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UFL/COEL-96/013
BEACH PROFILE RESPONSE TO ABRUPT
VOLUMETRIC PERTURBATIONS
by
Matthew S. Goodrich
Thesis
1996
BEACH PROFILE RESPONSE TO ABRUPT
VOLUMETRIC PERTURBATIONS
By
MATTHEW S. GOODRICH
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
1996
ACKNOWLEDGEMENTS
I wish to express a great deal of thanks to my advisor and supervisory committee
chairman, Dr. Robert G. Dean, for his support and guidance during my stay at the University
of Florida. I would also like to thank the members of my supervisory committee, Dr. Hsiang
Wang and Dr. Robert J. Theike.
My most sincere appreciation and gratitude belong to my parents, Ruth and Robert
Goodrich, for their unfaltering love and support that has enabled me to exceed in all my
endeavors.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ........................................... ii
LIST OF FIGURES ................................................. v
LIST OF TABLES .................................................. x
ABSTRA CT ..................................................... xi
CHAPTERS
1 INTRODUCTION ........................................ ....... 1
1.1 Descriptive Terms ......................................... 2
1.2 Profile Classification ....................... ................ 4
1.3 Fall Velocity ............................................. 4
1.4 Equilibrium Beach Profile .................................. 6
1.5 Empirical M odels ................................... ...... 6
1.6 Large Wave Tank Experiments ............................... 8
2 METHODOLOGY............................................... .. 10
2.1 Test Facilities ........................................... 10
2.2 Laboratory Experiments .................................... 14
3 RESULTS AND DISCUSSION ..................................... 19
3.1 Expected Results ...................... .................... 19
3.2 Data Analysis .................. .......................... 22
3.3 Experimental Results ....................................... 29
3.4 Perturbation Half-life ....................................... 92
3.5 Peak Transport Evolution ................................... 97
3.6 Nature of Profile Response to Volumetric Perturbations ............ 98
4 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER
STUD Y ..................................................... 108
4.1 Summary .................................... .......... 108
4.2 Conclusions ............................................ 109
4.3 Recommendations for Further Study ........................... 110
BIBLIOGRAPHY .................................................. 112
BIOGRAPHICAL SKETCH ......................................... 116
LIST OF FIGURES
1.1 Definition sketch of the beach profile, from Larson and Kraus (1989) ....... 3
2.1 Schematic of the Air-Sea Tank facility ............................... 11
2.2 Cumulative sand size distribution ................................... 12
2.3 Fall velocity of spherical grains as a function of size, Rouse (1937) ......... 13
2.4 Spectrum of an irregular wave train at the toe of the beach ................ 17
2.5 An irregular wave train at the toe of the beach ......................... 18
3.1 Expected response of an equilibrium profile to deposition of a volume of sand 21
3.2 Expected response of an equilibrium profile to removal of a volume of sand 21
3.3 Comparison of adjusted and unadjusted average sediment transport rates (Case
E, 120 to 125min) ............................................. 27
3.4 Summary of profile changes in Case A ............................... 31
3.5 Summary of average sediment transport rates in Case A .................. 31
3.6 Summary of profile changes in Case B ............................... 35
3.7 Summary of average sediment transport rates in Case B .................. 35
3.8 Summary of profile changes in Case C ............................. 37
3.9 Summary of average sediment transport rates in Case C .................. 37
3.10 Summary of profile changes in Case I .............................. 40
3.11 Summary of average sediment transport rates in Case I .................. 40
3.12 Summary of profiles at an elapsed time of 120 min for experiments with
regular waves (H = 0.14 m, T = 1.65 sec) ............................ 42
3.13 Summary of profile changes in Case D ................................... 44
3.14 Summary of average sediment transport rates in Case D .................. 44
3.15 Comparison of average sediment transport rates for Case D and Case I (unper-
turbed case) for the period 120 to 180 min ............................ 46
3.16 Comparison of profile changes for Case D and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 180 min ................. 47
3.17 Profile evolution with time for the period from 120 to 180 min for Case D ... 48
3.18 Case D: evolution of bar volume with elapsed time ..................... 49
3.19 Summary ofprofile changes in Case E .............................. 51
3.20 Summary of average sediment transport rates in Case E .................. 51
3.21 Mean profile evolution after the profile approached an equilibrium during
Experiment MT01. Elapsed times = 0, 242,297, 352, 407 and 476 min. Note
the substantial erosion of the area seaward of the bar and the deposition of the
area immediately landward of the bar trough. Note also the landward move-
ment of the bar (Oh, 1994) ................................. ...... 53
3.22 Profile evolution of Case E at elapsed times = 140 and 170 min ........... 53
3.23 Comparison of average sediment transport rates for Case E and Case I (unper-
turbed case) for the period 120 to 180 min ............................ 55
3.24 Comparison of profile changes for Case E and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 180 min ................. 56
3.25 Summary of profile changes in Case E .............................. 58
3.26 Summary of average sediment transport rates in Case E .................. 58
3.27 Comparison of average sediment transport rates for Case E and Case I (unper-
turbed case) for the period 120 to 180 min ........................... 59
3.28 Comparison of average sediment transport rates for Case E and Case I (unper-
turbed case) for the period 180 to 240 min ............................ 59
3.29 Comparison of profile changes for Case E and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 240 min ................. 61
3.30 Summary of profile changes in Case G .............................. 63
3.31 Summary of average sediment transport rates in Case G .................. 63
3.32 Comparison of average sediment transport rates for Case G and Case I (unper-
turbed case) for the period 120 to 180 min ............................ 65
3.33 Comparison of average sediment transport rates for Case G and Case I (unper-
turbed case) for the period 180 to 240 min ............................ 65
3.34 Comparison of profile changes for Case G and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 240 min ................. 66
3.35 Summary of profile changes in Case H .............................. 69
3.36 Summary of average sediment transport rates in Case H .................. 69
3.37 Comparison of average sediment transport rates for Case H and Case I (unper-
turbed case) for the period 120 to 180 min ............................ 71
3.38 Comparison of average sediment transport rates for Case H and Case I (unper-
turbed case) for the period 180 to 240 min ............................ 71
3.39 Comparison of average sediment transport rates for Case H and Case I (unper-
turbed case) for the period 240 to 300 min ............................ 72
3.40 Comparison of profile changes for Case H and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 300 min ................. 73
3.41 Summary of profile changes in Case J .............................. 76
3.42 Summary of average sediment transport rates in Case J .................. 76
3.43 Summary of profiles at an elapsed time of 120 min for experiments with
irregular waves (Pierson-Moskowitz spectrum, H, = 0.16 m, Tp = 1.65 sec) 77
3.44 Summary of profile changes in Case K .............................. 79
3.45 Summary of average sediment transport rates in Case K .................. 79
3.46 Comparison of average sediment transport rates for Case K and Case J (unper-
turbed case) for the period 120 to 180 min ............................ 82
3.47 Comparison of average sediment transport rates for Case K and Case J (unper-
turbed case) for the period 180 to 240 min ............................ 82
3.48 Comparison of average sediment transport rates for Case K and Case J (unper-
turbed case) for the period 240 to 300 min ............................ 83
3.49 Comparison of profile changes for Case K and Case J (unperturbed case) for
the interval from 120 min (after perturbation) to 300 min ................. 84
3.50 Summary of profile changes in Case L ............................. 87
3.51 Summary of average sediment transport rates in Case L .................. 87
3.52 Comparison of average sediment transport rates for Case L and Case J (unper-
turbed case) for the period 120 to 180 min ............................ 89
3.53 Comparison of average sediment transport rates for Case L and Case J (unper-
turbed case) for the period 180 to 240 min ........................... 89
3.54 Comparison of average sediment transport rates for Case L and Case J (unper-
turbed case) for the period 240 to 300 min ........................... 90
3.55 Comparison of profile changes for Case L and Case J (unperturbed case) for
the interval from 120 min (after perturbation) to 300 min ................. 91
3.56 Evolution of bar height and bar volume versus time for Case L ............ 93
3.57 Solution of Equation (5), from Dean and Zheng (1994) .................. 96
3.58 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases A and B ...................................... 99
3.59 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases C and D ..................................... 100
3.60 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases E and F ...................................... 101
3.61 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases G and H ...................................... 102
viii
3.62 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases I and J ........................................ 103
3.63 Evolution of peak offshore sediment transport rate and best-fit empirical
expression for Cases K and L ...................................... 104
LIST OF TABLES
1.1 Profile classification, from Oh (1994) ............................. 5
2.1 Summary of regular wave test conditions and profile modifications ..... 16
2.2 Summary of irregular wave test conditions and profile modifications .... 17
3.1 Average required change in elevation between profiles, in mm, in order to
achieve sediment volume conservation (change due to addition/removal
of sand at t = 120 min not included) ............................. 25
3.2 Average net change in elevation, in mm, over given intervals required to
achieve sediment volume conservation (change due to addition/removal
of sand at t = 120 min not included) ............................. 26
3.3 'Half-life' of increase in sediment transport due to perturbation, magnitude
of increase due to perturbation and description of perturbation ......... 94
3.4 Summary of least-squares fit parameters q and a for both before and after
perturbation of the experiment................................... 105
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
BEACH PROFILE RESPONSE TO ABRUPT
VOLUMETRIC PERTURBATIONS
By
MATTHEW S. GOODRICH
May 1996
Chairman: Dr. Robert Dean
Major Department: Coastal and Oceanographic Engineering
This study was conducted to develop an improved understanding of beach profile
morphology, more specifically, beach profile response to volumetric perturbations. Twelve
moveable bed studies were performed in a narrow wave tank that involved running waves
on an initially planar profile for 120 minutes, perturbing the profile by adding or removing
a volume of sand, and continuing the tests. The experiments included both regular and
irregular waves, and included both addition and removal of volumes of sediment.
The time scale of the response of the profile to the perturbations was analysed using
both a 'half-life' parameter as well as a best-fit expression for the time evolution of the peak
offshore transport, and it was found that with increasing perturbation volume, a decreased
profile response time scale resulted. Also, the data show that the response of a beach profile
to a volumetric perturbation is non-diffusionary in nature, although the response is complex,
the entire profile appears to respond in unison to the perturbation. Other conclusions are that
perturbations altering wave breaking cause the beach profile to evolve towards a new
equilibrium shape (the re-equilibrated profile is not simply the previous equilibrium profile
translated some uniform distance landward or seaward); a three-dimensional horizontal
circulation system may form in a narrow wave tank and produce a very significant impact
on cross-shore sediment transport rates; and a perturbation in the shape of a peaked bar
introduced to an irregular wave profile may help position the break point and result in a bar
form being maintained. The data resulting from the method employed in this study appear
useful for evaluating and improving cross-shore transport algorithms.
CHAPTER 1
INTRODUCTION
The prediction of beach profile evolution has been of paramount interest in the
coastal engineering field. The regulation and design of coastal construction requires a
quantitative understanding of profile evolution. For instance, coastal structure design
requires estimates of shoreline recession, and beach nourishment projects require estimates
of project lifespan, which are dictated, in part, by profile response of the projects.
However, the calculation of shoreline evolution is a difficult problem due to the
complex nature of the sediment transport processes that govern profile morphology. At
present, knowledge of the nonlinear unsteady hydrodynamics of the surf zone and sediment
fluid interaction is limited, and even if the hydrodynamics were known precisely, the
sediment transport mechanics are complex and poorly understood. Much remains to be
understood before an accurate physics-based model of sediment transport on the microscale
can be developed. When viewed on a macroscale, though, beach profile morphology appears
smooth, and thus, presents the most likely option for developing a working model of beach
profile evolution. This report endeavors to advance the understanding of beach profile
evolution at the macroscale through the use of laboratory model experiments.
