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APPENDIX CPrediction of Beach Nourishment Performance INTRODUCTION Beach nourishment is the placement of relatively large quantities of good- quality material on a beach to advance the shoreline seaward and to provide an elevation to adequately protect the upland area. Usually, beach nourishment is carried out in areas where the shore protection beach, the recreational beach, or both are inadequate to fulfill the intended function or functions. Beach width and elevation inadequacies can occur because the shoreline is retreating or by impru- dent location of upland construction. Erosion can be either natural or human induced. In the latter instance, it is important to attempt to remove or reduce the cause of erosion whenever possible. Beach nourishment material is usually placed on a steeper-than-equilibrium slope; it also represents a planform perturbation. These disequilibriums in both the planform and profile induce sediment flows that, over time, will reduce the disequilibrium, thereby approaching the equilibrium state. Retention structures can be employed to increase the longevity of the project, but in many situations they can also increase erosion on adjacent shorelines. Performance can be pre- dicted with simple, relatively rapid, inexpensive methods and also through the use of numerical models. The time scales associated with project equilibration are of considerable design interest and are critical to the economic viability of a project. Figure C-1 illustrates the complicated three-dimensional sediment trans- port patterns associated with various phases of project evolution. Although beach nourishment projects have been carried out actively for several decades, there is still not an adequate methodology to predict their de 167

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168 l BEACH NOURISHMENT AND PROTECTION Increasing Time ~ :=~3 I ~ Profiles ! (a) Offshore Transport on Over- (b) Onshore Transport on Flattened (c) Onshore Transport in Zone of steepened Profiles and Long- Profiles and Longshore Transport Flattened Profiles Due to Long shore Transport Due to Wave Due to Wave Obliquity. shore Transport Distribution Obliquity. Across the Surf Zone. FIGURE C-1 Three Phases of observed sediment transport in the vicinity of nourished projects. Note: cross-contour transport due to profile disequilibrium (from Dean et al. 19931. tailed performance. This is due in part to the complicated alongshore and cross- shore transport processes, the near uniqueness of every setting for such projects, and the generally inadequate monitoring of both the forces on and responses of past projects to provide a basis for assessment of available methodologies and guidance for their improvement. This appendix reviews simple analytical and numerical procedures available for prediction of beach nourishment project performance, introduces some less- well-known behavioral characteristics affecting performance, and provides esti- mates of predictability under various nourishment scenarios. METHODS FOR PREDICTING BEACH NOURISHMENT PROJECT EVOLUTION Simple Analytical Procedures The simple analytical prediction procedures are best suited for the less com- plex geometries and for preliminary design in the early phase and scoping of the volumes, costs, and renourishment intervals. More complex geometries, includ

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APPENDIX C 169 ing the effects of structures, require the use of numerical models and are dis- cussed later. Evolution of a beach nourishment project is a result of both cross-shore and alongshore sediment transport. For the simple case of a long nourishment project on a long straight beach, the time scales for cross-shore and planform equilibra- tion are disparate. The cross-shore and alongshore time scales are on the order of 2 to 3 years and decades, respectively. This discussion will assume that the profile adjustment occurs instantaneously. For this adjustment, predicting the equilibrium width of dry beach is the principal focus. For the alongshore equili- bration, the focus is on the time scales and evolutionary behavior. The disparity of time scales is fortunate because current knowledge of alongshore sediment transport has been developed over a period of 4 or 5 decades. The knowledge of alongshore sediment transport is much more advanced than for cross-shore trans- port, which has been studied actively for only about a decade. Equilibrium Dry Beach Width In cases in which the nourishment material is similar to the native beach material, the additional dry beach width after equilibration, /\yO, can be shown to be approximately V h* + B (C-1) in which V is the volume of fill added per unit beach length and h* + B represents the dimension of the active vertical profile, where h* is the depth of active motion (depth of closure) dependent on the upper ranges of wave height experienced, as given by Hallermeier (1978) and Birkemeier (1985), and B is usually selected as the height of the active natural berm but may exceed this elevation for flood control purposes. Dean (1991) has shown that for the general case in which the native and fill materials differ the additional dry beach width can differ substantially from that given by Equation (C-11. In this case, the best approach is to use the equilibrium beach profile concept, in which the simplest profile form is h=Ay where h is the depth at a distance y from the shoreline. (C-2) Equation (C-2) represents the ideal profile that occurs naturally and cannot represent bar features or effects of rock outcrops, hard bottoms, or coral reefs. Use of these idealized assumptions in applying Equation (C-2) has been criticized by Pilkey et al. (1993~. Equilibrium beach profile forms other than Equation (C- 2) have been proposed by Bodge (1992), Komar and McDougal (1993~; and

