Citation
Evaluation of beach and shoreface nourishment

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Title:
Evaluation of beach and shoreface nourishment a case study at Torsminde, Denmark
Series Title:
UFLCOEL-99005
Creator:
Grunnet, Nicholas Moulun
University of Florida -- Dept. of Civil and Coastal Engineering
Place of Publication:
Gainesville Fla
Publisher:
Coastal & Oceanographic Engineering Program, Dept. of Civil & Coastal Engineering, University of Florida
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English
Physical Description:
xi, 126 p. : ill., maps. ;

Subjects

Subjects / Keywords:
Beach erosion -- Denmark -- Torsminde ( lcsh )
Coast changes -- Denmark -- North Sea Coast ( lcsh )
Beach nourishment -- Management -- Denmark -- Torsminde ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (p. 122-126).
Statement of Responsibility:
by Nicholas Moulun Grunnet.

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University of Florida
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University of Florida
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All applicable rights reserved by the source institution and holding location.
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43305752 ( OCLC )

Full Text
UFL/COEL-99/005

EVALUATION OF BEACH AND SHOREFACE NOURISHMENT: A CASE STUDY AT
TORSMINDE, DENMARK by
Nicholas Moulun Grunnet Thesis

1999




EVALUATION OF BEACH AND SHOREFACE NOURISHMENT:
A CASE STUDY AT TORSMINDE, DENMARK
By
NICHOLAS MOULUN GRUNNET

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

1999




ACKNOWLEDGMENTS

First and foremost, I wish to express my deepest gratitude and appreciation to my advisor and supervisory committee chairman, Dr. Robert G. Dean, who provided much more than support and guidance. His attitude towards the field of coastal engineering is truly contagious. In possession of both zeal and passion for coastal processes, he faces the challenges with humility and courage. With such an inspiration thoughout my study, I hope to have been influenced enough to carry on in this spirit. However, Dr. Dean soon enough made me lose the tan, I had come to get under the Florida sun.
I would also like to thank Dr. Daniel M. Hanes and Dr. Robert J. Thieke for their participation as supervisory committee members and for their excellent lectures. Appreciation is extended to all.other faculty members and staff in the department whose contributions have made the completion of this thesis possible. They include Dr. Ashish J. Mehta and Dr. Michel K. Ochi for their inspiring lectures, Subarna B. Malakar for computer assistance, Helen Twedell for helping in the archives and to Becky Hudson and all other secretarial personnel in the department for their help and kindness.
Special thanks also go to the COWI Foundation for providing the financial support which made my stay at the University of Florida possible and even more so to COWI Head of Ports, Waterways and Coastal Engineering Department, Ole Juul Jensen, for encouragement and continuous support.
The collaboration with the Danish Coastal Authority and in particular their willingness in making the high quality NOURTEC data available for this study, is gratefully acknowledged.
Thanks are in order to many coastal and oceanographic engineering students, but to name one would be to omit another. However, special gratitude is due to my friends in the department




Edward Albada, Roberto Liotta and Guillermno Simon Fernandez for their friendship and assistance while sharing the same office. Thanks are extended to Albert E. Browder for his patience, valuable discussions and advice at most needed times.
I am forever indebted to Mathilde for sharing this unforgettable experience of joys and hardships with me. Her presence, both physical and moral, made the efforts less tortuous. Whether it was me or 1200 miles of sandy Florida beaches that attracted her to Gainesville, remains unsaid. Intensive pediatric research at Shands University Hospital also made Mathilde' s tan fade away, allowing her to better blend into the hectic environment of the Neonatal Intensive Care Unit.
Finally, this work is dedicated to my wonderful mother and father. Their attempt in understanding what coastal engineering research is about, is honorable. "Ask the fish, they must know," seems to be their valuable contribution to this field.




TABLE OF CONTENTS
ACKNOW LEDGM ENTS ............................................................................................................... ii
LIST OF FIGURES ........................................................................................................................ vi
LIST OF TABLES ......................................................................................................................... ix
ABSTRACT .................................................................................................................................... x
CHAPTERS
1 INTRODUCTION .................................................................................................................... 1
1.1 Problem Statement ............................................................................................................. 1
1.2 Objectives and Scope ......................................................................................................... 2
2 LITERATURE REVIEW .......................................................................................................... 4
2.1 Previous Shoreface Nourishm ent Projects .......................................................................... 6
2.2 Parameterization of Cross-Shore Sediment Transport ........................................................ 8
2.2.1 Classification of Berm s ............................................................................................. 9
2.2.2 Cross-Shore Transport Direction ............................................................................ 10
2.3 Cross-Shore Sediment Transport M odels ......................................................................... 14
2.3.1 Coastal Profile M odels ........................................................................................... 14
2.3.2 Other American M ethods ....................................................................................... 18
3 FIELD M ON ITORING DATA ............................................................................................... 19
3.1 Site Description ................................................................................................................ 19
3.1.1 H istorical Evolution ................................................................................................ 19
3.1.2 M orphology of Field Site ....................................................................................... 23
3.1.3 Nourishment Projects ............................................................................................. 23
3.1.4 Sediment Size Distribution ..................................................................................... 27
3.2 Hydrodynam ic Setting ...................................................................................................... 28
3.2.1 W ave, Tide and Current M easurements ................................................................. 29
3.2.2 W ind Characteristics ............................................................................................... 29
3.2.3 Littoral Drift ........................................................................................................... 29
4 M ORPHOLOGICAL DEVELOPM ENT ................................................................................ 31
4.1 Previous Study on Torsminde Data .................................................................................. 32
4. 1.1 M orphological Analysis ......................................................................................... 32
4.1.2 Relative Effect of the Two Nourishment Projects .................................................. 35




4.1.3 M odeling Results .................................................................................................... 38
4.2 Volumetric Profile Changes ............................................................................................. 41
4.2.1 Cross-Shore Sand Transport Rate Distribution ...................................................... 44
4.2.2 Longshore Volume Changes ................................................................................... 51
4.2.3 Cum ulative Volume Changes ................................................................................. 56
4.3 Longshore Variability ....................................................................................................... 61
4.3.1 Shoreline Positions ................................................................................................. 63
4.3.2 Sediment Transport Distribution ............................................................................ 63
4.4 Beach Nourishment Perform ance Prediction .................................................................... 66
4.4.1 Longevity of Nourishment Project ......................................................................... 67
4.4.2 M ultiple Nourishm ents in the Study Area .............................................................. 69
4.4.3 Effect of Distance to Groin Field ............................................................................ 75
4.5 Submerged Berm Response .............................................................................................. 78
4.5.1 M igration of the Berm ............................................................................................ 78
4.5.2 Breakwater and Feeder Effects ................................................................................ 80
5 M ODEL DERIVATION AND SOLUTION ........................................................................... 83
5.1 M odel Derivation ........................................... 83
5.1.1 Energetics Transport Model ............... 84
5.1.2 W ave-Based M odel of Berm M igration ................................................................. 86
5.1.3 M ethodology Lim itations ....................................................................................... 90
5.2 Numerical M odeling ......................................................................................................... 93
5.2.1 The QUICKEST Algorithm for Unsteady Flow ..................................................... 93
5.2.2 Stability Conditions ................................................................................................ 95
6 APPLICATION AN D M ODELING RESULTS ..................................................................... 96
6.1 Application of Torsminde Data ........................................................................................ 96
6. 1.1 Influence of Depth on Berm Behavior .................................................................... 96
6.1.2 Representative Profile Evolution ............................................................................ 98
6.2 Numerical M odeling Results .......................................................................................... 108
6.2.1 Estimate of Diffusion Coeffi cient ......................................................................... 108
6.2.2 Sim ulation of M orphological Evolution ............................................................... 109
6.2.3 M odel A ssessment ................................................................................................ 115
7 SUM M ARY AND CONCLUSIONS .................................................................................... 119
7.1 Summ ary ......................................................................................................................... 119
7.2 Conclusions .................................................................................................................... 120
REFERENCES ............................................................................................................................ 122
BIOGRAPHICAL SKETCH ............................................................................................... 127




LIST OF FIGURES

2.1 Prediction of cross-shore movement of outer bar, from Larson and Kraus (1992) ......... 11
2.2 Accretion (A) or erosion (E) beach profile condition as a function of
U. and Ut for field data, from Ahrens and Hands (1998) ............................................ 13
2.3 Velocity components calculated by NPM, LITCROSS, UNIBEST and SEDITEL
and 2-D current field calculated by SEDITEL,
from Broker Hedegaard et al. (1992) ......................................................................... 16
2.4 Cross-shore sediment transport calculated by NPM, L1TCROSS, UNIBEST,
SEDITEL and WATAN3, from Broker Hedegaard et al. (1992) ................................ 17
2.5 Comparison of measured and calculated coastal profiles after 4.3 hours of exposure,
from Broker Hedegaard et al. (1992) ......................................................................... 17
3.1 NOURTEC location map, from Laustrup et al. (1997a) ............................................ 20
3.2 Coastal protection measures 1978-1992, from Laustrup et al. (1997a) ....................... 22
3.3 Survey lines and positions for sediment sampling, from Laustrup et al. (1997b) ..... 24
3.4 Coastal profile surveys from March to June 1993 through ......................................... 26
(a) Shoreface nourishment at survey line 21880,
(b) Beach nourishment at survey line 22130.
3.5 Variation of grain size with depth, from Laustrup et al. (1997b) ................................. 27
3.6 Wind rose for the monitoring period, from Laustrup et al. (1997a) ............................ 30
4.1 Volume development in selected cells, from Laustrup et al. (1996) ........................... 33
4.2 Development of the bar system, from Laustrup et al. (1997b) ................................... 34
4.3 Definition of design parameters, from Laustrup et al. (1997b) ................................... 36
4.4 Nourishment effect on the design parameters, from Laustrup et al. (1996) ................ 37
4.5 Relative effect of the two nourishment methods, from Laustrup et al. (1996) ............ 38




4.6 Cross-shore transport calculated with Mike 21, from Laustrup et al. (1997b) ............ 39
4.7 Longshore transport for three different bathymetries, from Laustrup et al. (1997b) ....... 41
4.8 A verage survey lines .................................................................................................. 43
4.9 Net cross-shore sand transport rate distributions for ................................................... 45
(a) Pure Migration, (b) Pure diffusion.
4.10 Net cross-shore volumetric transport past any offshore location assuming no
longshore transport gradients. Results for average profiles 21840, 21870
and 21900 from June 10, 1993 to April 12, 1993 ....................................................... 47
4.11 Profile evolution for average profile 21870 ................................................................. 49
4.12 Net cross-shore volumetric transport past any offshore location assuming no
longshore transport gradients. Results for average profiles 21720, 21770
and 21970 from June 10, 1993 to April 12, 1993 ........................................................ 50
4.13 Longshore volume change from +8 m to -12 m .......................................................... 52
4.14 Longshore volume change from +8 m to -2 m .......................................................... 54
4.15 Longshore volume change from -2 m to -12 m .......................................................... 55
4.16 Cumulative volume change from +8 m to -12 m relative to March 1993.................. 57
4.17 Cumulative volume change from +8 m to -2 m relative to March 1993 ..................... 59
4.18 Cumulative volume change from -2 m to -12 m relative to March 1993 ................... 60
4.19 Shoreline change relative to June 10, 1993 position .................................................. 62
4.20 Shoreline change relative to March 29, 1993 position ................................................ 64
4.21 Northern 5 km stretch of study area ............................................................................ 71
4.22 Calculated planform evolution for multiple nourishment projects from 1985 to 1992 ... 74
4.23 Calculated planform evolution for beach nourishment located 5 km downdrift of
G robin Q ............................................................................................................................ 76
4.24 Calculated planform evolution for beach nourishment located 8 km downdrift of
G robin Q ............................................................................................................................ 77
4.25 Berm development for average profile 21900 ............................................................ 79
4.26 Measured and expected breakwater effects ................................................................ 81




6.1 Dependency of convection and diffusion coefficients with depth for a range of
3 wave heights in dotted and solid lines, respectively..................................... 98
6.2 Berm cross-section evolution from June 10, 1993 to July 15, 1993.................... 100
6.3 Berm cross-section evolution from August 26, 1993 to November 22, 1993 ......... 101
6.4 Berm cross-section evolution from November 22, 1993 to January 11, 1994......... 102
6.5 Berm cross-section evolution from February 8, 1994 to April 12, 1994................ 102
6.6 Hydrographic monitoring results from November 26, 1993 to January 11, 1994......104
(a) Wave height and period,
(b) Water level.
6.7 Hydrographic monitoring results from February 8, 1994 to April 12, 1994 .......... 105
(a) Wave height and period,
(b) Water level.
6.8 Initial bathymetry and profile development for average profile 21870................ 107
(a) From November 26, 1993 to January 11, 1994,
(b) From February 8, 1994 to April 12, 1994.
6.9 Predicted and measured diffused shapes following placement of sand................ 110
6.10 Comparison of Stokes' second order theory with SFWT for H = 2.0 m, T = 6 s
and h= 4.Om.......... ..................................................................... 112
(a) Near-bottom velocities,
(b) Velocities cubed.
6.11 Comparison of simulated and observed migration of berm in time period........... 114
(a) November 26, 1993 to January 11, 1994,
(b) February 8, 1994 to April 12, 1994.
6.12 Prediction of direction of cross-shore berm movement................................. 117
(a) From November 26, 1993 to January 11, 1994,
(b) From February 8, 1994 to April 12, 1994.




LIST OF TABLES

Table Page
2.1 Previous submerged berm projects, adapted from Otay (1994) .................................... 5
3.1 Wave statistics, March 1993 April 1995, Torsminde ............................................ 28




Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science EVALUATION OF BEACH AND SHOREFACE NOURISHMENT: A CASE STUDY AT TORSMINDE, DENMARK By
Nicholas Moulun Grunnet
May, 1999
Chairman: Dr. Robert G. Dean
Major Department: Coastal and Oceanographic Engineering
The morphological behavior of a beach and shoreface nourishment at Torsminde on the west coast of Denmark has been studied through analysis of survey data and numerical modeling. The two nourishment volumes of approximate equal size of 250,000 m3, showed a clear difference in stability. The beach nourishment was completely eroded within a year thus not fulfilling its design objectives, whereas most of the shoreface nourishment was still in its initial position two years following the implementation. The relative success of the shoreface nourishment and the subsequent morphological changes in the outer nearshore were studied in detail.
The shoreface nourishment, consisting of coarser than native beach quality sand, was placed on the offshore slope of the outermost breaker bar in an alongshore submerged berm. Extensive monitoring of the morphological development of the berm and the nearshore zone showed that the berm quickly became an integral part of the natural bar system. In the first two years of monitoring, the Torsminde shoreface nourishment had completely fulfilled all design




objectives through its pronounced breaker berm effect and reduced feeder effect. Not only was shoreline retreat compensated, a net seaward migration of the coastline was observed.
Volumetric analysis of cross-shore profiles was a useful means to describe the morphological changes induced by the placement of large volumes of sand in the nearshore zone. The natural variations of the longshore sediment transport were large compared to the changes introduced by the nourishment volumes which made it difficult to disassociate the natural processes re-shaping the nearshore profile from the processes caused by the implementation of the nourishment. The monitored area was soon found to be characterized by cross-shore as well as longshore natural variability implying that the nearshore processes are highly 3-dimensional.
With emphasis on the cross-shore redistribution of sediments after construction of the submerged berm, a model was derived to illustrate the shoreface profile development. The fundamental concept used was that wave asymmetry is primarily responsible for the onshore migration of the berm. The form of the berm was observed to migrate landward at a distinct speed while it diffused and lost height. This observed evolution in time was related to the measured hydrodynamics and reproduced by numerical simulation of the cross-sectional change of form and berm crest migration. Reasonable agreement with field observations was obtained.




