregular-wave-induced profile evolution to take longer than corresponding profile development in the regular wave tests is the same as observed by Mimura, Otsuka, and Watanabe (1986) and Uliczka and Dette (1987). Qualitatively, the morphological time scale factor between irregular and regular wave profile response was about 2; i.e., profile development took twice as long under irregular waves. This rate is somewhat faster than indicated by the data published by Uliczka and Dette (1987). 203. The tests described by Uliczka and Dette (1987) did not expose the 1:4 sloping concrete revetment because the sand berm was sufficiently wide so as to preclude that possibility. During the tests in the 6-ft tank, equilibrium was reached rapidly in both the regular and irregular wave cases after the revetment was exposed. This rapid move toward equilibrium may have been caused by sediment no longer being available for offshore transport. This may partially explain the differences in profile evolution times noted between the present tests and those of Uliczka and Dette. Conclusions Regarding Irregular Waves 204. Movable-bed physical model tests conducted using irregular waves successfully reproduced profile development observed using regular waves. Best results were obtained when the significant wave height of the irregular waves was chosen as the equivalent parameter to the regular wave height. This equivalence was in a water depth sufficiently deep so that the Rayleigh distribution assumption was still valid, and measured H,/3 was approximately the same as measured Hmo. 205. Profile evolution under irregular waves was slower by approximately a factor of two, although there are no strong physical arguments to justify this factor other than observation. The slowing of erosion may be caused by some waves in the irregular wave train moving sediment onshore. Qualitatively, this follows the same trend observed by other investigators. 206. Exposure of the revetment and subsequent depletion of the available sediment for transport on the upper profile lead to rapid formation of the equilibrium profile in the irregular wave tests. This resulted in the irregular wave case reaching equilibrium after nearly the same elapsed time as the regular wave case. Absence of the revetment very likely would result in more lengthy profile development times for the irregular wave case, as noted in the experiments of Uliczka and Dette (1987), and this was demonstrated during the irregular wave verification tests when the revetment was not exposed (see Part IV of this report). 82 370 Waves TO09 - Solid 170 Waves T03 - Dashed 750 Waves T09 - Solid 370 Waves T03 - Dashed 1450 Waves TO9 - Solid 750 Waves T03 - Dashed 4 6 RANGE - (ff) Figure 29. Time-shifted irregular wave comparison, T09 versus T03, H,/3 equals Hmono 83 PART VII: VERTICAL SEAWALL TESTS Background 207. Vertical seawalls placed on eroding beaches are designed to protect the land shoreward of the seawall location. Recently, seawalls have been cited as being either the cause of erosion to the beach fronting the seawall or contributing to increased rates of erosion to the beach profile (e.g., Pilkey and Wright 1988). This criticism and the projected rise in sea level will undoubtedly require engineers and coastal planners to make tough decisions on whether protection of upland investments warrants placement of structures such as seawalls. Because these decisions will be difficult, they ought to be based, to the maximum extent possible, on scientific facts and knowledge of the impacts of seawalls on fronting and adjacent beaches. 208. Opinions concerning the impact of seawalls on beaches are widely varied, mainly because insufficient scientific evidence is available to substantiate claims of the parties debating the issue. To date, the most comprehensive review and analysis of existing data and studies pertaining to seawall effects is that of Kraus (1988), which critically reviewed approximately 100 scientific papers related to seawall effects on the beach. The reader is referred to Kraus for his conclusions regarding seawall effects and additional details. (Note that Kraus (1988) appears in a volume dedicated to examining the effects of seawalls on beaches and the different viewpoints on the topic.) 209. One particular point addressed by Kraus (1988) was whether the volume of sand scoured locally on the profile in front of a seawall is greater or less than the volume eroded on adjacent beaches without seawalls. Expressed in another way, “Is the volume of sand being denied to the profile by the seawall similar to the volume of additional erosion observed in front of the seawall?” Kraus cites several field studies that indicate the volume of sediment withheld is approximately the same as the additional eroded volume over the profile of the seawalled beach. In one of the cited studies, Birkemeier (1980) used aerial photography to conclude that the eroded volumes of seawalled profiles and adjacent natural profiles were nearly the same. In another study, Kriebel (1987) reported that posthurricane field measurements on the “ Florida west coast indicated that the “... volume of sand lost due to scour at the seawall was approximately equal to the volume eroded on the adjacent beach without a seawall” . 210. Dean (1986) presented logical arguments founded on the principle of sediment conservation in discussing the potential effects of coastal armoring on fronting and adjacent beaches. One of Dean’s proposed “approximate principles” for the 2-D case was that the local volumetric scour in front of a coastal structure should be equal to or less than the volume that would have eroded if the structure had not been in place. 84 211. Barnett (1987) conducted 2-D laboratory tests using a movable-bed model scaled according to the criteria given by Equation 6. Tests were conducted using regular waves and sand with a median grain size of 0.15 mm. Profile measurements were made at 1/3 spacings across the wave tank and then averaged to compensate for the observed cross-tank variations. Erosive test cases without a seawall were compared with similar tests with a seawall located at different positions on the ‘profile. Volumetric comparisons of the “final” profiles indicated that the eroded volume in front of the seawall was less than the corresponding erosion on the natural profile in 10 of the 11 comparisons. On average (as determined by linear regression), 61-percent less volumetric erosion occurred on the seawalled profiles. (Also see Barnett and Wang 1988). Impact of Seawall 212. The approximate principle that the amount of sediment denied the profile by the presence of a seawall is balanced by additional erosion in front of the seawall was tested in cases T10 and T11. The primary difference between these tests and previous tests conducted in the flume was the presence in the flume of a vertical seawall constructed of marine plywood. The seawall was positioned on the sloping revetment approximately at the intersection of the still-water line and revetment. The seawall was constructed such that it effectively prevented sediment behind it from eroding as the revetment became exposed due to wave action. The presence of the sloping concrete revetment and subsequent wave-induced exposure of the revetment make these tests somewhat unique in comparison with previous laboratory studies that examined seawall impacts. Regular Wave Comparisons 213. Profile development under regular wave conditions with and without the vertical seawall is compared in Figure 30 for three different stages of development. The complete set of comparisons is given in Figure E19 in Appendix E, and associated experiment documentation is presented in the appropriate appendices. In Figure 30, the solid-line profiles (test T10) represent the profile development with the vertical seawall in position, and the dashed-line profiles are from test T03 (no vertical seawall). After 80 waves, profile development between the two tests is quite similar because the vertical seawall had just become exposed during the last few waves, and its effect was negligible to this point. Note that the sloping revetment is still covered with sand at the 80-waves profile. Even after 370 waves had impacted the initial plane-sloping beach, little difference between the tests in the profile development seaward of the vertical seawall was observed. Gradually, however, differences between the two tests began to appear after 85 370 waves (see plots in Figure E19 in Appendix E). At 750 waves, the profile with the vertical seawall showed increased scouring of the surf zone and decreased height of the offshore bar feature. At the equilibrium condition (after 1,650 waves), quite distinct differences were observed between tests T03 and T10, although the time required to reach the equilibrium profile appeared to be very similar in both tests. 214. The 1,650-wave comparison in Figure 30 shows that the seawall promoted increased erosion of material from the surf zone and caused a decrease in the offshore bar height. The extra material eroded was used to satisfy the sediment demand in the region immediately seaward of the bar feature. The removal of sediment from the bar crest was probably due to a combination of increased breaking wave height as the incident wave interacted with the wave reflected off the vertical wall and offshore return flow patterns different from those generated in the absence of a vertical seawall. However, wave statistics presented in Tables B3 and B10 (Appendix B) indicated that measured waves and reflection coefficients at the nearshore gages were quite similar for both tests, suggesting that any increased reflection caused by the vertical wall was attenuated as the reflected wave returned through the surf zone. 215. Cross-tank variations in the profile occurred during test T10 as well as test T03. Figure 31 compares the final profiles at the glass sidewall (top), the center line (middle), and the concrete wall (bottom). The additional eroded area resulting from the seawall was calculated for all three profile comparisons; then an average was subsequently calculated to determine the eroded volume for comparison with the withheld volume. The withheld volume per unit width of the flume was about 1.54 ft?/ft; and the calculated average volume of additional erosion was 1.58 ft?/ft, resulting in the eroded volume being only 3 percent greater. Eroded volumes per unit width for the individual profile comparisons were 1.92 ft?/ft at the glass wall, 2.13 ft?/ft on the center line, and 0.68 ft?/ft at the concrete wall, resulting in the average of 1.58 ft?/ft. 216. The near equivalence between the additional eroded volume in front of the seawall to the volume retained behind the seawall conforms to the field observations of earlier investigators, and it also follows the conclusions given by Dean (1986); however, the present result is substantially different from the average of laboratory results presented by Barnett (1987). The difference between the two may well lie in the fact that this is a single test result, whereas Barnett examined 11 different cases. Further tests are needed to examine a wider variety of vertical seawall conditions. Irregular Wave Comparisons 217. The irregular wave comparison consisted of running the same irregular waves used in test T09, but with the seawall installed on the sloping revetment as described above. Thus, the only difference influencing profile development between cases T09 and T11 was the presence of the seawall. Figure 32 shows comparison plots between vertical seawall test T11 (solid line) and non-seawalled test T09 (dashed 86 80 Waves T10 - Solid 80 Waves T03 - Dashed 370 Waves T10 - Solid 370 Waves T03 - Dashed 1650 Waves T10 - Solid 1650 Waves T03 - Dashed 4 6 RANGE - (ff) Figure 30. Seawall impact under regular waves, T10 versus T03 87 Glass Wall T10 - Solid Glass Wall TO3 - Dashed Centerline T10 - Solid Centerline TO03 - Dashed Cone, WalliimiOe eS olmia Conc. Wall TO03 - Dashed 4 6 RANGE - (ft) Figure 31. Seawall impact cross-tank variation, T10 versus T03 88 line) after approximately 80, 370, and 1,650 waves. Figure E20 in Appendix E contains the complete set of comparisons. Wave analyses, profile soundings, and profile plots for test T11 are given in Appendices B, C, and JD, respectively. 