2
The experiments conducted and described here are designed to study the response of
beach profiles to volumetric perturbations (the addition or removal of a volume of sediment
on a beach profile subjected to wave action). To simplify the problem, the experiments are
focused on sediment transport in the cross-shore direction, and attempt to achieve a two-
dimensional system by conducting the tests in a long, narrow wave flume. Through these
experiments it is desired that some fundamental questions concerning beach profile
morphology may be answered: On what time scale does the profile respond to the
perturbation in the cross-shore direction? Does the entire profile respond to the perturbation
simultaneously, or does the region affected by the perturbation increase with time (as it does
in the longshore direction)? Does the profile respond by reforming a similar shape to the pre-
perturbation profile, only translated seaward or landward, as simple equilibrium beach profile
theory predicts?
The remainder of this chapter presents the terminology associated with beach profiles
and a review of previous studies on beach profiles. The literature on the subject of beach
profile morphology is vast, however, this section will provide only a brief review of the
major contributions. For a more extensive review of published works on beach profile
change, see Larson and Kraus (1989).
1.1 Descriptive Terms
The beach profile is a cross-section of the beach taken perpendicular to the shoreline
(Figure 1.1). The profile is generally divided into four sections: the offshore, the nearshore,
the beach and the coast. The profile is shaped by waves that propagate from the offshore and
break in the nearshore zone. The waves are gradually shoaled by the sloping bottom of the
Figure 1.1 Definition sketch of the beach profile, from Larson and Kraus (1989)
profile and break when the wave height is approximately 0.8 times the water depth. The
submerged profile landward of wave breaking is denoted as the surf zone, and seaward is the
offshore. A bar feature is often formed in the region of wave breaking. The broken waves
continue to propagate landward and the remaining wave energy is dissipated in the swash
zone, or foreshore, as waves rush up on this steep portion of the profile. On the backshore,
accretionary features known as berms may exist, which are created by sediment deposited
by wave runup. The landward boundary of the beach is often defined by a line of dunes,
which are large ridges of sand transported by wind from the beach.
COASTAL AREA
NEARSHORE ZONE
COAST BEACH OR SHORE I
BACKSHORE INSHORE OFFSHORE
DUNE --FORESHORE
BERM STEP
L BREAKERS
LWL
BAR
TROUGH
HWL: HIGH WATER LEVEL
LWL: LOW WATER LEVEL
4
1.2 Profile Classification
Much of beach profile research has been focused on bar properties, the classification
of beach profiles based on bar and berm features, and the development of a criterion that can
delineate between bar and berm profiles.
Early field studies (Evans 1940, King and Williams 1949, and Shepard 1950) as well
as laboratory studies (Waters 1939, Keulegan 1948, Rector 1954, and Saville 1957) show
that breaking waves are the main cause of bar genesis. Based on these studies, as well as
later investigations (Hands 1976, Kriebel et al. 1986, Larson and Kraus 1989, etc.), it is
generally accepted that storm wave conditions result in offshore directed sediment transport,
profile erosion and the genesis of an offshore bar, while normal wave conditions result in
onshore sediment transport, and the development of a berm profile without an offshore bar.
Many criteria have been proposed to delineate bar and berm profile response. The
first criteria were based only on wave steepness (Johnson 1949, Saville 1957). Later criteria
included sediment size, fall velocity and beach slope. Table 1.1 summarizes some of these
criteria.
Since the formation of bar and berm features is closely related to the cross-shore
sediment transport direction, some criteria used to predict bar formation have been also used
as indicators of sediment transport direction (Rector 1954, Dean 1973).
1.3 Fall Velocity
Dean (1973) hypothesized that sediment was suspended during the passage of a wave
crest and if the fall time were less or greater than one half wave period, the net transport
would be landward or seaward, respectively. Considering the height of suspension to be
5
Table 1.1 Profile Classification Criteria, from Oh (1994)
Researcher Bar Formation Criteria Scales
Johnson (1949) H/L,, > 0.03 small
Rector (1954) HJ/L, > 29.4(D5s/L,)o8 small
Saville (1957) HjlL, > 0.025 small
Hj/L, > 0.0064 large
Dean (1973) Ho lT > 0.85 small
Sunamura and Horikawa (1974) HLo > C(tan p)-.27(D5s/L)0.67 small
Kriebel et al. (1986) Ho/Lo > A7t/wgT small, large
Larson and Kraus (1989) HO/L < 0.0007(H/GoT)3 large
Dalrymple (1992) gH2/(o3T > 9000 10400 large
where, in this table
Ho = Deep water wave height
Lo = Deep water wave length
T = Wave period
g = Gravitational acceleration
tan P = Initial beach slope
D5o = Median sediment diameter
o = Sediment fall velocity
A,C = Constants
proportional to the breaking wave height, the fall velocity parameter was defined as b
oT
whereHb is the breaking wave height, wis the fall velocity and Tis the wave period. Wave
tank tests conducted by Kriebel, Dally and Dean (1986) and Hughes and Fowler (1990)
support that the fall velocity parameter is a valid modeling parameter as a dynamic similarity
constraint. The fall velocity is scaled by the length scale as or = (Lr)12, which is consistent
with Froude modeling laws.
6
1.4 Equilibrium Beach Profile
One of the most basic assumptions in coastal engineering is that of the equilibrium
beach profile: given time, a beach under constant forcing will evolve to an equilibrium shape
and will cease to continue changing. Bruun (1954) developed a predictive equation for the
equilibrium profile with the form
h(y) = A(D)ym
where h is the depth, y is the distance offshore, and A is the scale parameter, which is a
function of sediment diameter D. The scale parameter was evaluated by Dean (1977) and
24 D
Moore (1982) and is given as A(D) = [ D ]m, where D is the equilibrium energy
5 pg 3/2
dissipation rate per unit volume, p is the fluid density, g is the acceleration due to gravity and
Kis the breaking index. Dean (1991) presents the scale parameter as a function of sediment
fall velocity.
Dean (1977) explained the power law profile given by Bruun (1954) on physical
grounds by assuming the profile was in equilibrium if the energy dissipation per unit water
volume due to wave breaking was uniform across the profile. Also, Dean (1977) analyzed
502 beach profiles on the United States Atlantic and Gulf of Mexico coastlines, and
concluded that the power law given by Bruun (1954) was the optimal function to describe
equilibrium profile shape.
1.5 Empirical Models
Many numerical models have been developed to predict profile evolution. A model
based on wave breaking was developed by Dally (1980) and Dally and Dean (1984). Models
7
based on the equilibrium concept have been developed by Kriebel (1982, 1986, 1989, 1990),
Kriebel and Dean (1985) [EDUNE], Larson and Kraus (1989) [SBEACH], Chiu and Dean
(1984, 1986) [CCCL], and Dean and Zheng (1994) [CROSS]. Zheng and Dean (1995)
provides brief descriptions of five equilibrium based models.
This report reviews only the concept used in Kriebel (1982), Kriebel and Dean (1985)
and Kriebel (1986, 1989, 1990), and first proposed by Dean (1977), which is an empirical
model in which the cross-shore transport rate is proportional to the degree of disequilibrium,
given by
Q = k(D(y)-D,)
where Q is the sediment transport rate [volume/time], and k is an empirical constant. D is
energy dissipation per unit water volume, and the value of D is given by
D = -5 p2 (gh) 2 dh
16 dy
where h is the water depth and y is the distance offshore. Since D is proportional to the
product of the square root of the local water depth and the bottom slope, a profile with
steeper or milder slope than the equilibrium will result in sediment transport offshore or
onshore, respectively.
The continuity equation is used to close the system, which is given by
ay aQ
at ah
where t is time.
8
In order to satisfy model scaling requirements, Dean and Zheng (1994) propose the
following transport model
Q = k(D-D.)ID-D.j"-
where n = 3. This value was supported by comparison with large wave tank data.
1.6 Large Wave Tank Experiments
One of the most useful tools in studying beach profile morphology is large wave tank
(LWT) experiment data. Many small scale laboratory experiments have been performed and
have been useful in identifying potential parameters related to beach profile change.
However, scaling distortion is a problem and generally applicable scaling laws for
interpreting small scale experiments have yet to be determined. The usefulness of field data
is diminished by our inability to extract cause and effect relationships between waves and
profile change due to: lack of high resolution in time and space of morphology and wave
data, spatial and temporal variability of waves, and the three-dimensional character of
nearshore bathymetry. Thus, the best alternative for the study of beach profile change is the
use of large scale wave tank experiments. Such experiments allow the control of wave and
sediment parameters, and can approximate a two-dimensional system. Also, scaling
problems are avoided, repeatability can be evaluated, and a high resolution of data can be
acquired.
LWT experiments performed with monochromatic waves include experiments
performed by the US Army Corps of Engineers (CE) in the years 1956-1957 and 1962
(Saville 1957, Caldwell 1959, Kraus and Larson 1988a) at Dalecarlia Reservation,
9
Washington, DC, experiments performed at the Central Research Institute of Electric Power
Industry (CRIEPI) in Chiba, Japan (Kajima et al. 1983a, b), and experiments performed in
a large German wave flume in Hannover (Dette and Uliczka, 1987a). Irregular wave LWT
experiments have also been performed (Vellinga 1986, Dette and Uliczka 1987b, Uliczka
and Dette 1987).
CHAPTER 2
METHODOLOGY
This chapter provides a description of the facilities and procedures used in the
experiments completed for this study.
2.1 Test Facilities
All experiments were conducted in the "Air-Sea Tank" at the University of Florida's
Coastal and Oceanographic Engineering Laboratory facility in Gainesville, Florida. The tank
measures approximately 37 m long, 2 m wide and 1.9 m deep (Figure 2.1). The test section
has been divided into two parallel test sections 0.9 m wide by a concrete block wall placed
along the centerline of the tank. The experiments used only the eastern half of the tank, of
which the outer wall is constructed of glass panels, thus enabling direct observation of the
experiments.
The tank is equipped with a hydraulically driven wave paddle measuring 1.8 m wide
by 1.2 m high. The wavemaker bulkhead is mounted on a carriage and is driven by two
hydraulic rams. The apparatus is configured such that independent control of the rams may
provide either piston or flap type motion, or any linear combination. For the experiments in
this study only piston type wavemaker motion was used to generate waves.
The wavemaker was controlled by a Seasim programmable spectrum signal generator
and a Pegasus Servo Controller/Amplifier capable of producing both regular and irregular
-3..m>-<--------
I Faw
Wave '
Scard
2-7m
lass Wall ?Sand Seacn Basin I ow
" 'zi av .... ^ .,,r2 *
P.'m Partiton / Wave
PLAN VIEW Wall AIsoming
L Seac= ,,
O.-=n Thick Wall
Steel Framework
S1Icmn Thick Plate G;ass
CROSS-SEC7sCN
- St Water Lavel
in Tank
Figure 2.1 Schematic of the Air-Sea Tank facility.
12
waves, both of which were used in the present study. Directly in front of the wavemaker is
an array of wave screens designed to prevent cross-tank variations in the generated waves.
The sand beach used for the experiments was located at the opposite end of the tank
from the wavemaker in the east bay. The material used was a fine brown sand with a median
grain diameter of 0.1 mm (Figure 2.2), and the size distribution was nearly uniform across
the profile. The mean fall velocity of this sediment is approximately 0.64 cm/sec, which was
estimated from the values of fall velocity of spherical grains given by Rouse (1937) (Figure
2.3).