CHAPTER 1
INTRODUCTION
1.1 Problem Statement
The beach is a dynamic system constantly changing under the action of the wave, tide, current and wind climate. Beachface accretion/recession is an equilibrium between storage of sediment on the foreshore and storage of sand offshore through creation of longshore bars that also act to reduce erosive energy reaching the beach by breaking the incident waves. In the crossshore plane, sediment moves between the beach face and bars according to the wave and water level conditions and the grain size of the beach material. During storms, which are characterized by higher waves and water levels, sediment moves from the beach face to form bars, whereas under lower waves, bars tend to move onshore. Sediment also moves alongshore in a direction mainly controlled by the angle of the incident waves.
The positive effects of bars for promoting beach growth and protecting beaches has made nearshore placement of sand an increasingly interesting option in the mitigation of shoreline erosion. Bars or "nearshore berms" are constructed with the intent of either to reduce the incoming wave energy by inducing breaking over the placed bars and/or to supply the beach with material. If a nearshore berm is not intended to migrate shoreward, it is referred to as a "stable berm," whereas if the berm is expected to migrate, it is referred to as an "active" or "feeder berm" due to its potential in supplying the beach face with material. This supplemental source of material can either result in an increase in beach volume or a reduction in the ongoing erosion.
To prevent coastal erosion, the earliest manmade changes along the coast were the construction of hard structures such as groins, jetties and seawalls. Designed to trap sediment moving alongshore, constrain the flow of water at tidal inlets or protect the foreshore, an




interruption of the natural bar-beach system with adverse effects on adjacent beaches was inherently associated with these coastal protective measures. Such undesired effects coupled with the increasing significance of the coastal areas for ecology, economy, culture and recreation, has promoted soft structures such as beach and nearshore nourishment.
Placing the sand in the nearshore instead of directly on the beach, has been shown to reduce costs and improve the overall cost-benefit ratio of a beach nourishment project (Laustrup et al. 1996). Placement of sand in a bar-like alongshore submerged berm, introduces only a small perturbation to the littoral processes in the cross-shore zone characterized by bars. The environmental impacts to the beaches are thus also improved with nearshore placement instead of direct beachfill because the sand moves ashore in the form of migrating sand bars instead of being placed by construction equipment.
However, as yet no quantitative methods have been developed as useful design and planning tools for predicting the long-term fate of nearshore berms. A primary design parameter is the depth of placement, which in the limited number of field nearshore nourishment projects has been based on rational choices and rules of thumb.
1.2 Objectives and Scope
In 1993, the NOURTEC project, an acronym for Innovative Nourishment Techniques Evaluation, was launched to study and explain the behavior of shoreface nourishment projects in different European coastal environments (Hoekstra et al. 1996, Knaack et al. 1996 and Laustrup et al. 1996). The final objective of the NOURTEC project was to study, determine and explain the feasibility, effectiveness and optimum design characteristics of shoreface nourishment techniques for different environmental conditions. The project was also intended to give an improved understanding of the morphological changes induced by placing large volumes of sand in a coastal environment.




As part of the NOURTEC project, the Danish Coastal Authority performed a full-scale test on beach and shoreface nourishment located at Torsminde on the west coast of Denmark. The hydrographic and bathymetric results of the comprehensive 2-year monitoring survey program were generously made available for the present study.
Through analysis of survey data, the morphological development of the nearshore can be studied following the implementation of the nourishment projects. Specifically, an attempt to disassociate the natural processes re-shaping the profile from the processes caused by the placement of the nourishments is valuable. However, the changes introduced by the nourishment volumes must be significant enough so as to disturb the natural system by an order of magnitude higher than its natural variations, both in time and space.
By analyzing the relative effects and stability of each nourishment project, the better nourishment option can be quantified in terms of stabilization of coastline, coastal protection and widening of the beach. At the end of the monitoring period, the extent of fulfillment of these design objectives forms the basis of a comparison of a beach and shoreface nourishment.
Previous studies have indicated that wave asymmetry can cause net onshore sediment movement and undertow can cause net offshore movement in the surf zone. The placement of the present berm is offshore of the outermost breaker bar, thus beyond the day-to-day surf zone, thereby enhancing the effect of wave asymmetry as the dominant forcing condition. The derivation of a model based on wave-asymmetry can describe such onshore berm migration.
With application of the Torsminde data, the predictive capability of the model can be evaluated in terms of agreement between measured and simulated profile evolution.




CHAPTER 2
LITERATURE REVIEW
A well documented history of field experimentation coupled with advances in sediment response modeling, have made nearshore placement of sand an attractive alternative to direct placement on the beach. Early nearshore nourishment experiments failed because material was placed too deep for mobilization by wave motion and other cross-shore flows. With the recognition of dredged material as a resource for nourishment sand and more recent successes in berm response with shallower placement, nearshore nourishment has proven its concept and is now used to mitigate chronic coastal erosion.
It is of fundamental importance to be able to predict the direction of sand transport for the design of nearshore dredged material berms intended to function as feeder berms. By studying the response of natural longshore bars with respect to the incident wave conditions, criteria have been developed for predicting the cross-shore direction of movement of berms placed in the nearshore. Several criteria for onshore and offshore bar movement are readily available.
A number of European and American coastal profile evolution models have been developed. Some numerical models are available to specifically simulate long-term berm movement. Due to the limited knowledge of sediment transport in the coastal environment, motivation is provided by the need for conceptually simple models to help explain the movement of sediments under waves. Simpler ways to quickly assess sediment stability have thus also been developed and may be sufficient in cases where detailed analysis is not needed. Whatever the different degrees of determinism/empiricism and refinement established in the modeling of




Table 2.1: Previous submerged berm projects, adapted from Otay (1994).

Location Date Placed Water Berm Sand Wave Wave On/Off- Shore Reference
Volume Depth Relief Size Height Period Shore Protection
[I m3] [ ml [ml [ mm] [ m] [s] Motion

Santa Barbara, CA Atlantic City, NJ Long Branch, NJ Durban, South Africa Copacabana Beach, Brazil Long Island Sound, CN Lake Erie, OH New River Inlet, NC Limfjord Barriers, Denmark Tauranga Bay, New Zealand Dam Neck, VA Sand Island, AL Fire Island, NY Jones Inlet, NY Mobile Outer Mound, AL Coos Bay, OR Silver Strand, CA Kira Beach, Australia Mt. Maunganui, New Zealand Port Canaveral, FL. Perdido Key, FL. Terschelling, the Netherlands Torsminde, Denmark

1935 154,000 1942 2,700,000 1948 460,000 1970 2,500,000 1970 2,000,000 1974 1,170,000 1975 18,000
1976 26,750 1976 22,000 1976 2,000,000 1982 650,000 1987 350,000 1987 320,000 1987 300,000 1988 14,300,000 1988 4,000,000 1988 113,000 1988 1,500,000 1988 80,000 1990 120,000 1992 3,000,000 1993 2,100,000 1993 250,000

6.1
4.6-7.6
11.5 7-16 4-6 18.3 17 2-4 4-5 11-17 10-11
5.8 4.9 4.9 10.7-13.7 20-26 4.6-5.5
7-10 4-7
5.3-6.8
5-6 5-7 5-6

1.5 0.18 stable none Hall and Herron (1950)
- 0.32 stable none
2.1 0.34 1-2 7-9 stable none
0-8.3 0.35 1-2 both indirect Zwambom et al. (1970)
- 0.4-0.5 0.7 10-14 onshore direct Vera-Cruz (1972)
9.1 silt 0.1 stable none Bokuniewicz et al. (1977)
0.36 silt 0.1 stable none Danek et al. (1978)
1-8 0.49 0.55 7.3 onshore direct Schwartz and Musialowski (1977)
2.1 0.25-0.3 onshore direct Mikkelsen (1977)
9 stable Healy et al. (1991)
3.3 0.08 stable Hands and DeLoach (1984)
1.8-2.1 0.22 onshore direct Hands and Bradley (1990)
2 McLellan et al. (1988)
2 -6.6 fine 0.3-0.8 3.4-4.6 stable indirect McLellan (1990)
4.6-7.6 0.25-0.3 2.7 11.5 loss none Hartman et al. (1991)
2.1 0.2 0.62 13.1 onshore direct Andrassy (1991)
2 4 8 onshore direct Smith and Jackson (1990)
2 0.5-1.5 5.9 direct Forster et al. (1994)
1.65 1.2 6.3 onshore direct Bodge (1994)
1.75 0.3 0.45 5.7 stable indirect Otay (1994)
1 0.2 1.08 7 onshore direct Hoekstra et al. (1996)
2.1 0.57 1.5 4-6 onshore direct Laustrup et al. (1996)




hydrodynamics, sediment transport and bed level evolution, these models seem to imply the important influence of wave asymmetry in the motion of sediment.
2.1 Previous Shoreface Nourishment Projects
A limited number of field shoreface nourishment projects have been carried out to construct bars or nearshore berms from dredged material with the intent of the placed material serving either as a submerged breaker berm and/or to supply the beach with material. Often, the nourishment only partly acts as a feeder berm as the actual success of the nourishment is also based on the impoundment of longshore sediment transport due to the damping of the wave energy leeward of the berm and the subsequent development of a salient effect. If a nearshore berm is not intended to move, it is referred to as a stable berm, whereas if the bar is expected to move, it is called an active or feeder berm with reference to its potential action of supplying material to the littoral zone of the beach.
The concept of placing dredged sand where the natural cross-shore currents would move it ashore, has a long history of mixed successes and disappointments. Periodic direct placement of material on the beach had already proven its abilities and been used as an acceptable means for restoring littoral drift downdrift of littoral barriers. With half a century of experience, feeder berms are now sited carefully for maximum exposure to onshore transport processes. A summary of previous submerged berms is presented together with their characteristics and overall stability in Table 2.1, adapted from Otay (1994).
Early disappointments with nearshore nourishment projects were reported by the U.S. Army Corps of Engineers (USACE). In 1935 at Santa Barbara, CA, a berm was built intended to mitigate extensive erosion downdrift of a newly constructed harbor. After 21 months, with no measurable movement of the berm or lessening of the coastal erosion, nearshore placement of sand was abandoned in favor of direct placement on the dry beach. At Atlantic City, NJ, larger volumes were placed in higher wave energy locations with hopes that they would more readily be




mobilized (Hall and Herron 1950). Monitoring for up to 10 years showed no migration of the nourishment nor any benefits to adjacent shores. Again, experiments with nearshore nourishment were dropped in favor of direct placement on the subaerial beach.
Despite the failure of initial nourishment projects, the idea persisted that under the right circumstances, properly designed offshore deposits could benefit adjacent beaches. A number of successes at Durban, South Africa (Zwamborn et al. 1970), Copacabana Beach, Brazil (VeraCruz 1972) and Limfjord Barriers, Denmark (Mikkelsen 1977) were reported as successes; extensive field monitoring programs had confirmed that the offshore berms had been of considerable benefit to the protection of the leeward beaches. The stable berms were reported to have reduced wave energy to a non-erosive level and active berms had induced an additional volumetric gain of the beach material; in some cases, the increasing grain sizes in beach sediment samples suggested an interaction with the offshore placement sites which were originally nourished with the coarser sand.
Coupled with the reported successes overseas and expanded mechanical abilities for precise placement in shallower water, a renewed interest led to a another series of shoreface nourishment projects performed by the USACE. At New River, NC, placement in 2 to 4 m depths proved that nourishment volumes could be returned to the littoral zone by shallow disposal (Schwartz and Musialowski 1977). Off the Virginia coast, nourishment tests were carried out with poor-quality material and constructed as stable stockpiles in 10 to 11 m water depths thus offering non-feeder benefits (Hands and DeLoach 1984). The nourishment tests demonstrated beneficial uses for formerly discarded beach quality material placed in deeper water.
Results from field studies at Kira Beach, Australia (Smith and Jackson 1990) and on the Mobile Outer Mound off Dauphin Island, AL, (McLellan 1990), showed positive berm responses in progressively deeper water. These tests proved the feasibility of constructing both stable berms and feeder deposits as nearshore nourishment had been demonstrated with increasingly deep




placement of medium to fine sand. Also, these studies helped narrow the gap between depths acceptable for sediment retention and depths suitable for feeding material to the nearshore zone.
In 1993, the NOURTEC program was launched to study and explain the behavior of shoreface nourishment projects in different European coastal environments. Two of the projects within this program, at Terschelling in the Netherlands and Torsminde in Denmark completely satisfied the design objectives in the first 2.5 years following the implementation of the nourishment volumes (Hoekstra et al. 1996, Laustrup et al. 1996). In Terschelling, the sediment was supplied to the nearshore zone, filling up the trough between the middle and outer breaker bar. In Torsminde, the sediment was placed on the offshore slope of the outermost bar. Both nourishment projects were found to only partly act as feeder berms as approximately only a third of the total gain of sediment in the inner nearshore could be explained by direct losses in the nourished zone. The projects illustrated the potential breaker berm function of the combination shoreface nourishment/nearshore breaker bar.
2.2 Parameterization of Cross-Shore Sediment Transport The criteria reviewed in this section deal with the parameterization of cross-shore sediment transport in a deterministic and probabilistic way. Guidelines for a suitable depth range for placement of nourishment sand were based on observed berm response at different sites and empirical berm stability was defined as a function of wave and sediment parameters. Detailed analysis was made of bar movement in order to develop empirical predictive expressions for the effective placement of nearshore berms. Such berms are placed in the form of long sandbars and are expected to behave similarly to natural bars, both in their movement and interaction with waves. The predictive criteria developed from field experiments appeared to have applicability to any site where longshore bars and constructed berms are modified primarily by wave action.
A general methodology was needed to determine the minimum depth assuring stability and the maximum depth where dispersion would occur.