218. The comparisons in Figure 32 were quite similar to the regular wave comparisons of T03 and T10. Initially, the profile development is very similar with little difference apparent between the two tests. Eventually, as the tests approached equilibrium, the seawall began to affect profile evolution with increased erosion in the surf zone region and removal of sediment across the crest and seaward slope of the slight bar feature as shown after 1,650 waves. Interestingly, there is a fairly uniform distribution of the additional erosion due to the vertical seawall, and the variety of waves in the irregular wave field helped to smooth the profile response. As in the regular wave case, no systematic differences in wave statistics or reflection coefficients were evident, and profile evolution also appeared to progress at similar rates. 219. As is typical in laboratory tests involving irregular waves, cross-tank variation in the profile was visually observed to be minor, although no sidewall profiles were obtained to document this observation for test T1l. The additional eroded area on the center-line profile seaward of the seawall was calculated to be 1.49 ft /ft compared with the measured withheld sediment quantity of 1.79 ft?/ft. Hence, the eroded volume for this case was about 83 percent of the withheld volume, a smaller percent than was obtained with regular waves, but still considerably higher than the average of 61 percent reported by Barnett (1987). Regular Versus Irregular Wave Effects 220. Test T11 with the vertical seawall in place represented the irregular wave counterpart of test T10 with H,,3 of the irregular wave train being nearly equal to the monochromatic wave height and the peak spectral period of the irregular waves equal to the period of the regular waves. Profile evolution for these two cases is compared in Figure 33 at 80, 370, and 1,650 waves. The complete set of comparisons is in Figure E21 in Appendix E. 221. Generally, the comparison is satisfactory throughout the profile development with the irregular wave condition (solid line) producing about 0.53 ft?/ft less surf zone erosion after 1,650 waves and exhibiting a smoother shape, as was expected. This result agrees with earlier comparisons between regular and irregular waves presented in Part VI and further supports the conclusion that the irregular wave parameter H/3 best represents the monochromatic wave height in the situation of profile development. 222. After the initial adjustment in the early stages of the experiment, time for profile evolution in the irregular case appeared to lag the regular wave profile development by a factor of approximately two. Figure 34 compares time-shifted profiles where the time for development in the irregular wave case is about twice as long as in the regular wave case. All time-shifted comparisons exhibit better correspondence than 89 80 Waves T11 - Solid 80 Waves TO9 - Dashed 370 Waves T11 - Solid 370 Waves TO9 - Dashed 1650 Waves T11 - Solid 1650 Waves TO9 - Dashed 4 6 RANGE - (ff) Figure 32. Seawall impact under irregular waves, T11 versus T09 90 80 Waves T11 - Solid 80 Waves T10 - Dashed 370 Waves T11 - Solid 370 Waves T10 - Dashed 1650 Waves T11 - Solid 1650 Waves T10 - Dashed 4 6 RANGE - (ff) Figure 33. Seawall irregular wave comparison, H1/3 equals Hmono 91 the no-time-lag comparisons in Figure 33. This was also previously noted in Part VI and demonstrated by Figure 29 for the comparisons with no vertical seawall. Vertical Seawall Summary and Conclusions 223. Modification of the basic testing arrangement in the 6-ft flume by addition of a vertical seawall provided the opportunity to examine Dean’s approzimate principle, which states that the volume of the additional scour in front of the seawall is approximately equal to the volume of sediment. denied to the profile by the seawall. Comparison of regular wave tests (with and without the vertical seawall) supported the approzimate principle, when averaged over the cross-tank profile variations, exhibiting a ratio of 1.03 for eroded volume over retained volume. Comparison tests using irregular waves were more uniform in the cross-tank dimension, but less erosion was observed, with a ratio of 0.83 for eroded over retained volume. Both results give ratios higher than that obtained by Barnett (1987); however, the present results represent only one condition, whereas Barnett’s results stem from 11 different test cases. 224. Comparison between vertical seawall tests using both irregular waves and regular waves support the earlier conclusion that the irregular wave height parameter H/3 provides best correspondence to the monochromatic wave height in terms of profile development. The regular wave period was represented by the peak spectral period. 225. Time for profile development under irregular wave action lagged the development caused by regular waves by a factor of approximately two. This also conforms to conclusions given earlier based on tests without a vertical seawall. 92 370 Waves T11 - Solid 170 Waves T10 - Dashed 750 Waves T11 - Solid 370 Waves T10 - Dashe 1450 Waves T11 - Soli d d 750 Waves 710 - Dashed 4 6 RANGE - (ft) Figure 34. Time-shifted seawall comparison with irregular waves, H,/3 equals H 93 mono PART VIII: SUMMARY OF RESULTS 226. Preceding sections of this report describe movable-bed physical model tests designed and conducted primarily to validate a selected set of scaling criteria for use in studying scour at and near coastal structures. A summary of the study results is presented below. Summary 227. A review of proposed movable-bed model scaling criteria applicable to turbulence-dominated regimes supported the criterion of maintaining the same value of the dimensionless sediment fall speed parameter between the model and the prototype situation. Two additional criteria for the selected guidance were that the model should be undistorted and hydrodynamics should be scaled according to the Froude scaling relationship. These criteria were adopted for testing and verification in this study. A similar sediment transport parameter suggested by Xie (1981) was examined and shown to be quite similar for turbulence-dominated situations. Applicability of the selected model scaling relationships was discussed, noting that most experience with this particular guidance was in 2-D situations. 228. Prototype-scale experiments conducted in the Grofer Wellenkanal served as the prototype to be reproduced at scale in CERC’s 6-ft wave flume. Tests using both regular and irregular wave trains were conducted at a prototype-to-model scale of 7.5:1, and the testing procedures were designed to duplicate those used in the GWK tests. 229. In the regular wave verification test where the sloping concrete revetment was exposed, a reasonable comparison between the model and the prototype profile evolution was obtained. However, the comparison improved when the model wave height was increased by about 10 percent over the original scaled value. An explanation for this discovery was given in terms of the difference in Xie’s parameter between prototype and model in the offshore region. Increasing the wave height resulted in closer agreement of Xie’s parameter between prototype and model, and sediment was moved farther offshore in the model. The resulting increased erosion of the inshore region adjacent to the exposed sloping revetment gave support to the concept that the offshore bar has a sediment storage capacity for a particular wave climate, and as long as this climate persists, the inshore region will continue to erode until this capacity is met. 230. Validation of the selected scaling criteria using irregular waves was considered highly successful. The model exhibited profile development that compared very well with the prototype profile development when the revetment was not exposed to wave action. In the irregular wave test, no increase in wave height was required as was done for the regular wave tests using the Xie parameter. Apparently, irregular wave 94 conditions extend the region of suspended sediment movement farther offshore due to variations in the location at which the waves break. 231. Experiment repeatability was shown to be well within acceptable limits, and overall, the attempts to validate the modeling guidance for the case of turbulence-induced scour of noncohesive sediment was judged by the authors to be successful. However, it was noted at present that this verification is encouraging only to the extent that prototype-scale wave tank tests can reproduce natural beach response without adverse laboratory effects. 232. Model tests in which wave parameters were slightly changed were conducted to assess the importance of the fall speed parameter on the profile response. Increasing the height of regular waves by 10 percent promoted additional offshore transport of sediment, as did decreasing the wave period by 10 percent. Similar profile development was seen when these slight variations in wave parameters resulted in the same value for the fall speed parameter, but this distortion of Froude-scaled hydrodynamics was not recommended for other than slight perturbations in the wave parameters. 233. Initial profile differences in the model experiments did not substantially affect the ultimate outcome of the experiments as the profile approached near-equilibrium; however, short-term differences were observed. It is possible that great differences in initial profile slopes could have an impact on final profile configuration, but no tests were conducted with radically different initial slopes. 234. Movable-bed tests in which the sloping revetment became exposed were conducted using irregular waves to determine which irregular wave parameter is best suited for use in comparing results from regular-wave tests. Best results at equilibrium were obtained when the significant wave height of the irregular waves was equivalent to the regular wave height, even though the irregular waves contained about 30 percent less total energy. Equivalent profile development took about twice as long under irregular waves, and a simple explanation is that the irregular wave train included accretive as well as erosive waves and it appeared that the larger waves were most responsible for profile development. 235. Placement of a vertical seawall on the sloping revetment effectively denied the profile of the sand shoreward of the seawall. Both regular and irregular wave tests were conducted to examine the 2-D impacts of this situation. The additional erosion observed in front of the seawall was approximately equal to the amount of sediment being held behind the seawall that otherwise would have eroded if the seawall were absent. For the irregular wave case, the additional eroded volume in front of the seawall was about 83 percent of the amount being withheld by the seawall. These findings are generally in agreement with results obtained by others. Comparisons between the irregular and regular wave tests with the seawall intact confirmed that making H/3 of the irregular waves equal to Hmono gives best correspondence between profile erosion tests. 