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170 - tr: UJ ~ 0.10 LL I: J o 0.01 BEACH NOURISHMENT AND PROTECTION SEDIMENT FALL VELOCITY, w (cm/s) 0.01 1.0 From Individual Field Profiles Where a Range of Sand Sizes was Given From Swartz's ~ Laboratory Results 0.1 I Suggested Empirical Relationship A vs. D (Moore) 1.0 10.0 100.0 From Hughes' FiRId Results ~;p ~~ Based on transforming _0- ~ A vs. D Curve Using Fall Velocity Relationship ff-' '0 ~~ A=0.067w0~44 0.01 0.1 1.0 10.0 100.0 SEDIMENT SIZE, D (mm) FIGURE C-2 Variation of sediment-scale parameter, A, with sediment size and fall velocity (from Dean, 1987~. Inman et al. (1993), however, these authors provide no guidance for applying these forms in cases where only the grain size is known. In order to apply Equation (C-2) to beach nourishment, a relationship is needed between the sediment-scale parameter, A, and the grain size, D, or equiva- lent sediment fall velocity, w. Such a relationship, originally developed by Moore (1982) and modified by Dean (1987), is shown in Figure C-2. In applying Equa- tion (C-2) the parameters for the native and fill materials will be indicated by subscripts N and F. respectively. In general, three types of nourished profiles can occur, depending primarily on the relative A parameters and the amounts of fill placed. These types, intersecting, nonintersecting, and submerged, are illustrated in Figure C-3. It can be shown that the nondimensional dry beach width, l~yO/W*, is a function of the three nondimensional variables: /\YO ~ V AF W* ~ BW* AN B h* = ~V', A,, hB ~ (C-3) where V is the volume added per unit beach length and B is the berm height. W* is the width of the active profile (to h*) on the native profile, that is, from Equation (C-2~: W*= h :312 ~AN) (C-4)

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APPENDIX C 171 (a) Intersecting Profile APA;N (b) Non-lntersecting Profile Ay<0 . . B Added Sand 2~ - `,~_ . . . ~ . _ .... . .~ 1' W* ~ ~ Aye Adds //// h* t h* :~7,)t :__ vv. ~ Virtual Origin of~ `;~ | Nourished Profile~ `_ 1 'an; ~ (c) Submerged Profile AF OCR for page 167
72 To W* on 10.0 0.001 . 1 1 1 _ AW = AVIBW,* = 10.0, T N1 =~:Z . I / =~ =: _ _ _ _ __ ~ 1 '1 At ymptot as' I toy= _ 1. 1 w I ~ _ 1 o~W-t i= SIB 46 - Definition Sketch . ~ \], s o.O ~ i tS on-lot `;,^ -~ _q',!~_ ~, ~ Em-. , 1, : . ~- W ll ~' Mel ... , . l ~ h* - ,_. ! ' 0 1.0 A = AF/AN BEA CH NO URISHMENT AND PR O TECTI ON v~=0.5 1 V. = 0.2 --r-r~ V. = 0.1 . a. 1 1 . V* = 0.05- i. T T T I _Y*=0.02 _ --t-T- V. = 0.01 _ ~ 1 - . l l 1 1 ~ = 0.005 -' 1 - 1 '- 1 1 = V/BOO. = 0.002 . __ . 2.0 FIGURE C-4 Variation of nondimensional shoreline advancement, /\yOIW*, with A' and results shown for h*lB = 2.0 (from Dean, 1991). Figures C-4 and C-5 present graphical solutions to Equation (C-3) for values of hJB of 2 and 4, respectively. Planform Evolution Planform evolution is influenced by the general morphology of the system to be nourished; the simplest case is a long straight beach. The planform of the nourishment can influence the performance; however, the initial discussions here will address the case of an initially rectangular planform for which analytical solutions exist.

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0.1 0.01 0.001 0.~01 . . = Non-lotomocting - . ._ - ~ =~=~ / ~ /] #~7 ~ - _ ^symp~tes J _ ~~=~= ~ . if-. ~ ~- `~ ~ . ~ ~- ,# ~ ~ . 'a.,, - :~ Dandy Sag n _ . _ 'If -- _ ~ ~ ~ . ~ 1 ~ ~ ~ loterse~ng Profile ~J-~- - i'=1 = _ go - go '' R1' . ~ = 0~1 _ = ~ + ~ ~ I 1 V'= 0.002 . 1 1 ~=~0~1 ~ __ ~ '- i 1 I . - ~ hi. AF ~ ~ ~=~ sw.) 1 ,.0 2.0 A'-A ~ F N FILMY C-5 V~adon of nondimensional sborobno advancement #0/^, Cab at' and results sbo~D for A~ = 4.0 (hoary Dean, 19917 7~

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174 BEACHNOURISHMENT AND PROTECTION Pelnard-Considere (1956) combined the linearized equation of sediment transport and the equation of continuity, considering the profiles to be displaced without change of form, to yield =G Y At~x2 (C-S) in which G is the so-called alongshore diffusivity and can be expressed in terms of breaking or deepwater wave conditions, respectively, as - ~ - ~(~ Ah B' (for breaking conditions) (C-6) KHo COO g 8~5 - 11~1 - p)C*K (h* + B) (for deepwater conditions) (C 7) in which K is a sediment transport factor usually taken as 0.77 but is probably a function of sediment grain size or other characteristics, H is the wave height, and K iS the ratio of breaking wave height to local water depth (usually taken as 0.781. CG is the wave group velocity, C* is celerity at the depth of closure, s is the ratio of the specific gravity of the sediment to that of the water in which it is immersed (a 2.65), p is the porosity (a 0.35), and g is the acceleration of gravity. The subscripts b and 0 denote breaking and deepwater wave conditions, respectively. Project Longevity for Simplest Case It can be shown that in the absence of background erosion the fraction of material remaining, M, in the region where fill is placed depends only on the parameter ~/~1{, in which His the length of the initially rectangular project and t is time (see Figure C-6~. For values of M between 0.5 and unity, it can be shown that within a 15 percent error band in M an approximate expression for the relationship in Figure C-6 is M=1- ~ (C-8) A useful result developed from Equation C-8 is the time (t50%) for 50 percent of the placed volume to be transported from the original project limits: e2 tSo% = K s/2 Hb (C-9) in which tSo% is expressed in years, and K'= 0.172 years m5/2/square kilometer for he in kilometers and Hb in meters.