2.2.1 Classification of Berms
Hands and Allison (1991) and Hands (1991) have proposed a method to help select depths appropriate for either dispersion or retention of placed materials. This method relates sediment stability and overall berm behavior to site specific berm and wave properties. As previously described, sand berms are classified as either stable or active based on repeated surveys; stable berms retain most of their original volume and remained at the placement site for years and active berms show significant movement within a few months.
Eleven nearshore berms on the open-ocean coast of the United States were classified according to their stability characteristics. The measured responses of the berms were compared to depth estimates using Hallermeier's (1981) concept of coastal profile zonation providing guidance on depths of sediment transport and profile variation for wave-dominated coasts. The inner and outer limit depths proposed, were the seaward limit for the active zone and the landward limit for the stable zone, respectively. The available berm data confirmed the validity of Hallermeier's limits as excellent site selection guidelines.
To estimate the stability of deposits at any depths, including the uncertain zone between Hallermeier's limits, a new limit criterion was introduced based on maximum near-bed oscillations. The distribution of long-term wave-induced near-bed velocities was shown to correctly categorize all the documented active and stable berm sites. Calculations using published wave climatology showed consistently that sand berms should not be expected to remain stable if the 75-percentile velocity exceeded 0.4 m/s or the 95-percentile velocity exceeded 0.7 m/s. For the eleven nearshore nourishment sites investigated, grain size, tidal currents and wind were assumed to not have a critical effect on the stability of the berms.
The Hands and Allison (1991) method is essentially empirical and does not attempt to explain migration direction. However, the proposed method implies that accounting for the




influence of velocity asymmetry on sand transport is recommended for modeling the fate of nearshore placed material.
2.2.2 Cross-Shore Transport Direction
Larson and Kraus (1989a, 1989b) presented different criteria for distinguishing between overall beach accretion and erosion. In the present context, beach accretion implies an onshore sand transport direction and vice-versa for beach erosion. Larson and Kraus (1992) later refined these criteria against field data obtained by examining the behavior of the offshore bar at DUCK, NC. Under the assumption that onshore sediment transport was associated with decreasing volumes of bar and vice-versa for increasing volumes, more appropriate threshold values were developed for differentiation between onshore and offshore bar movement. These criteria included the Dean number or fall velocity parameter H,, / wT, deep water wave steepness and ratio of deep water wave height to d50, and ratio of sediment fall velocity to gH. where H,, is the deep water wave height, T is the wave period and w is the sediment fall velocity.
One of the successful criterion was related to the Dean number presented by Dean (1973). The Dean number was first introduced as the ratio of sediment fall time to the wave period to describe the on/offshore motion of sediment particles suspended and transported by waves, thus used as a criterion for cross-shore transport formulations and for the formation of normal and storm beach profiles. Based on the Dean number, Larson and Kraus (1992) showed that a reasonable prediction of the cross-shore direction of bar migration could be given by the simple criterion H,, / wT = 7.2. Plotted against the deep water steepness, the prediction of crossshore movement of the outer bar for this combination of dimensionless parameters is displayed in Figure 2.1 for the DUCK experiments. A reasonable separation of accretionary and erosional events is seen to be achieved by the use of this criterion.




11
0.030
0o Ornshore
0.025 Offshore
- Criterion o
0.020 -- H/wT 7.2
I
0.015 o. .0
o o00 00
0 0 0
0.010
o
o
0 0
0
0.005 I I I I I I
3 4 5 6 7 8 9 10 14
H0/wT
Figure 2.1: Prediction of cross-shore movement of outer bar, from Larson and Kraus (1992).
Using the deep water wave climate time history at Torsminde, this criterion will be used to determine the wave events with accretionary and erosional potential, respectively.
Ahrens and Hands (1998) presented a different method to estimate the tendency of sediment to move onshore or offshore under the influence of waves in shallow water. Two dimensionless velocity parameters were developed to predict the tendency of sediment to move onshore under wave crests or offshore under wave troughs. The two versions of U were respectively Uc and U,, defined as the following ratio:
U-d maxcrest (2.1)
Ucrit
Ut U-d max,trough (2.2)
Ucrit
crit




where u-d max,crest and u-dm niax,trough are the instantaneous, maximum onshore near-bottom velocity under a wave crest and offshore velocity under the trough respectively, and ucrit is the critical velocity required to initiate sediment movement.
Near-bottom maximum velocities were estimated using the Stream Function wave theory as presented by Dean (1974) and led to the following expressions:
U-dmax,crest = (H / TXd / Lo)-O"579 exp [0.289-0.491(H / d)- 2.97(d / Lo)] (2.3)
Udmaxrough = -(H / T)exp [1.966 6.70(d / Lo)- 1.73(H /d)+ 5.58(H / Lo)] (2.4)
where d is the water depth, H is the wave height, T is the wave period and Lo is the deep water wave length.
Based on research by Hallermeier (1980), the critical velocity for the initiation of sediment movement for grain sizes smaller than 2.0 mm, was calculated as follows:
Ucrit = 8 g yd5 (2.5)
where g is the acceleration of gravity, y is the specific gravity of the sediment and d50 is the median sediment diameter.
Data from 98 beaches around the world tabulated in Kraus and Mason (1991), were used to develop criteria to discriminate between erosional and accretionary type beach profiles. Accretionary or erosional-type profiles are denoted in Figure 2.2 as a function of Uc and Ut. U, is seen to be a good discriminator between accretionary and erosional beach profiles at a value




around -2. Ahrens and Hands (1998) proposed using a value of U, = 1.90 as threshold level. Interestingly, even tests with high values of U,~ were erosional for U, around -2.

Figure 2.2: Accretion (A) or erosion (E) beach profile condition as a function of U.
and U, for field data, from Ahrens and Hands (1998).
Despite the simplicity of the method, the U, parameter showed considerable skill in predicting net cross-shore sediment movement for a large number of both laboratory and field observations. The method assumed that sediment movement responds only to near-bottom velocities produced by wave motion, neglecting other variables such as bottom slope and the presence of other cross-shore flows. However, it provided valuable insight on the processes that are important by showing a reasonable level of correlation over a wide range of observations of sediment movement.

A A A __ield Bedi Dsta
A
A AI
-2 4
all
-4E -4
WE -0~

WI for Hb




2.3 Cross-Shore Sediment Transport Models
Cross-shore sediment transport models are usually classified in two groups, closed loop and open loop models. Closed loop models are based on equilibrium, beach profile concepts (Bruun 1954 and Dean 1977) and assume that a profile will eventually reach equilibrium if exposed to the same conditions for a long time; cross-shore sediment transport is thus caused by deviations from an equilibrium profile. Open loop models are not constrained by reaching a final profile and the sediment transport is determined by sediment concentrations and fluid motions. Existing transport models will be reviewed briefly hereafter.
A number of European and American cross-shore sediment transport models have been developed to simulate morphological changes in coastal profile evolutions. However, other American conceptually simple methods have also been developed, specifically for determining the cross-shore transport of added sand placed on a coastal profile. These are of particular interest when considering the fate of constructed berms in the nearshore.
2.3.1 Coastal Profile Models
Early closed loop models only required that the form of the equilibrium profile be known; by assuming that a beach profile maintained its equilibrium form in immediate response to a water level rise, no sediment transport relationship was required. These models were in reality beach profile change models as no sediment transport was explicitely included. By introducing the concept of equilibrium wave energy dissipation per unit volume of water, wave energy dissipation related transport models such as EDUNE, Kriebel (1982), Kriebel and Dean (1985) and SBEACH Larson and Kraus (1989) were developed. According to equilibrium beach profile concepts, offshore transport continues until the wave energy dissipation per unit volume of water becomes uniform over the entire surf zone. The sediment transport rates across the nearshore active zone are thus related to the difference between the actual and equilibrium wave energy dissipation.




With varying degrees of modeling of the hydrodynamic processes, open loop models relate cross-shore sediment transport to the detailed physics of the flow field such as sediment concentration, fluid velocity and bottom shear stress. Open loop sediment transport models are usually based on one of the three following main transport relationships:
- product of flow velocity and sediment concentration,
- velocity powers,
- product of velocity and bottom shear stress.
The first type of models relate the net time-averaged flux of sediment to the product of flow velocity and sediment concentration. Such sediment transport models include the model presented by Dally (1980), Dally and Dean (1984) and LITCROSS developed by the Danish Hydraulic Institute, Broker Hedegaard et al. (1991).
The second type of sediment transport modeling is based on the concepts of stream flow transport by Bagnold (1963). Bailard and Inman (1981) later applied the Bagnold model to a coastal environment with time-varying oscillatory flow; a further description of this methodology will be given in Chapter 5. The following three coastal profile models have been developed based on Bailard's refined transport model: UNIBEST of Delft Hydraulics, NPM of Hydraulic Research and SEDITEL of Laboratoire National d'Hydraulique.
The third type of transport models determines the sediment transport in relation to local wave-current conditions and bottom shear stress. The total transport is thus a sum of contributions from mean currents and waves. An example hereof is the coastal profile model WATAN3 developed by the University of Liverpool.
In an intercomparison of coastal profile models, Broker Hedegaard et al. (1992) compared and evaluated five European models for short term coastal profile modeling. The five models are L1TCROSS of Danish Hydraulic Institute, UNIBEST of Delft Hydraulics, NPM of Hydraulic Research, WATAN3 of University of Liverpool and SEDITEL of Laboratoire National d'Hydraulique; all of which have been briefly introduced. The models were tested against




16
measured profile evolutions from a large wave flume under dune erosion conditions. The initial profile was a plane beach with an initial slope of 1:20 and the experiment was carried out with regular waves. In Figures 2.3 and 2.4, the vertical distribution of velocities and the cross-shore sediment transport are presented for all models, respectively. Figure 2.5 displays the comparison of measured and calculated coastal profiles after 4.3 hours of wave exposure. Even though large differences are seen to exist between the coastal profile models presented, all five models provided a reasonable agreement between the simulated and measured results. However, through the inherent uncertainties in sediment transport modeling, the intercomparison underlines the need for more profound understanding of the cross-shore processes.

zr

I U Ill W ~
I I I p
SWLI
I I I I
I P I I

DHI, Litcross
0.II I jim7
LNH, Seditel
""r E.0. .H
Ls f 1

I..,-a1 4 .0 0 44 2 40 0s 0.4 of 0.0 1.0
W-4

30 219 1.0

HR, NPM "_... ... tr ---7 J
-14- W.
.. . . ........

4.0 64 0 24 ,0. -. 0A O 0 ..
DH, Unibest
2"@ -- -__ 1"---- _20

-1.0 ',0.,I 4.0 ,,0 4 I 0. ,0 0 2 [, t4 01.0 0.0 P.O
20----L-S o1CM O.-of 52 111smog 0pei o I I

"".,20 "11 :: : ..... l

Figure 2.3: Velocity components calculated by NPM, LITCROSS, UNIBEST and SEDITEL and 2-D current field calculated by SEDITEL, from Broker Hedegaard et al. (1992).

,I'




z
5 -MvswI

I I i 100 i I
100 m

ONI. LUtcross ___SLN4H. Seditel -__I, .-'
il:

UL, Waton3

"1
.111 .144
.141

'"~ ;- i i j. i i s t t

Figure 2.4: Cross-shore sediment transport calculated by NPM, L1TCROSS, UNIBEST, SEDITEL and WATAN3, from Broker Hedegaard et al. (1992).

so NPM
4 0 NIMERCM RESULTS (nERWRAL MEMAITS
- ExPE71t4rI TAL RESUts Co
00-- 1 000 .
SO
So
- E.7RCAL RESULTS
--- EPEpuNAL. ntSULTS 20
- -f .. 0... yT-. . S .i
-'o000 10.00 3000 700 706.0 9000 (m) f so LITCROSS
so
-0 N00r0ICAL RESULTS
- WatnetMTAL ttsutts .20..
-00 10o on0 51o no so0 o9soo t o n(-)

SEDIEL

-0- - 4ERICM RET
I ~- EMPERIN. REtSULTS
20
-1000 o1000 3000 50.00 70n o00 (m) s.o. WATAN 3
680
------- N ERC -RESULTS -1 -tW~teMENAL RESuMtS
2.0.
*-1000 Won 3000 5000 70o.0o 0oo00 (m)
REGULAR WAS
H- .5n
d e 0.33m
Initial slopes lower beach 1:20 upper beach 1: 40

Figure 2.5: Comparison of measured and calculated coastal profiles after 4.3 hours of exposure, from Broker Hedegaard et al. (1992).

I 1

L

I

HR, NPM
9 -"" 7




2.3.2 Other American Methods
The other existing American methods for evaluating coastal profile evolution are more tuned to specifically estimating the long-term fate of sand placed in the nearshore. Motivated by the need to develop a systematic methodology for predicting the stability of dredged material disposal sites over long periods of time, methods have been developed so as to provide reliable predictions of the long-term dispersive or nondispersive characteristics of the site.
Scheffner (1991,1996) proposed linking a sediment transport model with a hydrodynamic model that includes the influence of waves indirectly through a modified bottom friction term. The result is a current velocity distribution at the site which is used to calculate the sediment transport. The migration of a berm south of Dauphin Island, Alabama (Hands and Allison 1991) was used for validation based on numerical simulation of the current field. Douglass et al. (1995) reported on a detailed analysis of the measured near-bottom currents at the same Alabama site: the cross-shore component of the mean near-bottom current was found to be offshore during the time the berm migrated landward. The sediment response to the mean currents was thus not able to satisfactorily explain the observed shoreward direction of berm migration. Evidently, Douglass demonstrated the fundamental problem with a model based on mean currents.
Based partly on these findings, Douglass (1995) proposed a different methodology for estimating landward migration of nearshore constructed sand berms. The fundamental concept was that the dominant driving force is the waves, specifically, the landward migration of sediment is due to the net landward transport by the asymmetry of finite-amplitude waves; the velocity asymmetry was described by Stokes' second order theory. The model considers net shoreward sand transport based on Bagnold's bedload sand transport equation. In conjunction with the equation of sand conservation, this lead to a convection-diffusion equation in which the speed of berm movement and the diffusion coefficient are expressed in terms of wave and sediment parameters. This model Will form the basis of the present study and is presented in Chapter 5.