95 Conclusions 236. Based on results obtained in this study, several important conclusions can be made about 2-D small-scale movable-bed physical modeling of coastal scour. a. Mid-scale test results support preservation of the dimensionless fall speed parameter in an undistorted Froude model as a viable method of scaling models intended to replicate wave erosion under turbulence-dominated situations. The guidance has been verified for 2-D cases, and must be further validated before it can be fully recommended for 3-D movable-bed model tests. b. For tests involving regular waves, model designers should consider augmenting the Froude-scaled experimental wave height to provide better prototype-to-model correspondence of the Xie parameter in the offshore region. This correspondence should be limited to the more active portions of the offshore and need not extend out to closure depth. c. Tests conducted using irregular waves do not require the augmentation described in (b) above. d. Small perturbations in the fall speed parameter between prototype and model can be tolerated without significant impact; however, this should be avoided if possible. e. Models in which temporal profile evolution results are important should begin with a reasonable approximation of the natural beach profile molded into the model. Accuracy in the offshore region is more important than surf zone detail. f. Comparable profile development can be achieved between regular and irregular wave models when the irregular significant wave height, H1/3, is equal to the regular wave height. Profile development will take between two and three times as long in the irregular wave model. g- Dean’s (1986) concept that the additional erosion experienced in front of a seawall is approximately equal to the amount of sediment behind the seawall that would erode in the seawall’s absence seems to hold for the 2-D situation investigated in the wave flume. 237. Further examination of these experimental results by others may reveal additional insights overlooked by the authors or inconsistencies in the conclusions stated above. Such scrutiny is desirable and encouraged by the authors in the spirit of scientific discovery. 96 REFERENCES Barnett, M. 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Thesis, Technical University of Braunschweig, Braunschweig, Federal Republic of Germany. Thompson, E. F., and Vincent, C. L. 1984. “Shallow Water Wave Height Parameters,” Journal of Waterway, Port, Coastal, and Ocean Engineering Division, Vol 110, No. 2, pp 293-299. . 1985. “Significant Wave Height for Shallow Water Design,” Journal of Waterway, Port, Coastal, and Ocean Engineering Division, Vol 111, No. 5, pp 828-842. Turner, K. A., and Durham, D. L. 1984. “Documentation of Wave Height and Tidal Analysis Programs for Automated Data Acquisition and Control Systems,” Miscellaneous Paper HL-84-2, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Uliczka, K., and Dette, H. 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Xie, S.-L. 1981. “Scouring Patterns in Front of Vertical Breakwaters and Their Influences on the Stability of the Foundations of the Breakwaters,” Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands. . 1985. “Scouring Patterns in Front of Vertical Breakwaters,” Acta Oceanologica Sinica, Vol 4, No. 1, pp 153-164. Yalin, M. S. 1971. Theory of Hydraulic Models, MacMillan Press, London, England. 101 m” fel es Haas Naw ‘hes APPENDIX A: DESCRIPTION OF WAVE ANALYSIS Data Acquisition and Analysis 1. Wave gages in the physical model were calibrated prior to collecting data. This was done by moving gage sensor rods through a series of vertical steps to obtain calibration coefficients from a least-squares linear or quadratic fit of the voltage versus submerged gage position. The US Army Engineer Waterways Experiment Station (WES) process IDCAL ensures that proper gage potentiometer coefficients are used, and it also generates descriptive information for documenting and archiving test output and data files. Wave data were collected in real-time, with a sampling rate of 20 Hz. Data acquisition and the wave board are driven by another WES process labeled SPLASH2. To assure smooth transition of the wave board between successive points, the command signal rate was set at 20 Hz. 2. Prior to data analysis, the calibration coefficients and header information created by the process IDCAL are combined with the water surface elevation data collected by process SPLASH2 and converted to engineering units for analysis by the WES process Time Series Analysis File (TSAF). Program TSAF is designed such that a user-defined process control file can be used to select which types of analysis to perform on the data. Among the analyses available in TSAF are single channel frequency analysis, multiple channel upcrossing analysis, multiple channel downcrossing analysis, and Goda analysis. The process control file contains information regarding how much of a particular data record to analyze, which channels are to be used in the data analysis, plotting instructions, whether or not to save certain values, and several other options. Hard copy output from TSAF can be in the form of printouts of parameters chosen, frequency plots, and strip charts as discussed below. Time Series Analysis File (TSAF) 3. The following description of the TSAF package is abstracted from Briggs’ and the TSAF package itself. Readers desiring more complete descriptions of the processes mentioned here should consult these references. In the TSAF code, the program reads and performs both time and frequency domain analysis on the collected water surface elevation data. In these analyses, the code assumes that the water surface 1 Briggs, M. J. 1988. “Unidirectional Spectral Wave Generation and Analysis in Wave Basins,” Volume I, Technical Report CERC-88-11, US Army Engineer Waterways Experiment Station, Vicksburg, MS Al elevation time series are discrete, real-valued sequences with equal time intervals of t = nAt with At the data collection interval. The total length of a time series is given by T = NAt where N is the total number of data points. The TSAF code consists of 11 processes that may or not be used during the data analysis sequence. These processes are concerned with either time domain or frequency domain analyses and are listed in Table Al. Table Al. Analysis Options Strip charts of raw data* Single channel frequency response* Zero upcrossing* Frequency response between 2 channels Zero downcrossing* Cross spectral density Crest height Goda reflection analysis* Trough height Coherence function Auto- and cross-correlation *Denotes those used in present study. 4. The strip chart option simply plots the raw time series data for one or more of the available gages. The time series plots are scaled to facilitate/enhance readability and presentability. An example of a strip chart plot of a typical raw water elevation time record recorded during an irregular wave test is presented at Figure Al. Examples of the output from the TSAF analysis program are presented at Figures A2—A4. The tables in Appendix B are derived from such output. 5. For the up and downcrossing analyses, the program calculates statistics of wave elevation, wave height, and period for the datum selected. This datum is typically the mean, but can be externally imposed. For the surface elevation, the mean, root mean square, standard deviation, minimum, and maximum values are calculated. Wave heights and periods corresponding to the difference between the minimum and maximum values between consecutive up or downcrossings are calculated (Figure A2). Averages of these values for each three-gage array are also computed (Figure A4). Also, the total number of waves (zero up or downcrossings) and maximum wave height are provided. Wave heights for each gage are saved for later plotting and use with other processes. If desired, cumulative probabilities and Wiebull distributions can be fitted and plotted. 6. Spectral densities are calculated for each of the individual gages after detrending and windowing the time series (Figure A3). Detrending options include removing the mean or a linear or second-order trend. Window options include 10- to 50-percent cosine bell or cubic polynomial. The data are Fourier transformed, band averaged between lower and upper cutoff frequencies, and plotted. Measured spectral estimates for each gage are then used in the calculation of frequency response estimates and reflection A2 1.0 7 0.8 0.6 0.4 0.2 Chan 6 (ft) -0.4 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. Time (sec) Figure Al. Irregular wave surface elevation time series FOCI IOI GOO IO III GIGI OIOIOCIIOIOIOCOCUIGIOCOIOOIOIIOIOOIIIOIOI IOI IOIOI I IE III IOI TOI IC RIK III I TK IKK KK * * * DOWNCROSSING ANALYSIS (PAGE 1) : * * 6 FT SCOUR TESTS, SPECTRAL, ST14WO5A ANALYSIS DATE 5-OCT-89 * * ANALYSIS TIME 1356 * * TIME STEP = 0.5000E-01 NUMBER OF TIME STEPS CONSIDERED = 3200 x * III IKK IOI II TICK I FOI I TIO TOK FOIE FOF KIO FOI TOK FOF KK I KOK KOFI TOI KOK TOK ICI FT KOK FTI TOK TOT I KT KOK IK IK OK KI KOK KK TOT ITO TOK KK II TK IKK IK IKK KK KKK KK KKK KKK KKK EK DATA CHANNEL = 1 CROSSING MODE = RECORD MEAN DATUM VALUE = -0.9802E-02 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.9802E-02 ETAMIN = -0.6102 T 1/3 = 2.092 H 1/3 = 0.6750 WEIBULL ALPHA = 1.762 ETARMS = 0.1817 ETAMAX = 0.5708 TBAR = 1.869 HBAR = 0.4531 WEIBULL BETA = 0.5812 ETASD = 0.1818 RHOHH = 0.4561 RHOHT = 0.5770 HMAX = 1.168 NUMBER OF WAVES = 84 FOI IO II III IOC OOOO OOOO III OO III IOI TOI IOI IO TOI IORI TOK IO III IT IOI TOK IKK IK IK IK DATA CHANNEL = 2 CROSSING MODE = RECORD- MEAN DATUM VALUE = -0.1347E-01 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.1347E-01 ETAMIN = -0.6015 T 1/3 = 2.101 H 1/3 = 0.6888 WEIBULL ALPHA = 2.213 ETARMS = 0.1848 ETAMAX = 0.6915 TBAR = 1.909 HBAR = 0.4678 WEIBULL BETA = 0.4916 ETASD = 0.1848 RHOHH = 0.4665 RHOHT = 0.4796 HMAX = 1.293 NUMBER OF WAVES = 83 FOI III CII OOOO IOI III TOO IO OOOO IO IOI IOI TO IO IOI IOI IOI TOT III IIR IO ATK RIK RR IK IK DATA CHANNEL = 3 CROSSING MODE = RECORD MEAN DATUM VALUE = -0.1312E-01 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.1312E-01 ETAMIN = -0.5239 T 1/3 = 2.105 H 1/3 = 0.6986 WEIBULL ALPHA = 2.112 ETARMS = 0.1836 ETAMAX = 0.6761 TBAR = 1.909 HBAR = 0.4655 WEIBULL BETA = 0.5092 ETASD = 0.1836 RHOHH = 0.3986 RHOHT = 0.4652 HMAX = 1.200 NUMBER OF WAVES = 83 FOI III IOI ICICI OOOO II IO OOOO III IOI IOI OO IO IOI TOTO IO IOI IO IO IOI OIC IOI TOK IK DATA CHANNEL = 4 CROSSING MODE = RECORD MEAN DATUM VALUE = -0.1542E-01 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.1542E-01 ETAMIN = -0.3566 T 1/3 = 2.048 H 1/3 = 0.6456 WEIBULL ALPHA = 2.181 ETARMS = 0.1642 ETAMAX = 0.6994 TBAR = abot ieht HBAR = 0.4191 WEIBULL BETA = 0.4931 ETASD = 0.1642 RHOHH = 0.4944 RHOHT = 0.3515 HMAX = 0.9490 NUMBER OF WAVES = 81 FOI III ICICI IO IOI COI IOI OTTO OIC III IO IO OO IO IO TOO IOI IO IIIT IIR IKK TOK ICICI IK DATA CHANNEL = 5 CROSSING MODE = RECORD MEAN DATUM VALUE = -0.1591E-01 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.1591E-01 ETAMIN = -0.3691 T 1/3 = 2.048 H 1/3 = 0.6361 WEIBULL ALPHA = 2.122 ETARMS = 0.1645 ETAMAX = 0.6439 TBAR = 1.907 HBAR = 0.4147 WEIBULL BETA = 0.4923 ETASD = 0.1645 RHOHH = 0.4536 RHOHT = 0.3731 HMAX = 0.9250 NUMBER OF WAVES = 82 FOI III OGIO IO III OO OI IOC III III IOI OI III TOI II IO TOIT RII IO I DATA CHANNEL = 6 CROSSING MODE = RECORD MEAN DATUM VALUE = -0.1590E-01 PLOTTED RESULTS? NO PLOT MODE = 0 ETABAR = -0.1590E-01 ETAMIN = -0.4021 T 1/3 = 2.150 H 1/3 = 0.6674 WEIBULL ALPHA = TLS) ETARMS = 0.1695 ETAMAX = 0.6499 TBAR = 11955) HBAR = 0.4221 WEIBULL BETA = 0.5704 ETASD = 0.1695 RHOHH = 0.3991 RHOHT = 0.3108 HMAX = 0.9410 NUMBER OF WAVES = 80 FOCI IOI OIC ICICI CTO OGIO OCI OOOO OOO OOOO IOI OOOO OO IORI IORI OIC IORI ICICI TIC I Figure