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APPENDIX C 1.0 :~ IL ~ o Z Us 'A o o lL ~ Z C' 0 0 5 ~-<( G G - 175 0.0 0.5 1.0 I I I I I rl ~ ~ T - 1 ~1 1 1 1 1 1 ~1 1 1 1 1 1 1 1 1 1 1 to Rime After Placement -\ ~ _ G ~ Alongshore Diffusivity - \ Asymptote 2 M = 1 - ` 0.0 1 1 1 1 1 1 1 1 1 Initial Fill Planform T L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T 0 1 2 3 4 5 6 ,~ FIGURE C-6 Proportion of material remaining, M, in region placed as a function of the parameter. Fill Performance with a Uniform Background Recession Rate, E For the case in which a uniform background shoreline recession rate, E, is present, it can be shown that for values of W' <0.5 the time required for a fraction (1-M) of the material placed to be removed from the project area (or equivalently for a fraction M of the material placed to remain in the project area) is tM = 2a -b + ~b2 _ 4ac in which and a = (EI ~yO)2, b = 2E(M- 1) 4 G_ /\YO 7r c= (1 _My2 in which l\yO is the initial dry beach width, as defined earlier. (C-10)

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76 BEACH NOURISHMENT AND PROTECTION Effect of Wave Refraction Around the Project It can be shown, consistent with intuition, that waves refract, wrapping around the nourishment planform and thereby tending to prolong its life. Equa- tion (C-6), applied in conjunction with Figure C-6, does not include the refraction effects, but they can be approximated simply by multiplying the G value in Equation (C-6) by the fraction Cb/C.*, in which C is the wave celerity and the subscripts b and ~ denote values at breaking and depth of closure h*, respectively. Since this ratio is generally less than unity, the effect is a greater project longevity with reduced G values. In some applications in Florida the effect of this correc- tion results in a t50% that is 40 percent greater than without this factor. Residual Bathymetry In contrast to the usual assumption that the entire placed beach profile moves without change of form during evolution of the project planform, in some cases the beach nourishment may extend to greater depths than will be mobilized, at least during the first few years following nourishment. If the initial placement is irregular, this can affect the quasi-equilibrium planform. In an idealized fashion the upper portions of the placed profile are "planed off'' by the alongshore trans- port, leaving the placed material below this level of activity as "residual bathym- etry." Although this residual bathymetry is not active in the transport processes, it does influence the wave transformation, in particular wave refraction. The effect of the wave refraction is to cause the quasi-equilibrium planform to remain irregular rather than to be straight, as would be the case if the entire placed planform moved in response to gradients in the alongshore sediment transport. The equilibrium shoreline planform will be a somewhat damped form of the offshore residual bathymetry. Denoting the celerity of the waves at the outer depth of the placed bathymetry as Cob and that at the depth of limiting motion, ha, as C2 (C~ > C2), it can be shown that the project-related transport, Qp, is KEoCGo cos(>o b :( - -i)~i + 2] (C ll) Eggs - 13~1 - P)C2 in which the ~ variables represent the azimuths of the outward normals of the various contours as depicted by their subscripts, and the /\13n are defined bY/~pn = 13n -130 p is the mass density of the water, and or is the azimuth from which the wave Is propagating In deep water. This result can be interpreted intuitively as the onshore contours "mimick- ing" those offshore. This phenomenon, as represented by Equation (C-ll), may explain why some beach nourishment projects experience erosional hot spots at which the beach erodes faster than the average for the project. Other possible causes of some erosional hot spots are a break in the offshore bar and wave refraction over an offshore mound, which allow wave energy to impact the shore

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APPENDIX C 177 line. Returning to the case in which the erosional hot spots are explained by Equation (C-ll), if for some unintended reason the placed material along the shoreline is not distributed uniformly and if the sediment at the deeper portions of the profile does not move at the same rate as that at the upper elevations, Equation (C-11) may provide an explanation of the cause of erosional hot spots. Regardless of their cause, Equation (C-11) may provide a basis for remedying such effects. For example, if the natural contours seaward of the placed material are such that they cause localized erosion, it may be possible (although not practical in all cases' to place material seaward of the active zone in a planform to refract the waves in a manner that balances the tendency for localized erosion. Equation (C- 11) can be used to find the shoreline of approximate planform equilibrium. This occurs, of course, for Qp = 0 and yields A~2 =~1-(Cc9-)l (C-12) from which it can be seen that if there is no residual bathymetry (C: = C1) the equilibrium shoreline orientation, p2 is equal to DO. As an example, if the plan- form relief in the offshore residual contours were 50 m and the celerity ratio C2/ Car = 0.5, the planform relief of the shoreline would be 25 m. Numerical Models for Predicting Beach Nourishment Performance Computer Models of Alongshore Shoreline Evolution An important tool in the design and implementation of many beach nourish- ment projects is the application of computer models that simulate the processes of alongshore sediment transport and the resulting evolution of the shoreline plan- form. Such models incorporate equations that relate sediment movements to the nearshore waves and currents. They also include a continuity equation that in essence keeps track of the total volume of beach sediment as it is redistributed alongshore and permits computations of the resulting patterns of shoreline reces- sion or advance. Such numerical simulation models have proved to be useful tools in a number of applications, including analyses of the impacts from con- struction of jetties and breakwaters on the shoreline configuration and predicting the patterns of shoreline change. Only in recent years have they been applied to beach nourishment projects. However, the use of numerical models has become a standard tool in the design of beach nourishment projects involving the U.S. Army Corps of Engineers (USAGE), although the application of this tool varies between USACE districts. The general approach to computer models of shoreline change involves the conceptual division of the shoreline into a large number of individual cells or compartments. Equations relating the alongshore sediment transport rate to the wave parameters that is, to wave heights or energies and to velocities of