CHAPTER 3
FIELD MONITORING DATA
As part of the NOURTEC project, the Danish Coastal Authority (DCA) performed a fullscale test on beach and shoreface nourishment located at Torsminde on the west coast of Denmark. A comprehensive 2-year monitoring survey program was initiated with the objective of a continuous record of hydrographic conditions during the period as well as numerous bathymetric surveys and sediment sampling. Waves, currents, water levels and winds were recorded from March 1993 to April 1995. The topographic and hydrographic characteristics of the monitored area presented in this section are taken from Laustrup et al (1997a).
All elevations are determined with respect to the Danish Normal Zero (DNN), related to the mean water level (MWL) by the relationship MWL = +0.14 m DNN.
3.1 Site Description
The Danish North Sea coast north of Torsminde was selected as an attractive test site due to severe profile retreat and regular bathymetry and few structures interfering in the longshore sediment transport immediately adjacent to the nourishment project area. Regular surveys in nearly 5 decades furthermore provided an extensive knowledge on the background coastal development in the area.
3.1.1 Historical Evolution
The Torsminde project area is located approximately 30 km south of Thyboron inlet on the west coast of Denmark. The inlet was formed naturally during a severe storm in 1862 when waves breached the narrow coastal barrier which separated the North Sea from the Limfjord. In




N
A
Groyne 0
Nourtec monitoring area

Figure 3.1: NOURTEC location map, from Laustrup et al. (1997a).




the years following the opening of the channel, the adjacent coastlines experienced substantial erosion which still today threatens the town of Thyboron. The net sediment transport into the inlet has been estimated to be in the order of 500,000 m3/year; this sediment is deposited on large flood shoals and is thereby lost from the littoral system.
Since the completion in 1875 of the first groin at the Thyboron tidal inlet, an extensive groin field comprising 58 groins was constructed south of the inlet; the groin field stretches from Thyboron to Fjaltring as illustrated in Figure 3.1. The terminal groin Q, situated 3 km north of the NOURTEC project site, was built in the 1960's. With a considerable southerly net littoral drift, downdrift erosion south of groin Q was inevitable.
To counteract the erosional development, a series of detached beach breakwaters and revetments in combination with nourishment were implemented from the late 1970's. A total of 5.8 km revetment and 28 breakwaters were built on a 3 km stretch south of groin Q. The shoreline retreat on this stretch, was thereby reduced from approximately 10 m/year prior to the coastal protection works to at present approximately 2.4 m/year.
Today, nourishment is the preferred solution. The continuing coastal erosion has been controlled by a comprehensive nourishment program for many years The nourishment volume has gradually increased and has now reached a level of about 3 million m3/year distributed along the west coast of Denmark, Laustrup et al. (1996). The chronological and spatial extent of all the coastal protection measures implemented in the NOURTEC area since 1978 and prior to the 1993 nourishment projects, are displayed in Figure 3.2.
Prior to 1993, shoreface nourishment had only been used occasionally. The aim of the NOURTEC project was to improve the understanding of the morphological changes induced by placing large volumes of sand on the shoreface. Following the positive experience with the NOURTEC shoreface nourishment, DCA in 1997 placed 1,25 million m3 sand as shoreface nourishment. This volume accounted for one third of the total nourishment volume in 1997.




Coastal protection measures: Breakwaters

00
r-D
=r 0
0
CD
0 D
0 C

1991
I I

Revetment Nourishment

1989
I

1983-85
1986 1984/85
1988 1987 1985 198 1986 1987
I I I I I I

1980 1982-84
1985
1987 1979

30000m3

73,000m3(shf.) 1983H-

24,000m3

42,00(

1987 78,000m3 42,000
1988 101,0Om3 127,00

19891 136,00m3
1990j 233,000m3

9,

2,000m3
19791 |
12,00Cm3
19801-Om
19870,000m3 + 23,00m3(shf.) 1981;
18,000m3
1982) 1
73,000m3(shf.) 73, (shf.)
11,00Cmn3
1985 11,00m3
107,000m3
S 24,00o m3
m
3 P 3
61,p0.3

19911 310,000m3 182,000m3
2 6500m3 170 00m3 (shf) 221000m3

0-1 1992
n
=$ West coast profiles numbers 5060 5180 10 m
CD
I I

I1

0n




3.1.2 Morphology of Field Site
There are no permanent offshore structures such as breakwaters or groins at the field site. However, a series of beach breakwaters extend from groin Q to approximately 500 m North of the beach nourishment. These breakwaters are normally covered by sand as the shoreline retreat has been arrested due to the mentioned nourishment program. Revetments are also present on the beach face extending from groin Q to approximately halfway between the beach and the shoreface nourishment; the revetments are always buried by the nourishment sand and thus are never evident on profile elevation surveys.
The cross-shore profiles reveal dunes, a beach and 1-3 longshore bars. The top of the dunes is at +8 m DNN with a dune foot located between +3.5 and +4.0 m DNN. MWL is located at +0.14 m DNN. The beach is approximately 100 m wide and consists of sediment ranging from fine sand to pebbles. The longshore bars are located shoreward of the 6 m depth contour with outer bar heights up to 3 m. The orientation of the shoreline at the field site is 3'-1830 with respect to true North.
The beach slope is approximately 1:20. The depth contours are straight and parallel to the shoreline and the shoreface slope is approximately 1:100. The depth of closure on the west coast of Denmark has been established at a depth of -16 m. However, the active profile zonation extends from +8 m to -12 m, from dune top to well beyond the day-to-day surf zone processes. Only on a very long time scale is there an interaction between the deep offshore region and shallower innershore region.
3.1.3 Nourishment Projects
Two nourishment projects, one beach nourishment and one shoreface nourishment, were located north of Torsminde in front of a 300-500 m wide barrier island and were implemented in April-May 1993. The alongshore dimension of the beach and shoreface nourishment were each 1 km separated by a distance of 2 km. The projects consisted of a beach and a shoreface




5080 5090

6100 5110
5120 5130
5140 5150 5160 -

51 70

Figure 3.3: Survey lines and positions for sediment sampling, from Laustrup et al. (1997b).




nourishment of approximately equal volumes on the order of 250,000 m3 of sand distributed alongshore with a density of 250 m3/m.
The beach nourishment was placed directly on the dry beach from the dune foot to the shoreline. The shoreface nourishment was located on the offshore side of the outermost bar. The pre-existing depth at the middle of the shoreface nourishment was approximately -5.5 m, located 500 m seaward of the shoreline. The shoreface nourishment resulted in a berm with a maximum relief of approximately 2.1 m.
The monitoring area was delimited by a southern boundary 2 km south of the shoreface nourishment and a northern boundary 1 km north of the beach nourishment, covering a total of 7 km alongshore. The alongshore spacing between the survey lines was 100 in. The cross-shore extent was 1500 m from the top of the dune at +8 in DNN to a water depth of approximately -12 m. A total of 17 survey campaigns was carried out during the 2-year monitoring period.
The southernmost survey line was line number 21620 and the northernmost was 22320. The shoreface nourishment was located approximately between lines 21820 and 21920 with the centerline of the berm at line 21870. The beach nourishment was placed between lines 22120 and line 22220. Figure 3.3 shows the extent of the monitoring area with the survey lines, the positions for sediment sampling and the location of the two nourishment projects.
A system of global survey lines is also shown on the same figure. These survey lines, with a spacing of 800-1000 m, have been surveyed regularly since 1938 and are used in establishing the historical development of the west coast of Denmark. A total of 13 of such profiles are located within the NOURTEC area, thereby providing information on background coastal retreat rates.
On Figure 3.4, two representative profiles through the beach and shoreface nourishment respectively, are shown. The initial bottom elevation of March 29, 1993 is shown together with the first post-nourishment survey, carried out on June 10, 1993. The profiles are seen to extend from 1000 to 2500 m seaward of the reference line behind the dunes.




108
6 4 z 2
Z
0
-6
2 -2 -..... .....
-8
-10
(a)
-12
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Distance Offshore [ m ]
108
6 4 z 2
Z
0
a
-4
-6
-8
-10
(b) _____-12
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Distance Offshore [ m ]
Figure 3.4: Coastal profile surveys form March to June 1993 through
(a) Shoreface nourishment at survey line 21880,
(b) Beach nourishment at survey line 22130.

- Mar-93
-Jun-93
MWL

2100 2200 2300 2400 2500

- Mar-93
-Jun-93
-MWL

2100 2200 2300 2400 2500




3.1.4 Sediment Size Distribution
Sediment samples were collected after each bathymetric survey in order to describe the variation in mean grain size and sorting along and perpendicular to the coast. Figure 3.5 shows the mean grain diameter d50% plotted against the water depth. The natural grain size is seen to vary between 0.2 and 0.45 mm, with the coarsest sand found on the beach face. As the offshore distance increases, the sand tends to be finer around 0.2 mm. However at the bar locations between 4 to 6 m water depth, a minor coarsening of sand is observed. This is also true at the seaward end of the surveyed profile. In the vicinity of the outer bar, a seasonal variation in mean grain size is observed, with coarser sand during winter than summer.
The mean grain size d50% for the beach nourishment sand was 0.32 mm and 0.57 mm for the shoreface nourishment.

D35 Microns
mop
. . .. . .. . . ., e , U
v* -- i ....-.. .. .. .
a % 0p we 12 N m ~~mi" ,m
__ U U :.a mL.,,.A1 &ut! .; :i
.
12.0 -10.0 -8.0 -6.0 -4.0 -2.(

.1400-

1000

--------- 800
.!

0 0.0

.1993.05
,n.1993.09
w1994.03
.1994.05 .1994.07
[.G1995.01
- - - --.- - -

2.0 4.0 m
Level

Figure 3.5: Variation of grain size with depth, from Laustrup et al. (1997b).




3.2 Hydrodynamic Setting
The wave height, period and direction were recorded by a waverider just north of the survey area in a water depth of 20 m. Wave-data were recorded for 20. minutes every 3 hours. Currents were measured by a current meter, initially placed at 14 m depth just seaward of the monitoring area and later at 4 m depth on the shoreface nourishment; the currents were recorded once every 15 minutes. The water level was recorded at a groin at Torsminde and at a groin 5 km north of the survey area once every 15 minutes. Wind speed and direction were recorded at Torsminde once every 15 minutes.
Table 3. 1. Wave statistics, March 1993 April 1995, Torsminde.

Time Period

March 1993 April 1993 May 1993 June 1993 July 1993 August 1993 September 1993 October 1993 November 1993 December 1993
January 1994 February 1994 March 1994 April 1994 May 1994 June 1994 July 1994 August 1994 September 1994 October 1994 November 1994 December1994
January 1995 February 1995 March 1995 April 1995

Mean H, [m]
N/A 0.81 0.91 1.31 1.39 1.31 0.91 N/A N/A 1.93
2.27 0.90
2.01 1.15
0.85
1.54
0.67 1.18 1.38
1.20 N/A 2.17
2.16 2.39 2.05
1.68

Max. H,
N/A
2.64 2.95 3.25 3.55 3.18 2.36 N/A N/A 5.68
6.34 3.32
4.33 4.04 3.60
4.03 1.89
4.43 3.38 2.33 N/A
4.28
8.97 8.57
6.27 6.00

Mean T [s]
N/A 3.8
4.2 4.3 4.6 4.4 3.9 N/A N/A 5.3
5.5
4.1 5.3
4.5
4.1 4.7 3.7
4.3 4.5
4.3 N/A 5.2
5.4 5.4 5.0
4.9

Mean Direction
[deg.]
N/A 272 293 301 291 287 290 N/A N/A
280
277 285 273
284 281 281 285
281 281 228 N/A 262
271 276 273
294




3.2.1 Wave, Tide and Current Measurements
For the entire monitoring period, the dominant deep water waves were from the Northwest. However, events of high waves above 2.0 m were most frequent from the Westnorthwest. The 100-year significant wave height is 8.1 m. The wave climate statistics for the monitoring period at Torsminde are displayed in Table 3.1. The wave statistics refer to the energy-based significant wave height, H,, and spectral period, T, measured in 20 n water depth. Both wave height and period were found from Fast Fourier Transform (FFT) analyses.
The tide is semi-diurnal with a tidal range of 0.6 m varying between mean low water level (MLW), MLW = -0.16 DNN and mean high water level (MHW), MHW = +0.44 m DNN. The 100-year water level is +3.40 m DNN. During the monitoring period, the water level was above +2 m DNN once, namely +2.05 m DNN on December 20, 1993.
The time-averaged currents were measured 1 m above the bottom. Due to the semidiurnal tide, the current direction changes 4 times a day. At 13 m depth, the dominant current was the tidal current with an amplitude of 0.4 m/s with a residual northerly directed current of 0.1 m/s. At 3 m depth, the current is also significantly influenced by the waves; the mean current is 0.7 m/s with a maximum velocity of 1.34 m/s.
3.2.2 Wind Characteristics
Wind from the Northwest is dominant and the 100-year wind speed is 33 rn/s. The wind rose for the monitoring period is displayed in Figure 3.6.
3.2.3 Littoral Drift
DCA has evaluated the annual littoral drift at Torsminde by two different approaches. First by accumulating the profile erosion from the nodal point for the littoral processes drift south of Thyboron and secondly by use of the CERC formula. The results yield a south-going littoral drift estimated in the interval 550,000 to 850,000 m3/year.




5 % of the time
- Above 15 ms
Period: 290393-240495 N 10-15 rn/s
2 5 rn/s
Below 2 mis
TMm Coastline
... ..J ......... ....... .. . .......... ... ~ :L ..
Figure 3.6: Wind rose for the monitoring period at Torsminde, from Laustrup et al. (1997a).
Groin Q at Fjaltring is not a perfect littoral barrier as suggested by the net littoral drift; sediment is bypassed on the bar outside of the groin. Construction of the groin field north of Torsminde has certainly reduced the rate of shoreline retreat. However, the tips of the groins are under severe pressure from the receding coastal profile, leading to their slow but progressive collapse.




CHAPTER 4
MORPHOLOGICAL DEVELOPMENT
The positive effects of placing large volumes of sand in the nearshore region has been shown to be an attractive way to protect the coast. However, at present no quantitative method exists to predict the long-term performance of the nearshore berms. Describing the morphological development following nearshore nourishment projects, can be valuable as to disassociate the natural processes re-shaping the profile from the processes caused by the implementation of the nourishment.
Profile survey data were analyzed to yield representative profiles to be used in the further analysis. The shapes of the chosen neighboring profiles were similar. However, longshore variability in volumetric changes was investigated to evaluate the applicability of a twodimensional approach. It was found that the monitored area is characterized by cross-shore as well as alongshore natural variability.
Average representative profiles were used in the analysis by averaging three neighboring profiles. If only one profile survey was selected for modeling, significant variability or deviation in calculated and measured results could be expected.
In the following, no attempt has been made to duplicate the modeling efforts previously conducted on the same data set, by using other equivalent coastal profile models. Rather, trying to supplement the existing analyses using a different approach to combine all the results, has been the motivation.