A2. Example of single channel downcrossing analysis A3 FOI I ITOK IOI TOK IOI I IOI ICI TOI I IOI TOK FIO IOI IK IIA II IOI IOI TOK III III I II IRD I III II IIA III III III IK III IASI III IIIS II IIASISICSISIAICSICIICI SII SISISICSACICACIC DAH SINGLE CHANNEL FREQUENCY DOMAIN ANALYSIS (PAGE 2) * * * * * x x, 6 FT SCOUR TESTS, SPECTRAL, ST14W05A ANALYSIS DATE 5-OCT-89 3 o ANALYSIS TIME 1356 “S * * « * FIFI IOI III IOI IIIT ICICI OK I IOI IOI III IOI TI I SOI I IK II IK III II III III I TIF III III III II IOI KIC II IK IK AISI IK III III ASIA ISI III SI SI II IASI AISI SISISDSISICSICSACAC IS: DATA CHANNEL 4 TIME STEP = 0.5000E-01 NUMBER OF TIME STEPS = 3200 BANDS AVERAGED = 10 PLOTTED RESULTS? YES DETREND MODE = 1 (MEAN REMOVED) WINDOW MODE = 1 (COSINE SQUARED) 10% OF RECORD TAPERED AT EACH END DETREND FUNCTION = (-0.1542E-01) + ( 0.0000E+00)*T + ( 0.0000E+00) * (T**2) FREQUENCY LIMITS 0.2000 TO 10.00 SPECTRAL PARAMETERS FPC = 0.4500 EMO = 0.2587E-01 FPS = 0.4500 TPC = 2.222 EM1 = 0.1387E-01 TPS = 2.222 HMO = 0.6434 EM2 = 0.8437E-02 FPD = 0.4500 QPG = 3.200 T02 = 1.751 TPD = 2.222 FRI IORI OI IOI IOI SII III TID IS II IK SII SI IOI I IIIS IISA ISSO I IIIS III IIA III IIIS I IK III IK II III III III II IAI III IIIS III IIIS AIS IIIA DATA CHANNEL 5 TIME STEP = 0.5000E-01 NUMBER OF TIME STEPS = 3200 BANDS AVERAGED = 10 PLOTTED RESULTS? YES DETREND MODE = 1 (MEAN REMOVED) WINDOW MODE = 1 (COSINE SQUARED) 10% OF RECORD TAPERED AT EACH END DETREND FUNCTION = (-0.1591E-01) + ( 0.0000E+00)*T + ( 0.0000E+00) * (T**2) FREQUENCY LIMITS 0.2000 TO 10.00 SPECTRAL PARAMETERS FPC = 0.4375 EMO = 0.2594E-01 FPS = 0.4500 TPC = 2.286 EM1 = 0.1389B-01 TPS = 2.222 HMO = 0.6443 EM2 = 0.8437E-02 FPD = 0.4500 QPG = 3.036 T02 = 1.754 TPD = 2.222 eK II IK IKI I IK KIKI IK FI IOI KI IK FI IOI TOI TOK KOFI KOI KK FIT KK FICK TOK KE TOK KKK ITT KITE KK TIT HIF KK HIT KKK TK IKK IAI KKH IAA KAKA KKK KK KKK KK KK KKK DATA CHANNEL 6 TIME STEP = 0.5000E-01 NUMBER OF TIME STEPS = 3200 BANDS AVERAGED = 10 | PLOTTED RESULTS? YES DETREND MODE = 1 (MEAN REMOVED) WINDOW MODE = 1 (COSINE SQUARED) 10% OF RECORD TAPERED AT EACH END DETREND FUNCTION = (-0.1590E-01) + ( 0.0000E+00)*T + ( 0.0000E+00) * (T**2) FREQUENCY LIMITS 0.2000 TO 10.00 SPECTRAL PARAMETERS EPC = 0.4375 EMO = 0.2798E-01 FPS = 0.4125 TPC = 2.286 EM1 = 0.1467E-01 TPS = 2.424 HMO = 0.6691 EM2 = 0.8697E-02 FPD = 0.4219 QPG = 333 T02 = 1.794 TPD = 2.370 FRI C OCI ICIUIOOIOIIOOCIOIIUIOICIIIOIIGOIIOIOOIIOIO IOIOIOIUIIOIIOI II OICIOCSOITOCTOIOAI TOI IIASA TIS TID ADD ADI IO AIDA ITI A IK Figure A3. Example of single channel frequency domain analysis (nearshore array) coefficients. The Coastal Engineering Research Center (CERC)/GODA three probe analysis for surface wave incidence and reflection is used to separate incident waves from reflected waves and calculate the reflection coefficient (Figure A4). Remarks About Wave Analysis Results 7. The experiments described in this report attempted to follow the wave-generating procedures used in the large-scale tests conducted in the GroSer Wellenkanal (GWK) in Germany. In the regular wave tests, this involved running wave bursts of up to 80 waves. Calibration before testing commenced indicated that this condition would keep the reflected wave components less than 20 percent, just as was done in the GWK tests. Examination of reflection coefficients calculated from data measured at the gage array closest to the wave board (Appendix B) reveals that this condition was reasonably met. 8. However, wave nonlinearities at the nearshore gage, combined with reflection from the profile (and sometimes the exposed revetment) acted to transform the nearshore wave field into a less than ideal set of regular waves. This is illustrated by Figure A5, which presents a typical wave times series from a A4 FOI III IOI IO IOI I IO IOI IO III IO IOI II IOI IO I IO IOI IO I IO I IORI ITO I IOI ITI IOI I TOI TIO I III III III II III III IIA IDA AI AAA AIK * * * CERC UNIDIRECTIONAL SPECTRAL INCIDENCE/REFLECTION ANALYSIS * * * * 6 FT SCOUR TESTS, SPECTRAL, ST14WO5A ANALYSIS DATE 5-OCT-89 * * ANALYSIS TIME 1356 * * OFFSHORE PROBE = DATA CHANNEL 4 CENTER PROBE = DATA CHANNEL 5 NEARSHORE PROBE = DATA CHANNEL 6 * * * * DX12 = 1.000 WATER DEPTH = 2.200 DETREND MODE = 1 (MEAN REMOVED) PLOTTED RESULTS? YES * * DX13 = 3.000 GRAVITY =i 2820 WINDOW MODE = 1 (COSINE SQUARED) 10% OF RECORD TAPERED AT EACH END * * TIME STEP = 0.5000E-01 NUMBER OF TIME STEPS ANALYZED = - 3200 * * * OPI IORI TO RIOT II IOI OIRO IOI IORI TORO TORII RTO IORI OOOO III TOIT IOI OK TOT OI TOK IO IIT ITOK TOK tO KK ka a Ik MEAN UPCROSSING ANALYSIS RESULTS (AVERAGES OF RESULTS FROM THREE PROBES) : ETABAR = -0.1574E-01 ETAMAX = 0.6644 H 1/3 = 0.6492 WEIBULL ALPHA = 1.989 ETARMS = 0.1660 ETAMIN = -0.3759 Tela 2.128 WEIBULL BETA = 0.5219 ETASD = 0.1661 HBAR = 0.4181 RHOHH = 0.5083 HMAX = 0.9430 TBAR = 1.938 RHOHT = 0.3374 MEAN DOWNCROSSING ANALYSIS RESULTS (AVERAGES OF RESULTS FROM THREE PROBES) : ETABAR = -0.1574E-01 ETAMAX = 0.6644 H 1/3 = 0.6497 WEIBULL ALPHA = 2.006 ETARMS = 0.1660 ETAMIN = -0.3759 T 1/3 = 2.082 WEIBULL BETA = 0.5186 ETASD = 0.1661 HBAR = 0.4186 RHOHH = 0.4490 HMAX = 0.9383 TBAR = 1.931 RHOHT = 0.3451 DETRENDING RESULTS: PROBE A B Cc FREQUENCY RANGE OVER WHICH SPECTRAL PARAMETERS ARE DETERMINED: (VALUES DEPEND ON OFFSHORE -0.1542E-01 0.0000E+00 0.0000E+00 DETREND MODE IM- CENTER -0.1591E-01 0.0000E+00 0.0000E+00 LOW FREQUENCY LIMIT = 0.2000 POSED) NEARSHORE -0.1590E-01 0.0000E+00 0.0000E+00 HIGH FREQUENCY LIMIT = 5.000 PARAMETERS OF INCIDENT SPECTRUM: FPC = 0.4375 EMO = 0.2773E-01 FPS = 0.4500 TPC = 2.286 EM1 = 0.1444E-01 TPS = 2.222 HMO = 0.6661 EM2 = 0.8291E-02 FPD = 0.4344 QPG = 3.422 T02 = 1.829 TPD = 2.302 PARAMETERS OF REFLECTED SPECTRUM: FRC = 0.4375 EMO = 0.2014E-02 FPS = 0.4125 TPC = 2.286 EM1 = 0.1202E-02 TPS = 2.424 HMO = 0.1795 EM2 = 0.9067E-03 FeRD = 0.4125 QPG = 2.908 T02 = 1.490 TPD = 2.424 MEAN REFLECTION COEFFICIENT = 0.2695 FIR OI OO C CIO OIC OIG IOI IO I IOI Ik Figure A4. Example of three-gage average values and reflection analysis (nearshore array) monochromatic test. The upper record was obtained at the offshore array, while the lower record was measured at the nearshore array. The nonuniformity in the regular wave field did not impact the outcome of the experiments because it can be assumed that similar effects occurred in the large-scale experiments. 9. This nonuniformity in regular waves can, however, impact the results from the wave analysis program. Usually, a portion of the record containing between 30 to 50 waves was selected for analysis. Depending upon which section of record was analyzed, it was possible to obtain values for the statistical wave height parameters that showed considerable variation. For the most part, the same region of record was analyzed, but this was not always the case, and variations between nearshore averages seen in the Appendix B results can usually be attributed to this cause. 10. Variations in nearshore wave statistics between experiments that are claimed to have identical wave input may give the impression that the experiments were not the same, but the important point to remember is that these cases all had the same input wave board signal. Examination of the offshore wave statistics between experiments gives a better indication of the similarity of regular wave input. 11. The authors advise anyone who may use these experimental profile evolution results to validate numerical models that it would be better to drive the numerical model with the measured offshore wave Ad ; : EY SUC 60. 70. 80. Time (sec) Le * SARAH plot) values rather than those values reported for the nearshore wave gage array. 12. Irregular wave analyses seemed to provide more stable statistical values between analyzed bursts. Figure A6 shows a typical wave record at the offshore array (upper plot) and the nearshore array (lower plot). However, reflection and nonlinear waves also influence the statistical results; and that combined with the relatively small number of waves analyzed probably explains the variations observed in the Appendix B tables for irregular wave experiments. Chan 3 (ft) 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. Time (sec) Chan 5 (ft) Figure A6. Typical irregular wave measurement at offshore array (upper plot) and nearshore array (lower plot) AT APPENDIX B: WAVE ANALYSIS RESULTS FOR EXPERIMENTS 1. This appendix contains analyzed results for the time series of water surfaces elevations collected by the gage arrays at the two locations in the wave flume during the experimental test series. Each documented experiment has a table of values for the offshore gage array and the nearshore gage array. All wave parameter values in each table represent the average of the three gages comprising the array. 2. Each wave data collection is denoted by a unique filename. The first two characters are the same for all files; the third and fourth characters represent the experiment number (e.g., T03); the fifth character is the same for all; the seventh and eighth characters correspond to a series of wave bursts between profiling stops; and the final character is the burst sequence within the wave series. For example, STO1WO5A was the first set of waves run after a profiling stop, and STOLWO5E was the final set, so five bursts of waves were run between profiling stops. 3. For all tables except Table B14, the column "Total Waves" is the approximate cumulative total of waves run in the wave flume. The corresponding column on Table B14 is labeled "Number Waves," and it gives the total analyzed number of irregular waves for each burst of waves. 4. The parameters listed on the tables are defined as below: H,. - Energy-based significant wave height found as four times the standard deviation of sea surface elevations. Hpar - Average wave height as determined from zero down-crossing method. H,,;3 - Significant wave height obtained as the average of the highest 1/3 waves determined from zero down-crossing method. Hnax - Highest wave determined from zero down-crossing method. TpC - Wave period associated with the spectral peak. Tyar - Average wave period determined from zero down-crossing method. T,;3 - Average wave period associated with the highest 1/3 waves determined from zero down-crossing method. Reflection coefficients were determined from analysis of the three gage array. Bl Test TOL TO2 TO3 TO4 TO5 T06 TO7 TO08 TO9 T1O T1ll T12 DS T14 Description of Test Reproduction of prototype experiment using 10-m horizontal width berm Repeat of TOl1 to demonstrate repeatability Reproduction of prototype experiment using 1l-m horizontal width berm (same as prototype) Repeat of TO3 with wave height increased by 10 percent to examine impact of height variations Repeat of T03 using absorbing wave paddle Repeat of TO3 starting with the prototype profile at 40 waves molded in the flume Repeat of T0O3 with wave period decreased 10 percent to examine impact of period variations Repeat of T03 using irregular waves having Hj,,3 equal to 110 percent of monochromatic wave height Repeat of TO3 using irregular waves having H,/3 equal to the monochromatic wave height Repeat of TO3 using regular waves with a vertical seawall at the intersection of the revetment and still-water level Repeat of T10 using irregular waves with Hj,,3 equal to the monochromatic wave height Undocumented repeat test of T08 Aborted irregular wave test Reproduction of prototype irregular wave test B2 Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Number Bl B2 B3 B4 B5 B6 B7 B8 B9 B10 Bll B12 B13 B14 (peanut UOD) TpLsO) -cOGte, G6Lsc Volo | vir-08 92950 — SI9°0). 