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78 BEACHNOURISHMENT AND PROTECTION alongshore currents are employed to calculate the shift of sand from one cell to the next. The continuity equation, based on the conservation of sediment, makes sure that none is unaccountably created or destroyed. But more importantly, it can convert volumes of sand entering or exiting a particular cell into the resulting shoreline changes, whether these changes are net advances or recessions. In general, sand enters a particular cell from one direction and exits in the same direction, so it is the net volume of these transfers that ultimately governs whether there is recession or advance of the shoreline as represented by that cell. Such an analysis involves many computations of sand exchanges between cells and the resulting net volumes of sand in the many cells, and such a computationally intensive analysis requires the use of a computer. Furthermore, the model is run through time so as to simulate the shoreline evolution spanning months to de- cades. In some cases, the models must be run on large powerful computers if an extended stretch of shoreline is being analyzed for predicted shoreline changes spanning many years. Reduced versions of such model analyses are also avail- able for desktop computer applications. Early examples of computer models of shoreline change that have a range of applications are provided by Price et al. (1973), Komar (1973, 1977), and Perlin and Dean ( 1979~. These early studies established the validity of computer models and demonstrated their reliability in a number of applications. The study by Price et al., an analysis of the impoundment of sand by groins, is especially noteworthy in that it provided the first comparison between the results from a computer model and a physical model undertaken in a laboratory wave basin. The most recent advances in numerical models used to simulate shoreline changes have been incorporated into GENESIS, an acronym for generalized model for simulating shoreline change. GENESIS was developed by the USACE. Details of the technical development of GENESIS are given in a report by Hanson and Kraus (1989), and a report by Gravens et al. (1991) serves as a workbook and user's manual. One of the chief contributions of the GENESIS model is that it provides a flexible basis for analyses that can be applied to an arbitrary prototype situation a basis that calculates wave transformations as they shoal and undergo refraction and diffraction, calculates the patterns of alongshore sediment trans- port, and then determines the resulting shoreline changes. One of the principal modifications of the GENESIS model from earlier models is in the calculation of alongshore sediment transport rates, an approach that includes the transport caused by waves breaking obliquely to the shoreline and alongshore variations in wave breaker heights. This modification enhances the capability of GENESIS to simulate shoreline changes in proximity to structures such as jetties and groins, where local sheltering from Offshore waves is a factor. The importance of this inclusion in numerical shoreline models was first demonstrated by Kraus and Harikai (1983) in their analyses of Oarai Beach, Japan, where wave diffraction at a long breakwater is a dominant process, and subsequently in some of the appli- cations of GENESIS that also include shoreline structures.

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APPENDIX C 179 Hanson et al. (1988) applied GENESIS to a simulation of the shoreline development on Homer Spit, Alaska, and the erosion downdrift from a seawall on Sandy Hook, New Jersey. The most complex analysis, examined in great detail by Hanson and Kraus (1991a), was of shoreline changes at Lakeview Park, in Lorain, Ohio, on Lake Erie. This analysis simulated the shoreline changes ob- served following the construction of three detached breakwaters in the offshore and two bounding groins and the addition of sand to create a new beach. The simulation involved analysis of wave diffraction through the gaps between the breakwaters and of the resulting readjustment of the shoreline from its original smooth curvature after sand emplacement. Cusps or salients developed in the sheltered region behind each breakwater, with intervening bays opposite the gaps between the breakwaters. The agreement between the measured shoreline and that computed by GENESIS was excellent. However, the result represents a calibration of the model that included some adjustment of empirical coefficients to optimize the fit. After the model had been calibrated and tested versus ob- served shoreline changes, Hanson and Kraus (1991a) explored alternative project designs for maintaining the beach fill. This included analyses of the beach reten- tion for various lengths of the bounding groins and for the absence of any groins. Such analyses demonstrate the usefulness of numerical shoreline models in gen- eral and GENESIS specifically, as many alternative designs can be examined at minimal expense. Hanson and Kraus (1991b) compared GENESIS predictions to the results obtained in physical models, again for a series of detached breakwaters such as those at Lakeview Park but also for the impoundment of sand in a series of groins built across the beach. In all cases, the numerical models closely repro- duced the shoreline changes that occurred in the physical models. GENESIS includes analyses of wave refraction in the offshore. Therefore, its use can incorporate design and implementation aspects involving predictions of potential impacts that result, for example, from changes in offshore water depths that are produced by dredging in the source area for sand for nourishment. These potential impacts are illustrated by the earlier study of Motyka and Willis (1975), which also developed shoreline simulation models coupled with wave refraction/ diffraction analyses. The necessity for computing wave refraction patterns con- siderably increases the complexity of the model in that it requires an offshore array to account for the bottom topography as well as to define the shoreline position, with the possibility of both evolving through time. The problem ana- lyzed by Motyka and Willis involved an examination of whether dredging of sediment from the continental shelf could alter the wave refraction to a sufficient degree that it induces shoreline erosion. One example of the model calculations of Motyka and Willis (1975) is the consideration of the effects of dredging a 4-m-deep hole in water that is 7 m deep and 500 m offshore. The model used realistic profiles of the beach and offshore and had a dredged hole inserted. The root-mean-square wave height was 0.4 m, and periods of 5 and 8 seconds were used. Wave directions were selected so as to