Although the nourishment projects consisted of a beach and shoreface nourishment of approximately equal volumes, focus is made on the evolution and processes around the nearshore berm.
4.1 Previous Study on Torsminde Data
An extensive study on the interpretation of the Torsminde data has previously been performed by the Danish Coastal Authority (DCA) in cooperation with the Danish Hydraulic Institute (DHI); the results hereof are presented in Laustrup et al. (1996) and Laustrup et al. (1997a). By using numerical modeling systems developed by DHI, part of the aim of the study was an attempt to reproduce numerically the long-term profile evolution over the monitoring period. Only the most important findings of these modeling results are mentioned in this section.
4.1.1 Morphological Analysis
The volume changes in the monitored area have been analyzed by the use of a system of cells with fixed horizontal boundaries. In Figure 4.1 the system of cells is shown together with the calculated volume development in selected cells. Immediately following the completion of the shoreface nourishment in cell H, a volume increase of approximately 100,000 m3 is observed. Landward of the shoreface nourishment, a gradual increase in volume is seen in cells A, B and C throughout the monitoring period. This increase is significant downdrift of the nourishment and less accentuated updrift. Although the volume in cell H containing the shoreface nourishment appears constant, the berm migrated 50-75 m onshore and lost approximately 0.5 m of its height over the monitoring period. The beach nourishment sand in cell E is seen to be eroded in approximately 3/4 year. Tracer results indicated that part of this sand migrated towards the south in the shoreline region.
The horizontal development of the bar system is shown in Figure 4.2. Just after completion of the nourishment, it appears that the berm becomes an integral part of the bar




system. South of the shoreface nourishment, the bar becomes continuous due to increased wave breaking over the very wide and shallow berm which in return enhances southerly sediment transport on the bar. This bar remains continuous for the rest of the monitoring period.

Volume 1000 m3

* .

* S
*
U SS~
* S U S U
S S U
U .5

Z
0 0 0
F V H d
-A-IB-C j
Figure 4.1: Volume development in selected cells, from Laustrup et al. (1996)

At the end of the monitoring period, the bar had migrated shoreward 50-75 m. A simultaneous southern migration of the berm was also observed together with a weakening of the northern end of the berm. A continuous bar developed landward of the shoreface nourishment. The bar development in the northern half of the monitoring area is less clear, as the bars are fragmented. A tendency towards alignment with the bar developed landward of the shoreface nourishment is however observed. Following the nourishment works, the lack of a consistent bar outside the beach nourishment probably contributed to the fast erosion of the beach nourishment.
Earlier surveys in the Torsminde monitoring area have documented the average vertical erosion in the offshore end of the survey profile at 12 m depth to be approximately 20 cm/year over the entire longshore stretch. Although the amount of erosion at the offshore end of the

M P a
K "P




Just before nourishment

~- ~% -

Just after

8 months after

10 months after

18 months after

23 months after

>m-z

0 0,5 1 km

Figure 4.2: Development of the bar system, from Laustrup et al. (1997b).

~Bar




surveyed area is approximately equal, the cross-shore sediment transport is not evenly distributed in the longshore direction. This is probably due to the presence of migrating bed forms. However, the longshore variation in cross-shore transport has not yet been successfully correlated with the migrating bed forms.
Results from sediment sampling in the nourishment area show that 60% of the nourishment sand was still in the initial position at the end of the monitoring period. The 40% loss of the nourishment sand only accounted for 1/3 of the total accretion shoreward of the nourishment. The shoreface nourishment had therefore an obvious breakwater effect. Similarly to a detached breakwater, the nourishment reduced the longshore transport landward resulting in an accretion at the shoreline.
Overall a considerable erosion took place even though 0.5 million of in3 sand had been supplied to the area.
4.1.2 Relative Effect of the Two Nourishment Projects
In order to obtain an improved understanding of the morphological changes induced by placing large volumes of sand in a coastal environment, general design objectives were chosen in the planning of the nourishment projects. The design objectives of the nourishment projects were
- stabilization of the shoreline,
- coastal protection,
- widening of the beach.
The effects of each of the nourishment projects on the coastal profile development as well as the relative effect of the two types of nourishment have been analyzed based on their ability to fulfil the design objectives. In Figure 4.3, the definition of the corresponding design parameters are shown. The design parameters are obtained by transforming the volumes to an average horizontal position by dividing by the height of the zone used in the volume calculations. The result is a horizontal distance to the chosen reference line on the landward side of the dune top.




Duna top
Dune foot L
Beach width '
44
-4
Figure 4.3: Definition of design parameters, from Laustrup et al. (1997b).
The level +4 m DNN corresponds to the beach level at the dune foot. The longshore extension of the nourishment effect has been determined to be approximately 3 km located symmetrically around the two project areas. Together with the natural development of the coastal profile, the development of the three design parameters for the southern and the northern 3 km stretches is shown in Figure 4.4.
It appears that the beach nourishment stabilized the coastline and improved the coastal protection but the beach width had not been improved. On the other hand, the shoreface nourishment fulfilled all three design objectives. By the end of the monitoring period, the shoreface nourishment had an effect on the coastal stability of 10.4 m for the 3 km stretch while the similar effect of the beach nourishment was 9.0 m. Similarly the effect on the coastal protection was 9.0 m for the 3 km stretch for the shoreface nourishment and 5.4 m for the beach nourishment.
Figure 4.5 compares the relative effects of the two nourishment projects in terms of the design parameters. The net effects thereby obtained show again that the shoreface nourishment is the better option for all parameters, even though the beach nourishment in the first -year was




more effective. The better relative effects of the shoreface nourishment is even increased as the actual price to nourish on the shoreface was 30% cheaper than to nourish on the beach.

3 km with shoreface nourishment 3 km with beach nourishment
Position of the coastline coastal stability Posftilon of the coastline coastal stability
mrn ODistance from reference ine" m Distance from reference kwne
225 175
200 ISO
-t ,, w. p 1 2.8
175 125
93 94 95 96 Year 93 94 95 96Year
Position of the upper part of the profile coastal Protectonfl Position of the upper part of the profile coastal protection m Distance tom reference ine m Distance from reference line
25 25
-25 -2S
93 94 95 96 Year 93 94 95 96Year
Beach vdwidth widening of the beach Beech width widening of the beach
m Width m Width
125 100
.100 75 me= -4.3
75 50
93 94 95 96Year 93 94 95 96 Year
Figure 4.4: Nourishment effect on the design parameters, from Laustrup et al. (1996).

Shoreface nourishment seems to be a more stable solution than the beach nourishment. This is partly due to the coarser sand in the shoreface nourishment. But even more contributory to the stability of the shoreface nourishment, is its placement in a natural bar zone where the nourishment immediately becomes an integrated part of the bar system instead of being eroded away. Placing sand on a natural outer bar, thereby increasing its volume, does not bring a considerable change to the system and will therefore not disturb the natural processes in a significant way.




Relative effect on the design parameters
Position of the coSetline coastal stability
m Southern nonhern section
20
10
0
-10
93 e4 95 96ear
Posllon of the upper part of the profile coastal protection
m Southern northern section
20
10
-10
03 94 95 96Year
Beach width widening of the beach
m Southern nothem section
20
to
- 0
-20
93 94 4S 96 Year
Figure 4.5: Relative effect of the two nourishment methods, from Laustrup et al. (1996).

4.1.3 Modeling Results
The computational modeling of hydrodynamics and sediment transport processes was based on the use of the models LITPACK and MIKE 21, both models developed by DHI. LITPACK is a 1-dimensional deterministic modeling system for littoral processes and coastline kinetics. MIKE 21 is a 2-dimensional deterministic modeling system for coastal waters and seas. The purpose of using the models was to analyze the effect of coarser grain size in the shoreface nourishment and to calculate sediment budgets.
Due to the dominant role of the longshore sediment transport, no cross-shore transport was considered in the use of LITPACK. After calibrating LITPACK to the annual south-going net littoral drift estimated to be in the interval of 550,000-850,000 m3/year, the longshore littoral




Shoreface nourishment
After:

Before:

Bathymetry : 93.01
Wave ongle :JJ dog Grain size : 0.32 mm
8 m contour 170
140-
130
120
110
atoo
-154000-10000 -5000 0 000
transport (m'/m/y.ar)

- H,,..= 1.50 m
- H,_ 2.25 m
H..,. 3.00 mn

Bothymetry : 93.05
Wave angle : 313 deqg Grain size : 0.32 mm
S 8 mn contour
140
.2 140i
30
&120
.2"
110
100
-15000-1000 -5000 0 5000
transport (m /m/yeor)

Beach nourishment
After:

Before:

B4thymetry : 93.01
Wave angle : 313 deg Grain size : 0.32 mm
310 8 m contour
300--Fo
*270-5230
240
-15000-1000 0-00 500
transport (m/m/rnyear)

- H.. ~ 1.50 m
- H... = 2.25 m .-.- H,. 3.00 m
4 m contour
'1
'I I
, //
-1:000-tOOD -500 0 5000
transport (m'/m/year)

Bathymetr : 93.05
Wave nge : 313 deog Grain ize : 0.32 mrn
o 8 m contour
310
290
3 00
270
C
026
2O
250
240
-15 000-10000 -5000 0 5000
transport (m'/m/year)

- H,. 1.50 m
-- H,,. 2.25 mn **-- H,,.- 3.00 m
4 m contour
;I
//
-15000-1000 -5000 0 50
transport (m'/m/year)

Figure 4.6: Cross-shore transport calculated with Mike 21, from Laustrup et al. (1997b).
transport across the survey lines was determined by modeling. Better agreement was found with the shoreface nourishment than with the beach nourishment. The LITPACK results were then applied to the calibration of MIKE 21.

H,. 1.50 m SH.., 2.25 m .*** H,.. 3.00 m




The simulated conditions with the MIKE 21 model were limited to 3 wave heights and corresponding water levels, 2 wave directions, 3 bathymetries and 4 different types of sediments. For both nourishment projects, significant wave heights of 1 to 2 m were found to cause most of the sediment transport; this range of wave heights was thus chosen in the modeling. Wave directions from Southwest and Northwest were chosen, both 400 off the coast normal. The bathymetries chosen were an initial bathymetry before nourishment, a "summer" bathymetry with nourishment and a "winter" bathymetry with nourishment.
In Figure 4.6, the effect of the beach and shoreface nourishment on the potential crossshore transport is shown as calculated by MIKE 21. The beach nourishment is seen to have nearly no influence on the cross-shore transport at 4 m depth and deeper. In the case of the shoreface nourishment, the increased sand volume in the berm and the local breaking of incoming waves, induced a significant increase in the cross-shore transport. In both cases, bathymetric variations due to the presence of the nourishment caused a longshore variation of the cross-shore transport.
The results for the longshore transport presented in Figure 4.7, show that even small morphological changes are highly reflected in the sediment transport pattern. The modeling results show a significant longshore variation of the longshore transport. The wave-driven current field is very sensitive to even small bathymetric irregularities, such as longshore variations in the bar system. These irregularities in turn have an enhanced effect in the longshore sediment transport pattern. The changes in the longshore transport introduced by the beach and shoreface nourishment appear to be nearly insignificant compared to the natural longshore bathymetric variations. The volume and location of the shoreface nourishment are such that the stability of the total bathymetry has not been disturbed significantly.
Although helpful in understanding details of some of the processes which contribute to the natural re-shaping of the monitored area, the modeling results could not be combined in such a way to satisfactorily reproduce the observed losses and gains of sediment. The coastal profile




development could not be reproduced and thus could not be used in a predictive way. The modeling efforts showed that the processes in the nearshore region are highly 3-dimensional.

Longshore transport Effect of nourishment only
F
2

Longshore transport 'Summer' and 'winter'

) C
C.
C1 '. IA ";,o
----- -----2-" I
i i ., -t -i
o o 0 0 o C 0 0 0 0 0
,0.-lo Figure 4.7: Longshore transport for three different bathymetries, from Laustrup et al. (1997b).
4.2 Volumetric Profile Changes In the following, emphasis was given to the changes of the nourishment volumes themselves and to the changes caused by placing the nourishment sand. The first year of monitoring was of greater interest than the second year since the effect of the disturbance due to the implementation of the nourishment projects, decreases with time as the natural processes tend to restore an equilibrated profile.




The reference line for all the surveys was chosen at the top of the dune and nearly parallel to the shoreface nourishment. With the chosen reference line, the initial position of the shoreline landward of the shoreface nourishment is approximately 1175 m. The cross-shore bathymetry perpendicular to the shoreline and through the shoreface nourishment is characterized by two offshore bars nearly parallel to the shoreline. The inner bar is located in the interval 1250-1400 m with a crest at approximately 1300 m and the outer bar in the interval 1400-1600 m with a crest at approximately 1525 m. The starting and ending points of the bars are here to a large degree defined arbitrarily. The shoreface nourishment was placed on the offshore slope of the outer bar, located in the interval 1575-1750 m with its crest at approximately 1650 m. The above locations relate to the time just after completion of the nourishment works.
Due to the large amount of survey lines, only representative sections of the monitored area were selected. Figure 4.8 shows the selected survey lines, three of which represent one third of the shoreface nourishment. To serve as control beaches, three additional survey lines were used, one survey line 500 m north on the updrift side and two lines 500 m and 1000 m south on the downdrift side of the nourishment. Only one survey line north of the shoreface nourishment was chosen due to the migration of the eroded beach nourishment sand towards the south. This survey line was thus probably not affected much by the beach nourishment sand. The survey dates used were selected as being the most characteristic to describe the development of the coastal profile during the elapsed time between the surveys. These were the initial June 10, 1993 survey and the April 12, 1994 survey.
Prior to the NOURTEC nourishment project, the average coastal retreat was 2.4 m/year corresponding to a volume loss of 48 m3/m/year between the dune top at +4 m DNN and estimated depth of closure at -16 m DNN, Laustrup et al. (1997a). This erosion volume must be considered in comparison with the nourishment volume of approximately 250 m3/m.




21970 21900 21870
21840
21770 21720

Figure 4.8: Average survey lines.

00.5 1 KM




4.2.1 Cross-shore Sand Transport Rate Distribution
In the following, a right-hand coordinate system was defined with the x -axis oriented alongshore to the right when looking seaward and the y -axis oriented offshore. The cross-shore sand transport rate distributions were determined from the development of consecutive profiles by integrating the mass conservation equation
Ah+ DqX + Dqy + s=O
at ax y(4.1)
where h represents the water depth, q, and qy are the longshore and cross-shore transport rates, respectively and s is the volume rate of sand added per unit plan area.
In an initial attempt to two-dimensionalize the sediment transport pattern by neglecting gradients in the longshore transport, the second term in the Eq. (4.1) was reduced to zero and s is also taken as zero. By choosing a stable reference point on the dune top where no changes occur between consecutive profile surveys, the cross-shore rate transport distribution was obtained as Y.Dh ay
qY (Y) = -J ay (4.2)
where q is the accumulated cross-shore transport until a seaward distance y.
The transport rate distribution thereby obtained represents an average net rate for the period between the two profile surveys. By calculating the cross-shore transport rate distribution between such two profiles, a picture of the overall morphological response within the profile is obtained.




(a) pure migration
z[m]
q,[m3/m ]

(b) pure diffusion

y[m] Sy[m] y[m]

Figure 4.9: Net cross-shore sand transport rate distributions for
(a) Pure Migration, (b) Pure Diffusion.