82850 9ST°C 679°0 60MTO.LS SSIe= = 90 80MTOLS 9L2°2 ~=90L*0 OLOMTOLS 9L¢-c- _V69-0 a ZOMTO.LS OL Gae 92930 WLOMTOLS peprzcosy eed ON CIOMTOLS CGE OLEI0) SEL10 I90MTO.LS [EEA GLO (40YEX0) H9OMTOLS EGE 2c [69s0) sbv970 SIOMTOLS 6257) VL9 10) v.90 AI0OMTOLS Sele 08940) 1679)40 A90MTOLS 6LT°2 6L9°O0 O¥v9°O C90MTOLS Sbce 96905 86920 O90MTOLS €€T°c LGL°O 9TL°O a90MTOLS €€T°c 6GL°O OTL°O W9OMTOLS €€T°? 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LLS (33) SEAM ou] §=TeIOL sureueTtd B29 Pie OF ea ; oe e poe aa ae iP , 2 i ' hy hae < : Wer fo te Pei f ge Vue te Be mt }) pie ake a pie aia i ey 7 My, APPENDIX C: TABLES OF EXPERIMENT PROFILES 1. This appendix contains profile range and elevation coordinates (model units) for all profiles recorded during the experimental test series. Elevation measurements are relative to still-water level in the wave tank. Profiles have been named using the following convention. The first three characters of the name denote the test number. The fourth character is typically "P" (meaning center line), but can be "G" (glass sidewall) or "C" (concrete sidewall). The rest of the name (two to four characters) represents the number of waves from the start of the test. For example, profile TO4P1450 is a center-line profile from test TO4 after 1,450 waves. Cl Test Description of Test Table Number TOL Reproduction of prototype experiment using Table Cl 10-m horizontal width berm TO2 Repeat of TO1 to demonstrate repeatability Table C2 T03 Reproduction of prototype experiment using Table C3 11-m horizontal width berm (same as prototype) TO4 Repeat of T03 with wave height increased by Table C4 10 percent to examine impact of height variations TO5 Repeat of T0O3 using absorbing wave paddle Table C5 TO06 Repeat of TO3 starting with the prototype Table C6 profile at 40 waves molded in the flume TO7 Repeat of TO3 with wave period decreased Table C/ 10 percent to examine impact of period variations TO8 Repeat of T03 using irregular waves having H,/3 Table C8 equal to 110 percent of monochromatic wave height TO9 Repeat of TO3 using irregular waves having Hj); Table C9 equal to the monochromatic wave height T1O Repeat of TO3 using regular waves with a Table C10 vertical seawall at the intersection of the revetment and still-water level Talli Repeat of T10 using irregular waves with Hj/3 Table Cll equal to the monochromatic wave height T12 Undocumented repeat test of T08 Table C12 TS Aborted irregular wave test Table C13 T14 Reproduction of prototype irregular wave test Table C14 C2 Table Cl Profile Survey Data, Test TO1l Profile TO1LSTART Profile TO1P40 Profile TO1P80 Profile TO1P170 Range Elev. Range Elev. Range Elev. OS. Do - te 0 -1.97 12.00 -1.93 13.00 -1.97 11.00 -1.54 -2.00 132.00 -2.01 14.00 -2.00 12.00 -1.78 -2.09 14.00 -2.04 15.00 -2.09 13.00 -1.93 -2.12 15200 -2.09 16.00 -2.12 14.00 -1.99 -2.17 16.00 a2) 163) 17.00 2197) 15.00 -2.05 =22 9 17.00 -2.17 18.00 -2.19 16.00 -2.10 18.00 -2.18 17 OO) -2.14 18.00 = yell] (Continued) (Sheet 1 of 3) C3 Table Cl (Continued) Profile T0O1P370 Profile TO1P/50 Profile TO1P1450 Profile TO1P1650 Elev. (Continued) (Sheet 2 of 3) C4 Table Cl (Concluded) Profile TO1P1850 Profile TO1P2050 Profile T01G1650 Profile T0O1C1650 Range Elev. Range Elev. Range Elev. (£t) (ft) (£t) (ft) (ft) (ft) Elev. (ft) 0.00 -0.26 =-3.70 0.82 -3.80 0.82 0.50 -0.39 -3.59 0.63 -3.73 0.67 1.00 -0.49 -2.00 0.24 -1.00 -0.01 eo) -0.60 -1.00 0.00 0.00 -0.26 2.00 -0.61 0.00 -0.27 0.80 -0.46 2.50 -0.63 0.90 -0.47 1.00 -0.48 3.00 -0.63 1.00 -0.48 1.50 -0.43 3500) -0.68 15.0 -0.43 2.00 -0.43 4.00 -0.78 2.00 -0.46 25,0 -0.50 4.50 -0.86 20) =) 3.00 -0.53 5.00 -0.84 3.00 -0.54 3050 -0.47 2) 4209) -0.83 350 -0.47 4.00 -0.44 6.00 =0.96 4.00 -0.44 4.50 =O0%52 6.50 -1518 4.50 -0.51 5.00 -0.66 7.00 = 1, S72 5.00 -0.64 >) 5 a\0) -0.82 Hs )0) -1.32 BY 5 210) -0.82 6.00 -0.91 8.00 Sua ksh 6.00 —OR 92 6.50 -0.86 850 -0.84 6.50 -0.87 7.00 -0.74 9.00 -0.74 7.00 =O. 71 150 -0.63 9.50 -0.77 7.50 -0.62 8.00 0859 00 -0.81 8.00 -0.59 8.50 -0).63 50 -0.84 8.50 -0.62 9.00 -0.68 00 -0.89 9.00 -0.69 10.00 -0.82 00 -1.07 9.50 -0.74 11.00 -1.00 00 = 167 10.00 -0.83 12.00 StS )2 00 = 9/2. 11.00 -1.00 13.00 -1.74 00 al, 8) 12.00 SAS 2 14.00 -1.88 00 -2.02 13.00 oll. 75) 15.00 SIL OY 00 -1.99 14.00 -1.89 16.00 -2.01 00 Big EP 150.0 ll, 5 ES) 17.00 -2.07 16.00 -2.03 18.00 Sete? 17.00 =21:07 18.00 -2. (Sheet 3 of 3) c5 Table C2 Profile Survey Data, Test TO2 TO2P170 Profile TO2START Profile TO2P40 Profile TO2P80 Profile Range Elev Range Elev Range Elev (ft) (ft) (ft) (ft) (ft) (ft) -5)..00 0.90 -3.00 ORO -3.00 OOH -4.00 0.90 -2.00 On92 -2.00 0.92 -3.00 0.90 -1.00 0.90 -1.00 0.90 -2.00 OR Sil! -0.60 0.87 -0.60 0.83 -1.00 0.90 0.00 0.63 -0.30 0.15 0.00 0.72 0.30 0.02 0.00 0.08 0 1.00 0.51 0.80 -0.06 0.50 -0.04 0 f 2.00 0.28 1.00 =02 10 1.00 -0.13 1.00 -0.17 3.00 0.03 2.00 -0.23 2.00 -0.29 2.00 -0.28 4.00 -0.13 3.00 -0.35 3.00 -0.40 2.50 -0..32 5.00 -0.50 4.00 -0.45 35,0 -0.41 3.00 =0).39 6.00 -0.72 5.00 -0.54 4.00 -0.48 3550 -0.44 7.00 -0.93 5.50 -0.56 4.80 -0.67 4.00 -0.46 7.87 lu adeS) 6.00 -0.61 5.00 -0.65 4.50 =(0)55)// 8.00 ma elk 6.50 -0.68 5 30) -0.59 5.00 -0.76 9.00 ob 29) 7.00 -0.78 6.00 -0.59 D0 -0.80 10.00 -1.64 7.50 -0.90 6.50 -0.64 6.00 -0.70 11.00 -1.85 8.00 -1.04 7.00 -0.72 6.50 -0.62 12.00 -2.03 8.50 Sls IL 7/ 73,0) -0.80 7.00 -0.63 13.00 = 278 9.00 -1.27 8.00 -0.90 Ug 20) -0.67 10.00 -1.46 8.50 =0599 8.00 -0.74 11.00 -1.64 9.00 -1.14 8.50 -0.82 12.00 -1.83 10.00 -1.40 9.00 -0.94 13.00 -2.01 11.00 -1.61 10.00 -1.26 14.00 -2.08 12.00 -1.80 10.50 39 15.00 <2 163, 13.00 -2.01 11.00 -1.53 16.00 = 2116 14.00 -2.08 12.00 = 276 17.00 -2.118 15.00 -2.13 13.00 = OY 18.00 -2.19 16.00 =o ALD) 14.00 -2.08 17.00 -2.18 15.00 ele 18.00 7) cL) 16.00 =-2.14 17.00 oie dk7) 18.00 32 oily) (Continued) (Sheet 1 of 3) C6 Table C2 (Continued) Profile T0O2P370 Profile T0O2P750 Profile T0O2P1450 Profile TO2P1650 Range Elev. Range Elev. Range Elev. (ft) (ft) (ft) (ft) (ft) (ft) -3.50 0.89 -3.60 0.86 0.00 -0.27 -2.90 0.90 -3.40 0.58 0.50 SQ), 37/ -2.80 0.45 -3.00 0.50 1.00 -0.43 -2.00 0.23 -2.00 0.25 15,0 -0.44 -1.00 -0.02 -1.00 -0.01 2.00 -0.45 0.00 -0.23 0.00 -0.25 2.50 -0.42 0.50 -0.26 0.50 -0.36 3.00 -0.53 1.00 -0.28 1.00 -0.41 3.50 -0.59 1.50 -0.30 1.50 -0.42 4.00 -0.56 2.00 -0.32 2.00 -0.40 4.50 -0.52 250) -0.36 2.50 -0.42 5.00 -0.54 31100 -0.45 3.00 -0.47 50 -0.58 3/90 -0.54 3.50 -0.57 6.00 -0.76 4.00 -0.58 4.00 -0.57 6.50 -0.92 4.50 -0.57 4.50 -0.53 7.00 -0.89 5.00 -0.58 5.00 -0.54 750 -0.74 550) -0.66 5.50 -0.58 8.00 -0.59 6.00 -0.87 6.00 -0.75 8.50 -0.60 6.50 -0.93 6.50 -0.91 9.00 -0.67 7.00 -0.84 7.00 -0.88 9.50 -0.74 7.50 -0.67 U5 D0) -0.72 10.00 -0.80 8.00 -0.62 8.00 -0.61 11.00 -0.93 8.50 -0.64 8.50 -0.61 a 50) -1.04 9.00 -0.72 900) -0.67 12.00 aks 27 10.00 -0.85 10.00 -0.80 WD .5\0) -1.53 10.50 -0.91 11.00 -0.96 13.00 -1.79 11.00 -1.01 12.00 -1.29 14.00 -1.97 12.00 -1.45 13.00 -1.84 15.00 -2.01 13.00 -1.88 14.00 -1.96 16.00 -2.06 14.00 -1.97 15.00 -2.00 17.00 -2.10 15.00 -2.04 16.00 -2.05 18.00 a7) alls} 16.00 -2.09 15/00) -2.09 17.00 -2.12 18.00 = 23 18.00 -2.14 (Continued) (Sheet 2 of 3) C7 Table C2 (Concluded) Profile T02G1650 Profile T02C1650 Range Elev. Range (ft) (ft) (ft) ODO WMWONNAAUNUUNFHFWWNNFF OO 0. an. Ie Die De By Br 4, 4. Di. 26 6. 6. is Ws 8. 8. OF Be 10. ub eo Wh Pree aNu allen oo NI (Sheet 3 of 3) c8 Table C3 Profile Survey Data, Test TO3 Profile TO3START Profile TO3P40 Profile TO3P80 Profile TO3P1/70 (Continued) (Sheet 1 of 3) C9 Table C3 (Continued) Profile T03P3/70 Profile T0O3P/50 Profile TO3P1450 Profile T0O3P1650 Range Elev. Range Elev. Range Elev. Range Elev. (ft) (ft) (ft) (ft) (ft) (ft) (ft) (ft) .00 0.94 -3.00 0.94 -3.50 0.95 -3.30 .00 0.92 -2.70 0.92 -3.20 0.91 -3.10 80 0.30 -2.50 0.35 -2.90 0.46 -2.00 50 0.22 -2.00 0.24 -2.00 0.24 -1.00 00 0.12 -1.50 (0) 2 -1.00 -0.01 0.00 00 -0.09 -1.00 0.04 -0.50 -0.13 0.50 50 -0.17 -0.50 -0.07 0.00 = 0/23 1.00 00 -0.21 0.00 “07 16 0.50 =0),25 10) 50 -0.25 0.50 -0.20 1.00 -0.32 2.00 00 -0.29 1.00 -0.24 1.50 -0.33 2.50 50 -0.36 1.50 -0.25 2.00 -0.32 3.00 00 -0.40 2.00 -0.29 2.50 -0.35 3g) 50 -0.44 2.50 -0.32 3.00 -0.38 4.00 00 -0.46 3.00 -0.36 3550) -0.43 4.50 50 -0.49 350 -0.43 4.00 -0.50 5.00 00 -0.53 4.00 -0.49 4.50 -0.52 Deo 0) 50 -0.65 4.50 -0.53 5.00 =0.51 6.00 00 -0.85 5.00 -0.50 5) 320) -0.51 6.50 50 -0.88 5.50 -0.56 6.00 -0.61 7.00 00 -0.78 6.00 -0.74 6.50 -0.76 Toa) 50 -0.62 6.50 -0.89 7.00 -0.84 8.00 00 -0.61 7.00 -0.83 750 -0.77 8.50 50 -0.65 7.50 -0.67 8.00 -0.64 9.00 00 -0.71 8.00 -0.60 8.50 -0.59 5 0) 00 -0.86 8.50 -0.62 9.00 -0.62 10.00 00 -1.10 9.00 -0.66 9.50 -0.68 10.50 00 -1.54 sa) -0.72 10.00 -0.75 11.00 00 -1.86 10.00 -0.79 10.50 -0.81 12.00 00 =o, 11.00 -0.94 11.00 -0.89 1310.0 00 -2.04 12.00 -1.38 12.00 -1.18 14.00 00 -2.07 13.00 -1.83 13.00 -1.68 15.00 00 =Dynelled 14.00 -1.93 14.00 -1.93 16.00 00 -2.15 15.00 -1.98 15.00 =n 5) 17.00 16.00 -2.04 16.00 -2.03 18.00 17.00 -2.09 17.00 -2.05 18.00 = Aq ILS) 18.00 -2.10 (Continued) (Sheet 2 of 3) C10 Table C3 (Concluded) Profile T03G1650 Profile T03C1650 Profile T0O3P1850 Range Elev. (ft) -0. -0. -0. -0. -0. -0. -0. -0. -0. OF 0. ‘lie Ale oe 2 3. 3): 4. 4. Dis ae 6. Oe Ties Ts 8. 8. OF Ne (Sheet 3 of 3) cll Table C4 Profile Survey Data, Test TO4 Profile TO4START Profile TO4P40 Profile TO4P80 Profile TO4P1/70 Range Elev. (Continued) (Sheet 1 of 3) C12 Table C4 (Continued) Profile TO4P370 Profile TO4P750 Profile TO4P1450 Profile TO4P1650 Range Elev. 5 Range Elev. (izle) GE) -3. -3. ooh 0. 0. i Iie 2 Lee 3h oh6 4. 4. Se 5)6 6. 6. Tee Te 8) 8. oF OF (Continued) (Sheet 2 of 3) C13 Table C4 (Concluded) Profile T04G1650 Profile TO4C1650 Profile 7041850| Elev. Range Elev. Range Elev. (ft) (ft) (ft) (ft) (ft) -0.26 0.00 -0.26 -3.90 0.91 -0.50 1.00 -0.51 -3.80 0.69 -0.51 150 -0.61 0.00 -0.26 -0.49 2.00 -0.61 1.00 -0.45 -0.52 2.50 -0.59 50 -0.46 -0.59 3.00 -0.62 2.00 -0.46 -0.68 3750 -0.70 250 -0.43 -0.69 4.00 -0.80 3.00 -0.50 -0.63 4.50 -0.88 SeD0 -0.56 -0.62 5.00 -0.88 4.00 -0.57 -0.66 Da) -0.86 4.50 -0.52 -0.85 6.00 -0.87 5.00 -0.52 -1.02 6.50 -1.03 5.50 -0.56 -1.06 7.00 -1.26 6.00 -0.67 -0.93 T3530 -1.42 6.50 -0.89 -0.78 8.00 -1.43 7.00 -1.00 -0.70 8.50 ell 2y ToDo Sil @il -0.69 9.00 -1.00 8.00 -0.88 -0.71 950 =0..81 8.50 -0.73 -0.82 10.00 -0.80 9.00 -0.65 -0.82 10.50 -0.83 950 -0.66 -0.92 11.00 -0.88 10.00 -0.71 -0.97 ile) -0.93 11.00 -0.82 -1.04 12.00 -0.99 12.00 -0.95 =35 13.00 -1.19 13.00 -1.16 -1.76 14.00 =D) 13550 -1.36 -1.91 15.00 =1 293 14.00 -1.67 eke) 16.00 ibn es) 15.00 =19.0 -2.02 IZ! SO”) -2.04 16.00 =o o2 -2.09 18.00 -2.10 17.00 -1.98 18.00 -2.06 (Sheet 3 of 3) C14 Table C5 Profile Survey Data, Test TO5 Profiles) TOSP17.0 Profile TOSSTART Profile TO5P40 Profile TO5P80 Elev Range Elev (ft) (ft) (ft) -5.00 Ono -3.00 0.96 -3.00 0895 -4.00 ORO, -2.00 ORS Ae) 0.88 -3.00 0.96 -1.00 0.81 Sil eo) Ont -2.00 ORS -0.80 0.82 0.00 -0.16 -1.00 0.83 -0.70 0.08 0.50 -0.23 0.00 ORM 0.00 -0.06 1.00 -0.31 1.00 0.69 0.50 -0.16 150) -0.37 2.00 0.45 1.00 -0.22 2.00 -0.40 3.00 0.21 0, -0.30 7) 50) -0.42 4.00 -0.05 2.00 -0.38 3.00 -0.47 5.00 -0.39 250) -0.51 390) -0.57 6.00 -0.62 3.00 -0.61 4.00 -0.67 7.00 -0.77 3.50 -0.63 4.50 -0.69 7.87 as es 0) 4.00 -0.62 5.00 -0.62 8.00 -1.15 4.50 -0.62 3/50 -0.60 9.00 -1.40 5.00 -0.64 6.00 -0.62 10.00 -1.65 5), 50) -0.66 6.50 -0.66 11.00 -1.87 6.00 -0.67 7.00 -0.72 12.00 -2.02 6.50 =0), 73 Uo) -0.80 13.00 -2.12 7.00 -0.80 8.00 -0.91 14.00 -2.20 7.50 -0.90 8.50 -1.04 8 .00 -1.01 9.00 -1.18 8.50 -1.14 D5 0) =Na3 2 9.00 -1.24 10.00 -1.43 10.00 -1.47 11.00 dle 3)// 11.00 -1.60 12.00 -1.65 12.00 -1.67 13.00 -1.70 13100 =u /all 14.00 ales) 14.00 -1.74 15.00 -1.81 14.00 alba e2. 15.00 -1.81 16.00 -1.85 15.00 ells Hs} 16.00 -1.86 17.00 -1.89 16.00 -1.84 17.00 -1.89 18.00 Sil ey) 17.00 -1.87 18.00 -1.94 18.00 -1.96 (Continued) (Sheet 1 of 2) C15 Table C5 (Concluded) Profile T05P3/0 Profile TO5P750 Profile TO5P1450 Profile TO5P1650 Range Elev. Range Elev. Range (ft) (£t) (ft) (ft) (£t) o4 Ww OM WONWNAADUUNFHFWWNHNNRFRFOOrF OWWMWMANNAHAUUNFHFWWNNEKEF OF -1. 