An examination of the dependence of mud shore profiles on the nearshore environment

UFLICOEL-96/002

AN EXAMINATION OF THE DEPENDENCE OF MUD
SHORE PROFILES ON THE NEARSHORE
ENVIRONMENT

by

A.P. Mulia Tarigan

Thesis

1996

AN EXAMINATION OF THE DEPENDENCE OF MUD SHORE PROFILES
ON THE NEARSHORE ENVIRONMENT

A. P. MULIA TARIGAN

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

ACKNOWLEDGMENTS

First and foremost, I would like to express my deepest gratitude to my advisor and

the chairman of my supervisory committee, Professor Ashish J. Mehta, who supported,

guided and trained me throughout my study. It has been an unforgettable experience that has

shown me the joys of challenges.

I wish to thank Dr. Say-Chong Lee who previously initiated the study on the dynamics

of mud profile geometry to which this study is closely related. Thanks and appreciation are

extended to Professor Robert G. Dean who supplied essential knowledge through his lectures,

discussions and research. Special thanks are extended to Dr. Li-Hwa Lin for encouragement

and technical discussions at various times. Thanks and appreciation are also due to Professor

Donald M. Sheppard for his participation as a supervisory committee member.

My gratitude is extended to the staff of Badan Pengkajian dan Penerapan Teknologi

(BPPT), or the Agency for the Assessment and Application of Technology, in Jakarta.

Information on the study areas, i.e., Pantai Madura, Pantai Surabaya, and Teluk Waru, used

in this study is based on reports submitted to BPPT. Gegar Sapta Prasetya deserves special

acknowledgment for helping me obtain and describe the field information.

I would also like to thank George Chappel, Jim Joiner, and Sidney Schofield for their

assistance during the experimental phase of this research. Special thanks go to the staff of

the Coastal and Oceanographic Engineering Department, with special acknowledgment to

Helen Twedell and John Davis for their friendly greetings that made life easier during my stay.

The contribution of my fellow student colleagues in many ways has had a special place

throughout my study. Wayne Walker, Paul Divine, Yigong Li, Renjie Chen, Lee Chee Gwan,

Marshal Bridges, Kat Marussin, Miller, and Doynov are among those who provided much

more than just nice conversations.

My study was funded by the Natural Resources Management Project assisted by

USAID. In this respect, the assistance given by Patricia S. Link of the Institute of

International Education (New York) in supervising the academic aspects of my study is

specially acknowledged.

Most important of all, I am deeply indebted to my parents who have rendered me with

sincere love, support and encouragement to do the best. Lastly, I would like to express my

appreciation for the support of my family and Indonesian friends in Gainesville.

TABLE OF CONTENTS

ACKNOWLEDGMENT ................................................... ......................... ii

LIST OF FIGURES ........................................................................................... vi

LIST OF TABLES ........................................................................................... xi

LIST O F SY M BO LS ........................................................................................... xiii

ABSTRACT .................................................................... xvi

CHAPTERS

1 INTRODUCTION ......................................................................... 1

1.1 Problem Statement ................................................................ 1
1.2 Objective and Scope ....................................................................... 7
1.3 Outline of Presentation ................................................................ 8

2 FIELD INFORM ATION ........................................................................... 9

2.1 Site D descriptions .......................................................................... 9
2.2 Hydrodynamic Information ........................................ ......... 14
2.3 Sedimentary Characteristics ............................................... ........ 17
2.4 Beach Profiles ...................................................................... 18

3 PROFILE ANALYSIS ....................................................................... 24

3.1 Introduction ............................................................................... 24
3.2 Coarse-Grained Profile Equation .................................... ......... 26
3.3 Fine-Grained Profile Equation .................................... .......... 31
3.4 Field Profile Analysis ............................................................. 37