The general characteristics of the transport rate distributions can be classified as the following three main types:
- Accretionary; the accumulated transport rate at the seaward end of the profile is negative,
- Erosional; the accumulated transport rate at the seaward end of the profile is positive,
- Mixed accretionary and erosional; the transport is directed onshore along the seaward part of
the profile and offshore along the shoreward part of the profile or vice-versa.
Equilibrium distributions can be obtained if there is conservation of sand within the consecutive profiles indicating transport only in the cross-shore direction. At an unchanged point in time, corresponding to the stable established reference line on land, the transport is zero and if the profile experiences conservation of sand, a zero transport rate at the seaward extremity of the survey follows. Having neglected the effect of the longshore transport in Eq. (4.2), an equilibrium distribution should not be expected. The net transport rate value at the seaward extremity of the survey at 2500 mn, will thus be an indicator of the gradient of longshore transport at the profile cross section. This transport rate value quantifies the integrated loss/gain of sand volume over the entire length of the surveyed profile. The volume is either lost to or gained from neighboring profiles. By performing such net cross-shore sand transport rate distributions for adjacent profiles along the shoreline, the longshore variation of the longshore sediment transport can be obtained.
Characteristics of net cross-shore sand transport rate distributions are presented in Figure 4.9, for the case of pure convection and pure diffusion respectively, for the reshaping of a berm under wave action. Conservation of sand is seen to be assumed as no loss/gain of sand volume occurred in the berm cross-section.
Figure 4.10 illustrates the net cross-shore sand transport rate distributions for the representative shoreface nourishment profiles, average profile 21840, 21870 and 21900 respectively. The general characteristics of all three transport rate distributions are a shoreward migration of the berm and vertical erosion of the sea bed over the entire offshore stretch seaward




-50
-100
-150
-200
-250

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
Distance Offshore [ n ]
Figure 4.10: Net cross-shore volumetric transport past any offshore location assuming no longshore transport gradients. Results for average profiles 21840, 21870 and 21900 from June 10, 1993 to April 12, 1993.




of the nourishment. The total amount of erosion varies significantly with a volume change of approximately -90 m3/m, -191 m3/m and +33 m3/m, respectively.
A decreasing transport rate in the interval 1550-1625 m, indicates a deposition of sediment shoreward of the shoreface nourishment. An increasing transport rate in the interval 1625-1750 m immediately seaward hereof, illustrates the loss of height of the shoreface nourishment. Altogether, this corresponds to the observed 50-75 m shoreward migration of the berm during the first year. On the offshore side of the shoreface nourishment, a decreasing transport rate illustrates the effect of the strong diffusive processes; the natural re-shaping of the seaward side of the berm is obtained by sediment moving offshore and depositing into a milder equilibrated slope.
Seaward of 1900 m, a steady increase over the entire length of the shoreface nourishment illustrates the ongoing vertical erosion. This offshore erosion appears to be independent of the morphological changes occurring in the nearshore.
The northern 1/3 of the shoreface nourishment, average profile 21900, is seen to experience an accretion at the shoreline until the inner bar. This does not occur as consequently in the central and southern 1/3 of the profile, implying a temporary stronger deposition of sediment in the northern part. However, the deposited sand is probably eroded sediment from the beach nourishment and not a result of the breakwater effect of the shoreface nourishment. Sampling of sediment in the nearshore at neighboring profile 21920, did show a concentration of fluorescent tracer originally mixed with the beach fill, thus confirming the southern movement of the beach fill into the shoreface nourishment area, Laustrup et al (1997a).
In conjunction with corresponding profile surveys, the cross-shore morphological changes are best illustrated. Figure 4.11 shows a typical profile evolution across the shoreface nourishment, here chosen as the central average profile 21870.
The net cross-shore transport rates for the three control beaches, average profile 21720, 21770 and 21970, are displayed in Figure 4.12. The same graph scaling as for the shoreface




Mar-93
-Jun-93 S Apr-94
- Apr-95
- MWL

Figure 4.11: Profile evolution for average profile 21870.

6
4
2
z0
0
z
E
-2
o Ca
a)
[U -4
-6
-8
-10

-12,.
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
Distance Offshore [ m ]

! ... .. ... ... .. ..




- Average Profile 21720
- Average Profile 21770
-Average Profile 21970 IShoreface Nourishment

-250 4
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
Distance Offshore [ m ]

Figure 4.12: Net cross-shore volumetric transport past any offshore location assuming no longshore transport gradients. Results for average profiles 21720, 21770 and 21970 from June 10, 1993 to April 12, 1993.

200 150 100
50
E
0~
-50 -100 -150
-200




nourishment profiles in Figure 4.10 was chosen, in order to facilitate an intercomparison of the magnitude of the transport rates.
In the nearshore zone of the two neighboring downdrift profiles, a smaller amount of activity is seen to occur. This relates to the fact that no immediate disturbance of the system was introduced at that location. No parallel development is seen in the profiles downdrift of the shoreface nourishment. In the nearshore zone, longshore fluctuations in the transport rates are attributed in part to profile changes introduced by small variations in forcing conditions.
North of the shoreface nourishment, the bathymetry is developing from a profile with one bar to a profile with two bars. The increased transport rate seen in average profile 21970 relates to this change in bathymetry. As mentioned previously, the beach face accretion corresponding to the decreasing transport rate in the interval 1175-1300, is not a sheltering effect due to the shoreface nourishment, but sand transported from the beach nourishment. The negative accumulated transport rate at the end of the profile is seen to be caused by the gain of sediment in the 500 m nearshore. No impact of migrated beach nourishment sand is seen in the offshore, where vertical erosion is predominant, as earlier described for neighboring profiles.
By superimposing the two downdrift profiles, it can be seen that the cross-shore sediment transport in the nearshore is unevenly distributed in the longshore direction implying a transport direction that is not so distinct.
4.2.2 Longshore Volume Changes
The longshore volumetric changes were computed directly from the surveyed coastal profiles by integrating the gains/losses over the entire length of the profiles, from dune top to the offshore limit of the profile. In order to determine the cross-shore variation of longshore volumetric changes, the profiles were also divided into two zones, a nearshore zone in the interval from +8 m to -2 m and an offshore zone from -2 m to -12 m. The bathymetry just after nourishment was used as the reference profile. Two following bathymetries were used to describe




200
, iA
-200
-800 ..jun93-apr95
-nourishment
'III
Shoreface Nourishmnerit ''
-1000
21620 21670 21720 21770 21820 21870 21920 21970 22020
-6Survey Line No.
jun93-apr94 I
-800 . .. -jun93-apr95 i .... .......... .i. ............ .. .
Shoreface Nourishmerit
21620 21670 21720 21770 21820 21870 21920 21970 22020
Survey Line No.

22070 22120 22170 22220 22270 22320

Figure 4.13: Longshore volume change from +8 m to -12 m.




the development during the monitoring period. The selected surveys were April 12, 1994 and the last survey April 24, 1995.
The overall longshore volumetric changes from dune top to offshore limit of the surveyed area are presented in Figure 4.13. Considerable fluctuations alongshore are observed. Erosion and accretion appear to follow a spatial periodicity of approximately 500 m. In time, longshore migration of the erosional and accretionary effects is observed; no distinct migration directions seem to prevail. However, extensive erosion is characteristic in the beach nourishment segment. By integrating the volumetric changes over the entire length of the profile, the breakwater effect of the shoreface nourishment is not very accentuated as the nearshore accretion is added to the offshore erosion.
Looking at the nearshore changes displayed in Figure 4.14, three characteristics appear: the downdrift accretion adjacent to the shoreface nourishment, the erosion at the beach nourishment and the mixed accretion/erosion fluctuations in the remaining shoreline stretches. All three effects seem to intensify during the monitoring period.
During the first year, the downdrift accretion over a length of 1000 m adjacent to the shoreface nourishment is observed with an average gain of 70 m3/m/yr. During the second year, this effect seems to grow as the accretion migrated further downdrift to a total length of 1500 m with a supplemental average gain of 65 m3/m/yr. The breakwater effect is clear.
The beach nourishment sand is seen to be totally eroded during the first year and this erosion continues in the second year. The major losses from beach fills occur through the diffusive losses at the project ends by longshore sediment transport. However, the nearshore fluctuations are seen to be a small part of the total fluctuations shown in Figure 4.13, as a significant offshore loss is observed also to have taken place seaward of the beach nourishment. It is of interest that at the end of the 2-year monitoring period, the total loss in the beach nourishment area exceeds almost by a factor of 2 the amount of beach nourishment, leading to a considerable profile steepening.




400 200 -

-200
-400
-600
-800 -

I
V V
jun93-apr94
- -jun93-apr95 nourishment

-1000 i
21620 21670 21720 21770

A

Net Longshord Sedimen Transport i i ,'
A,\i

V, i

Shoreface Nourishment

21820 21870 21920 21970 22020 Survey Line No.

Beach NoUrishment

22070 22120 22170 22220 22270

Figure 4.14: Longshore volume change from +8 m to -2 m.

22320

I l = t I




400
Net Longshore Sediment Transport
I ,'.'i
200
-200-r E1
E/
> III
-400
I... I.... ..\
LA
-600
- jun93-apr94
!i I it
-800 -. -- jun93-apr95
-nourishment
Shoreface Nourishmer Beach Nourishment
-1000
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320
Survey Line No.

Figure 4.15: Longshore volume change from -2 m to -12 m.




Even in the offshore zone, a great amount of fluctuation describes the longshore changes, see Figure 4.15. The same spatial periodicity as in Figure 4.13 is observed. However, a general erosional trend can be seen from one year to the next. Again, it appears that most of the ongoing erosion in the beach nourishment stretch, took place in the offshore zone.
4.2.3 Cumulative Volume Changes
The longshore volumetric changes previously calculated were integrated alongshore. Again in order to determine the cross-shore variation of volumetric changes, the profiles were also divided into two zones, a nearshore zone in the interval from +8 m to -2 m and an offshore zone from -2 m to -12 m. The initial bathymetry before nourishment was used as the reference profile. Three bathymetries were used to describe the development during the monitoring period. The selected surveys were again June 10, 1993 and April 12, 1994 to which the last survey April 24, 1995 was added.
Figure 4.16 shows the measured cumulative volumetric changes for the entire 7 x 1.5 km monitored area, starting from the southernmost survey line 21620. Integrating over the entire length of the profile, the overall morphological changes are highlighted. Approximately 1,000,000 m3 of material was lost from the survey area over the two-year monitoring period. The accretionary effect in the profiles containing the shoreface nourishment, seem to be slightly decreasing from the first to the second year. However, the erosional effect in the profile containing the beach nourishment seems to be increasing. A further division in cross-shore regions will be more precise in showing where on the profile these volume changes occurred.
Also displayed in Figure 4.16, are the expected cumulative volumetric changes when only considering the established local background erosion rate of 48 m3/m/yr and the added nourishment volumes. That is, not taking into consideration the changes introduced in the nearshore littoral processes by the nourishment projects. For all three time periods shown, the expected changes differ somewhat from the measured. The offshore deposition of sand in the




700 600 500
400 300
E
0
0
o 200 100
0
-100 -200 -300

Figure 4.16: Cumulative volume change from +8 m to -12 m relative to March 1993.

-4001 i,
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320
Survey Line No.




berm area is not accounted for, but the greatest difference is however related to the significant erosion in the beach nourishment area, also not accounted for. The comparison between the measured and expected cumulative volume changes underlines both the significant impact of the nourishment project in disturbing the natural littoral processes and as well the natural longshore variability in these processes.
The cumulative volume changes in the nearshore zone are presented in Figure 4.17. In two consecutive years following the completion of the nourishment projects, the breakwater effect of the shoreface nourishment is clearly seen; a gradual accretion immediately downdrift of the shoreface nourishment is observed. A total of approximately 150,000 m3 sand was deposited over a distance of 1500 m at the end of the monitoring period. Directly landward of the shoreface nourishment, only a slight accretion occurred just after completion of the nourishment; this effect was not present in the remaining time of the monitoring. The beach nourishment sand is seen to be completely eroded after a year. After the first and the second year, there appears to be a small periodic fluctuation between accretion and erosion at the shoreline but no general trend is seen.
Similarly, the cumulative volume changes in the offshore zone are presented in Figure 4.18. The overall characteristics in the offshore zone appear to be similar to the characteristics for the entire profile, suggesting that by far most of the erosion took place in the deeper end of the profile thus creating a steeper profile. An immediate volume increase downdrift of the shoreface nourishment following its completion is seen; the longshore transport on the berm is increased due to extensive wave breaking over the berm. After two years, the bar system seems to be stabilizing as the alongshore volume changes diminish.
A very extensive erosion seaward of the beach nourishment at an amount much greater than the nourishment volume itself is observed. The bathymetry in front of the beach nourishment is characterized by the presence of only one bar, an inner bar not very pronounced and discontinuous. As was shown in Figure 4.2, the nearshore area in this coastline stretch has not the benefit of an outer bar to dissipate the incoming wave energy. A loss of approximately 100,000




500
400 300
200 100
E
C0
0
-100
-200 -300
-400

Figure 4.17: Cumulative volume change from +8 m to -2 m relative to March 1993.

*-50
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320 Survey Line No.




500
-400 Jun-93
400
- -- Apr-94
...... ----Apr-95
300
- Nourishment
200
100
E / --,00 .
x ..
"-- ," i o" Io --. I . .
- 1 0 0 " .. . .. . . . } . . . ..I
I =I I I'
I ii :
-200
-300.
-400 i
2 Shoreface Nourishment IBeach Nourishment .--... '
-500
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320
Survey Line No.

Figure 4.18: Cumulative volume change from -2 m to -12 m relative to March 1993.




m3 occurred during the first year followed in the second year by a loss of approximately 300,000 in3. This increase in erosion from the first to the second year was probably also caused by the extremely strong erosion in the winter in 1994-95 outside the beach nourishment.
4.3 Longshore Variability
Placing nearly half a million m3 of sand in a littoral system might seem to be a large nourishment volume capable of a considerable perturbation to a system in dynamic equilibrium. However, the system experiences natural background "noise" and as the effect of the perturbation decreases with time due to the re-shaping of the profile, it becomes even more difficult to disassociate the natural processes from nourishment introduced processes as the natural background noise increases with time. The above inevitably raises the question of whether the perturbations introduced by the nourishment volumes were great enough in a system with such a high degree of variability.
The longshore volumetric changes in the whole monitoring area suggest a lack of coherency in the longshore processes. A considerable spatial and temporal variability in the littoral processes seems to characterize the area. This natural variability will also be found in the alongshore variation of shoreline positions. The development of the shoreline position will thus illustrate the effect of the nourishment projects.
The dominant role of the longshore sediment transport pattern has been shown. Both the cross-shore and longshore sediment transport seem to be very sensitive to the bathymetric variations in the nearshore region. The implementation of the nourishment volumes in addition to the lack of uniformity in the coastal profiles will therefore result in a variable alongshore distribution of the sediment transport pattern.