0. OF ile i De 2h oF 3 4. 4. 5. 2). 6. 6. Us We 8. 8. oF oF (Sheet 2 of 2) C16 Table C6 Profile Survey Data, Test T06 Profile TO6P40 Profile TO6P80 Profile TO6P170 Profile T06P3/70 (Continued) (Sheet 1 of 3) C17 Table C6 (Continued) Profile TO6P750 Profile TO6P1450 Profile TO6P1650 Profile T06G1650 Elev. (ft) Elev. (ft) Range (ft) Range (ft) 0 0-0 1 OWOWMWANNAADUMNHFHSFWWNNFRFOORNNWE (Continued) (Sheet 2 of 3) C18 Table C6 (Concluded) Profile T06C1650 Profile TO6P1850 Range Elev. Range ‘Elev. (ft) (ft) (ft) (ft) 0.00 =(0) 525) -4.00 1.00 0.50 -0.33 3) 9.0 0.72 1.00 -0.46 =O) 0.12 1.50 -0.58 0.00 -0.26 2.00 -0.58 0.50 -0.39 20) -0.60 1.00 -0.44 3.00 -0.67 1.50 -0.45 Sg a0) -0.76 2.00 -0.45 4.00 -0.81 2.50 -0.46 4.50 (0) OV/7/ 3.00 -0.42 5.00 -0.72 3F50 -0.40 5.50 -0.81 4.00 OK497 6.00 23k 50)5) 4.50 -0.61 6.50 oll, 25 5.00 -0.78 7.00 33 320) 0589 750 =1523 6.00 -0°91 8.00 =0R 98 6.50 -0.84 8.50 -0.74 7.00 -0.69 9.00 -0). 70 7.50 -0.57 5 aX0) 0575 8.00 20) 55) 7/ 10.00 0R79 8.50 -0.61 11.00 -0.90 9.00 -0.66 12.00 -1.10 9.50 -0.74 00 =a 6 10.00 -0.82 00 SS y/ 7 11.00 -1.00 00 84 12.00 -1.46 00 39 13.00 Sis 7S 00 -1.94 14.00 = .9) 00 240 0X0) 15.00 als OW) 16.00 Sha al 17.00 = b3 7) 18.00 2502 Sheet 3 of 3) C19 ablienGy, Profile Survey Data, Test TO/ Profile TO/7START Profile TO/P40 Profile TO/P80 Profile TO/7P1/0 Range Elev. (ft) (ft) (Continued) (Sheet 1 of 3) C20 Table C7 (Continued) Profile T0O7P370 Profile T0O7P/50 Profile TO/7P1450 Profile TO/P1650 (Continued) (Sheet 2 of 3) C21 Table C7 (Concluded) Profile T0O/C1650 Range Elev. (ft) (ft) Profile T0O/G1650 OU MOAN WAAUUNFPHEwWwWNNHYRrOS (Sheet 3 of 3) C22 Table C8 Profile Survey Data, Test T08 Profile TO8START Profile TO8P40 Profile T0O8&P80 Profile TO8P170 Range Elev. : Range Elev. (ft) (ft) -4.00 0.97 -3.00 0.92 -2.00 0.84 -1.50 0.33 -1.00 OF23 0.00 0.03 0.50 -0.03 10,0 -0.09 1 5 5X0) -0.16 2.00 -0.21 23,0 -0.29 3.00 -0.35 3.50 -0.40 4.00 -0.44 4.50 -0.48 5.00 -0.55 5.50 -0.61 6.00 -0.68 6.50 -0.71 7.00 -0.72 7550, -0.72 8.00 -0.77 8.50 -0.84 9.00 -0.91 9.50 -1.01 10.00 =e) 11.00 -1.37 12.00 -1.64 13.00 -1.84 14.00 -1.96 1520.0 -2.01 16.00 -2.07 17.00 7) lla 18.00 = 2), 1) (Continued) (Sheet 1 of 2) C23 TO8P370 Profile Profile Range (ft) Table C8 (Concluded) TO8P750 Profile TO8P1450 Profile T08P1650 Elev. Range Elev. Range Elev. (ft) (ft) (ft) (ft) (ft) 0.98 -1.50 0.89 0.00 : 0.62 0.50 O. OZ 1.00 O. =O Leo) ie -0.24 2.00 IL -0.29 2.50 2: -0.33 3.00 2s =0-316 3.50 Be =0.39 4.00 3% : -0.43 4.50 -0.62 4.00 S059 -0.46 5.00 -0.66 4.50 -0.64 -0.50 3/390 -0.69 5.00 05 (57/ -0.54 6.00 -0.70 5.50 -0.68 -0).59 6.50 -0.74 6.00 -0.69 -0.64 7.00 -0.80 6.50 0-73 -0.67 7.50 -0.90 7.00 -0.81 -0.73 8.00 -0.98 7350 -0.88 —On9 8.50 -0.98 8.00 -0.98 -0.86 9.00 -0.93 8.50 =I On -0.86 9.50 -0.88 9.00 =O 97 -0.84 10.00 -0.89 2250) -0.94 -0.83 11.00 -0.92 10.00 -0.87 -0.83 12.00 =1./05 11.00 -0.90 -0.88 13.00 als ad 12.00 -1 02 -1.00 14.00 -1.49 13.00 eile ly ait, 7 15.00 -1.84 14.00 -1.41 -1.48 16.00 =1 591 15.00 ail. JY -1.80 17.00 - 1.96 16.00 =1 788 Sale sQilt 18.00 = 2502 17.00 -1.95 -1.97 18.00 -1.98 =2;. Ol -2.07 (Sheet 2 of 2) C24 Table C9 Profile Survey Data, Test T09 Profile TO9START Profile TO9P40 Profile TO9P80 Profile TO9P170 Range Elev. (ft) (ft) (Continued) (Sheet 1 of 3) C25 Table C9 (Continued) Profile T0O9P370 Profile TO9P750 Profile TO9P1450 Profile TO9P1650 (Continued) (Sheet 2 of 3) C26 Table C9 (Concluded) Profile TO9P1850 Profile T09G1850 Profile T09C1850 Range Elev. Range Elev. ’ Range Elev. (ft) (ft) (ft) (ft) (ft) (ft) .00 0.89 0.00 -0.19 0.00 =O)5211 52.0 0.85 0.50 -0.26 0.50 =0) 31 . 00 0.51 1.00 -0.30 1.00 -0).33 .00 0.03 1, 30) -0.34 1.50 =0'.39 . 00 (0) 1K) 2.00 -0.38 2.00 -0.43 520) -0.23 25,0 -0.42 2.50 -0.46 .00 -0.26 3.00 -0.45 3.00 -0.50 .50 -0.30 350 =O 52 3.50 -0.53 .00 =(0) 553k 4.00 =057/ 4.00 -0.59 . 50 -0.34 4.50 -0.62 4.50 -0.64 .00 -0.38 5.00 -0.65 5.00 -0.69 .50 -0.42 5) 5,.5)0) -0.66 5.50 -0.74 .00 -0.47 6.00 -0.66 6.00 -0.77 .50 -0.49 6.50 =O8)7al 6.50 = ORS .00 =0..51 7.00 -0.77 7.00 =0., 81 .50 =0),5i5 7 530) -0.81 7.50 -0.86 .00 -0.60 8.00 -0.84 8.00 -0.90 .50 -0.66 8.50 -0.81 8.50 S090 .00 -0.73 9.00 -0.79 9.00 -0.88 5,0) (0) 8 7/i 5210) -0.81 950 -0.86 .00 Oh 10.00 -0.87 10.00 -0.90 #20 -0.70 11.00 -1.05 10.50 -0.94 .00 -0.68 12.00 =a 11.00 -1..02 .50 -0=73 13.00 =H eal 12.00 -1.26 .00 -0.79 14.00 =1e.98 13.00 Sse) . 00 SOs 9)7/ 15.00 =i 3 )7/ 14.00 Sl Sy .00 mls ZS) 16.00 =2).05 15.00 -2.05 .00 -1.66 17.00 -2.07 16.00 SO .00 =A 92. 18.00 -2.10 17.00 =iDvreles) 00 =A 8 18.00 =2relS .00 -2.04 00 209 00 =2.10 (Sheet 3 of 3) C27 Profile T1OSTART Table C10 Profile Survey Data, Test T10 Profile T10P40 Profile T10P80 Range Elev. Range Elev. Elev (ft) (ft) (ft) (ft) (£t) 0.87 -4.00 0.86 -4.00 0.86 0.89 -0.66 0.86 -3.00 0.86 0.87 -0.65 0.82 -2.00 0.86 0.86 -0.55 0.81 -0.66 0.86 0.86 0.00 0.59 -0.65 0.20 0.79 0.30 0.05 -0.55 0.18 0.52 0.50 0.01 0.00 0.08 0.32 1.00 -0.07 0.50 -0.01 0.10 1.50 -0.14 1.00 -0.10 -0.14 2.00 -0.21 Ip 2X0) -0.17 -0.38 2.50 -0.25 2.00 -0.21 -0.60 3.00 -0.29 2.50 -0.28 -0.84 3.50 -0.33 3.00 -0.32 -1.04 4.00 -0.39 B50 -0.35 -1.07 4.50 -0.47 4.00 -0.42 -1.32 5.00 -0.52 4.50 -0.55 -1.59 5.50 -0.53 5.00 -0.64 -1.81 6.00 -0.54 5.50 -0.61 -2.05 6.50 -0.61 6.00 -0.58 -2.15 7.00 -0.72 6.50 -0.60 -2.19 7.50 -0.83 7.00 -0.64 8.00 -0.98 VoDo) -0.73 8.50 Sik als} 8.00 -0.81 9.00 -1.24 8.50 -0.91 9.50 -1.37 9.00 -1.03 10.00 -1.49 9.50 -1.20 10.50 -1.57 10.00 -1.36 11.00 -1.64 10.50 -1.48 12.00 alg 2 11.00 -1.57 13.00 -1.82 12.00 -1.69 14.00 -1.90 13.00 -1.78 15.00 -2.01 14.00 -1.88 16.00 -2.10 15.00 -2.00 17.00 -2.14 16.00 -2.09 18.00 =r 07, 17.00 -2.14 18.00 -2.17 (Continued) C28 Profile T10P170 (ft) (ft) -4.00 0.86 -3.00 0.86 -0.65 0.86 -0.65 0.03 -0.55 0.01 0.00 -0.08 0.50 -0.16 1.00 -0.22 1.50 -0.26 2.00 -0.29 2.50 -0.33 3.00 -0.40 3.50 -0.49 4.00 -0.51 4.50 -0.55 5.00 -0.74 5.50 -0.79 6.00 -0.73 6.50 -0.63 7.00 -0.62 7.50 -0.64 8.00 -0.70 8.50 -0.77 9.00 -0.84 ea) -0.99 10.00 -1.14 10.50 =o 33 11.00 -1.47 12.00 -1.68 13.00 = 14.00 -1.88 15.00 =i99 16.00 -2.08 17.00 -2.13 18.00 oon ILE) (Sheet 1 of 3) Table C10 (Continued) Profile T10P370 Profile T10P750 Profile T10P1450 Profile T10P1650 Range Elev. (Continued) (Sheet 2 of 3) C29 Table C10 (Concluded) Profile T10P1850 Profile T10G1850 Profile T10C1850 Range Elev. Range Elev. (ft) (ft) (ft) (ft) OWOMAANNAAUNFHLFWBWNHNEE OS 0. ibs ky aM Die 3. S)5 4. 4. De 5: 6. Ge Tiss Ti 8. 8. e) OF (Sheet 3 of 3) C30 Profile T1L1ISTART Range (ft) Elev. (ft) Oey OOO EO EC © Profile Table Cll Profile Survey Data, Test Tll Range (ft) T11P40 Profile Elev. Range (ft) (ft) 0.94 -4.00 0.94 -3.00 0.94 -2.00 OF93 -0.66 0.69 -0.65 0.09 -0.55 0.00 0.00 -0.08 0.10 -0.16 0.50 -0.23 1.00 -0.31 15,0 -0.35 2.00 -0.40 22350) -0.43 3.00 -0.48 5 50) = Oya 4.00 -0.57 4.50 -0.64 5.00 -0.73 Bye 210) -0.80 6.00 -0.90 6.50 -1.02 7.00 = 2 750 -1.24 8.00 -1.36 8.50 -1.46 9.00 -1.59 9.50 -1.81 10.00 -1.99 10.50 -2.04 11.00 -2.09 12.00 =20 182) 13.00 SOG 14.00 -2.18 15.00 16.00 17.00 18.00 (Continued) C31 T11P80 Profile: TASIPAy.O Range Elev. (ft) (£t) -4.00 0.94 -3.00 0.94 -0.65 0.94 -0.65 O) 5 ALY) =0).55 0.17 0.00 0.08 0.50 0.01 1.00 -0.08 Meo) =0.15 2.00 sO 23 2590 -0.26 3.00 (0), 50 S50) = 01.35 4.00 -0.39 4.50 -0.45 5.00 -0.50 5) 5 0) 30) 5 2)3) 6.00 -0.56 6.50 -0.60 7.00 =0F 63 7.50 -0.69 8.00 -0.74 8.50 -0.82 9.00 -0.90 550) -1..03 10.00 abe ALY) 10.50 -1.34 11.00 =H. 5,0 12.00 -1.76 13.00 10 5 oXs) 14.00 -2.02 15.00 =2.07 16.00 Sw Ale 17.00 -2.14 18.00 Sq dk// (Sheet 1 of 3) Table Cll (Continued) Profile T11P370 Profile T11P750 Profile T11P1450 Profile T11P1650 Elev. ; Range Elev. (ft) (ft) (Continued) (Sheet 2 of 3) C32 Table Cll (Concluded) Profile T11P1850 (Sheet 3 of 3) C33 Table C12 Profile Survey Data - Test T12 Profile Profile Profile Range Elev. Range Elev. Range Elev. Range Elev. (ft) (ft) (ft) (ft) (ft) (ft) (ft) (ft) This Table intentionally left blank. Profile data were recorded and plotted in Figure E18 in Appendix E. C34 Table C13 Profile Survey Data - Test T13 Profile Profile Range Elev. Range Elev. Range Elev. (ft) (ft) (GEE) (ft) (ft) (ft) This Table intentionally left blank. Profile data were recorded but not plotted in this report. Profile Range (ft) Elev. (ft) C35 Table C14 Profile Survey Data, Test T14 T14P40 Profile T14P80 Profile T14P200 Profile Profile T14START Elev. (ft) Elev. (ft) Range (ft) QOoooe © lip (Continued) (Sheet 1 of 5) C36 Table C14 (Continued) Profile T14P470 Profile T14P720 Profile T14P1200 Profile T14P1640 Range Elev. Range ~_ Elev. (ft) (ft) (Continued) (Sheet 2 of 5) C37 Table C14 (Continued) Profile T14P2140 Profile T14P27/0 Profile T14P3420 Profile T14P3940 (Continued) (Sheet 3 of 5) C38 Table C14 (Continued) Profile T14P4590 Profile T14P5250 Profile T14P5770 Profile T14P6290 Range Elev. (Gz) (ft) (Continued) (Sheet 4 of 5) C39 Table C14 (Concluded) Profile T14P6810 Profile T14P6810 Range Elev. (ft) (ft) 0. 0. ibe Ik, DD ae 3). 3): 4. 4. De Die 6. (Sheet 5 of 5) c40 6 physical model plotted in model units. APPENDIX D: PLOTS OF EXPERIMENT PROFILES The plots shown in this appendix are results from the movable-bed The solid profile line represents the profile recorded after the specified number of waves, whereas the dashed profile line marks the position of the previously recorded profile. All profiles are center-line profiles except those denoted with an uppercase G (glass sidewall) or an uppercase C (concrete sidewall). T13 have been purposely omitted from this appendix. Test TOL TO2 TO3 TO4 TO5 TO06 TO7 T08 TO9 T1O ala T14 Description of Test Reproduction of prototype experiment using 10-m horizontal width berm Repeat of TO1 to demonstrate repeatability Reproduction of prototype experiment using 11-m horizontal width berm (same as prototype) Repeat of T03 with wave height increased by 10 percent to examine impact of height variations Repeat of T03 using absorbing wave paddle Repeat of TO3 starting with the prototype profile at 40 waves molded in the flume to examine effect of initial profile on evolution. Repeat of T03 with wave period decreased 10 percent to examine impact of period variations Repeat of T03 using irregular waves having H,/3 equal to 141 percent of monochromatic wave height Repeat of TO3 using irregular waves having Hj,3 equal to the monochromatic wave height Repeat of TO3 using regular waves with a vertical seawall at the intersection of the revetment and SWL Repeat of T10 using irregular waves with Hj,; equal to the monochromatic wave height Reproduction of prototype irregular wave test D1 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Profiles of T1l2 and Figure Number D1 D2 D3 D4 D5 D6 D7 D8 D9 D1O D11 D12 ELEV. - (ff) ELEV. - (ft) ELEV. - (ff) TEST TO‘ 40 Waves - Solid -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) al 80 Waves - Solid 40 Waves - Dashed -4 2 0 2 4 6 8 10 12 14 16 RANGE - (ff) 1 a CSE SSeS an eee eae | Nee as ee 170 Waves - Solid val E : ee 80 Waves - Dashed \ ? E alee (da seen ' pax RANGE - (ff) Figure Dl. Test TO1 profile development (Sheet 1 of 4) D2 ELEV. - (ft) ELEV. - (ft) ELEV. - (ft) Figure Dl. (Sheet 2 of 4) TEST TO‘ 4 6 RANGE - (ff) RANGE - (ft) D3 370 Waves 170 Waves ?50 Waves 370 Waves 1450 Waves 7250 Waves = {SXo)\|!fi - Dashed = Soild - Dashed = Solid - Dashed ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) -4 -2 Figure Dl. 0 e (Sheet 3 of 4) TEST 101 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D4 1650 Waves - 1450 Waves - 1650 -G Waves 1650-P Waves 1650 -C Waves 1650 -P Waves Solid Dashed - Solid - Dashed =" Soiliiic - Dashed ELEV. - (ff) ELEV. - (ft) TEST TO‘ 1850 Waves - Solid 1650 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) —— = 2050 Waves - Solid = 1850 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) Figure Dl. (Sheet 4 of 4) D5 