100
80 ------ --------------------- ----------------
60 -- - - - - - - - - - - - - - - - - - - - - --
80
40- - - - - - - - - - - -
20
0 --------------i- i i-t
0.01 0.1 1
Grain Size (mm)
Figure 2.2: Cumulative Sand Size Distribution
-- ---*----___ _- 'i'
3 t
t i l I
d 1 i i I i i i
rI ww
i -.i I. .1
I I ,_ i \1 1 1 1 l '~,I iii .? 1 i .:. -
a 0 o j n aC 'I a n 1 '.a a i. i to 6 a i a a i' w
Figure 2.3: Fall Velocity of Spherical Grains as a Function of Size, Rouse (1937)
\ iI 1, T 5 i i ';ti i " l i, ;
I I L i i ; | N I i I I I I'z+
1 I4 -i"+ ,--! -i--i- i ,- -. l i" II 1 itl
3.01 via0 ,, ao o '1 A i 8 1 i. I 1O a +.0 i ii o a i -
Figure 2.3: Fall Velocity of Spherical Grains as a Function of Size, Rouse (1937)
14
The experimental profiles were measured using a mobile cart system equipped with
a profiling rod. The cart rides along level rails mounted on top of the walls of the east bay
of the Air-Sea tank. The top of the eastern-most wall is graduated at 2 cm intervals to
provide a horizontal reference scale. The profiling rod mounted on the cart is graduated in
millimeters and was used to measure the elevation of the beach profile during surveys.
The wave conditions during each experiment were measured using a capacitance type
wave gage mounted to the mobile cart. The gage was connected to an IBM compatible PC
and surface elevation data was recorded at a sampling rate of 20 Hz using the data acquisition
module of a Global Lab software package.
2.2 Laboratory Experiments
The objective of the laboratory experiments was to measure, analyze and interpret the
response of beach profiles to instantaneous additions or removals of sediment volume.
Ideally, the beach profile would be in equilibrium for the given wave condition before the
profile was perturbed. Thus, the evolution of the profile following the perturbation could be
attributed exclusively to the deposition/removal of the volume of sediment. However,
achieving an equilibrium shape by running waves for a long time on the beach profile is not
practical for this study because of the large amount of time that would be required for each
experiment. In large wave tank (LWT) experiments performed by the Corps of Engineers
(CE) at Dalecarlia Reservation, Washington, DC, and experiments performed at the Central
Research Institute of Electric Power Industry (CRIEPI) in Chiba, Japan, experiments using
waves of similar steepness to those in this study, significant volume changes were still
occurring after 100 hours of wave action (Larson and Kraus 1989). Therefore, the model
15
tests were not designed to be in equilibrium before the profiles were perturbed. Instead, the
experimental profiles were subjected to waves for a sufficient amount of time for the
sediment transport rate to subside enough such that following the perturbation of the beach
profile, the increase in sediment transport would be very noticeable.
2.3 Experimental Procedure
First, the initial beach profile of uniform slope 1:20 was constructed in the following
manner: (1) the initial profile was drawn on the outside of the glass wall of the tank with a
marker; (2) the sediment in the wave tank was redistributed to conform to an elevation
slightly higher than the initial slope dictated by the drawn line; (3) the material was
compacted using a 30 pound tamper; (4) the profile was then scraped with a board equal in
length to the width of the tank to conform to the line on the glass wall while special attention
was given to keeping the profile uniform across the tank width, which was aided by the use
of a level. The tank was then filled with water to the required depth and the initial profile
was surveyed.
The beach profile was subjected to waves for 120 minutes, while being stopped at
intervals to allow the completion of surveys after elapsed times of 10, 20, 40, 80, 110 and
120 minutes. A volume of sand was then deposited or removed at various location on the
beach profile, and the newly perturbed profile was surveyed. The waves were then continued
for another 60 minutes while being stopped at total elapsed times of 125, 130, 140, 170 and
180 minutes to allow for profile surveys. The later experiments ran for longer durations: 240
minutes and 300 minutes with additional surveys conducted at 30 minute intervals. Shorter
durations of wave action were run between surveys at the beginning of the experiment and
16
immediately before and after the perturbation to allow higher resolution of sediment transport
information at these points of increased profile disequilibrium.
2.4 Test Conditions
A total of twelve experiments was conducted with various wave conditions and
profile modifications. The first nine experiments used regular waves, and the remaining
three used random waves (Tables 2.1 and 2.2). Tests A, B and C were subjected to larger
wave heights and the resulting profiles had broad, diffuse bar formations. The subsequent
regular wave cases used smaller waves to produce a more peaked bar formation. The
irregular wave cases were modeled by a Pierson-Moskowitz spectrum with a peak wave
period of 1.65 sec and significant wave height of 0.16 m (Figures 2.4 and 2.5). A brief
description of the profile modification for each experiment is also provided in Tables 2.1 and
2.2.
Table 2.1: Summary of Regular Wave Test Conditions and Profile Modifications
Test Wave Wave Water Grain Test Profile
height period depth size dura- modification
(m) (sec) (m) (mm) tion
(min)
A 16.5 0.465 180 bar removed
B 16.0 0.45 180 bar removed
C 16.0 0.45 180 seaward section of bar
removed
D 14.0 1.65 0.45 0.10 180 landward section of bar
removed
E 14.0 0.45 180 volume deposited in trough
F 14.0 0.45 240 volume deposited on beach
face
G 14.0 0.45 240 volume deposited just
landward of trough
H 14.0 0.45 300 volume deposited just
seaward of beach face
I 14.0 _0.45 _300 unperturbed case
17
Table 2.2: Summary of Irregular Wave Test Conditions and Profile Modifications
Test Significant Peak Water Sand Test Profile
wave height period depth size duration modification
(m) (sec) (m) (mm) (min)
J unperturbed case
K 0.16 1.65 0.45 0.10 300 deposition at mid-surf
zone
L deposition at break
point
an
C )
Co
O0
C-
O'3
3.5
3
2.5
2
1.5
1
0.5
2 4 6 8
frequency [Hz]
w
Figure 2.4: Spectrum of an Irregular Wave Train at the Toe of the Beach
10
-10-
-15
0 5 10 15 20 25 30
Time (sec)
Figure 2.5: An Irregular Wave Train at the Toe of the Beach
CHAPTER 3
RESULTS AND DISCUSSION
This chapter presents the results of the wave tank experiments and attempts to
interpret these results to provide meaningful conclusions relating to cross-shore sediment
transport processes. Included is a discussion of the expected results, according to
equilibrium beach profile theory, as well as a description of the procedures used in the
analysis of the experimental data.
3.1 Expected Results
The concept of the equilibrium beach profile is widely accepted and commonly used
in coastal engineering. A comparison of the experimental results with the expected results
according to equilibrium beach profile theory would provide insight aiding the analysis and
interpretation of the data. It may also provide a basis for evaluating the existing cross-shore
sediment transport relationships and proposing new relationships. This section discusses the
general expected response of an equilibrium profile to a deposition or removal of a volume
of sand.
Dean (1991) asserts that when a volume of fill is added to a beach profile, and the
sediment characteristics of both are identical, it is assumed that it will equilibrate eventually
to the pre-fill equilibrium profile shape translated a uniform horizontal distance seaward
across the entire active profile. If this assumption is true, it raises the question: in what
manner is the deposited fill volume redistributed?
20
Pelnard-Considere (1956) described the evolution of a rectangular planform fill using
an equation similar to a heat diffusion equation, where the planform is gradually smoothed-
out over time as the sand diffuses along an increasing length of shoreline. Perhaps this
applies to a perturbation in a two-dimensional beach profile system in a similar manner: the
perturbation is gradually smoothed-out, with the affected region of the profile gradually
increasing. The expected responses of the profiles to the perturbations are based on this
assumption.
The expected response of an equilibrium profile to a deposit of a volume of sand is
shown if Figure 3.1. Included are both the short-term and long-term expectations of the
beach profile shape, as well as the approximate sediment transport rate curves for the short
and long-term profile changes. In the short-term forecast the perturbation begins to be
smoothed-out by the wave action, and sand is transported both landward and seaward of the
perturbation. On a longer term basis, the same transport form will occur, but will be smaller
in magnitude and distributed over a larger portion of the profile. The predicted equilibrium
is the result of redistribution of the deposited sand over the entire active profile resulting in
the translation of every point of the initial active equilibrium beach profile a uniform distance
seaward.
The impact of the removal of a volume of sediment is presented in Figure 3.2. The
short- term profile change is the smoothing-out of the depression by the transport of sediment
into the removal area from both onshore and offshore directions. The equilibrium response
is the uniform translation of the equilibrium profile landward. The rates at which different
elevations on the active profile approach equilibrium will depend on the elevation.
Sre-equilibrated profile
'. initial perturbation
S short-term
.- 7-'long-term
equilibrium profile '- .
rQ /short-term
\ long-term
X
Figure 3.1 Expected response of an equilibrium profile to deposition of a volume of sand
re-equilibrated profile _
equilibrium profile
initial perturbation-> g-
\ long-term
/ \ short-term
long-term
Figure 3.2 Expected response of an equilibrium profile to removal of a volume of sand
22
The anticipated response of each of the experimental cases is presented and compared
to the results for each case in the experimental results section.
3.2 Data Analysis
The measured experimental data consist of profile data and water surface elevation
data. To assist interpretation of these results, various quantities are calculated using these
data sets. The most important of these quantities is the average sediment transport rate
between surveys, which is the variable indicator used to assess the impact of the perturbation
on the beach profile system. The procedures used in calculating the transport rates and some
other quantities are given below.
Sediment Transport Rate Calculation
The equation describing the relation between the profiles and sediment transport rate
is given by the two-dimensional sediment conservation equation, which is
ah aq
at ax )
where h is the profile elevation at a given point x and time t, x is the offshore distance, and
q is the time-averaged sediment transport rate per unit length of shoreline.
Integrating Equation (3.1) with respect to x from the landward end of the profile, xo,
to any point x, and setting q(x,) = 0 as the landward closure yields
q(x) = (3.2)
0x, at
with
8h [h(x,t2) h(x,ti)]
-- (3.3)
at t2-t
Since h, t and x are measured in each experiment, the time-averaged sediment transport rate
between the times of any two profiles may be calculated using Equations 3.2 and 3.3.
Application of these equations to the experimental data presents a problem: the
transport rates are not necessarily found to be zero at the offshore closure depth as they
should be theoretically. This is the result of three effects. First, sediment may not
necessarily be conserved, because there may have been some transport of material beyond
the offshore measurement depth. However, from visual observations it was concluded that
this effect was very small. Second, in attempts to model a two-dimensional system in a long,
narrow wave tank, the assumption of a two-dimensional system is often not strictly correct.
Three-dimensional morphology was present at times to some degree in every experiment.
Thirdly, although sand mass is conserved, sand volume may not be. Transported sand may
be deposited in a state of increased or decreased porosity relative to its initial condition.
To facilitate interpretation and comparison of the sediment transport curves, the
curves were adjusted to obtain closure at the offshore end of the profiles. This was
accomplished by subtracting uniformly across the entire profile the average change in
elevation between profiles from the later profile used in the transport rate calculation. Thus,
the average sediment transport rates were adjusted by a uniformly increasing/decreasing rate
across the entire profile. Table 3.1 tabulates the average change in elevation between
24
adjacent profile surveys that were used for the closure adjustments. Table 3.2 summarizes
the net change in elevation required to achieve closure over the intervals 0 to 120 min, 120
to 180 min, 120 to 240 min and 120 to 300 min. For the interval 0 to 120 min, the net change
in elevation required was negative in all experiments, which indicates that the system gained
sediment volume during the first 120 min of each experiment. For the interval 120 to 180
min, seven of the ten perturbed experiments and both of the control experiments required
negative net adjustments.
The adjustment was made uniformly across the profile because the sources of non-
closure could not be isolated. The location of the three-dimensional areas could not be
isolated by visual observations (due to the high turbidity associated with the fine sediment
used in the experiments), and, unfortunately, no additional profiles were taken to document
the three-dimensionalities. However, when the wave tank was drained (when the
perturbation was added or at the end of an experiment), it was noted that the primary location
of the 3-D effects was the region seaward of the beach face and landward of the bar/trough
formation. Oftentimes trough-like formations occurred along the walls of this region, with
maximum depths up to approximately 0.1 m below the centerline elevation.