4 LABORATORY EXPERIMENTS .............................................. ......... 55

4.1 Introduction ................................................... ....................... 55
4.2 Equipm ent .................................................... ........................ 56
4.3 Sedim ents ................................................................................. 61
4.4 Test Conditions ................................................ ..................... 61
4.5 Experimental Procedure ........................................................... 63
4.6 Corrections for Wave Data ......................................................... 67
4.7 Profile Change Data and Discussion ........................................ 70
4.8 Wave Envelope Data .................................................................... 85

5 DISCUSSION AND CONCLUSION .................................... ........... 90

5.1 Mud versus Sand Profile Geometry ......................................... ...... 90
5.2 Erosional and Accretionary Mud Profile Cycles .......................... 93
5.3 Concluding Remarks ................................................................... 95
5.4 Recommendations for Future Work ........................................ ..... 98

BIBLIOGRAPHY ....................................... ............... ................................. 99

APPENDICES

A PROFILE SEDIMENT CHARACTERISTICS ...................................... 103

B LEAST SQUARES FIT RESULTS ..................................................... 107

C FIELD PROFILES ..................................................... ................... 119

D BEST-FIT PLOTS OF EQUATIONS 3.2 AND 3.29 TO
LABORATORY PROFILES ................................................................. 130

E EIGEN VALUE ANALYSIS ................................................................. 135

BIOGRAPHICAL SKETCH ............................................................................... 142

LIST OF FIGURES

1.1 Typical normal and storm profiles along a sandy shoreline ........................... 3

1.2 Long-term profile change along a glacial till profile at Grimsby, Lake
Ontario, Canada (after Coakley et al., 1988) .......................................... 4

1.3 Spatial changes between periodic surveys for a mud profile along the
southwestern Louisiana chernier plain (after Lee, 1995) ............................... 5

1.4 Spatial changes between periodic surveys for a clayey mud profile in
a laboratory flume (after Lee, 1995) ......................................... ............. 6

1.5 Spatial changes between periodic surveys of a profile composed of a
loess in a laboratory flume (after Lee, 1995) ........................................... 7

2.1 Map of Indonesia. Locations ofPantai Madura, Surabaya, and Teluk
Waru are indicated by letters A and B with arrows pointing to the areas. ........ 9

2.2 Locations of Pantai Madura and Surabaya. Both are in the vicinity of an
area (enclosed by rectangle) designated for building a bridge connecting the
two islands. Pantai Madura is on the Madura side of the area, while Pantai
Surabaya is on the Surabaya side. ............................................ ............ 10

2.3 Photograph of the study site in Madura taken on August 13, 1994. The
shoreline is in Kecamatan (village) Labang of Kabupaten (county)
Bangkalan-M adura ................................................................................... 11

2.4 Photograph of the study site in Surabaya taken on August 13, 1994.
The shoreline is in Kecamatan (village) Kenjeran of Kabupaten (county)
Surabaya ..................................................... ............................................. 12

2.5 Teluk Waru site (Amsari, 1994). This site is located about 50 km south
of Mataram, the capital city ofNusa Tenggara Barat Province. Lembar,

a small natural harbor just north of Teluk Waru, can be reached easily by
boat from Bali. The rectangular area indicates the region surveyed. .............. 13

2.6 Photograph of the study site in Teluk Waru taken on May 19, 1993. The
shoreline is in Desa (village) Teluk Waru of Kabupaten (county) Labuhan
Tereng Lom bok Barat. ............................................................................ 14

2.7 Textural classification of sediment for beach profiles from Madura and
Surabaya. Data points represent the median particle size. Circle data
points are for samples from Surabaya, and rectangular points are from
Madura. The data points for both areas are clustered by open ovals,
indicating that the sediment can be classified in two dominant size ranges. .... 20

2.8 Textural classification for beach profiles from Teluk Waru. Circle data
points represent the median particle size. Two open ovals cluster the
data points into two dominant size ranges. ................................................. 21

2.9 Sketch showing beach profile lines at Madura and Surabaya. Dashed
lines, from the shoreline toward offshore, represent the profiles. Lengths of
profiles depicted do not reflect the actual lengths digitized. Numbers 1 and
7 following the letter M for Madura profiles, and 4 and 5 following letter S
for Surabaya profiles are associated with the sheet numbers of the
bathym etric m aps. ................................................................................... 22