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80 BEACH NOURISHMENT AND PROTECTION yield a net alongshore sediment transport of 30,000 m3/year. The results demon- strate that the dredged hole would cause recession of the shoreline in its lee and an advance to either side. The pattern is asymmetrical owing to the superimposed alongshore sediment transport that results from an overall oblique wave approach. The shoreline alterations are greater with the 8-second waves than with the 5- second waves because the longer-period waves undergo more refraction. The models predict major erosion that results from offshore dredging-a shoreline retreat of 20 to 35 m that exists over a kilometer of shoreline length. Another example of shoreline recession induced by offshore dredging for a beach nourish- ment project can be seen at Grand Isle, Louisiana (Combe and Soileau, 19873. The dredging there occurred over a wide area about 500 m offshore and lowered the bottom by 3 to 6 m. The resulting development of an erosional embayment between accretional cusps is very similar to that obtained in the numerical models of Motyka and Willis (1975~. Although Combe and Soileau confirmed that the impact at Grand Isle was due to the effects of the dredged hole on wave refrac- tion, detailed numerical analyses were not undertaken. In a somewhat comparable fashion, offshore shoals can focus the wave en- ergy on specific stretches of shoreline through their effects on the patterns of wave refraction over the shallower water. In some instances, this process may account for erosional hot spots in nourishment projects. The process has been suggested as a cause of the erosional hot spots that have occurred at Ocean City, Maryland. Analyses using shoreline models such as GENESIS that include wave refraction have the potential for predicting locations of erosional hot spots and could be used to analyze whether the focus of erosion might be eliminated by dredging the offshore shoals to some determined water depth. Shoreline models such as GENESIS have been discussed here as an aspect of the design of beach nourishment projects and have been used to predict the shoreline evolution of the sand fill. They can be equally useful during the moni- toring phase of a project because the models unite measurements of beach pro- files that can be used to determine the actual resulting patterns of shoreline recession and advance. This is illustrated by Work (1993), who analyzed moni- toring data for the nourishment project at Perdido Key, Florida. The continued use of numerical shoreline models in the monitoring phase of this project has provided an additional basis for improvements in the models themselves and a greater confidence in future projects, especially at this site. One advantage of computer models is that they allow determination of the effects of particular placement configurations and wave variability. For example, Hanson and Kraus (1993) have investigated the effectiveness of transitioning the ends of a project to reduce total costs, including that of renourishment. The numerical methods could use actual wave data or a simulation of serial wave data rather than an equivalent wave height, period, and direction, or a combination of the three. At present, the prediction of shoreline position by numerical models in some applications may be limited by the accuracy of available wave information.

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APPENDIX C 181 There are at least two options to account for the background erosion rates with numerical models. In applying GENESIS the model should be calibrated with historical shoreline changes, so that it can faithfully represent the causes of the background erosion. A second procedure, recommended by Dean and Yoo (1992), is that the empirical background erosion be represented as background sediment transport and be superimposed on the transport induced by the nourish- ment project. In the absence of nourishment, this method ensures that the back- ground erosion will be reproduced exactly. The numerical models of shoreline evolution are based on the same equa- tions as the analytical method described earlier, except that one of the equations is linearized in the analytical method. Generally, if the two methods are applied to the same initial planform and wave conditions, the results are essentially the same. The numerical models also share many of the uncertainties in applications with the analytical models discussed earlier. Model predictions are limited by the ability to predict alongshore sediment transport rates. Any uncertainties in the transport calculations carry over into the model predictions of the shoreline evo- lution. The dependence of the alongshore transport on sediment grain sizes is not well established. This especially affects the ability to model the evolution of a beach fill where the nourishment material does not fully match the grain-size distribution of the native beach sand. Although full three-dimensional models that account simultaneously for cross-shore and alongshore sediment transport are available, the commonly applied models such as GENESIS deal only with alongshore evolution of the shoreline, and separate models, such as SBEACH, analyze the cross-shore sediment transport. The models sometimes need recalibration for the specific site of the application or verification during the monitoring phase of a nourishment program because of uncertainties in the trans- port calculations and because of simplified assumptions that are used in develop- ing the shoreline evolution models. Prof le Evolution Numerical models are also available to represent profile evolution and can, in principle, be used to simulate the equilibration of a placed profile or the profile response during a storm. The structure of these models is similar to that described for planform evolution that is, there is a dynamic or transport equation that prescribes the sediment flow across the profile and a continuity equation that conducts the bookkeeping of differences between sediment flows in and out of a computational cell and equates those differences to changes in profile elevation. These computational models have been employed and verified to a limited degree in the equilibration phase of a fill; however, only limited efforts have been de- voted to the recovery phase following storms. The earliest profile evolution models include those of Edelman (1972), who assumed that the profile maintained the same shape as the original while it is