These 3-D effects are similar to the findings documented by Oh (1994), who
conducted regular wave experiments in a narrow wave tank with 2-D initial conditions.
After four hours of testing, Oh found 3-D features associated with fairly strong horizontal
cellular circulation and rapid net landward sediment transport and shoreline advancement.
Later in the testing, the profile returned to nearly 2-D conditions with the exception of a deep
and narrow return channel near one of the tank walls. Oh concluded that there is a relatively
Table 3.1 Average required change in elevation between profiles, in mm, in order to achieve
sediment volume conservation (change due to addition/removal of sand at t = 120 min not
included)
survey :
30 40 60 80 110 120 125 130 140
Time
10
-0.71
-1.64
-0.6
0.306
-0.56
-2.28
-3.5
-2.42
-1.05
-1.38
-1.51
-0.4
-0.52
0.648
-1.07
0.41
0.44
0.85
-1.41
-2.06
-0.33
0.12
-0.59
-1.41
-0.51
-0.78
0.16
-0.1 -0.17
-0.48 0.16
-0.14
-1.4
-0.58
-1.01
-0.25
-0.62
0.55
-0.52
0.67
-0.34
0.198
-0.25
1.32
0.856
0.02
-1.31
-0.1
0.817
0.147
0.244
0.457
0.216
-0.3
-0.44
-0.5
-0.16
0.459
-0.51
0.156
-0.14
-0.2
1.17
1.106
-1.33
-0.63
0.03
-0.61
-0.1
-0.18
-0.49
150 160 170 180 200 210
230 240 270 300
0.359 -0.11
-0.92 0.358
-1.71
-0.72
-0.71
-0.37
0.225
-2.15 -2.77
-0.1 -0.47
0.79
0 0.02
-0.43 0.129
Case:
-0.88
-0.1
-1.05
-0.1
-0.3
0.5
-0.37
-0.87
0
-0.48
of
20
-1.12
-1.79
-1.36
-0.66
-0.53
-0.72
-0.51
-0.34
0.695
0.04
-1.21
-0.28
-2.55
-1.22
-1.84
0.5
-1.49
1.465
0.395
-0.72
-0.27
0.164
-0.77
0.577
0.315
-0.85
0.27
-0.43
0.22
-1.4
-0.91
-0.61
-0.1
0.104
-0.44
0.22
-1.67
0.219
-0.36
26
Table 3.2 Average net change in elevation, in mm, over given intervals required to
achieve sediment volume conservation (change due to addition/removal of sand at t = 120
min not included)
Case 0 120 min 120 180 min 120 240 min 120 300 min
A -2.85 -3.10
B -6.34 1.55
C -6.17 -0.003
D -1.15 -2.16
E -2.54 -3.32
F -3.30 1.42 1.23
G -4.80 0.312 -3.03
H -3.81 -1.92 -5.30 -10.22
I -2.37 -0.91 -1.63 -2.20
J -1.84 -0.61 -1.32 -0.53
K -0.887 -0.446 -0.597 -0.577
L -1.41 0.035 -0.10 -0.401
slow feedback between the hydrodynamics and the morphology that leads to the initiation
and growth of 3-D features.
An extreme example of the resulting change in the transport curves due to the closure
adjustment is shown in Figure 3.3. This particular case required a large sediment transport
rate adjustment to achieve offshore closure, and it was selected to illustrate the difficulties
associated with interpreting profile changes presented in two-dimensions when, in fact, it is
evident that the beach system had very significant three-dimensional changes.
0.003 -
0.002
0.001
E
S o-
-0.001
-0.002
-0 .0 0 3 , . . -
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
adjusted unadjusted
Figure 3.3 Comparison of adjusted and unadjusted average sediment transport rates
28
It should be noted that although the closure adjustments sometimes had a large affect
on the sediment transport curves, the closure adjustments were generally on the order of 1
mm and thus are reasonably small.
Calculation of Other Ouantities
Various other quantities were calculated and used, when helpful, to aid in the
evaluation of the impact of the perturbation on the beach profile system. They include:
change in profile elevation, maximum time-averaged sediment transport rate, shoreline
position, bar height, bar volume, 'half-life' of perturbation and best-fit of empirical
expression to peak transport data. A brief description of each and the procedures used to
calculate them are described below.
The change in profile elevation was calculated for the last profile available in each
experiment. The change in elevation was defined as the difference in the final profile
elevation from the profile elevation at an elapsed time of 120 min (after the volume of sand
was added/removed).
The shoreline position was plotted versus time for each experiment. The shoreline
position was taken as the interception of the still water line with the beach profile. This
quantity, however, was found to have poor repeatability between tests, and thus, was judged
to be a poor indicator of profile response.
The bar height was calculated as the difference in elevation between the minimum
elevation in the trough adjacent to the bar and the maximum elevation at the peak of the
bar. The bar volume in the regular waves experiments was taken as the volume of material
between the interception points of the bar feature with the initial profile.
29
In order to evaluate the time scale of the changes in sediment transport rate induced
by the perturbation, the 'half-life' of the changes was calculated for each case. The 'half-life'
was defined as the time required for the maximum sediment transport rate in the experiment
to decay to a magnitude that was equal to half the increase in maximum transport rate due
to the perturbation plus the pre-perturbation rate. In order to find this value it was necessary
to assign the maximum sediment transport rate for each interval to the midpoint of that time
interval, and to interpolate between the measured maximum sediment transport rates to solve
for the half-life value.
The maximum time-averaged positive sediment transport rate was plotted versus
elapsed time for each experiment to provide an approximate gage of the magnitude of the
offshore sediment transport at a given time. The adjustments made to the sediment transport
rates to achieve closure have a significant influence on the maxima, and thus, these results
are only approximate.
An empirical expression was least-squares fitted to the time evolution of the peak
q
sediment transport rate data. The expression selected was qm =- which was found
1 + at
by Larson and Kraus (1989) to have the best general agreement with CE and CRIEPI data.
3.3 Experimental Results
This section describes the changes made to the experimental profile and presents a
brief description of the expected response of the profile to the perturbation. Also, both a
general statement of evaluation following the perturbation is given as well as a more detailed
account of the results.
3.3.1 Case A
3.3.1.1 Volume removed and experiment duration
The experiment in Case A was modified by the removal of the volume of sediment
that composed the broad offshore bar after an elapsed time of 120 min (Figure 3.4). The
experiment was run for 180 min.
3.3.1.2 Expected response
The expected immediate response of the profile was an increase in the energy
dissipation rate per unit volume landward of the perturbation, since the removal of the bar
would allow more wave energy to propagate past the location where the bar previously
existed and be dissipated closer to the shoreline. This would increase the offshore directed
sediment transport rate landward of the perturbation, and it would cause increased shoreline
recession and increased deposition in the region where the bar was removed. The longer-
term expected response was the reformation of the bar and the development of a profile
somewhat similar to the pre-perturbation profile translated slightly landward.
3.3.1.3 General results
The general response of the beach profile to the perturbation was a significant
increase in offshore transport landward of the perturbation and the deposition of sand in the
region where the bar was removed (Figure 3.5). The experimental results agree with the
anticipated results, in that the perturbation resulted in an increase in offshore directed
sediment transport rate. However, it was not expected that the perturbation would induce a
dramatic increase in erosion of the beach face as rapidly as occurred in Case A. Also, most
of the profile experienced a shift landward as expected. However, the bar position did not
shift landward, but instead, the bar reformed at the same location as the pre-perturbation bar.
0.1
0-
-0.1
o= -0.2
Q3
S-0.3
-0.4
-0.5 .
-1 0 1 2 3 4 5 6 7 8 9
Offshore Distance (m)
- t = 0 min -- t= 120 min, before --- t = 120 min, after --- t = 180 min
Figure 3.4 Summary of profile changes in Case A
0.0016
0.0014
0.0012
0.001 -
E
- 0.0008 -
E
C'2
' 0.0006
0.0004
0.0002
0--
-0.0002 -..----
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
S t= 40-120 min -t= 120-130 min t =130-150min t= 150- 180 min
Figure 3.5 Summary of average sediment transport rates in Case A
32
3.3.1.4 Detailed description and discussion of results
The sediment transport rate for the interval immediately following the perturbation
(120 to 130 min) shows an increase in offshore sediment transport both in the region
immediately landward of the perturbation and also, to an even greater extent, in the region
from -0.5 to 2.3 m offshore. This suggests that instantaneous profile alterations are not
necessarily just smoothed out across the profile, with the perturbation affecting adjacent
areas of the profile that increase in size with time. Instead, from this experiment it appears
that the removal of a volume of sand may have an immediate influence on the sediment
transport at all points of the profile landward of the perturbation.
The sediment transport curves for the next intervals though 180 min generally show
a slight increase in offshore transport over the profile from -0.5 to 4.6 m and decrease in
transport from 4.6 to 8.5 m offshore, relative to the pre-perturbation rates. During this time
the bar reformed in a shape similar to that of the pre-perturbation form, but by the end of the
experiment it had not yet regained the size of the pre-perturbation bar. Also, the location of
the bar was the same as that of the pre-perturbation bar.
The experiment in Case A was performed as a preliminary experiment, and this
experiment established that more frequent surveys were necessary in order to quantify the
perturbation induced transport. Thus, in subsequent experiments more frequent profiles were
measured, particularly for the times immediately before and after the perturbation of the
profiles.
3.3.2 Case B
3.3.2.1 Volume removed & experiment duration
Similar to Case A, but with slightly decreased water depth and wave conditions, Case
B also was altered by removal of the bar formation near the toe of the beach (Figure 3.6).
The experiment was run for 180 min.
3.3.2.2 Expected response
The expected response of Case B was the same as that of Case A, except the
magnitudes of the sediment transport rates were expected to be slightly smaller because of
the smaller wave height used in this case.
3.3.2.3 General results
The response to the removal of the bar was a large increase in offshore sediment
transport rate over the profile from 0.9 m offshore to the seaward end of the profile, and
onshore directed transport in the beach face region, which accelerated the growth of the berm
feature. In the 60 min following the removal, the sand being transported seaward was
deposited in the region where the bar previously existed. In comparison to Case A, the
experimental results agree better with the expected results, as there was not such a dramatic
increase in the erosion of the beach face region immediately following the perturbation.
Also, the magnitude of the offshore transport following the perturbation in Case B was found
to be much larger than that of Case A, which was due to the more frequent sampling
intervals.
34
3.3.2.4 Detailed description and discussion of results
The adjusted average sediment transport rates are presented in Figure 3.7. For the
interval from 120 to 125 min, the average change in profile elevation was 1.32 mm, and thus,
the transport rate for this interval required a large negative adjustment. The post-perturbation
curve shows onshore directed transport in the beach face area, which resulted in the growth
of the berm. Dominant is the large increase in offshore directed transport from 1 to 9.5 m
offshore induced by the removal of the offshore bar.
The subsequent intervals through 180 min generally showed offshore transport over
most of the profile with the peak offshore transport much closer to the pre-perturbation peak
rate. It was surprising to find that in the region -1.5 m to 0.8 m offshore the sediment
transport rates were always less than the pre-perturbation rates for this region. This is
counter-intuitive, since it was anticipated that the removal of the bar would increase erosion
in this region, as it clearly had in Case A.
Further comparison with Case A shows similar magnitudes of maximum sediment
transport rates immediately preceding the removal of the bar volumes. However, the
sediment transport rate immediately following the perturbation was much larger in Case B
than in Case A, with the increase in maximum average sediment transport following the
alteration approximately twice that of Case A. Also, the shape of the transport is much more
peaked in Case B. These variations are due, in part, to the increased resolution of profile
data in Case B immediately following the removal of the bar. The larger increase in Case
B may also be due to the perturbation resulting in a large shift away from the equilibrium
profile shape. Note that after the sand was removed in Case A a small bar formation still
remained approximately 5.75 m offshore, where in Case B no bar formation remained at all.