ELEV. - (ff) ELEV. - (ft) ELEV. - (ff) Figure D2. TEST TO2 MS 40 Waves - Solid — =S SS a al 5 TSS Res Ss 0 2 4 6 8 10 le 14 16 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ff) Test TO2 profile development (Sheet 1 of 3) D6 TEST TO2 370 Waves - Solid 170 Waves - Dashed ELEV. - (ff) -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) ee cS 750 Waves - Solid zi 370 Waves - Dashed Sa al Ye — 4 a a el aT i 4 “e 4 -4 aA) 0 2 4 6 8 10 12 14 16 RANGE - (ff) 1450 Waves - Solid 7°50 Waves - Dashed ELEV. - (ff) A -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure D2. (Sheet 2 of 3) D7 ELEV. - (ff) ELEV. - (ft) ELEV. - (ft) Figure D2. (Sheet 3 of 3) TEST TO2 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ft) D8 1650 Waves 1450 Waves —Soiliire - Dashed 1650-G Waves - Solid 1650 -P Waves - Dashed 1650 -C Waves - Solid 1650-P Waves - Dashed ELEV. - (ft) ELEV. - (ft) ELEV. - (ff) Figure D3. TEST TO3 40 Waves - Solid 0 2 4 6 8 10 12 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ft) Test TO3 profile development (Sheet 1 of 4) D9 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) Figure D3. (Sheet 2 of 4) TEST TO3 4 6 RANGE - (ft) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D10 370 Waves 170 Waves 8 10 = Soll fic - Dashed ?S50 Waves 370 Waves = So)l) JG) - Dashed 8 10 le 14 1450 Waves - Solid 750 Waves - Dashed SS S SS N SS N SS ss ~— 8 10 12 14 16 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) TEST TO3 1650 Waves - Solid 14S0 Waves - Dashed -4 =2 0 2 4 6 8 10 12 14 16 RANGE - (ft) il a ag em es re i er ee me aa a a a Pl | ——- eS j = 1650-G Waves - Solid 1650-P Waves - Dashed / / Le Ns es a oe : a4 Me te a = SS N =u . al —~ — ty S ~—— 2 xia SS -4 =e 0 2 4 6 8 10 le 14 16 RANGE - (ft) 1650 -C Waves 1650-P Waves 2) Soll ial - Dashed -4 “2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure D3. (Sheet 3 of 4) D11 ELEV. - (ft) Figure D3. (Sheet 4 of 4) TEST TO3 4 6 RANGE - (ft) D12 1850 Waves - Solid 1650 Waves - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) TEST T04 40 Waves - Solid “A -2 0 2 4 6 8 10 12 14 le RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed -4 -2 0 2 4 6 8 10 ine 16 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure D4. Test TO4 profile development (Sheet 1 of 4) D13 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) TEST TO4 370 Waves - Solid 170 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) at 750 Waves - Solid 370 Waves - Dashed -4 “2 0 2 4 6 8 10 ia 1 16 RANGE - (ft) 1450 Waves - Solid 750 Waves - Dashed S) ey aay Pee ' inv) -4 2 0 2 4 6 8 10 ieee 16 RANGE - (ff) Figure D4. (Sheet 2 of 4) D14 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) TEST TO4 RCo anemia is Ress Se 1650 Waves - Solid = (a SS 1450 Waves - Dashed S| Se a 0 = SS ~ zi = ~ ey i — > SS i zi _— ne MS TL -4 “2 0 2 4 6 8 10 12 14 16 RANGE - (ff) [Parana ace 1650-G Waves - Solid 1650-P Waves - Dashed 2 -4 uD 0 2 4 6 8 10 12 14 16 RANGE - (ff) ne Oe ey x aU ee 1650-C Waves - Solid = SS 1650-P Waves - Dashed zal — 0 2 SS a 4 z i eS te SS 7 SSS rs] “i Ve a Ee Sais SS 2Fy | eer a SS esi 2A 2 0 2 4 6 8 10 12 14 1G RANGE - (ff) Figure D4. (Sheet 3 of 4) D15 ELEV. - (ft) Figure D4. (Sheet 4 of 4) TEST TO04 4 6 RANGE - (ft) D16 1850 Waves - Solid 1650 Waves - Dashed ELEV. - (ft) ELEV. - (ft) ELEV. - (ft) Figure D5. TEST TO5 40 Waves - Solid 0 2 4 6 8 10 12 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ff) Test TO5 profile development (Sheet 1 of 3) D17 ELEV. - (ff) ELEV. - (ft) ELEV. - (ff) TEST TOS ] 370 Waves - Solid E 170 Waves - Dashed 0 E oe [i 2. -4 -2 0 2 4 6 8 10 he 14 16 RANGE - (ff) 1 escape aoe Uc = Guam | On| (Pua Mineman | Ramune lCatattan lntroow neeassorcon lnmeact Unuigey licen Uloraens AO oel fe Big po 750 Waves - Solid — 370 Waves - Dashed es fies | poo -] | li =2 -4 = 0 2 4 6 8 10 12 14 16 RANGE - (ff) 1 Saat Leite ee [euees ama ak 1450 Waves - Solid FJ E ™S Se 750 Waves - Dashed am ; SS E oa Lae a E Se + -| Ss SS E e ~ “al SS ~ -2 E i = [Seperate a Ss -4 -2 0 2 4 6 8 10 1e 14 16 RANGE - (ff) Figure D5. (Sheet 2 of 3) D18 ELEV. - (ff) Figure D5. (Sheet 3 of 3) TEST TOS 4 6 RANGE - (ft) D19 1650 Waves - Solid 1450 Waves - Dashed aS ea ellico tales eee ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) Figure Dé. TEST TO6 40 Waves - Solid 0 2 4 6 8 10 12 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ff) 170 Waves - Solid 80 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ff) Test T06 profile development (Sheet 1 of 4) D20 ELEV. - (ft) ELEV. - (ft) ELEV. - (ff) Figure D6. (Sheet 2 of 4) TEST TO6 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D21 370 Waves 170 Waves 7S0 Waves 370 Waves = Soillird - Dashed = Soillaie - Dashed 1450 Waves - Solid ?50 Waves - Dashed ELEV. - (ff) ELEV. - (ft) ELEV. - (ft) TEST TO6 1650 Waves - Solid 1450 Waves - Dashed =4 32 0 2 4 6 8 10 re 14 16 1650-G Waves - Solid 1650 -P Waves - Dashed -4 s2 0 2 4 6 8 10 ie 14 16 RANGE - (ff) | Gos ey Ss 16S50-C Waves - Solid = 1650 -P Waves - Dashed 0 =} =f) -4 =e 0 2 4 6 8 10 le 14 16 RANGE - (ft) Figure D6. (Sheet 3 of 4) D22 ELEV. - (ft) Figure D6. (Sheet 4 of 4) TEST TO6 4 6 RANGE - (ff) D23 1850 Waves - Solid 1650 Waves - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) TEST 107 40 Waves - Solid 0 2 4 6 8 10 12 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 0 2 4 6 8 10 12 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed Figure D7. RANGE - (ff) Test TO7 profile development (Sheet 1 of 3) D24 14 16 ELEV. - (ft) ELEV. - (ff) ELEV. - (ft) Figure D/. (Sheet 2 of 3) TEST TO7 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D25 370 Waves - Solid 170 Waves - Dashed 750 Waves - Solid 370 Waves - Dashed 1450 Waves - Solid ?50 Waves - Dashed 16 ELEV. - (ff) ELEV. - (ft) ELEV. - (ff) Figure D/. (Sheet 3 of 3) TEST TO7 4 6 RANGE - (ft) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D26 1650 Waves - 1450 Waves - 1650 -G Waves 1650 -P Waves 1650 -C Waves 1650 -P Waves Solid Dashed ie 14 = So) jal - Dashed SUN ne ~ le 14 2a-Soll ic) - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ft) TEST TO8 40 Waves - Solid -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 80 Waves - Solid 40 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure D8. Test TO8 profile development (Sheet 1 of 3) D27 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) Figure D8. (Sheet 2 of 3) TEST TO08 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D28 370 Waves 170 Waves 8 10 750 Waves 370 Waves 1450 Waves 750 Waves eS Oilisiicl - Dashed = ‘Soilkiicd - Dashed =7 Sy) || FG! - Dashed 16 ELEV. - (ff) Figure D8. (Sheet 3 of 3) TEST TO8 4 6 RANGE - (ff) D29 1650 Waves - Solid 1450 Waves - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ft) TEST TO9 40 Waves - Solid re 0 2 4 6 8 10 ie 14 16 RANGE - (ff) ) je Ses = Ba a: a 80 Waves - Solid a re \ Ss 40 Waves - Dashed = 0 ee S = sl es on as SS a i = a oe eS =e > | See — = -4 =e 0 2 4 6 8 10 le 14 16 RANGE - (ff) Tk ae Mr ay 170 Waves - Solid \ SS 80 Waves - Dashed : OEE 1 i eae a [ie =e) -4 -2 0 2 4 6 8 10 le 14 16 RANGE - (ff) Figure D9. Test TO9 profile development (Sheet 1 of 4) D30 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) Figure D9. (Sheet 2 of 4) TEST TO9 4 6 RANGE - (ff) 4 6 RANGE - (ft) 4 6 RANGE - (ff) D31 370 Waves - Solid 170 Waves - Dashed 8 10 le 14 750 Waves - Solid 370 Waves - Dashed 1450 Waves - Solid 750 Waves - Dashed SS \ SS N SS SS TS SES > Ss 8 10 le 14 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) Figure D9. TEST TO9 4 6 RANGE - (ft) (Sheet 3 of 4) 4 6 RANGE - (ft) 4 6 RANGE - (ft) D32 1650 Waves 1450 Waves 1850 Waves 1650 Waves SES Oiliicl - Dashed = §Soiliia - Dashed 1850-G Waves - Solid 18S0-P Waves - Dashed ELEV. - (ff) Figure D9. (Sheet 4 of 4) TEST TO9 4 6 RANGE - (ff) D33 1850-C Waves - Solid 1850-P Waves - Dashed ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) TEST 110 40 Waves - Solid 80 Waves - Solid 40 Waves - Dashed -4 oe 0 2 4 6 8 10 12 14 16 RANGE - (ft) 170 Waves - Solid 80 Waves - Dashed RANGE - (ff) Figure D10. Test T10 profile development (Sheet 1 of 4) D34 ELEV. - (ft) ELEV. - (ft) ELEV. - (ft) TEST 110 370 Waves - Solid 170 Waves - Dashed fea ee fame er is SS N ~ SS —— > SS -4 Te 0 2 4 6 8 10 re 14 16 RANGE - (ft) 250 Waves - Solid 370 Waves - Dashed “4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 1450 Waves - Solid ?50 Waves - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure D10. (Sheet 2 of 4) D35 ELEV. - (ft) ELEV. - (ff) ELEV. - (ft) Figure D10. (Sheet 3 of 4) TEST 110 4 6 RANGE - (ff) 4 6 RANGE - (ff) 4 6 RANGE - (ff) D36 1650 Waves - 1450 Waves - 1850 Waves - 1650 Waves - 1850 -G Waves 1850-P Waves Solid Dashed Solid Dashed = SO ilpiicl - Dashed ELEV. - (ft) Figure D10. (Sheet 4 of 4) TEST 110 4 6 RANGE - (ff) D37 1850-C Waves - Solid 1850 -P Waves - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) TEST 111 0 2 4 6 RANGE - (ft) Figure Dll. 0 2 4 6 RANGE - (ft) RANGE - (ff) 40 Waves - Solid 8 10 le 80 Waves - Solid 40 Waves - Dashed 8 10 le 170 Waves - Solid 80 Waves - Dashed Test Tll profile development (Sheet 1 of 3) D38 a TEST 111 370 Waves - Solid 170 Waves - Dashed ELEV. - (ff) 750 Waves 370 Waves = Soll fie! - Dashed ELEV. - (ft) 1450 Waves - Solid 750 Waves - Dashed ELEV. - (ff) RANGE - (ff) Figure Dil. (Sheet 2,06 3) D39 ELEV. - (ff) ELEV. - (ft) TEST 141 1650 Waves - Solid 1450 Waves - Dashed -4 -2 0 2 4 6 8 10 2 14 16 RANGE - (ff) 1850 Waves - Solid 1650 Waves - Dashed -4 “2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure Dll. (Sheet 3 of 3) D40 TEST 114 40 Waves 4 S 12 14 16 RANGE - (ff) 80 Waves - Solid 40 Waves - Dashed 10 le 14 16 4 6 RANGE - (ff) 200 Waves - Solid 80 Waves - Dashed 10 ire 14 16 4 6 RANGE - (ff) Figure D12. Test T14 profile development (Sheet 1 of 6) D41 TEST 114 470 Waves 200 Waves - Solid - Dashed 720 Waves - Solid 470 Waves - Dashed 1200 Waves - Solid 720 Waves - Dashed 4 6 RANGE - (ff) Figure D12. (Sheet 2 of 6) D42 TEST 114 1640 Waves - Solid 1200 Waves - Dashed 4 6 10 12 14 16 RANGE - (ft) 2140 Waves 1640 Waves = Solid - Dashed 2770 Waves 2140 Waves = S¥e}l| NG) - Dashed 4 6 RANGE - (ff) Figure D12. (Sheet 3 of 6) D43 TEST 114 3420 Waves - Solid 2140 Waves - Dashed 4 6 RANGE - (ff) 3940 Waves - Solid 3420 Waves - Dashed 4590 Waves - Solid 3940 Waves - Dashed 4 6 RANGE - (ff) Figure D12. (Sheet 4 of 6) D44 TEST 114 S250 Waves - Solid 4590 Waves - Dashed S?70 Waves S250 Waves = Soiltiid - Dashed 4 6 RANGE - (ff) 6230 Waves - Solid S?70 Waves - Dashed 4 6 RANGE - (ft) Figure D12. (Sheet 5 of 6) D45 ELEV. - (ft) Figure D12. TEST 114 4 6 RANGE - (ff) (Sheet 6 of 6) D46 6810 Waves - Solid 6290 Waves - Dashed 10 le APPENDIX E: PLOTS OF PROFILE COMPARISONS The plots shown in this appendix are comparisons between various profiles from both the midscale and the Grosser Wellenkanal (GWK) prototype- scale tests. Midscale physical model profiles are scaled to prototype units when compared with GWK prototype profiles. Profile comparisons between midscale tests are plotted in model units. All profiles are center-line profiles except those denoted with an uppercase G (glass sidewall) or an uppercase C (concrete sidewall). Description of Comparison Figure Number Test TOl1 versus prototype El Test T03 versus prototype E2 Test TO4 versus prototype E3 Test TO5 versus prototype E4 Test T06 versus prototype E5 Test TO7 versus prototype E6 Irregular test T14 versus prototype E/7 Repeatability test, TOl versus TO2 E8 Wave height perturbation, T0O4 versus T03 E9 Wave period perturbation, TO7 versus T03 E10 Equal H/wT parameters, T0O4 versus TO7 Ell Initial profile at 40 waves, T06 versus TO3 E12 Reduced sediment comparison, TOl versus TO3 E13 Absorbing wave board test, TO5 versus T03 E14 Irregular wave comparison, H,,;3 equals Hono E15 Irregular wave comparison, H,,3 equals 141% Hono E16 Irregular wave