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82 BEACH NOURISHMENT AND PROTECTION translated and that the profile equilibration processes kept pace with the rising sea level. Swart (1974) developed a complex computational model based on a series of laboratory tests. Moore (1982), Kriebel (1982), and Kriebel and Dean (1985) have described a profile response model based on a transport that is proportional to the difference between the actual and equilibrium wave energy dissipation per unit of water volume. Limited evaluations of prototype and laboratory data pro- vide support for this transport relationship. Kriebel et al. (1991) and Kriebel and Dean (1993) have described an analytical method, based on observations from numerical models, in which the profile tends to approach the equilibrium in an exponential manner for a constant water level. Kriebel (1990) has described modifications to his model that allow the effects of seawalls and overwash to be represented. The Kriebel and Dean (1985) model (EDUNE) was used to some extent in the design of the Ocean City, Maryland, beach nourishment project, although its use was limited because it was not calibrated or verified for erosion events at Ocean City. The numerical modeling system and storm erosion models were used to evaluate and compare the relative effectiveness of each plan rather than to determine the dimensions of the alternative proposed plans. The profile evolution model employed by the USACE is called SBEACH (Larson and Kraus, 1989a, 1991) and uses a modified form of the transport equation described earlier. This model is well documented and is in the public domain. It differs from the others described earlier in that it can predict the formation of bars-in the eroding profile. The model has been calibrated and verified for both laboratory and prototype profiles. Larson and Kraus (1989b, 1990) have compared SBEACH predictions with results from a test using a large wave tank and field data from Duck, North Carolina. The model was also used to analyze the design of the Ocean City nourishment project after the storm of January 4, 1992. It was tested both with and without overwash, a feature that was added to the model to attempt to represent the processes contributing to profile changes during the storm (Kraus and Wise, 1993; Wise and Kraus, 1993~. SBEACH allows the effects of seawalls to be represented. With respect to SBEACH simulations for the Ocean City project, the model calibration param- eter was 20 percent below that determined in an earlier publication treating a lesser storm on a smaller fill section at the same site. For Ocean City, Maryland, Hansen and Byrnes (1991) quote an SBEACH transport coefficient of 1.0 x 10-6 m4/N, Kraus and Wise (1993) quote 1.5 x 10-6 m4/N, and Wise and Kraus (1993) quote 1.2 x 10-6 m4/N. The SBEACH simulations were not correlated with the original application of the Kriebel-Dean model. The present version of SBEACH (Version 3.0) contains additional improvements not found in the versions used in either of the previous studies mentioned. NOURISHMENT IN THE PRESENCE OF STRUCTURES Coastal structures can be used to increase the longevity of beach nourish- ment projects. Structures for this purpose include groins, terminal structures, and

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APPENDIX C 183 submerged or emergent offshore breakwaters. In addition, some projects will be carried out in areas where seawalls are present. Due to the complexity of the interaction of sediment transport processes with coastal structures, prediction of the performance of beach nourishment projects in the presence of coastal struc- tures will usually require the use of numerical models. Knowledge of the interac- tion of coastal structures with beach systems is on the edge of the state of the art. Retention Structures The "spreading out" losses due to alongshore sediment transport can be reduced by placing retention structures near or at the ends of a project. These structures, also frequently referred to as "terminal structures," increase the lon- gevity of the project by reducing transport from the project to adjacent areas. In considering the use of such structures, careful consideration must be given to the possibility and degree to which they might affect the shorelines adjacent to the project. The potential for impact is much greater in those cases where a substan- tial alongshore sediment transport exists. To partially alleviate the early impacts of transport interruption, a surcharge of sand can be placed on the downdrift side of the downdrift retention structure. Seawalls A limiting effect of mismatch of the native and nourishment materials occurs when nourishment is placed in front of a shoreline that is backed by seawalls and has alongshore transport potential but little sediment-to-transport potential. In this case, it can be shown that the planform evolution is markedly different from nourishment on a beach of compatible sand. The behavior of the beach planform has been modeled in GENESIS since its inception and is documented in both the technical reference and specialized publications (Hanson and Kraus, l991a,b; Gravens et al., 1991~. Dean and Yoo (1994) have shown theoretically, numeri- cally, and experimentally that the planform evolution is critically dependent on the transport characteristics near a project's end, in particular for those portions of the project where the "active" profile does not extend up to the free surface. The general differences include a downdrift migration of the planform centroid, with initially increasing and later decreasing speed, and a spreading of the plan- form, which can be significantly less or greater than would occur on a beach with compatible sand. The behavior of the beach planform in front of seawalls was previously incorporated into GENESIS (Hanson and Kraus, 1985, 19893. Figure C-7 presents an example of a calculated planform and volumetric evolution for the case of nourishment in front of a seawall and under the action of oblique waves. The upper panel shows the shoreline displacement and the lower panel the volumetric distributions. The "threshold volume" is that associated with an incipient dry beach; that is, sufficient sand is present to just fill the profile to the water line at the seawall. The planform migrational tendency shown in the

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184 120 100 - z 80 ~60 In cat IIJ z40 up o I20 Oh 1 200 1 000 800 by600 LL 400 o 200 O BEACH NOURISHMENT AND PROTECTION a) Planforms at Years: 0, 1, 3, 5, 10, 15 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Longshore Distance, (m) b) Volume Densities at Years: 0, 1, 3, 5, 10, 15 - ~;~ Threshold Volume tt:405 m' ~ 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Longshore Distance, (m) FIGURE C-7 Calculated planform and volumetric evolution of an initially rectangular beach nourishment project fronting a seawall. Deepwater waves at 10 to shore normal (from Dean and Yoo, 19941.