'ii 1
- - - - - - - - - - -
-- -- - -- - - - -- - - - - - - - - -
- --- -- -- -- -- -- -- ------------------ --
-- -- - - - - - - - - - - - - - - - -
0 1 2 3 4 5
Offshore distance (m)
6 7 8 9
=0min - t = 120 min, before
-- t = 120 min, after -- t = 180 min
Figure 3.6 Summary of profile changes in Case B
0.0025
0.0018
S0.0011
0.0004
-0.0003
-0.001 ... i .. .. I
-2 -1 0 1 2 3 4 5 6
Offshore Distance (m)
7 8 9 10
t = 110-120 min t = 120-125 min t = 125-130 min
t = 130-140 min t =140-170 min t = 170-180 min
Figure 3.7 Summary of average sediment transport rates in Case B
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-2 -1
3.3.3 Case C
3.3.3.1 Volume removed & experiment duration
The profile in Case C was altered by the removal of a seaward section of the bar
formation while the peaked portion of the bar remained undisturbed (Figure 3.8). The
experiment was run for 180 min.
3,3.3.2 Expected response
The expected response of the profile was an increase in sediment transport rate
landward of the perturbation and a decrease in transport seaward of the perturbation, as in
Cases A and B, except smaller in magnitude. The bar was expected to regenerate its
previous form, and the position of the bar was expected to be slightly landward of the
location of the pre-perturbation bar.
3.3.3.3 General results
The results of Case C are summarized by the sediment transport rates plotted in
Figure 3.9. The perturbation resulted in a large increase in sediment transport rate over the
seaward half of the profile and a reduction in sediment transport rate over the landward half
of the profile. The largest increase in sediment transport rate occurs just landward of the
perturbation, which agrees with the expected results. However, the reduction in transport
over the landward half of the profile and the increase in transport seaward of the perturbation
are inconsistent with the expected results.
3.3.3.4 Detailed description and discussion of results
The immediate response of the profile (t = 120 to 125 min) is difficult to interpret due
to the magnitude of the closure adjustment. In the region x = -1 to 1 m the transport curve
0.1
0-
-0. -
E
W -0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
-- t = 0 min
- t = 120 min, before t = 120 min, after t = 180 min
Figure 3.8 Summary of profile changes in Case C
0.002
0.0015
0.001
0.0005 -
0
-0.0005 . .. .
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
--t = 110-120 min t = 120-125 min t= 125-130 min
t = 130-140 min t = 140-170 min t = 170-180 min
Figure 3.9 Summary of average sediment transport rates in Case C
I
38
shows onshore transport, which is counter-intuitive for the perturbation imposed. This may
have been caused by the negative transport rate adjustment used to achieve closure. An
inspection of the unadjusted profiles shows a recession of the profile in this area, and the
profile in this region was relatively two-dimensional. This suggests that the sediment
transport rate was actually directed offshore over the region in question. Thus, the transport
rate was probably directed offshore over the entire profile.
In comparison with the pre-perturbation transport rate, this transport curve shows an
increased offshore transport rate in the region of x = 4.5 9.5 m. The subsequent profiles
display a gradual reduction in the transport rate across the profile.
It is likely that the increased sediment transport rates in the bar region were caused
by the steepened seaward slope of the bar, which resulted in more sudden shoaling and
breaking of the waves. Also, one may hypothesize that since the maximum elevation of the
bar was not reduced by the perturbation, increased wave energy would not have been
transmitted beyond the wave breaking zone. Thus, the shoreward half of the profile did not
experience increased erosion, and the offshore transport in this region decayed with time as
it would have, were the profile undisturbed.
Also, it was expected that seaward of the perturbation the sediment transport would
be directed landward. However, this did not occur for the interval 120 to 125 min, but it did
occur for the intervals 125 to 130 and 140 to 170 min.
3.3.4 Case I
This experiment was conducted as the control for the experiments subjected to
regular waves with a wave height of 0.14 m and a wave period of 1.65 sec. The experiment
was run for 300 min without any removal or deposition of sediment.
3.3.4.1 General results
The experiment conducted in Case I produced a barred, erosional profile. The profile
evolution and the calculated sediment transport rates are shown in Figures 3.10 and 3.11,
respectively. A bar developed in the region approximately 3 m offshore, similar to those
developed in the other regular wave cases prior to being perturbed. Also, on a longer time
scale than the mid-profile bar, an offshore bar developed in the region approximately 7 m
offshore. As this offshore bar grew, it caused a reduction in wave energy passing the bar,
thus resulting in a reduction in size of the mid-profile bar.
3.3.4.2 Detailed description and discussion of results
After being subjected to waves for 120 min, the profile developed into a barred
profile with a peaked bar at x = 3.5 m. A comparison of the profiles shows the bar crest
moving in the offshore direction over the first 120 min.
For the next 60 min (t = 120 to 180 min) the profile was relatively stable over the
region landward of the bar, with the exception of the berm still continuing to build up. The
bar shifted landward approximately 0.3 m. The region seaward of the bar experienced
offshore transport, and deposition of material near the seaward end of the profile began to
build a broad bar feature about 7 m offshore. This offshore bar caused some waves to begin
spilling earlier, and thus, allowed less wave energy to reach the inner bar. This was likely the
cause for the landward shift of the bar.
From t = 180 to 240 min, the profile experienced increased offshore transport over
most of the profile, deposition built up the broad offshore bar, and the landward bar shifted
further landward.
0.1
0
-0.1
0* -0.2
-0.3
-0.4
-0.5 ----- I I ----
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
t = 0 min t = 120 min -- t = 180 min -t = 240 min t = 300min
Figure 3.10 Summary of profile changes in Case I
0.002 .
0.0015
-" 0.001 -
E
- 0.0005 -
0
-0.0005 I ,. .. I
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
t = 0 to 120 t = 120 to 180 t = 180 to 240 t =240 to 300
Figure 3.11 Summary of average sediment transport rates in Case I
41
From t = 240 to 300 min the profile experienced even more increased offshore
transport over the profile, and the continued build-up of the offshore bar, but the inner bar
shifted slightly seaward.
3.3.4.3 Assessment of repeatability
In order to use this experiment as a control to which the perturbed experiments are
compared, it must be assumed that had the other experiments not been perturbed, they would
have experienced a similar profile evolution. Therefore, to evaluate the validity of this
assumption, it is necessary to evaluate the repeatability of the experiments. Figure 3.12
illustrates a comparison of the profiles after an elapsed time of 120 min for all the regular
wave experiments subjected to the same wave conditions as Case I. All of the profiles have
the same basic shape, with a few exceptions. Most notably, the bar in Case E is located
farther seaward than the other 5 cases. Also, there is a significant amount of variation in the
volume of material deposited near the toe of the beach.
3.3.5 Case D
Beginning with Case D the wave height was reduced in order to produce a smaller,
more peaked bar formation.
33.35.1 Volume removed & experiment duration
The profile in Case D was altered by the removal of a landward section of the bar
formation which included the peak of the bar (Figure 3.13). The experiment was run for 180
min.
0.1
0
-0.1
E
-- -0.2
-0.3
-0.4
-0.5 -
0 1 2 3 4 5 6 7 8 9 10 11 12
Offshore distance (m)
test D test E test F test G test H test I
Figure 3.12 Summary of profiles at an elapsed time of 120 min for experiments with
regular waves (H = 0.14 m, T = 1.65 sec)
3.3.5.2 Expected response
The expected impact of the perturbation was an increase in offshore sediment
transport rate landward of the perturbation and a decrease in transport rate seaward of the
perturbation. The bar was expected to regenerate its previous form, and the position of the
bar was expected to be slightly landward of the location of the pre-perturbation bar.
3.3.5.3 General results
The impact of the perturbation on the profile landward of the perturbation was a large
increase in offshore directed sediment transport rate, as anticipated. Surprisingly, the bar did
not begin to rebuild immediately. Instead, the bar system collapsed first, and then began to
reform approximately 0.5 m further landward than the previous bar position.
3.3.5.4 Detailed description and discussion
In the first 5 min following the perturbation (t = 120 to 125 min) the profile
experienced increased erosion over most of the profile landward of the bar (Figure 3.14). In
the region of the perturbation and approximately 0.5 m seaward of the perturbation there was
considerable negative transport as the bar collapsed and was transported landward into the
trough formation.
For t = 125 to 130 min, the profile continued to erode over the region x = -1.5 to 3.4
m. The onshore transport in the bar region was more pronounced as the bar began to reform
landward of its location prior to the perturbation.
The remainder of the experiment up to t = 180 min showed a gradual reduction in the
magnitude of the sediment transport rates. The bar was rebuilt at a position approximately
0.5 m landward of the pre-perturbation position, and was still shifting landward during the
interval from t = 170 to 180 min.
0.1
0--
0 -0.2
S-0.3
-0.4
-0.5 --..--.i-i -
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--t = 0 min -t = 120 min, before
-- t = 120 min, after t = 180 min
Figure 3.13 Summary of profile changes in Case D
0.0015
0.001 -
0.0005 -
E- 0
-0.0005
-0.001
-0.0015
-0.002 -.-----
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
t= 110-120 min t = 120-125 min -- t = 125-130 min
t = 130-140 min t = 140-170 min t = 170-180 min
Figure 3.14 Summary of average sediment transport rates in Case D
45
A comparison with the unperturbed case is presented in Figures 3.15 and 3.16. These
show that the impact of the removal of the landward section of the bar was a considerable
increase in the erosion of the profile landward of the perturbation. This agrees well with
what one would anticipate intuitively for the same reasons as in the previous three cases: a
removal of sediment from the bar increases the amount of wave energy transmitted past the
bar and dissipated in the region landward of the bar/trough system.
An interesting occurrence is the collapse and reformation of the bar system following
the removal of sediment. Inspection of the profile morphology in Figure 3.17 and the
evolution of bar volume in Figure 3.18 shows a continued reduction in the size of the bar for
the 10 minutes following the perturbation. The bar then grows over then next 40 minutes,
and the last 10 minutes show a slight reduction in bar volume.
3.3.6 Case E
3.3.6.1 Volume added & experiment duration
Case E was altered by the deposition of a volume of sediment in the trough region
of the profile (Figure 3.19). The experiment was run for 180 min.
3.3.6.2 Expected response
The expected response of the profile to the perturbation was the transport of the
deposited sediment both landward and seaward. The bar/trough formation was expected to
regenerate a form similar to its pre-perturbation form, and the profile was expected to be
shifted slightly seaward from the unperturbed case.
0.001
0.0008
0.0006
E
E
0.0004
E
O
0.0002
0
-0.0002
-
2 -1
2~ 3 4 5
2 3 4 5 6
Offshore distance (m)
- Case I Case D
Figure 3.15 Comparison of average sediment transport rates for Case D and Case I
(unperturbed case) for the period 120 to 180 min
1
0.1
Case I
0.05- Case D
o
-0.05
-2 0 2 4 6 8 10
Offshore distance (m)
0.1
0
1.-0.1 -
CU
Case D, t = 120 min a 0.
-0.4 o ....... o Case I, t = 180 min
--+ Case D, t = 180 min
-0.5 '
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.16 Comparison of profile changes for Case D and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 180 min
0.1
0
--0.1
o -0.2
w -0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
t = 120 min, after t = 125 min -- t = 130 min
t = 140 min t = 180 min
Figure 3.17 Profile evolution with time for the period from 120 to 180 min for Case D
30 60 90 120 150
Elapsed time (min)
Figure 3.18 Case D: evolution of bar volume with elapsed time
0.05
0.04
E
0.03
()
E
0 0.02
0.01
0
180
3.3.6.3 General results
The general response to the perturbation appeared to be the redistribution of the
deposited sediment both landward and seaward, as anticipated. However, the exact response
of the profile to the perturbation was difficult to determine in Case E. The results were
obscured by both a large closure adjustment required for the interval from 120 to 125 min
and an apparent 3-D circulation that dominated sediment transport during the interval from
140 to 170 min.