perturbation, T09 versus T08 E17 Irregular wave repeatability, T12 versus T08 E18 Seawall impacts under regular waves, T10 versus TO3 E19 Seawall impacts wenGlere Streveesraqvilieee waves, Tll versus TO9 E20 Seawall irregular wave comparison, H,,;3 equals Hono E21 El ELEV. - (m) ELEV. - (m) ELEV. - (m) Figure El. TEST T01 vs. PROTOTYPE 40 WOVES Model - Solid Proto - Dashed 10 20 30 40 RANGE - (m) Model - Solid Proto - Dashed 10 20 30 40 RANGE - (m) 170 WAVES Model - Solid Proto - Dashed 10 20 30 40 RANGE - (m) Test TOl versus prototype (Sheet 1 of 3) E2 SO ELEV. - (m) ELEV. - (m) ELEV. - (m) Figure El. TEST T0414 vs. PROTOTYPE Model Proto 3°70 WAVES 10 20 30 RANGE - (m) 750. WAUES Hoan Proto 10 20 30 RANGE - (m) Mode | < i450 WAVES Baas 10 20 30 RANGE - (m) (Sheet 2 of 3) E3 = So}lsic - Dashed = SOllniicl - Dashed = SSoy ( a 1 =a S Ww a ~ —s ~ \ Pe NS | Se Sahae Se == -4 =e 0 2 4 6 8 10 lie 14 16 RANGE - (ff) = al = Sie} I} ial - Dashe SH 1650-C Waves T04 1650-C Waves T03 ELEV. - (ff) -4 oe 0 2 4 6 8 10 1e 14 16 RANGE - (ff) Figure E9. (Sheet 3 of 4) E31 ELEV. - (ft) Figure E9. WAVE HEIGHT PERTURBATION 1850 Waves T04 - 1850 Waves T03 - RANGE - (ft) (Sheet 4 of 4) E32 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) WAVE PERIOD PERTURBATION 40 Waves T0? - Solid 40 Waves T03 - Dashed -4 <2 0 2 4 6 8 10 12 14 16 RANGE - (ft) j ale li Ez LP 80 Waves TO? - Solid = “= : ~ 80 Waves T03 - Dashed 4 0 eS al = 4 ce ass -4 =a 0 2 4 6 8 10 12 14 16 RANGE - (ft) 170 Waves 10? - Solid 170 Waves T03 - Dashed RANGE - (ff) Figure E10. Wave period perturbation, TO/7 versus TO03 Gheetwigok s3)) E33 ELEV. - (ft) ELEV. - (ft) ELEV. - (ff) WAVE PERIOD PERTURBATION UE MAE: TeaRPoAR 370-laves TO? - Solid i Ss 370 Waves T03 - Dashed “2 0 2 4 6 8 10 12 14 16 RANGE - (ff) 750 Waves T07 - Solid : 7S0 Waves 103 - Dashed 2 0 2 4 6 8 10 12 14 RANGE - (ff) 1450 Waves TO? - Solid 1450 Waves T03 - Dashed 2 0 2 4 6 8 10 12 14 16 RANGE - (ft) Figure E10. (Sheet 2 of 3) E34 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) WAVE PERIOD PERTURBATION eae 1650-P Waves TO? - Solid 7 S 16S50-P Waves T03 - Dashed SS a Al es Resin 5 We eS < Gi = N — XN Re x sd ors Es -4 = 0 2 4 6 8 10 1e 14 16 RANGE - (ff) 1650-G Waves T0? - Solid] 1650-G Waves T03 - Dashe -4 =2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 1650-6 Waves 0M N= sSoeiliiid 1650-C Waves T03 - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) Figure E10. (Sheet 3 of 3) E35 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) EQUAL H/wT PARAMETERS 40 Waves T04 - Solid 40 Waves T0? - Dashed -4 “e 0 2 4 6 8 10 12 14 RANGE - (ff) _~ 80 Waves 104 - Solid 80 Waves TO? - Dashed le ES ees ai -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 170 Waves T04 - Solid 170 Waves T0? - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) Figure Ell. Equal H/wI parameters, T04 versus TO7 (Sheet iL @ie S}) E36 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) EQUAL H/wT PARAMETERS 370 Waves T04 - Solid 370 Waves TO? - Dashed -4 =2 0 2 4 6 8 10 12 14 16 RANGE - (ff) me ?50 Waves T04 - Solid 750 Waves TO? - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) 1450 Waves T04 - Solid 1450 Waves T0? - Dashed -4 -2 0 2 4 6 8 10 ie me 16 RANGE - (ff) Ficure Edd (Sheet 2 of 3) E37 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) EQUAL H/wT PARAMETERS 1650-P Waves 104 - Solid 1650 -P Waves T0? - Dashed -4 “2 0 2 4 6 8 10 12 14 16 RANGE - (ff) S S > ee SS (ef al es Pl cs a DSS -4 Re 0 2 4 6 8 10 RANGE - (ff) 750 Waves TO05 750 Waves T03 “2 0 2 4 6 8 RANGE - (ff) 1450 Waves T05S - Solid - Dashed = Soll 1G - Dashed = So) ficl 1450 Waves T03 - Dashed ae 0 2 4 6 8 RANGE - (ff) Figure E14. (Sheet 2 of 3) E48 ELEV. - (ff) ABSORBING WAVE BOARD ey. Cae (68) Haves Tes = Goi 1650 Waves T03 - Dashed RANGE - (ft) Figure E14. (Sheet 3 of 3) E49 ELEV. - (ff) ELEV. - (ff) ELEV. - (ft) IRREGULAR H1/3 = Hmono 40 Waves T0939 - Solid 40 Waves T03 - Dashed -4 =2 0 2 4 6 8 10 12 14 RANGE - (ff) 80 Waves T09 - Solid 80 Waves T03 - Dashed -4 -2 0 2 4 6 8 10 12 14 RANGE - (ff) 170 Waves T09 - Solid 170 Waves T03 - Dashed -4 “2 0 2 4 6 8 10 12 14 RANGE - (ff) Figure E15. Irregular wave comparison, H,,3 equals Hpono (Sheet 1 of 3) E50 ELEV. - (ft) ELEV. - (ff) ELEV. - (ff) IRREGULAR H1/3 = Hmono 370 Waves T0939 - Solid 370 Waves T03 - Dashed -4 22 0 2 4 6 8 10 12 14 16 RANGE - (ft) ?S0 Waves T03 - Dashed 750 Waves T0939 - Solid ra -4 -2 0 2 4 6 8 10 12 14 RANGE - (ff) 1450 Waves T0939 - Solid 1450 Waves T03 - Dashed -4 =e 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure E15. (Sheet 2 of 3) E51 ELEV. - (ff) Figure E15. IRREGULAR H1/3 = Hmono 1650 Waves T09 1650 Waves T03 0 2 4 6 8 10 12 RANGE - (ff) (Sheet 3 of 3) E52 = Soll jG - Dashed IRREGULAR H1/3 = 141% Hmono 40 Waves T08 - Solid 40 Waves T03 - Dashed 80 Waves T08 - Solid 80 Waves T03 - Dashed 170 Waves T08 - Solid 170 Waves T03 - Dashed 4 6 RANGE - (ff) Figure E16. Irregular wave comparison, H,,;3; equals 141 percent Hea (Sheets) lof 3) E53 IRREGULAR H1/3 = 141% Hmono 370 Waves T08 - Solid 370 Waves T03 - Dashed 750 Waves T08 - Solid 750 Waves T03 - Dashed 1450 Waves T08 - Solid 1450 Waves T03 - Dashed Figure E16. (Sheet 2 of 3) E54 ELEV. - (ff) Figure El6. IRREGULAR H1/3 = 141% Hmono 1650 Waves T08 1650 Waves T03 (Sheet 3 of 3) E55 = Soild - Dashed ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) IRREGULAR WAVE PERTURBATION 40 Waves T09 - Solid 40 Waves T08 - Dashed ahh -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) 80 Waves T09 - Solid 80 Waves T08 - Dashed -4 -2 0 @ 4 6 8 10 1e 14 6 RANGE - (ft) fee ett a : Care 170 Waves T09 - Solid s SS 170 Waves T08 - Dashed =] -4 -2 5 2 4 6 8 10 12 14 16 RANGE - (ff) Figure El7. Irregular wave perturbation, TO9 versus T08 (Sheet 1 of 3) E56 ELEV. - (ft) ELEV. - (ff) ELEV. - (ft) IRREGULAR WAVE PERTURBATION 370 Waves T09 - Solid 370 Waves T08 - Dashed -4 ae. 0 2 4 6 8 10 12 14 16 RANGE - (ft) 750 Waves T0939 - Solid 750 Waves T08 - Dashed -4 “2 0 2 4 6 8 10 12 14 16 RANGE - (ft) we 1450 Waves T0939 - Solid 4 1450 Waves T08 - Dashed “4 =2 0 2 4 6 8 10 12 (vue si RANGE - (ff) Figure El7. (Sheet 2 of 3) E57 ELEV. - (ff) IRREGULAR WAVE PERTURBATION 1650 Waves T09 - Solid 16S0 Waves T08 - Dashed -4 “2 0 2 4 6 8 10 12 14 RANGE - (ff) Figure El7. (Sheet 3 of 3) E58 IRREGULAR T12 VERSUS T08 40 Waves Tle - Solid 40 Waves T08 - Dashed 80 Waves Tle - Solid 80 Waves T08 - Dashed 170 Waves Tile - Solid 170 Waves T08 - Dashed 4 6 10 12 14 16 RANGE - (ff) Figure E18. Irregular wave repeatability, T12 versus T08 (Sheet 1 of 3) E59 Figure E18. IRREGULAR T12 VERSUS T08 370 Waves Tle - Solid 370 Waves T08 - Dashed 750 Waves Tle - Solid 750 Waves T08 - Dashed 1450 Waves Tle - Solid 1450 Waves T08° - Dashed (Sheet 2 of 3) E60 ELEV. - (ff) Figure E18. IRREGULAR T12 VERSUS T08 1650 Waves Tle - 1650 Waves 108 - 4 6 8 RANGE - (ff) (Sheet 3 of 3) E61 ELEV. - (ff) ELEV. - (ff) ELEV. - (ft) SEAWALL IMPACT - MONO. WAVES 40 Waves T10 - Solid 40 Waves T03 - Dashed -4 52 0 2 4 6 8 10 12 14 RANGE - (ff) 80 Waves T10 - Solid 80 Waves T03 - Dashed sa -2 0 2 4 6 8 10 12 14 16 RANGE - (ft) 170 Waves 710 - Solid 170 Waves T03 - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) Figure E19. Seawall impacts under regular waves, T10 versus TO3 (Sheet 1 of 3) E62 ELEV. - (ff) ELEV. - (ft) ELEV. - (ff) SEAWALL IMPACT - MONO. WAVES Figure E19. (Sheet 2 of 3) 4 6 RANGE - (ff) 4 6 RANGE - (ft) 4 6 RANGE - (ff) E63 370 Waves T10 - Solid 370 Waves T03 - Dashed 250 Waves T10 - Solid 250 Waves T03 - Dashed 8 10 , eae area ate earn Tea ns ly celta reel yer all eal eal ema Teae Irlernaliee melee] 1450 Waves T10 - Solid 1450 Waves T03 - Dashed ELEV. - (ff) ELEV. - (ft) SEAWALL IMPACT - MONO. WAVES 1650 Waves T10 - Solid =| 1650 Waves T03 - Dashed — -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) 1850 Waves T10 - 1850 Waves T03 - RANGE - (ft) Figure E19. (Sheet 3 of 3) E64 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) SEAWALL IMPACT - IRREGULAR WAVES Figure E20. 40 Waves T11 - Solid 40 Waves T0939 - Dashed 0 2 4 6 8 10 12 14 16 RANGE - (ff) 80 Waves T11 - Solid 80 Waves T0939 - Dashed 170 Waves T11 - Solid Ss 170 Waves T0939 - Dashed = 0 2 4 6 8 10 12 14 16 RANGE - (ff) Seawall impacts under irregular waves, T1ll versus TO9 (Sheet 1 of 3) E65 ELEV. - (ff) ELEV. - (ff) ELEV. - (ff) SEAWALL IMPACT - IRREGULAR WAVES 370 Waves T11 - Solid 370 Waves TO9 - Dashed -4 2 0 2 4 6 8 10 12 14 RANGE - (ff) 750 Waves T11 - Solid 750 Waves T0939 - Dashed -4 -2 0 2 4 6 8 10 12 14 RANGE - (ff) 1450 Waves T11 - Solid 1450 Waves T0939 - Dashed -4 =2 0 2 4 6 8 10 12 14 RANGE - (ff) Figure E20. (Sheet 2 of 3) E66 al ELEV. - (ft) ELEV. - (ff) SEAWALL IMPACT - IRREGULAR WAVES 16S0 Waves T11 - Solid 1650 Waves T0939 - Dashed -4 22 0 2 4 6 8 10 12 14 RANGE - (ff) 1850 Waves T11 - Solid 1850 Waves T0939 - Dashed -4 -2 0 2 4 6 8 10 12 14 RANGE - (ff) Figure E20. (Sheet 3 of 3) E67 ELEV. - (ft) ELEV. - (ft) ELEV. - (ff) SEAWALL - IRREGULAR H1/3 = Hmono Figure E21. 40 Waves T11 - Solid 40 Waves T10 - Dashed 0 2 4 6 8 10 12 14 RANGE - (ff) 80 Waves T11 - Solid 80 Waves 110 - Dashed 0 2 4 6 8 10 12 14 RANGE - (ff) 170 Waves T11 - Solid 170 Waves T10 - Dashed 0 e 4 6 8 10 12 14 RANGE - (ff) Seawall irregular wave comparison, H,,;3 equals Hyono (Sheet 1 of 3) E68 ELEV. - (ff) ELEV. - (fi) ELEV. - (ff) SEAWALL - IRREGULAR H1/3 = Hmono 370 Waves T11 - Solid 370 Waves T10 Dashed -4 “2 0 2 4 6 8 10 12 14 RANGE - (ft) ?50 Waves T11 - Solid 750 Waves T10 Dashed -4 se 0 2 4 6 8 10 ioe RANGE - (ff) 1450 Waves T11 - Solid 1450 Waves T10 Dashed -4 -2 0 2 4 6 8 10 12 14 RANGE - (ff) Figure E21. (Sheet 2 of 3) E69 ELEV. - (ft) ELEV. - (ff) SEAWALL - IRREGULAR H1/3 = Hmono 1650 Waves T11 - Solid 1650 Waves T10 - Dashed -4 -2 0 2 4 6 8 10 12 14 16 RANGE - (ff) FE Sey: aaa eer nese ase SSS SSS SS — 1850 Waves T11 - Solid 1850 Waves T10 - Dashed 4 RANGE - (ft) Figure E21. (Sheet 3 of 3) E70 APPENDIX F: NOTATION C Profile along concrete sidewall of 6-ft flume d Sediment mean grain size diameter dso Median grain size g Gravitational acceleration G Profiles along glass sidewall of 6-ft flume h Water depth hm Model profile elevation h, Prototype profile elevation H Wave height Hmo Primary energy-based wave height Hmono Monochromatic wave height H, Deepwater wave height H,ms Root-mean-square wave height Hy/3 Significant wave height equal to average of the highest one-third irregular waves H/L Wave steepness H,/L. Deepwater wave steepness K, Reflection coefficient L_ Local wavelength L, Deepwater wavelength m Subcript representing model N _ Prototype-to-model ratio of the subscripted parameter N, Gravity scale Nz Length scale N, Time scale N. Fall speed scale N, Scale based on horizontal velocities p Subscript representing prototype P Center-line profile time T Wave period Umar Maximum orbital water particle velocity near the bed U, Critical velocity for incipient motion of the sediment w Fall speed of median grain sediment size y Spectral width parameter +! Immersed specific weight of sediment Fl i aM iy mi Ne ; "dbl ecole earY i es: ance Wiese ieorh ot mh a ayn wv of aia grout sya rrCnun gies | tag ies. ibe Se Ue Ould Goel , POR es Saks Satedael ase os O \" J 1 oe pe natn Sr er 7 he’ ‘ i APY Coo ves “hs gendesho ‘ta Fat I cy ? ee aw: tty May ih oe m Ai ( sic ; i fats) y i! finsaricion ‘eye * J is ; : His ate ltt * ] Ms \ y She ey A ras 4 } , \ i ( Lek eS aa, AG . i ih ibaa) tale qe hating eet ah FR Res ; Or Pa es ae By Sy Ad L : Ni ven i Lek ipa iia, 6 ntuontixa a i 4) a 4 AY Z 0 + auth wie uit Seca Ge Brivek, iWin eile cel Ayo Manny Ki DEPARTMENT OF THE ARMY WATERWAYS EXPERIMENT STATIO N, CORPS OF ENGINEERS 3909 HALLS FERR Y ROAD VICKSBURG, MISSISSIPP| 39180-6199 —_—, Official Business CEWES-IM-MI-S DIRECTOR COAS TAL MANAGEMENT 100 CAMBRIDGE Sil BOSTON MA 02202-0001 37928/012/0)