2.10 Sketch showing Teluk Waru profile lines. Dashed lines, from the shoreline
toward offshore, represent the profiles. Lengths of profiles do not in
general reflect their actual lengths digitized. .......................................... 23

3.1 Two-dimensional beach profile illustrating the coordinate adopted. Point (0,0)
is the shoreline position, while (h, y,) is a profile point denoting an arbitrary
position with depth h. and distance yi from the shoreline. Point (ho, Yo) is the
offshore terminus beyond which the profile does not change significantly. ...... 24

3.2 Plot of profile M7-14 from Pantai Madura, showing the selected location of
the offshore terminus. All the field profiles from the three areas are given in
A ppendix C ............................................................................................ 36

3.3 Two examples of fitting Equation 3.2 and Equation 3.29 to Madura profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed
line is for the iteration method. The log-log method is found to fit the profiles
better than iteration method for all Madura profiles. Equation 3.29 is shown
by a dotted line. ..................................................... ............................ 38

3.4 Two examples of fitting Equation 3.2 and Equation 3.29 to Surabaya profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed
line is for the iteration method. For profile S4-01, the log-log method gives a
better fit, but not for profile S5-20. However most of the Surabaya profiles
are better fitted by log-log method tahn by iteration method. Equation 3.29
is shown by a dotted line. ................................................................... 38

3.5 Two examples of fitting Equation 3.2 and Equation 3.29 to Waru profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed
line is for the iteration method. Unlike for the other two areas, the iteration
method fits all of the Waru profiles better tahn log-log method does. Fitting
of Equation 3.29 (mud profile equation) is presented by a dotted line. ....... 39

3.6 Histogram of parameters A and n for Madura profiles ............................ 40

3.7 Histogram of parameters A and n for Surabaya profiles .......................... 41

3.8 Histogram of parameters A and n for Teluk Waru profiles ...................... 42

3.9 Histogram of parameters A and n for all profiles ................................ 44

3.10 Profile scale parameter, A, as a function of sediment settling velocity, w,
Box shows the domain of values obtained for field mud profiles analyzed
by Lee (1995) and of mean values in the present study. ....................... 47

3.11 Histograms of k, and K for all field profiles examined ............................. 50

3.12 Histograms ofF and P for all field profiles examined ............................ 51

4.1 Schematic of the flumes. The two subflumes used were A and B. ................ 57

4.2 Photograph of flume with the wavemaker at the end of seaward portion
of subflumes A and B ....................................................................... 58

4.3 Schematic of sediment coring device .................................... ........... 60

4.4 Time-evolving profile for mud bottom of Run 1 ....................................... 72

4.5 Time-evolving profiles for sand bottom of Run 1 .................................... 73

4.6 Initial and final profiles of mud and sand bottoms of Run 1 ................... 74

4.7 Initial and final profiles of mud and sand bottoms of Run 2 ...................... 75

4.8 Initial and final profiles of mud and sand bottoms of Run 3 ................... 76

4.9 Schematic section showing the sedimentary formations of
multiple bars of sandy banks and of mud deposits in the
western part of the Bay of Mont-Saint-Michel (after Caline, 1994) ............... 77

4.10 Initial and final profiles of mud and sand bottoms of Run 4 ..................... 78

4.11 Initial and final profiles of mud and sand bottoms of Run 5 .................... 79

4.12 Spatial changes between surveys, for mud and sand profiles of Run 1 ......... 80

4.13 Spatial changes between surveys, for mud and sand profiles of Run 2 ......... 81

4.14 Plots of sediment mass changes for mud and sand over the profile
for all runs .............................................................................................. 83

4.15 Wave height envelope in Run 1 before and after side-wall and linear
shoaling corrections .................................................. .......................... 86