3.3.6.4 Detailed description and discussion
The immediate response of the profile (t = 120 to 125 min) is difficult to interpret
from the calculated sediment transport rates due to the large adjustment required to achieve
closure. The transport curve in Figure 3.20 for this interval shows offshore transport seaward
of the perturbation and onshore transport over the 3 m landward of the perturbation as one
would anticipate. However, it also shows increased offshore transport over the region -1.5
to 0.25 m offshore, which is counter-intuitive (one does not expect an offshore deposition
of sand to increase beach face erosion). This increased offshore transport may be the result
of the adjustment made to the transport rate to achieve offshore closure (a plot of the adjusted
and unadjusted transport curves is shown in Figure 3.3). This region was not erosional
according to the unadjusted profiles, and since the region was nearly 2-D, and the deposited
volume of sand was not near this region, the closure adjustment probably does not apply to
this region. Thus, it is plausible that the perturbation did not induce increased erosion of the
beach face area. Also, the profiles at t = 120 and 125 min show a large amount of erosion
in the perturbation area due to the reformation of a trough. It appears that most of the eroded
volume was deposited just seaward of the new trough, which increased the bar height.
0.1
0
-0.1
E
.-S
-0.2
-0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--t = min - t = 120 min, before
--t = 120 min, after t = 180 min
Figure 3.19 Summary of profile changes in Case E
0.0025
0.0018
0.0011 -
0.0004
-0.0003 -
-0 .00 1 .. . . i . .
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
t = 110-120 min t = 120-125 min -- t = 125-130 min
t = 130-140 min t = 140-170 min t = 170-180 min
Figure 3.20 Summary of average sediment transport rates in Case E
52
The interval from t = 125 to 130 min shows erosion in the region x = -1.5 to 2.5 m
offshore. Onshore transport occurred in the regions x = 2.5 to 3.7 m, which was the transport
of some of the deposited material to the area immediately landward of the deposition site.
Seaward transport occurred from x = 3.7 to 4.5 m and onshore transport occurred from x =
4.5 to 6 m, which deepened the trough feature and built the bar formation.
From t = 130 to 140 min there was a small amount of onshore transport in the region
of the trough (x = 2.7 to 3.75 m), and seaward transport occurred over the remainder of the
profile. The elevation of the bottom of the trough remained the same, and the bar shifted
slightly seaward.
The changes in the profile between t = 140 and 170 min were very different than the
trends in profile morphology shown from t = 120 to 140 min. During this interval there was
little change in the profile from -1.5 to 2 m, but there was a considerable amount of onshore
transport over the remainder of the profile. The size of the bar dramatically reduced while
much of the bar material was apparently deposited over the 2 m length of profile just
landward of the trough formation. Material was also transported shoreward from the region
6.5 to 8.5 m offshore. The effects of a 3-D current system were documented by Oh (1994),
and a comparison of Oh's results with the current results in figures 3.21 and 3.22 suggest that
the onshore transport may have been caused by a 3-D current system.
The final 10 min of the experiment showed offshore directed transport dominating
over most of the profile. The bar formation continued to reduce in size as sand was
transported seaward from the bar region and deposited near the toe of the beach.
O.1 5
0.10
0.15
C0o
a: -o.os
w -0.20
Ck
-0. ..----.--.-
-0.3'0rANK BOTTOM"'-Y
-0.30 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (zr)
Figure 3.21 Mean profile evolution after the profile approached an equilibrium during Experiment
MT01. Elapsed times = 0, 242,297, 352, 407 and 476 min. Note the substantial erosion of the area
seaward of the bar and the deposition of the area immediately landward of the bar trough. Note also
the landward movement of the bar (Oh, 1994).
0.1
0
- -0.1
o -0.2
; .
LL -0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5
Offshore distance (m)
6 7 8 9
I- t = 140min t = 170min
\Figure 3.22 Profile evolution of Case E at elapsed times = 140 and 170 min.
------ -------- --------------- --- ------
- - - - - - - - - - - - - - - - - - - - - -
- ------------------------------------- ------
54
A comparison with Case I of the average transport rates for the interval t = 120 to 180
min is presented in Figure 3.23, and a comparison of the changes in profile elevation is
shown for the same interval in Figure 3.24. Unfortunately, the large apparent 3-D effect in
Case E reduces confidence in the interpretation of the graph, and it is difficult to draw
conclusions from this plot concerning the impact of the perturbation.
3.3.7 Case F
3.3.7.1 Volume added & experiment duration
The profile in Case F was altered by the deposition of a volume of sand in the beach
face region (Figure 3.25). The experiment was run for 240 min.
3.3.7.2 Expected response
The expected response of the profile was the transport of most of the deposited
material seaward and only a very slight amount of sand transport landward. The profile was
expected to evolve toward the form the active profile would have had if unperturbed, but
translated slightly seaward.
3.3.7.3 General results
The immediate response of the profile to the sand deposit was a small onshore
transport of sand and a large offshore transport of sand from the fill, as anticipated. A
comparison of sediment transport rates with the unperturbed case shows that the deposit of
sand induced greater offshore transport rates over most of the fill region (except for the berm
region). A comparison of the final profile and the profile elevation changes with the
unperturbed case shows that at the end of the experiment the fill resulted in the shift of the
beach face seaward and the bar position was also shifted seaward relative to the unperturbed
case. The perturbation did not appear to have a major effect on the remainder of the profile.
0.0004
0.0002
- 0
E
- -0.0002
0 -0.0004
-0.0006
-0.0008 --I--- I I I I '
-2 -1 0 1 2 3 4 5 6
Offshore distance (m)
7 8 9 10
- Case E, 120-180 unadjusted Case E, 120-180, adjusted
-Case I, 120-180, adjusted
Figure 3.23 Comparison of average sediment transport rates for Case E and Case I
(unperturbed case) for the period from 120 to 180 min
0.08 Case I
0.06
Case E
0.04-
0.02
-0.02
-0.04
-0.06
-2 0 2 4 6 8 10
Offshore distance (m)
0.1
0
-.-0.1
o -0.2 :- o
S-0.3 ...... Case t= 120 min 'o.o.
Case E, t = 120 min 0.
-0.4 o- ....- o Case I, t = 180 min :
-I Case E, t= 180 min
-0.5 I
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.24 Comparison of profile changes for Case E and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 180 min
3.3.7.4 Detailed description and discussion
The transport in the 5 min following the perturbation exhibited increased offshore
transport across nearly the entire profile, except for the beach face (Figure 3.26). Onshore
directed transport occurred over a landward section of the beach face region, which resulted
in a build up of the berm. The seaward portion of the sand deposit eroded substantially.
Also, note the landward shift in the bar formation.
In the interval from t = 125 to 230 min the profile continued to experience increased
erosion with offshore transport occurring everywhere except near the peak of the berm. The
shoreline showed a large recession, as one would expect. The bar position oscillated in its
horizontal position around 3 m offshore.
The final 10 min (t = 230 to 240 min) showed a minimal accretion in the beach face
area as the shoreline advanced slightly. Also, the bar/trough formation shifted landward.
A comparison with the unperturbed case for the interval t = 120 to 180 min (Figure
3.27) shows greatly increased offshore transport in the region 0 to 4 m offshore. Also, the
comparison displays an increased onshore transport rate in the region from -0.3 to -1.2 m
offshore, thus, resulting in a larger berm than in the unperturbed case.
For the period t = 180 to 240 min, the comparison with Case I shows much smaller
differences (Figure 3.28). Case F experienced slightly greater offshore transport over the
entire profile, save the region -1 to 0 m offshore, which had greater onshore directed
transport than Case I. Obviously, the deposit had a considerably lessened impact on the
transport rate after it had been somewhat smoothed out over the 60 min following the
deposition.
0.1
0
-0.1
E
S-2 -1 0 1 2 3
-- t = 0 min - t = 120 min, before --- t = 120 min, after
-0.3
0.0015
-0.5001 -
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
t=0min - t=120min, before--t=120min, after
-t = 180 min t = 240 min
Figure 3.25 Summary of profile changes in Case F
0.0005
0
-0.0005
-0.001
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
- t = 110-120 min t = 120-125 min -- t = 125-130 min t = 130-140 min
- t = 140-160 min t = 160-180 min t = 180-230 min t = 230-240 min
Figure 3.26 Summary of average sediment transport rates in Case F
0.0004
0.0003
S0.0002-
0
-0.0001' ,
-0.0001 -'---I-t-F----- ---'--- I--- :-
-2 -1 0 1 2 3 4 5 6
Offshore distance (m)
7 8 9 10
- Case F - Case I
Figure 3.27 Comparison of average sediment transport rates for Case F and Case I
(unperturbed case) for the interval from 120 to 180 min
0.0005
0.0004-
0.0003 -
A 0.0002-
E
0.0001
-0.0001 I ,I,---, i-l ] I
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
-- Case F - Case I
Figure 3.28 Comparison of average sediment transport rates for Case F and Case I
(unperturbed case) for the interval from 180 to 240 min
60
A comparison with the unperturbed case of changes in profile elevation over the
interval from 120 to 240 min is presented in Figure 3.29. Here it can be seen that the
deposition caused berm growth over the landward third of the fill area and greatly increased
erosion of the seaward two-thirds of the fill area. The perturbation seemed to have little
effect on the profile between the fill area and the bar/trough formation, but the perturbation
did seem to have an impact on the bar. The bar in Case F shifted landward less than half the
distance the bar in Case I shifted landward. Also, the bar crest elevation increased, whereas
the bar crest elevation decreased in the unperturbed case. Overall, the perturbation caused
a seaward shift in the shoreline and bar formation relative to the unperturbed case, and
appeared to have little effect on the remainder of the profile.
3.3.8 Case G
3,3.8.1 Volume added & experiment duration
A volume of sand was deposited just landward of the trough formation in Case G
(Figure 3.30). The experiment was run for 240 min.
3.3.8.2 Expected response
The general expected response of the profile to the perturbation was the transport of
the deposited sediment both landward and seaward. The immediate expected result was the
reduction in wave energy propagating beyond the fill area, and thus, a decrease in sediment
transport rate landward of the fill, as well as an increase in offshore sediment transport rate
in the region of the fill. The long term expected result was the redistribution of the material
across the profile, resulting in a seaward shift of the profile from the unperturbed case.
61
0.15
0.1-
Case I
0.05- --- Case F
0 0.
0-
-0.05
-0.1 '
-2 0 2 4 6 8 10
Offshore distance (m)
0.1
0
--0.1 -.
E o
-0.2
-0.3- ......... Case 1l,t=120 min -.-o
Case F, t = 120 min .mo
-0.4 o ....... Case I, t = 240 min
--- Case F, t = 240 min
-0.5 '
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.29 Comparison of profile changes for Case F and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 240 min
3.3.8.3 General results
The sediment transport curves calculated for the experiment show that the immediate
response of the profile to the sand deposit was a small onshore transport of sand and a large
offshore transport of sand from the fill, as anticipated. A comparison of sediment transport
rates with the unperturbed case shows that the deposit of sand induced greater offshore
transport rates over most of the profile seaward of the perturbation, as expected, but for the
interval 120 to 180 min the sediment transport curves did not show any noticeable difference
in the region landward of the perturbation. However, for the interval from 180 to 240 min
there was a reduction in offshore sediment transport rate relative to the unperturbed case for
the region landward of the fill area. A comparison of the final profile and the profile
elevation changes with the unperturbed case shows that at the end of the experiment the sand
deposit appeared to be smoothed out over the profile and produced a seaward shift in most
of the profile relative to the unperturbed case, as expected.