' I I
501
-Apr-94
\ / 1
40 .. .... -Apr-9
20
10' '':
o1
Ef
.10I
CO 0
-10.
I j I
-20I
-30-.
-40
' ...~ ~~ ,*\ / ........
-50 i Shoreface Nburishment IBea6h Nourishment
-50,
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320
Survey Line No.
Figure 4.19: Shoreline change relative to June 10, 1993 position.




4.3.1 Shoreline Positions
The changes in shoreline positions between consecutive profiles were calculated by determining the change of volume in the zone MLW -0.25 mn and MLW +0.25 mn. The obtained volume was then divided by 0.50 m which yielded horizontal distances from the reference line to the updated shoreline.
The shoreline changes relative to the June 10, 1993 survey, just after completion of the nourishment works, are given in Figure 4.19. A main characteristic of the development of the shoreline position during the two years of monitoring, seem to be a spatial as well as a temporal variation. An alongshore fluctuation between shoreline retreat and shoreline advance is present over the entire stretch. No distinct direction of migration of the fluctuating pattern seems to prevail.
The considerable retreat of the shoreline at the beach nourishment location indicates the eroded nourishment volume by the end of the first year. However during the second year, the retreat becomes much greater than the imposed shoreline advance due to the nourishment volume. This is highlighted in Figure 4.20, showing the shoreline changes relative the March 29, 1993 survey before nourishment. It supplements the former figure by showing that the natural alongshore variability in shoreline position, seem to follow the same pattern at the beach nourishment as for the rest of the stretch.
The positive effect of the shoreface nourishment is a distinct average shoreline advance of approximately 30 m over a distance of 1000 m downdrift. This effect is visible at the end of the second year and correlates with the accretion previously observed in the longshore volumetric changes.
4.3.2 Sediment Transport Distribution
The cross-shore distribution of the longshore sediment transport was shown to be very sensitive to the local shape of the shoreface nourishment on the outer bar. Even small




50
Apr-94
40- ----Apr-95
I V |I I
, 1 Nourishment
30 ,.
20
--10
E /
e ,\ i\/" "1
-10 /1
1 ""1 1 1 1/
.20 .
-30 .
-40 I
Shoreface liourishmen Beach Nourishment
-50 I.
21620 21670 21720 21770 21820 21870 21920 21970 22020 22070 22120 22170 22220 22270 22320
Survey Line No.

Figure 4.20: Shoreline change relative to March 29, 1993 position.




morphological changes were reflected in the sediment transport pattern, making it difficult to distinguish between the sediment transport caused by the natural variations and the sediment transport caused by the nourishment volumes. In an attempt to eliminate all other changes but the ones caused by the nourishment volumes, Laustrup et al. (1996) integrated the longshore transport in depth intervals of +4 m to -4 m and of -4 m to -8 m; these intervals correspond to the shoreline zone and the shoreface nourishment zone respectively. Figure 4.7 showed examples of calculated 2-dimensional sediment transport fields and integrated longshore sediment transport for these intervals. It appears that the changes introduced by the nourishment volumes are nearly insignificant compared to the natural variations in both space and in time.
The sediment transport distribution was shown to be not particularly affected by the beach nourishment since it extended only a small distance seaward.
The modeling results showed that for both the shoreface and the beach nourishment areas during the monitoring period, waves with a significant wave height of 1 to 2 m caused most of the sediment transport with the net sediment transport being towards South.
Migrating bed forms in deep water in the interval 15-20 m, influence the direction of the incoming waves by refraction and thus through focusing, have an effect on the local longshore sediment transport. The migration rate of these bed forms has been established at a velocity up to 80 m/year directed towards the North. This migration furthermore induces a yearly variation in incoming wave field. However, the correlation between the instability of the sediment transport and the migrating bed forms in the seaward end of the coastal profile has not been found to be significant enough to draw conclusions.
Unequal amounts of alongshore volumetric changes would suggest that even with similar forcing conditions along the region examined, differentials in longshore sediment transport were important. In the immediate vicinity of the nourishment projects, coastal structures were not present in such a way as to create differentials in longshore transport; i.e. during the monitoring period, the revetments were always buried on the beach and the beach breakwaters normally




covered by nourishment sand so as not to protrude in the nearshore. However, the overall erosional state of the coastline is inherently related to the groin field 3 km updrift, but the variability in longshore transport was probably not due to localized processes associated with the updrift groin field as the variability is on a much smaller spatial and temporal scale than would be expected if the groin field were responsible.
4.4 Beach Nourishment Performance Prediction
Beach nourishment projects are generally placed with profiles which are steeper than the natural profiles for the size of sediment that is used in the beach nourishment project. Over the years, an offshore transport of sediment results as the profile will tend to equilibrate to its natural shape, consistent with the grain size used in the nourishment. The qualitative effect of grain size in terms of the dry beach width for the same added volume per unit length of beach has been investigated by Dean (1998).
In addition to the cross-shore profile equilibration, the placement of a beach nourishment project results in a planformn anomaly which interacts with the waves to result in sediment transport away from this anomaly. This process of mobilization of sediments by waves has been referred to as "spreading out" losses in which the transport is occurring away from the anomaly. These losses relate to a longshore redistribution of the sediment and not a total loss to the system but rather a loss from the region in which the sediment initially was placed. The spreading out losses from the nourished area are thus manifested by a relative gain of sediment volume in areas adjacent to the beach nourishment.
Simple analytical methods are readily developed for predicting the performance of beach nourishment projects, Dean (1983). These methods are valuable in providing an estimate of overall beach nourishment performance such as project longevity and remaining volume in the project area. To allow for greater flexibility in the modeling of shoreline evolution, Dean and Grant (1989) have developed methodologies for calculating the response of shorelines in the




vicinity of beach nourishment projects. Their numerical approach provides the capability to include site specific features such as arbitrary initial shoreline position, background erosion rates and littoral barriers. The study area at Torsminde has such features and will thus also be modeled numerically.
4.4.1 Longevity of Nourishment Project
One-line models of shoreline evolution have been proposed by many investigators and these models have been shown to perform effectively in many different beach nourishment projects of engineering interest. A one-line model is the simplest model to describe the time history of a nourishment project along a shoreline. In the absence of background erosion, PelnardConsidere (1956) combined the conservation equation and the linearized transport equation which resulted in the classical heat-conduction equation
Y =Ga2' (4.3)
at a2
in which the longshore diffusivity, G is defined as
KHb512gJ7 (4.4)
8(s-1!)(1- p)(h. + B)
where K is a sediment transport parameter, Hb is the breaking wave height, g is the acceleration of gravity, ic is a proportionality constant relating breaking wave height to water depth, s is the ratio of mass densities of sediment to water, p is the in-place sediment porosity, h. is the depth of limiting sediment motion and B is the berm elevation.




The above one-line model can be used to predict the planform evolution of a beach fill. It is thus possible to obtain information on the proportion of sand remaining at the placement site at any time following the nourishment works. For estimating the "half-life". of a beach nourishment project on a long straight shoreline with no background erosion, corresponding to half the initial fill volume still within the project length, Dean (1983) defined the half-life t50% as
12 (4.5)
t50% ": 0. 21
G
where I is the project length and G the shoreline diffusivity defined in Eq. (4.4).
In determining the longshore diffusivity of the present beach nourishment project, common constants and coefficients were set to known values, such as K =0.78, s = 2.65 and p = 0.35. Other site specific parameters were arbitrarily chosen as best estimates based on the available data, such as K= 1.10 based on the beach fill mean sediment grain size 0.32 mm, Hb = 1.5 m, h4 = 16 mi and B = 6 m based on monitoring survey results. (It is noted that the relationship between the sediment parameter and the sediment grain size is based on effective wave height as defined by a Rayleigh distribution. The present representative significant wave characteristics are based on energy spectrum, thus requiring a correction of the wave height by a factor of 0.73 5).
The estimated longevity yields a half life of t50% = 3.1 months for the beach nourishment at Torsminde. The monitoring results showed that the beach fill was totally eroded after 9 months. As the erosion rate of planform anomaly tends to decrease as the remaining nourishment volume diminishes, the predicted longevity is found to be in order of magnitude in agreement with the measured performance.




The rapid erosion of the entire beach fill suggests the importance of the short project length of only 1 kmn. As can be deduced from Eq. (4.5), t50% is seen to be proportional to the square of the project length, thus doubling the project length would result in extending its longevity by a factor of 4.
4.4.2 Multiple Nourishments in the Study Area
As described in Chapter 3, a system of coastal profiles has been surveyed regularly since 1938, 13 of which are located within or adjacent to the NOURTEC area, thus providing the historical development of the shoreline position in the study area. Decadal variation in wind and wave conditions and implementation of extensive coastal protection measures at different times, has altered the shoreline trend lines for separate periods. DCA has selected the period 1985-1992 to determine the representative development of the area. The choice of 1985 relates to the significant commencement of nourishment volumes. Figure 3.2 shows the coastal measures implemented in the NOURTEC area since 1978; specifically the chronological and spatial extent of the multiple nourishment projects is of interest. With knowledge of the annual shoreline retreat, the wave characteristics and the added nourishment volumes, the effect of the multiple nourishments can be modeled.
The numerical model DNRBS (Department of Natural Resources, Beaches and Shores) developed by Dean and Grant (1989) predicts shoreline change in the vicinity of a beach nourishment projects. The shoreline modeling utilizes a deep water wave equivalent for the oneline model presented briefly in the previous section. A slightly modified version of the DNRBS model also includes the effects of subsequent multiple nourishment projects on the same updated shoreline.
The DNRBS model assumes straight and parallel contours seaward of the depth of closure, h., and contours parallel to the nourished shoreline landward of h.. By considering the




ratio of the wave celerity at h., C., and the deep water wave celerity, C0, the longshore diffusivity is entirely expressed in terms of deep water wave quantities, with the exception of a., the incoming wave angle at h., and C.. The longshore diffusivity is now expressed as
KH02.4CGo12g 0.4 [cos"2 (13o -ao )cos 2(0 -a.)]
G = (46
8(s-_1)(1-_p)C.K0O4 (h. ;+B) [cos(130, -a.) ](4.6)
where the subscript "o" denotes deep water conditions; H, is the deep water wave height, CGO is the deep water group celerity, P,, is the azimuth of the outward normal to the ambient depth contours in deep water and cxo is the deep water incoming wave angle.
Starting from the sediment transport equation at the breaker line, using conservation of energy considerations coupled with Snell's Law and the continuity equation, the transport equation used for numerical analysis was derived to yield
-KHo 2.4 CGO 1.2"g.4 cos"2 (P -aO)sin(f
8(s _-1)(1 P )C.IC4 (4.7)
where fis is the azimuth of the outward normal to the depth contours within the depth limit affected by the nourishment project. With the exception of the trigonometric term involving (fls a.) and the term C., all quantities are again expressed in terms of deep water conditions.
The DNRBS model was applied to the NOURTEC area over a 10 km longshore stretch immediately south of groin Q. Figure 4.21 displays the northern 5 km of the study area with the shoreline indentation south of groin Q, the location of the beach nourishment, the revetments and the multiple beach breakwaters located at the shoreline; the southern 5 km half of the modeled




A
Groin Q Beach Breakwater >
Shoreline
Revetment
II
z
A A
Figure 4.21: Northern 5 km stretch of study area.




stretch has no manmade features or irregularities in its nearly uniform shoreline and is thus not shown on the figure.
The model is capable of including the downdrift erosion adjacent to a partial littoral barrier such as groin Q. In order to include the proper amount of sediment bypassing the groin, an annual sediment budget for the 10 km stretch was developed. Provided that the longshore volumetric sand transport rate, Q, for any alongshore location on a beach, x, is known, beach changes can be predicted by the continuity equation
aQ aV (4.8)
a)x )t
where s is an additional source term indicating any material added per unit length per unit time and V is the volumetric change per unit beach length over a time period t. After profile equilibration occurs under the assumption that as beaches erode or accrete, the profile moves without change of form in a landward or seaward direction, respectively, this volumetric change can be shown to be given by the Bruun rule
1 aV (4.9)
AY= (h. + B) at
where Ay is the shoreline change for a given volumetric change AV. In the considered period from 1985 to 1992, the annual shoreline retreat at Torsminde is 1.4 m/year, accounting for the average nourishment-related shoreline advance of 1.0 m/year, Laustrup et al. (1997a).
The sediment transport capacity of the incident waves can be computed from Eq. (4.7). Using representative wave and site characteristics for the monitoring period: H. = 1.5 m, A, =




2730 and ix, = a.= 2830, the annual net southerly sediment transport is estimated to be on the order of 1.5 million m3/year.
In the time period 1985 to 1992, an average of approximately 250,000 m3/year was supplied to the study area as nourishment, largely as beach nourishment. The small amount of volume placed as shoreface nourishment before 1992, represents 6% of the total added volume and was thus included in the average annual supply.
Under the assumption that the extensive annual nourishment prior to 1993 nourishment have established a uniform alignment of the shoreline and following integration of the continuity equation, Eq. (4.8), over the 10 km stretch, the amount of sediment bypassing groin Q was found to be approximately 750,000 m3/year. This volume was included in the model as a constant sediment supply at the location of the groin Q.
The DNRBS model neglects wave diffraction in the lee of a littoral barrier or more precisely in this modeled case, downdrift of a sediment sink as the amount of sand bypassing the groin is less than the transport capacity of the waves. Thus, accentuated erosion immediately downdrift of groin Q should be expected in the modeling of planform evolution. In reality, this erosion is limited locally and distributed downdrift as the shoreline stretch south of the groin features several beach-parallel breakwaters and continuous revetments.
Figure 4.22 displays on a distorted scale the calculated planform evolution from 1985 to 1992 for the 10 km modeled stretch. The shoreline progresses from South to North from the left of the plot at 0 km to the right at 10 km at the location of groin Q. All 18 nourishment projects from 1985 to 1992 have been included at their respective locations and with their actual distributed densities, although only selected years are displayed for clarity.
The shoreline is seen to retreat downdrift of groin Q and advance at the location of the greatest nourishment density. The computed alongshore average of shoreline variation was found to be -1.34 m. In other words, all the different volumetric changes within the modeled stretch




20
Q
10
0
2 3 4 5 6 7
E
-10
o
a,
W
0
-20
0
-30
1987
-1989
-40
- 1991 1993
-50
Shoreline Length [ km ]
Figure 4.22: Calculated planform evolution for multiple nourishment projects from 1985 to 1992.




were reasonably accounted for. A -1.4 m average shoreline change was expected as it resulted from the sediment budget in which the annual erosion was not incorporated.
The resulting -1.4 m shoreline change infers that the 10 km shoreline stretch downdrift of the groin field was in approximate volumetric sediment equilibrium with a background coastal retreat rate of 2.4 m/year and with a nourishment rate of 250,000 m/year corresponding to a shoreline advance rate of 1.0 m/year. Thus, the remaining shoreline retreat rate of 1.4 m/year should be expected with the actual annual nourishment rate.
4.4.3 Effect of Distance to Groin Field
The proximity of the updrift groin field with its terminal groin Q and the inevitable downdrift erosion into the study area, might be in part responsible for the rapid erosion of the beach nourishment. Although the previously predicted project longevity was in reasonable agreement with the observed lifetime without taking the effect of the adjacent groin field into account, the effect of the distance from the beach fill relative to groin Q, can be significant. Placement of sand in an area prone to extensive erosion, for example, downdrift of a partial littoral barrier, is certainly where it is most needed but at the same time where it is inherently most unstable. By varying the location of the beach nourishment, the effect of the distance to the groin field can be estimated.
Figures 4.23 and 4.24 display the planform evolution for the centerline of the beach nourishment located 5 km and 8 km downdrift of groin Q, respectively. Both nourishment volumes were 250,000 m3 of sand distributed alongshore with a density of 250 m3/m. The initial dry beach width was chosen as 45 m from consecutive surveyed profile elevations before and after implementation of the nourishment.
The computed percentages of remaining volume after the first as well as the second year were for each location nearly equal; 23% remained after the first year and 17% after the second year. However, these percentages are not in agreement with the observed evolution of the beach




40
Q
20
0
2O
40 0-40
...... Year0
-60-- Yearl
-Year 2
-80-
Shoreline Length [kin] Figure 4.23: Calculated planform evolution for beach nourishment located 5 km downdrift of groin Q.