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APPENDIX C TABLE C-1 Beach Nourishment Invariants 185 Description of Invariant Initially symmetric planforms remain nearly symmetric even under oblique wave attack (Note: this implies that wave direction is relatively unimportant) Planform evolution at any time is independent Same as above of the sequencing of the previous waves causing the evolution Good-quality sand remains in the active beach profile Conditions Nourishment on a long, straight beach with compatible sediment Good-quality sand has the same general size characteristics as that originally present on the beach figure can be interpreted as due to the oblique waves "cannibalizing" the sand on the updrift end of the project and depositing it on the downdrift end. In the case of nourishment on a shoreline of compatible sand, owing to the small aspect ratio of the project, the transport patterns can be linearized approximately as the superim- position of alongshore transport on an unperturbed shoreline and normally inci- dent waves acting on the nourishment project. This is the reason that nourishment on a beach of compatible sand will result in little downdrift migration or plan- form asymmetry. In those cases in which nourishment occurs in front of a sea- wall, there is a much greater need to establish the directional characteristics of the waves than for nourishment on a beach of compatible sand. INVARIANTS Although there are uncertainties associated with the design of beach nourish- ment projects, there are also some invariants or performance characteristics that are insensitive to some physical processes. Three relevant design invariants are characterized in Table C-1. REFERENCES Birkemeier, W. A. 1985. Field data on seaward limit of profile change. Journal of the Waterway, Port, Coastal, and Ocean Engineering 3(3):598-602. Bodge, K. R. 1992. Representing equilibrium beach profiles with an exponential expression. Journal of Coastal Research 8(1):47-55.

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86 BEACH NOURISHMENT AND PROTECTION Combe, A. J., and C. W. Soileau. 1987. Behavior of man-made beach and dune, Grand Isle, Louisi- ana. Pp. 1232-1242 in Proceedings of Coastal Sediments '87, Specialty Conference on Ad- vances in Understanding of Coastal Sediment Processes, Vol. 2. New York: American Society of Civil Engineers. Dean, R. G. 1987. Coastal sediment processes: toward engineering, solutions. Pp. 1-24 in Proceed- ings of Coastal Sediments '87, Specialty Conference on Advances in Understanding of Coastal Sediment Processes, Vol. 1. New York: American Society of Civil Engineers. Dean, R. G. 1991. Equilibrium beach profiles: characteristics and applications. Journal of Coastal Research 7(1):53-84. Dean, R. G., and C-H. Yoo. 1992. Beach nourishment performance predictions. Journal of the Wa- terway, Port, Coastal and Ocean Engineering, 118(6):557-586. Dean, R. G., and C-H. Yoo. 1994. Beach nourishment in the presence of seawalls. Journal of the Waterway, Port, Coastal, and Ocean Engineering 120(3):302-316. Dean, R. G., T. R. Healy, and A. Dommerholt. 1993. A "blind-folded" test of equilibrium beach profile concepts with New Zealand data. Marine Geology 109:253-266. Edelman, T. 1972. Dune erosion during storm conditions. Pp. 1305-1311 in Proceedings of the 13th Coastal Engineering Conference. New York: American Society of Civil Engineers. Gravens, M. B.' N. C. Kraus and H. Hanson. 1991. GENESIS: generalized model for simulating shoreline change. In: Report 2: Workbook and System User's Manual. Technical Report CERC- 89-19. Vicksburg, Miss.: Coastal Engineering Research Center, U.S. Army Engineer Water- ways Experiment Station, U.S. Army Corps of Engineers. Hallermeier, R. J. 1978. Uses for a calculated limit depth to beach erosion. Pp. 1493-1512 in Pro- ceedings of the 16th International Conference on Coastal Engineering. New York: American Society of Civil Engineers. Hanson, M. E., and M. R. Byrnes. 1991. Development of optimum beach fill design cross-section. Pp. 2067-2080 in Proceedings of Coastal Sediments '91. New York: American Society of Civil Engineers. Hanson, M. E., and N. C. Kraus. 1985. Seawall constraint in the shoreline numerical model. Journal of Waterways, Ports, Coastal and Ocean Engineering 111(6): 1079-1083. Hanson, H., and N. C. Kraus. 1989. GENESIS: generalized model for simulating shoreline change. In Report 1: Reference Manual and Users Guide. Technical Report No. CERC-89- 19. Vicksburg, Miss.: Coastal Engineering Research Center, U.S. Army Engineer Waterways Ex- periment Station, U.S. Army Corps of Engineers. Hanson, H., and N. C. Kraus. 1991a. Numerical simulation of shoreline change at Lorain, Ohio. Journal of Waterway, Port, Coastal and Ocean Engineering 117:1-18. Hanson, H., and N. C. Kraus. l991b. Comparison of shoreline change obtained with physical and numerical models. Pp. 1785-1799 in Proceedings of Coastal Sediments '91. New York: Ameri- can Society of Civil Engineers. Hanson, H., and N. C. Kraus. 1993. Optimization of beach fill transitions. Pp. 103-117 in D. K. Stauble and N. C. Kraus, eds., Volume on Beach Nourishment Engineering and Management Considerations, Proceedings of Coastal Zone '93. New York: American Society of Civil Engi neers. Hanson, H., M. B. Gravens, and N. C. Kraus. 1988. Prototype applications of a generalized shoreline change numerical model. Pp. 1265-1279 in Proceedings of the 21st Coastal Engineering Con ference. New York: American Society of Civil Engineers. Inman, D. L., M. H. S. Elwany, and S. A. Jenkins. 1993. Shorerise and bar-berm profiles on ocean beaches. Journal of Geophysical Research 98(C10)18, 181-18, 199. Komar, P. D. 1973. Computer models of delta growth due to sediment input from rivers and longshore transport. Geological Society of America Bulletin 84:2217-2226. Komar, P. D. 1977. Modeling of sand transport on beaches and the resulting shoreline evolution. Pp. 499-513 in E. Goldberg et al., eds., The Sea, vol. 6. New York: John Wiley & Sons.