3.3.8.4 Detailed description and discussion
The sediment transport rates for the experiment are presented in Figure 3.31. It is
important to note that the closure adjustments for the intervals from 120 to 125 min and 125
to 130 min are relatively large. The average change in elevation for the two intervals were
0.817 mm and -0.51 mm, respectively.
For the interval immediately following the perturbation (120 to 125 min) the transport
curve is directed onshore in the region -2 to 1 m offshore. However, the large negative
closure adjustment may be responsible for much of this apparent onshore sediment transport.
Despite the large adjustment of the transport curve, it is clear that the perturbation induced
0.1
0
-0.1
E
a,
.o -0.2
LU
-0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
--t = 0 min - t= 120 min, before -t = 120, after
St = 180 min -- t = 240 min
Figure 3.30 Summary of profile changes in Case G
0.002
0.0015
-E
- 0.001
0.0005
-0.0005
-2 -1 0 1 2 3 4 5 6 7 8 9
Offshore distance (m)
- t = 110-120 min t = 120-125 min t = 125-130 min t = 130-140 min
- t = 140-160 min t = 160-200 min --- t = 200-230 min t = 230-240 min
Figure 3.31 Summary of average sediment transport rates in Case G
64
strong offshore transport over the portion of the profile seaward of the landward edge of the
deposited sediment volume. This is confirmed by a comparison of the profiles at elapsed
times of 120 and 125 min, which show erosion of the deposited volume, a reduction in bar
height, a shift of the bar landward and deposition offshore.
For the interval t = 125 to 130 min the deposition area eroded further, the bar
continued to shift landward and there was some deposition in the offshore area.
For the next 100 min, up to t = 230 min, the sand deposited at t = 120 min continued
to erode and be transported seaward until the perturbation was mostly smoothed-out at t =
200 min. Then, the profile landward of the region where the sand deposit previously existed
began to erode. Also, the bar position oscillated as the bar grew in height.
In the last 10 min, t = 230 to 240 min, the bar suddenly decreased in height,
apparently becoming unstable after reaching its maximum height at t = 230 min.
A comparison with the unperturbed case for t = 120 to 180 min shows increased
offshore transport over the profile seaward of 1.5 m offshore (Figure 3.32). This is
reasonable, but the lack of shoreward transport (relative to the unperturbed case) landward
of the perturbation is surprising.
The comparison with Case I for t = 180 to 240 min is more intuitively consistent, in
that the perturbation did appear to cause some shoreward transport landward of the
deposition area, although the beach face experienced slightly increased erosion (Figure 3.33).
Seaward of the deposition region showed increased offshore transport, as expected.
A comparison with the unperturbed case of changes in profile elevation over the
interval from 120 to 240 min is presented in Figure 3.34. This plot shows a large negative
0.0006
0.0005
.5 0.0003 --
,E
E 0.0002 /
0.0001 'I
0 .....
-0.0001 I I i' 1 1 I I I
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--Case G - Case I
Figure 3.32 Comparison of average sediment transport rates for Case G and Case I
(unperturbed case) for the interval from 120 to 180 min
0.0005
0.0004
0.0003
0.0002
0.0001
0 ----""-------
-0.0001I I I -I ii
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--Case G - Case I
Figure 3.33 Comparison of average sediment transport rates for Case G and Case I
(unperturbed case) for the interval from 180 to 240 min
66
0.12
0.1
0.08-
08 ........ Case I
0.06
Case G
E 0.04
0.02
0 .
-0.02
-0.04
-0.06 '
-2 0 2 4 6 8 10
Offshore distance (m)
0.1
0
oO"o
EG
u -0.2 .
S-0.3 ........ Case 1, t = 120 min
Case G, t = 120 min
-0.4- ....... o Case I, t = 240 min
----- Case G, t = 240 min
-0.5 '
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.34 Comparison of profile changes for Case G and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 240 min
67
change in the Case G profile elevation in the region where the fill was deposited, which was
caused by the smoothing out of the perturbation, as expected. Landward of the sand deposit
site the Case G profile showed almost no change, whereas the unperturbed case showed
erosion in this region (except the berm area). Thus, the perturbation induced a positive
elevation change in this region, relative to the unperturbed case. Also shown in this figure,
the bar in Case G shifted landward, but only about half the distance that the bar shifted
landward in Case I. This suggests that the perturbation affected the bar by shifting it seaward
relative to the unperturbed case. Seaward of the bar, up to an offshore distance of 7 m, the
figure shows a positive elevation change in Case G relative to the unperturbed case. Overall,
the sand deposit appeared to be smoothed out over the profile and produced a seaward shift
in most of the profile relative to the unperturbed case, as expected.
3.3.9 Case H
3.3.9.1 Volume added & experiment duration
In Case H a volume of sand was deposited at a location between the deposition sites
chosen in Cases F and G (Figure 3.35). The experiment was run for 300 min.
3.3.9.2 Expected response
As in the previous deposition cases, the general expected response of the profile to
the perturbation was the transport of the deposited sediment both landward and seaward. The
immediate expected result was the reduction in wave energy propagating beyond the fill area,
and thus, a decrease in sediment transport rate landward of the fill, as well as an increase in
offshore sediment transport rate in the region of the fill. The long term expected result was
the redistribution of the material across the profile, resulting in a seaward shift of the profile
from the unperturbed case.
3.3.9.3 General results
The results of the experiment in Case H are very similar to those of Case G, and it
appears that the change in position of the fill area between these experiments did not have
a large effect on the results. The sediment transport curves calculated for the experiment
show that the immediate response of the profile to the sand deposit was a small onshore
transport of sand and a large offshore transport of sand from the fill, as anticipated. A
comparison of sediment transport rates with the unperturbed case shows that the deposit of
sand induced greater offshore transport rates over most of the profile seaward of the
perturbation and decreased offshore sediment transport landward of the perturbation, as
expected. A comparison of the final profile and the profile elevation changes with the
unperturbed case shows that at the end of the experiment the sand deposit appeared to be
smoothed out over the profile and produced a seaward shift over most of the profile relative
to the unperturbed case, as expected.
3.3.9.4 Detailed description and discussion
The transport curve for t = 120 to 125 min, shown if Figure 3.36, required only a
small adjustment for closure (there was only a 0.147 mm average change in elevation over
the active profile) and may be a fairly accurate description of the sediment transport rate for
the 5 min interval. It shows some onshore directed transport in the berm and beach face
region, as one would anticipate due to a deposit of sand this size so close to the beach face.
Dominant is the large increase in the offshore directed sediment transport rate over the region
1 to 7 m offshore. A slight decrease in the bar height as well as a shift landward in the bar
position occurred. Also, note the onshore transport at the toe of the profile.
0.1
0
-0.1 -
E
.o -0.2
-0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
-t = 0 min - t =120 min, before t = 120 min, after
St = 180 min t = 240 min -- t = 300 min
Figure 3.35 Summary of profile changes in Case H
0.002
0.0015
0.001
E
S0.0005
0
0
-0.0005
-2 -1 0 1 2 3 4 5 6
Offshore distance (m)
7 8 9 10
t = 130-140 min
- t = 270-300 min
Figure 3.36 Summary of average sediment transport rates in Case H
- t = 110-120 min t = 120-125 min t= 125-130 min
- t = 140-180 min t = 160-180 min t = 210-240 min
70
The period from t = 125 to 180 min showed much of the same behavior. There was
offshore directed sediment transport over most of the profile, though of much lesser
magnitude, and there was slight onshore transport at the landward end of the perturbation.
The bar position oscillated and the bar height varied slightly. The offshore bar approximately
7 m offshore continued to develop and become more pronounced.
For t = 180 to 240 min, offshore directed sediment transport over the entire profile
occurred. The offshore bar formation became more developed and an inner bar formed about
1 m offshore.
The final 60 min of the experiment experienced the same trends as the previous 60
min. The transport over the entire region was directed offshore. The inner bar at 1 m
offshore became more peaked, the main bar at 3.5 m offshore remained relatively stable and
the offshore bar continued to build.
A comparison with the unperturbed case for t = 120 to 180 min, shown in Figure
3.37, displays greatly increased offshore directed sediment transport from 0.5 m to 6.5 m
offshore. There is little change in transport landward of the deposit area, except for a small
increase in onshore transport immediately adjacent to the landward edge of the perturbation.
For t = 180 to 240 min, a comparison with Case I displays a reduction in offshore sediment
transport in the region -1 to 1.5 m offshore and an increase in offshore transport 2.5 to 9 m
offshore (Figure 3.38). For t = 240 to 300 min, the offshore sediment transport in Case H is
less than that of Case I over most of the profile (Figure 3.39).
A comparison with the unperturbed case of changes in profile elevation over the
interval from 120 to 300 min is presented in Figure 3.40. This plot shows a large negative
0.0006
0.0004-
E
E
0
S0.0002 -
-0.0002 l '------I l'--I--- II- I I I I I
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
- Case H - Case I
Figure 3.37 Comparison of average sediment transport rates for Case H and Case I
(unperturbed case) for the interval from 120 to 180 min
0.0006
0.0004-
0 --- ^ ^ --------------- -------------
- 0.0002
<
0
-0.0002 I -----I-- I I I I I
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--Case H - Case I
Figure 3.38 Comparison of average sediment transport rates for Case H and Case I
(unperturbed case) for the interval from 180 to 240 min
0.0006
0.0004 -
E
- 0.0002
E
CO
-0.0002 l i I I l i l l
-2 -1 0 1 2 3 4 5 6
Offshore distance (m)
7 8 9 10
I- Case H - Case I
Figure 3.39 Comparison of average sediment transport rates for Case H and Case I
(unperturbed case) for the period 240 to 300 min
E 0.02
"( 0 -- -
-0.02 -
-0.04
-0.06
-0.08
-2 0 2 4 6 8 10
Offshore distance (m)
0.1
0
0'-
= -0.2
LU-0.3- ......... Case I, t= 120 min
Case H, t = 120 min
-0.4 o ....... o Case I, t = 300 min
-- I Case H, t = 300 min
-0.5 I I '
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.40 Comparison of profile changes for Case H and Case I (unperturbed case) for
the interval from 120 min (after perturbation) to 300 min
74
change in the Case H profile elevation in the region where the fill was deposited, which was
caused by the smoothing out of the perturbation, as expected. Landward of the sand deposit
site the Case H profile showed only small changes, whereas the unperturbed case showed
erosion in this region (except the berm area). Thus, the perturbation induced a positive
elevation change in this region, relative to the unperturbed case. Also shown in this figure,
the bar in Case H shifted landward, but only about half the distance that the bar shifted
landward in Case I. This suggests that the perturbation affected the bar by shifting it seaward
relative to the unperturbed case. Seaward of the bar, up to an offshore distance of 7.5 m, the
figure shows a positive elevation change in Case H relative to the unperturbed case. Overall,
the perturbation in this case produced results very similar to those of Case G: the sand
deposit appeared to be smoothed out over the profile and produced a seaward shift over most
of the profile relative to the unperturbed case, as expected. This suggests that the change in
position of the fill area between Cases G and H has little influence on the results.
3.3.10 Case J
Case J was conducted as the control experiment for the irregular wave experiments.
Random waves (H, = 0.16 m, Tp = 1.65 sec) were run on the 1:20 slope initial profile for
300 min without any perturbation introduced to the profile by the deposition or removal of
sand.
3.3.10.1 General results
The summary of profile evolution for the experiment is presented in Figure 3.41. The
profile developed a shape similar to a power law profile in the region -1 to 4 m offshore.
Also, a small "step" feature formed approximately 0.6 m seaward of the still water line.