60
.. .. ......
40
40
0
C 1)1 2 34 5 67 9
CO
* i
* I
* i
20
----- Year 0
-60 -- -Year 1
-Year 2
80
Shoreline Length [km ] Figure 4.24: Calculated planform evolution for beach nourishment located 8 km downdrift of groin Q.
0
(1,
0
-40
-60 __Year____1
-80
Shoreline Length [ kin] Figure 4.24: Calculated planform evolution for beach nourishment located 8 km downdrift of groin Q.




nourishment project, which eroded entirely within the first year. This lack in predictive capability is probably related to the assumption that the volume of beach nourishment sand is evenly distributed over the entire height of the active profile, from dune top at .+6 mn DNN to depth of closure at -16 m DNN. The beach nourishment project was placed with much steeper profile from +4 mn DNN to -2 mn DNN and was likely eroded before it ever nearly reached equilibrium in the cross-shore direction.
Nevertheless, the present results suggest that the relative performance of the beach nourishment compared with shoreface nourishment is not related to its proximity to the groin field. As noted previously, the presence of the shore armoring would tend to distribute some of the predicted erosion immediately downdrift of groin Q, further downdrift and would place greater erosion on the beach nourishment.
4.5 Submerged Berm Response
4.5.1 Migration of the Berm
The shoreface nourishment was constructed as a nearly symmetrical berm. Immediately following its completion, the berm cross-section became asymmetrical with a steeper landward slope. In part, this asymmetry reflects the initial diffusive processes or the spreading of sediment down-slope into the approaching waves. As the berm migrated, the asymmetry continued throughout the monitoring period. This asymmetry reflects the shoreward transport as waves carry sand over the crest to deposit on the leeward side of the berm.
During the first year of monitoring, the location of the initial trough between the inner and outer bar became the location of the new crest as the berm migrated shoreward. The inner bar also migrated shoreward. The berm responded along its entire length in the same persistent shoreward fashion; a typical profile development in the region of the nearshore berm is presented




Figure 4.25: Berm development for average profile 21900.

-1
-2
-3
z
z
9
E
--4
0
Ca
0
-5
-6
-7
-8
1400

1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950
Distance Offshore[ n]

2000




in Figure 4.25 for average profile 21900. Over the monitoring period, the berm migrated 50-75 mn onshore and the level of the top of the berm was reduced by approximately 0.5 m.
4.5.2 Breakcwater and Feeder Effects
The shoreface nourishment was constructed with the intent of both reducing incoming wave energy and causing breaking over the berm and to supply material to the littoral zone of the beach. Both effects were found to be occurring. The breakwater effect of the berm was most pronounced by visibly increasing beach volume on some stretches and by reducing erosion on other stretches. The feeder effect was determined by corings taken on the beach face and analyzed for the coarser shoreface nourishment material.
The performance of an offshore breakwater is based on the principle of reducing the amount of wave energy that reaches a coastline in order to reduce shoreline erosion. As in the case of a shoreface nourishment, the breakwater can be effective even if it is not emergent. Wave diffraction landward of the breakwater, will lead to an equilibrating shoreline planform characterized by a depositional feature behind the breakwater, referred to as a salient. If the incoming wave angle is nearly normal to the shoreline, the salient is located symmetrically around the breakwater. The reduction of wave height by diffraction implies a decreasing local transport, resulting in impoundment of sediment. Ultimately there is a downdrift erosion due to this impoundment of sand by the advanced shoreline.
According to the hydrographic results for the whole monitoring period, the annual average wave direction was oriented approximately 2830 relative to true North. The coast normal is 273' along the entire shoreline, in other words, the average incident deep water wave angle can arbitrarily be taken as 100 off the shore normal.
The nearshore in the surveyed area is characterized by straight and parallel offshore contours, hence each wave refracts similarly along the beach in the longshore direction. As incoming waves shoal, this change in wave direction further reduces the incoming wave angle to




3330

N
2830

Figure 4.26: Measured and expected breakwater effects.




the shoreline, thereby justifying the nearly symmetrical depositional feature behind an offshore breakwater.
The measured breakwater effects induced by the shoreface nourishment are given in Figure 4.26. Together with these monitored effects, are superimposed the breakwater effects as would be expected by the measured hydrographic results and as described above. As mentioned in the previous section, a shoreline accretion was seen to occur directly downdrift of the nourishment and not behind the nourishment. This would correspond to an incoming wave angle approximately 500 off the actual measured wave angle. The dotted line corresponds to the expected shoreline development under the measured average wave direction; wave refraction is not taken into account, but if so, would increase the discrepancy.
The observed accretionary and erosional effects on the shoreline behind the nourishment can not be attributed completely to the breakwater effect of the shoreface nourishment. The shoreline development as it occurred is not typical of a pattern caused by an offshore breakwater. Other processes must have strongly interacted, such as those induced by the considerable southgoing littoral drift, and might in part be responsible for the observed development.
The effect of the berm serving as a supplemental source of feeder material, was much less pronounced. Through sediment sampling, it was found that the 40% loss of the nourishment sand at the end of the monitoring period, only accounted for 1/3 of the total accretion landward of the nourishment. This relates to the placement of sand on the outer bar where the nourishment quickly becomes an integral part of the natural bar system. Instead of being eroded away, the nourishment behaves like a longshore bar in dynamic equilibrium with the nearshore littoral processes. The feeder effects are thus reduced.




CHAPTER 5
MODEL DERIVATION AND SOLUTION
A model for the migration of submerged berms constructed offshore of the day-to-day surf zone but within the depths disturbed by waves during storm events was proposed by Douglass (1995). The model assumes that landward migration of the nourishment is due primarily to the net landward transport by the velocity asymmetry of finite-amplitude waves, and is based on Bagnold' s bedload-sand transport equation and Stokes' second-order wave theory. Conservation of sand considerations in the cross-shore direction lead to the classical convectiondiffusion model equation. In the present study, this model is derived and forms the basis for further investigation.
The combined convection-diffusion model equation presented, is a classical nonlinear partial differential equation. By using readily established methods in computational fluid dynamics, the equation can be solved numerically. Given a specified sea state in form of a wave climate time history, the equation predicts the behavior of a berm; it implies that the form of a berm will migrate landward while it diffuses.
5.1 Model Derivation
To illustrate the coastal profile development under onshore-offshore transport from a basic sediment transport model, the equations proposed by Bagnold (1963) have been used. Bagnold' s approach has been applied fairly successfully in a wide variety of sedimentological problems and will thus also be used in this study in an attempt to determine quantitative predictions of onshore-offshore transport.




Bailard and Inman (1981) applied Bagnold's transport model to a coastal environment as a basis for the development of a total load model of time varying sediment transport over a plane sloping bed. This model will be used in the cross-shore direction under the assumption that all water motion is directly onshore or offshore.
Neashore placement of sand is typically placed seaward of the surf zone. A fundamental concept for the model is that in such depths, the dominant driving force is the waves. Specifically, the landward migration of sediment is due to the net landward transport by the asymmetry of finite-amplitude waves. Douglass (1995) applied Stokes' second order wave theory to describe this velocity asymmetry.
Consideration of conservation of sand with the wave theory and transport model will lead to a wave-based model of berm migration.
5. 1.1 Energetics Transport Model
Current sediment transport models reflect two distinct approaches: an energetics approach and a traction approach. In both cases, these approaches are based on adaptation of stream flow sediment transport models. The energetics approach, which is used in the present study, is based on the stream transport model developed by Bagnold (1963).
Bagnold' s energetics-based sediment transport model assumes that the sediment is transported in two distinct modes, each differing according to the support of the sediment grains. Sediment transported as bedload is supported on the bed via grain to grain interactions, while sediment transported as suspended load is supported by the stream fluid via turbulent diffusion. In both modes, energy is dissipated by the stream by transporting the sediment load. Bagnold, comparing the stream to a machine, defined the sediment transport efficiency as the ratio of the rate of energy expended in transporting the bed load, divided by the total rate of energy production of the stream.




For steady, two-dimensional stream flow, Bagnold (1963) developed the following total load sediment transport equation:
L b + E
( tano-tanf (W/l)-tanp) (5.1)
where it is the total immersed weight sediment transport rate composed of the sum of the bedload transport rate, ib, and the suspended load transport rate, is, (0 is the rate of energy production of the stream, u is the mean velocity of the stream, tan fP is the slope of the stream bed, 0 is the internal angle of friction of the sediment, W is the fall velocity of the sediment and Lb and E, are the bedload and suspended load efficiencies respectively.
For oscillatory flows, such as those found in the surf zone, Inman and Bagnold (1963) further developed a conceptual sediment transport model, currently the most widely accepted and equivalent to the equation recommended by the Shore Protection Manual (1984). Based on Bagnold's models, Bailard and Inman (1981) presented a total load sediment transport model developed for time-varying flow over an arbitrarily sloping planar bed. The model predicts the local, near-bottom sediment transport rate as a function of the near-bottom water velocity vector.
Following Bailard and Inman (1981), by integrating the instantaneous bedload and suspended load sediment transport equations in time, the total load sediment transport is obtained as
(')= PC t-no tan 0
+I -C 1.) 3 f) 1
+ PCf W (IWIi7-tan/3I~i)' (5.2)




where p is the density of water, C, is a friction coefficient, the velocity vector ii has an
arbitrary orientation to the y -axis, j is a unit vector pointing shoreward and ()means average in time over one wave period.
In both bedload and suspended load, the transport vectors are found to be composed of a velocity-induced component directed parallel to the instantaneous velocity vector and a gravityinduced component in the cross-shore direction.
5.1.2 Wave-Based Model of Berm Migration
The success of a shoreface nourishment project is directly dependent on the depth in which the nourishment is placed. If placed within the outer limit of sand-transport initiation by waves, the nourishment is expected to migrate onshore. Nearshore nourishment of sand is typically placed offshore of the location of the outer bar in depths beyond the day-to-day surf zone but within depths where the wave orbital velocities are capable of moving sediment during higher waves and storm events. In these water depths, wave breaking-induced turbulence is m-inimal. As turbulence is the most important factor in the suspension of sediment, bedload transport can reasonably be assumed to be the dominant transport mechanism outside the surf zone. Thus, in the following, only bedload transport is considered in the cross-shore sediment transport. This assumption simplifies greatly the sediment transport equation, as the second term in Eq. (5.2) reduces to zero.
In order to enhance the longevity of a shoreface nourishment project and the overall performance of the project, nourishment material was chosen coarser than the native material at the same cross-shore location. The suspension of such coarse material would require a highly turbulent flow field, which is not present at the nourishment location. Hence, the use of coarse sediment further justifies bedload as being the main cross-shore sediment transport mode outside the surf zone.




Another simplifying assumption can be made, by only considering water motion in the cross-shore direction. This assumption is consistent with the interest in the onshore migration of the nourishment and the corresponding cross-shore transport. By incorporating all the above assumptions into Eq. (5.2), the bedload transport rate becomes
tan 2 (5.3)
Flows induced by dissipation of wave energy in the nearshore, play a dominant role in sediment transport. A variety of cross-shore flows, such as asymmetric oscillatory flow, breaking induced turbulent flow and momentum decay-induced undertow have been identified by Roelvink and Stive (1989), with the aim of revealing the role of each of the flow mechanisms in the twodimensional case of modeling bar generation. One of these flows is the breaking-induced undertow, the role of which in the bar generation was first described qualitatively by DyhrNielsen and Sorensen (1970). A study of Stive (1986) shows that it is important to account for the effects of wave asymmetry. These studies indicate that some of the main bar-generating crossshore flow mechanism are identified.
As the shoreface nourishment was, placed on the offshore flank of the outermost bar beyond the day-to-day surf zone, the effects of undertow are reduced and wave asymmetry mechanism dominate. Considering depths beyond the day-to-day surf zone, this fundamental concept is used by Douglass (1995) in assuming that the wave asymmetry mechanism dominates the water motion.
In intermediate depths, the velocity profile of a finite-amplitude wave is characterized by larger forward velocities under the crest than the backward velocities under the trough; the wave profile is much more peaked at the wave crest and flatter at the wave trough. Douglass proposed using Stokes' second-order wave theory, the lowest order wave theory with wave asymmetry, to




describe the orbital water velocities. Stokes' second order wave theory predicts near-bottom velocities of
HgT cos(2rt/Tl) 3 7r2H2 cos(47rt/T)
u=+
2L cosh(2rhlL) 4 LT sinh4(2rh/L) (5.4)
where u is the near-bottom water velocity, H is the wave height, L is the wave length, T is the wave period and h is the water depth. Substituting Eq. (5.4) into Eq. (5.3) and following integration with respect to time, the bedload transport rate is
97r2 pg2Cfe'b H4T_ 2
Q(ib 2 t fb (tan -tanf P) Tsech2(27r h/L)csch4(27r hl L)
64 tan2 L (5.5)
The volumetric bed load sediment transport is obtained as ibPs
q- (P P)g (5.6)
Substitution of Eq. (5.5) into Eq.(5.6) yields
q= 92 pgCfEb (tan -tan) 4T sech2(27rh/L)csch4(27rh/L)
64 (p,-pla'tano L (5.7)
where a' is the ratio of total volume to volume of solids and p, is the sand density. Considering the one-dimensional conservation of sand in the cross-shore direction, h = q, (5.8)
at Dy