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Al APPENDIX C 187 Komar, P. D., and W. G. McDougall 1993. The analysis of exponential beach profiles. Journal of Coastal Research 10(1):59-69. Kraus, N. C., and S. Harikai. 1983. Numerical model of the shoreline at Oarai Beach: Coastal Engineering 7:1-28. Kraus, N. C., and R. A. Wise. 1993. Simulation of January 4, 1992 storm erosion at Ocean City, Maryland. Shore and Beach 61(1):34-41. Kriebel, D. L. 1982. Beach and Dune Response to Hurricanes. Master's thesis, University of Dela- ware, Newark. Kriebel, D. L. 1990. Advances in numerical modeling of dune erosion. Pp. 2304-2317 in And International Conference on Coastal Engineering. New York: American Society of Civil Engi neers. Kriebel, D. L., and R. G. Dean. 1985. Numerical simulation of time-dependent beach and dune erosion. Coastal Engineering 9:221-245. Kriebel, D. L., and R. G. Dean. 1993. Convolution method for time-dependent beach profile re- sponse. Journal of Waterway, Port, Ocean and Coastal Engineering 119(2):204-227. Kriebel, D. L., N. C. Kraus, and M. Larson. 1991. Engineering methods for predicting beach profile response. Pp. 557-571 in Proceedings of Coastal Sediments '91. New York: American Society of Civil Engineers. Larson, M. 1988. Quantification of beach profile change. Report No. 1008. Department of Water Resources and Engineering, University of Lund, Lund, Sweden. Larson, M., and N. C. Kraus. 1989a. Prediction of beach fill response to varying waves and water level. Pp. 607-621 in Proceedings of Coastal Zone '89. New York: American Society of Civil Engineers. Larson, M., and N. C. Kraus. 1989b. SBEACH: Numerical Model for Simulating Storm-Induced Beach Change. Report 1: Empirical Foundation and Model Development. Technical Report No. CERC-89-9. Vicksburg, Miss.: Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, U.S. Army Corps of Engineers. Larson, M., and N. C. Kraus. 1990. SBEACH: Numerical Model for Simulating Storm-Induced Beach Change. Report 2, Numerical Foundation and Model Tests. Technical Report CERC-89- 9. Vicksburg, Miss.: Coastal Engineering Research Center, U. S. Army Engineer Waterways Experiment Station, U.S. Army Corps of Engineers. Larson, M., and N. C. Kraus. 1991. Mathematical modeling of the fate of beach fill. Coastal Engi- neering 16:83-114. Larson, M., N. C. Kraus, and M. R. Byrnes. 1990. SBEACH: Numerical Model for Simulating Storm-Induced Beach Change. Report 2: Numerical Formulation and Model Tests. Technical Report CERC-89-9. Vicksburg, Miss.: Coastal Engineering Research Center, U.S. Army Engi- neer Waterways Experiment Station, U.S. Arrny Corps ~ Engineers. Moore, B. D. 1989. Beach Profile Evolution in Response to Changes in Water Level and Wave Height. Unpublished master's thesis, Department of Civil Engineering, University of Dela ware. Motyka, J. M., and D. H. Willis. 1975. The effect of refraction over dredged holes. Pp. 615-625 in Proceedings of the 14th Conference on Coastal Engineering. New York: American Society of Civil Engineers. Pelnard-Considere, R. 1956. Essai de Theorie de l' evolution des Formes de Rivate en Plages de Sable et de Galets. 4th Journees de l'Hydraulique, Les Energies de la Mer, Question III, Rap- port No. 1 (in French). Vicksburg, Miss.: U.S. Army Engineer Waterways Experiment Station, U.S. Army Corps of Engineers. Perlin, M., and R. G. Dean. 1979. Prediction of beach planforms with littoral controls. Pp. 1818-1838 in Proceedings of the 16th Coastal Engineering Conference. New York: American Society of Civil Engineers.

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88 BEACH NOURISHMENT AND PROTECTION Pilkey, O. H., R. S. Young, S. R. Riggs, A. W. S. Smith, H. Wu, and W. D. Pilkey. 1993. The concept of shoreface profile equilibrium: a critical review. Journal of Coastal Research 9(1):255- 278. Price, W. A., K. W. Tomlinson, and D. H. Willis. 1973. Predicting changes in the plan shape of beaches. Pp. 1321-1329 in Proceedings of the 13th Conference on Coastal Engineering. New York: American Society of Civil Engineers. Swart, D. H. 1974. Offshore Sediment Transport and Equilibrium Beach Profiles. Publication No. 131. Delft, The Netherlands: Delft Hydraulics Laboratory. Wise, R. A., and N. C. Kraus. 1993. Simulation of beach fill response to multiple storms, Ocean City Maryland. Pp. 133-147 in Proceedings of Coastal Zone '93. New York: American Society of Civil Engineers. Work, P. A. 1993. Monitoring the evolution of a beach nourishment project. Pp. 57-70 in D. K. Stauble and N. C. Kraus, eds., Proceedings of Beach Nourishment Engineering and Manage- ment Considerations. New York: American Society of Civil Engineers.