4.16 Two examples of exponential fitting (using Equation 3.18) to wave
height envelope over mud profile ......................................... ............. .. 87

5.1 Erosional and accretional stages of a coastal mud beach and associated
sedimentary fluxes ................................................... ........................... 96

A.1 Sediment samples from the Madura area ................................................ 105

A.2 Sediment samples from the Surabaya area .............................................. 106

A.3 Sediment samples from the Teluk Waru area ........................................... 106

B.1 Histograms of parameter ki and K for Madura profiles ............................ 113

B.2 Histograms of parameters F and P for Madura profiles .......................... 114

B.3 Histograms of parameter ki and K for Surabaya profiles .............................. 115

B.4 Histograms of parameters F and p for Surabaya profiles .............................. 116

B.5 Histograms of parameter ki and K for Teluk Waru profiles ......................... 117

B.6 Histograms of parameters F and P for Teluk Waru profiles .......................... 118

C.1 through C.51 Profiles M1-00 through TW-10 ............................... 119- 129

D.1 Best-fit plots of Equations 3.29 and 3.2 to mud and sand profiles,
respectively, for Run 1 .................................................................................. 130

D.2 Best-fit plots of Equations 3.29 and 3.2 to mud and sand profiles,
respectively, for Run 2 ................................................................................ 131

D.3 Best-fit plots of Equations 3.29 and 3.2 to mud and sand profiles,
respectively, for Run 3 ................................................................................ 132

D.4 Best-fit plots of Equations 3.29 and 3.2 to mud and sand profiles,
respectively, for Run 4 ................................................................................ 133

D.5 Best-fit plots of Equations 3.29 and 3.2 to mud and sand profiles,
respectively, for Run 5 .................................................................................. 134

E.1 First mode of temporal and spatial eigen functions for Run 2 ..................... 138

E.2 Second mode of temporal and spatial eigen functions for Run 2 ................... 139

E.3 First mode of temporal and spatial eigen functions for Run 3 ....................... 140

E.4 Second mode of temporal and spatial eigen functions for Run 3 .................... 141

LIST OF TABLES

2.1 Hydrodynamic Characteristics of Pantai Madura, Surabaya, and Teluk
W aru ................................................................ .................................... 16

3.1 Mean values of the three parameters in Equation 3.29 for each study area ......... 52

3.2 Values of parameters in Equation 3.29 for erosional and accretionary
profile configurations using K= 0.15 as the demarcation value .................. 53

3.3 Results of profile divisions into erosional and accretionary configurations
(after Lee, 1995) using K = 0.15 as the demarcation value ...............................
53

4.1 Summary of test conditions .................................................................... 62

4.2 Results of mud density measurement ....................................... ............ 67

4.3 Results of fitting Equation 3.2 to final sandy profile data from laboratory
experim ents ........................................................... ................................ 84

4.4 Results of fitting Equation 3.29 to final mud profile data from laboratory
experim ents ........................................................... ................................ 85

4.5 Wave attenuation coefficients (k,) obtained from exponential fitting of
Equation 3.5 to the measured wave height envelopes in each run ................ 88

5.1 Summary of test results for mud profiles .................................... ........... 95

A.1 Grain size characteristics of Madura and Surabaya study areas ..................... 103

A.2 Grain size characteristics of the Teluk Waru study area ................................ 104

A.3 Grain size characteristics of all the three areas from sieve analysis
conducted at the Coastal Engineering Laboratory of the University
of Florida .................................................................................................... 105

B. 1 Results of least squares fit of Equation 3.2 for Madura profiles ................... 107

B.2 Results of least squares fit of Equation 3.2 for Surabaya profiles .................... 108

B.3 Results of least squares fit of Equation 3.2 for Teluk Waru profiles .............. 109

B.4 Results of least squares fit of Equation 3.29 for Madura profiles .................. 110

B.5 Results of least squares fit of Equation 3.29 for Surabaya profiles ............... 111

B.6 Results of least squares fit of Equation 3.29 for Teluk Waru profiles .......... 112