3.3.10.2 Detailed description and discussion
In the first 120 min of the experiment, the sediment transport rate was directed
onshore over x = -1 to 0 m which built up a berm at -1 m (Figure 3.42). The transport was
directed offshore for x = 0 to 6 m and onshore for x = 6 to 10 m. In the region -1 to 4 m
offshore, where most of the waves broke, the profile developed an exponential shape similar
to that of the h = Ax.3 power law profile proposed by Bruun (1954) and Dean (1973).
For the next 180 min, the experiment continued along very similar trends with only
slightly modified sediment transport rates across the profile. At an elapsed time of 240 min
a small step in the profile developed about 0.6 m offshore and became more pronounced at
t = 300 min.
3.3.10.3 Assessment of repeatability
Since this experiment is used as a control to which the perturbed cases are compared,
it is necessary to assess the repeatability of the experiments with irregular waves. Figure
3.43 shows the profiles of Cases J, K and L at an elapsed time of 120 min. The profiles are
very similar, showing only minor differences, with the exception of Case J showing a greater
erosion near the beach face and a slightly lesser beach face slope.
3.3.11 Case K
3.3.11.1 Volume added & experiment duration
The experimental profile in Case K was altered at t = 120 min by the deposition of
a volume of sand in the area 2 to 3 m offshore (Figure 3.44). The experiment was run for
300 min.
0.2
0.1
0
E -0.2
-0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
-- t = min t = 120min -- t = 180min -t = 240min -t =300 min
Figure 3.41 Summary of profile changes in Case J
0.0006
0.0004
" 0.0002
-0.0002
-0.0004 .-..-.--.-
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
t = 0 to 120 min t = 120 to 180 min
t = 180 to 240 min t = 240 to 300 min
Figure 3.42 Summary of average sediment transport rates in Case J
2 3 4 5 6 7 8 9
I I I I I I I I I
2 3 4 5 6 7 8 9
Offshore distance (m)
case J case K case L
10 11
Figure 3.43 Summary of profiles at an elapsed time of 120 min for experiments with
irregular waves (Pierson-Moskowitz spectrum, Hs = 0.16 m, T, = 1.65 sec)
0.2
0.1 -
0
E- 0.1-
2.
| -0.2 -
wL
-0.3 -
-0.4 -
-0.5
) 1
3.3.11.2 Expected response
As in the previous deposition cases, the general expected response of the profile to
the perturbation was the transport of the deposited sediment both landward and seaward. The
immediate expected result was the reduction in wave energy propagating beyond the fill area,
and thus, a decrease in sediment transport rate landward of the fill, as well as an increase in
offshore sediment transport rate in the region of the fill. The long term expected result was
the redistribution of the material across the profile, resulting in a seaward shift of the profile
from the unperturbed case.
3.3.11.3 General results
For the 60 min following the perturbation the results were mostly consistent with
expectations. A comparison of sediment transport rates with the unperturbed case shows that
the deposit of sand induced greater offshore transport rates over most of the profile seaward
of the perturbation and decreased offshore sediment transport landward of the perturbation,
as expected. However, for the subsequent intervals the perturbation did not induce any
onshore transport relative to the unperturbed case. A comparison of the final profile and the
profile elevation changes with the unperturbed case shows that at the end of the experiment
the sand deposit appeared to have a negative impact on the profile from -0.2 to 0.9 m
offshore, which is contrary to what was expected.
3.3.11.4 Detailed description and discussion
The average sediment transport rates are presented in Figure 3.45. An odd occurrence
in this experiment was the sediment transport directed onshore for the 10 min preceding the
perturbation. Although relatively small, this did not occur in the other random waves case
-0.1
> -0.2
-0.3
-0.4
-0.5 ---
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--t = 0 min - t = 120 min, before -- t = 120 min, after
--- t = 180 min t = 240 min -- t = 300 min
Figure 3.44 Summary of profile changes in Case K
0.002
0.0015
- 0.001
0.0005
0
-0.0005
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
- t = 110-120 min -- t = 120-125 min t = 125-130 min t = 130-140 min
- t = 140-160 min t = 160-180 min -- t = 210-240 min t = 270-300 min
Figure 3.45 Summary of average sediment transport rates in Case K
80
in which transport was measured for the same interval (Case L). This is due, in part, to the
negative closure adjustment made for that interval.
In the 5 min following the perturbation there was moderate offshore sediment
transport from -2 to 1.9 m offshore. It is surprising that the addition of the volume of
sediment caused this increase in offshore sediment transport in this region. There was a
'spike' of onshore directed transport from 1.9 to 2.2 m offshore, the position of which
corresponded approximately to the landward edge of the fill area. Also, there was a large
amount of offshore sediment transport over the profile 2.25 m offshore and seaward.
During the next 5 min, from t = 125 to 130 min, offshore sediment transport occurred
seaward of 1 m offshore, but unlike the previous 5 min, onshore transport occurred from -2
to 1 m offshore.
Through an elapsed time of 180 min the perturbation was smoothed out. Offshore
directed transport occurred over x = 1 to 6 m and slight onshore transport occurred over the
beach face region.
From 180 to 300 min the same trends of sediment transport continued: offshore
transport in the middle of the profile and onshore directed transport at the ends of the profile.
The berm continued to build as well as the 'bar' at 4.5 m offshore. Also, the same feature
as noted in Case J, a rather abrupt drop-off about 0.5 m offshore, developed during this
interval.
The comparison with Case J for t = 120 to 180 min displays considerable change in
sediment transport rates (Figure 3.46). The perturbation induced a negative impact on the
transport rate landward of the deposition area, and a large positive impact on the transport
81
rate seaward of the deposition area. Note that the magnitude of the maximum transport rate
in Case K is twice that of Case J.
For the interval t = 180 to 240 min, the sediment transport rates for Cases J and K are
very similar (Figure 3.47). During this interval the perturbation is well smoothed out, but
the added volume has altered the profile in the region of the deposit by flattening the slope
compared to the unperturbed case. It is odd that this is not reflected by greater differences
in sediment transport rates.
For t = 240 to 300 min, the comparison of sediment transport rates (Figure 3.48)
yields results that are more explainable than those in Figure 3.47. Case K exhibits increased
offshore transport from 2 to 9 m offshore, and from this plot it is clear that the added volume
does, in fact, still influence the sediment transport rates.
A comparison with the unperturbed case of changes in profile elevation over the
interval from 120 to 300 min is presented in Figure 3.49. This plot shows a large negative
change in the Case K profile elevation in the region where the fill was deposited, which was
caused by the smoothing out of the perturbation, as expected. Landward of the sand deposit
site the Case K profile showed both expected and unexpected changes. Case K showed
positive profile changes relative to Case J at the berm and from about 0.9 m to 2 m offshore.
However, unexpected and unexplainable changes occur in the region from 0 to 0.9 m
offshore, where Case K shows a negative profile change relative to the unperturbed case.
Seaward of the deposit area the figure shows a positive elevation change in Case K relative
to the unperturbed case over most of the profile. Overall, the sand deposit appeared to be
smoothed out over the profile and produced a seaward shift in the most of the profile relative
0.0006
0.0004
E
H 0.0002
0
-0.0002
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
- Case K - CaseJ I
Figure 3.46 Comparison of average sediment transport rates for Case K and Case J
(unperturbed case) for the interval from 120 to 180 min
0.0006
0.0004
E
c 0.0002-
-0.0002
-2 -1 0
1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
-- Case K - Case J
Figure 3.47 Comparison of average sediment transport rates for Case K and Case J
0.08 Case J
0.06
Case K
0.04
0.02
E
-cr
0
-0.02
-0.04
-0.06
-0.08 '
-2 0 2 4 6 8 10
Offshore distance (m)
0.2
0.1
E
.0
> -0.2 -
-0.3- .......Case J, t= 120 min
Case K, t = 120 min
-0.4 ..... o Case J, t = 300 min
i--- Case K, t = 300 min
-0.5 '
-2 0 2 4 6 8 10
Offshore distance (m)
Figure 3.49 Comparison of profile changes for Case K and Case J (unperturbed case) for
the interval from 120 min (after perturbation) to 300 min
0.0006
0.0004
CE
S0.0002- ------
0-
-0.0002 ----
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
Case K - Case J
Figure 3.48 Comparison of average sediment transport rates for Case K and Case J
(unperturbed case) for the period 240 to 300 min
85
to the unperturbed case, with the exception of the region from -0.7 m to 0.9 m offshore.
Thus, the experimental results generally agreed with the expected results for most of the
profile, except for the beach face and the region immediately adjacent offshore, which gave
unexpected results.
3.3.12 Case L
3.3.12.1 Volume added & experiment duration
The purpose of the experiment conducted in Case L was to test the hypothesis that
a peaked bar formation created during a storm by somewhat regular waves may act to
position the break point and thus maintain the bar in a similar shape under irregular waves.
Thus, a volume of sand was deposited at t = 120 min in the area 4 to 5 m offshore in a shape
similar to that of the bars formed during the regular wave cases (Figure 3.50). The location
of the deposition was selected as the point where most of the plunging breakers occurred and
where a peaking in the profile had formed under the irregular waves. The experiment was
run for 300 min.
3.3.12.2 Expected response
The general expected response of a profile to a deposit of sediment is the transport
of the deposited sediment both landward and seaward as the sediment is redistributed across
the profile. However, in this particular case it was expected that the deposited volume might
be maintained in a bar formation by positioning a break point at the location of the fill. It
was not expected that the exact form of the deposit be preserved, but instead, reformation of
the deposited sand while retaining a bar form was expected. The extent of the redistribution
of the fill material to be expected was unknown. It was anticipated that the redistribution of
86
the fill might cease at some point while a bar formation still existed at the location of the
perturbation, and that bar formation might be maintained.
3.3.12.3 General results
The volume of sand that constituted the emplaced bar was largely redistributed both
landward and seaward, though primarily seaward. However, a large amount of the sand was
not redistributed far from the fill area, but rather was redistributed to form a broader, flatter
bar than that which was emplaced. The evolution of the bar characteristics of volume and
height suggest that the broad, flat bar was stable and may have continued to grow with the
continuation of the experiment.
3.3.12.4 Detailed description and discussion
The perturbation caused waves to break in a much more rapid, plunging manner over
the newly introduced bar. An inspection of the average sediment transport rates for the
interval t = 120 to 125 min shows surprising results (Figure 3.51). The transport rate greatly
increased in the region 0 to 3 m offshore, which is counter-intuitive. One would expect that
the bar would reduce the amount of wave energy propagating past the bar and reduce the
erosion of the nearshore area.
For the interval t = 125 to 130 min, a comparison with the pre-perturbation transport
curve (t = 110 to 120 min) shows the bar inducing a 'spike' of increased offshore transport
over a 1 m length of the profile corresponding to the bar location, and a region of increased
onshore transport over a 1.5 m length of the profile just seaward of the bar.
Up to t = 180 min the sediment transport was directed predominantly offshore over
the entire profile. The bar was smoothed out considerably, and the 'step' feature began to
form about 0.6 m offshore, as it had in the previous irregular wave experiments.
0.2
0.1
0
-0.1
.-0.2
-0.3
-0.4
-0.5
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Offshore distance (m)
--t = 0 min - t = 120 min, before t = 120 min, after
t = 180 min t = 240 min t = 300 min
Figure 3.50 Summary of profile changes in Case L
0.0008
0.0006
0.0004
E 0.0002 -
-0.0002
-0.0002 -
-0.0004 . .. .. .
-2 -1 0 1 2 3 4 5 6
Offshore distance (m)
-t = 110-120 min -
- t = 140-160 min -
7 8 9 10
t = 120-125 min t = 125-130 min t = 130-140 min
t = 160-180 min -- t = 210-240 min t = 270-300 min
Figure 3.51 Summary of average sediment transport rates in Case L
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