LIST OF SYMBOLS

A = Profile scale parameter in Equations 3.1 and 3.5

b = Width of subflume

c(t) = Temporal eigen function

C, = Nearshore depth correction

dso = Sediment median size

d(y) = Spatial (offshore distance) eigen function

De = Equilibrium value of wave-mean rate of energy dissipation per
unit water volume

erm = Root-mean square error

Eeq = Equilibrium value of wave-mean rate of energy dissipation per
unit bed area

F = Bottom slope at the shoreline in Equation 3.29

Fs = Beach slope in Equation 3.34

g = Acceleration due to gravity

h, h, = Water depth; water depth at any point along the profile length

hmn = Profile measurement at the m-th location and n-th time in Equation D. 1

h, = Depth at the seaward terminus of the profile

h, = Predicted depth

h = Non-dimensional water depth

H = Wave height or matrix of time-varying profile data in Equation D. 1

H, = Breaking wave height

Hf = Corrected wave height

Ho = Incident wave height/Deep water wave height

I, j = Index for direction

k, = Wave attenuation coefficient

ko = Wave number

k, = Shoaling coefficient

k,, = Wave attenuation coefficient due to side-wall friction

k1 = Profile averaged wave attenuation coefficient

K = Non-dimensional wave attenuation parameter

m = Exponent in Equation 3.2

N = Number of measured profile data points

Re, = Wave Reynolds number

t = Time

T = Wave period

wi = Weighting factor in Equation D.2

w, = Sediment fall velocity

y = Horizontal axis normal to the shoreline located at the
mean water level, or offshore distance

y, = Offshore distance at any point along the profile length

y, = Offshore distance at the offshore terminus or profile length

9 = Non-dimensional value of the y-coordinate

p = Parameter characterizing depth correction due to wave breaking and related
effects in Equation 3.29

A = Eigen value

F = Wave energy flux

K = Spilling breaker index

p, = Water density

Pd = Dry density of mud

pf = Fluid mud density

o = Angular wave frequency in radians

v, = Kinematic viscosity of water

At = Time increment

Ay = Distance between two adjacent measuring stations

Abstract of Thesis Presented to Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

AN EXAMINATION OF THE DEPENDENCE OF MUD SHORE PROFILES
ON THE NEARSHORE ENVIRONMENT

By

A. P. Mulia Tarigan

May 1996

Chairman: Dr. Ashish J. Mehta
Major Department: Coastal and Oceanographic Engineering

A preliminary study has been carried out to examine the nature of beach profiles

composed of fine-grained sediment and their response to wave forcing. The well known

power-law equation for sandy profiles and a recently developed profile equation for muddy

shores have been best-fitted to fifty-one fine-grain dominated profiles from Indonesia. It is

shown that the second equation provides a better profile representation because of the very

flat profile slopes, and because the profiles do not always show concavity characteristic of

sandy shores.

A previous observation, based on an analysis of the response of muddy coast profiles

to oceanic forcing, is further explored in laboratory tests. This observation is that when a

muddy profile erodes, the resuspended material, with a low settling velocity and relatively

easy transportability, neither necessarily forms an offshore bar characteristic of sandy beaches,

nor necessarily remains within the active profile length. Profiles composed of clayey mud

beds were prepared and a thin blanket of fluid mud was initially poured uniformly over the

profiles. These profiles were then subjected to suitably high and low monochromatic waves.

Fluid mud caused the incoming waves to dampen measurably with a comparatively low

degree of breaking restricted to the very nearshore region. In a test with high incident waves,

after several hours the fluid mud flowed offshore to the flume bottom, where it deposited

uniformly without significant surface features. Also, wave breaking became more intense as

the fluid mud layer was depleted. In a test with low waves the fluid mud was largely retained

on the profile, with some erosion in the proximity of the shoreline. Wave damping continued

to remain significant throughout the test. In contrast to these tests, other tests carried out

with profiles composed of very fine sand under the same wave conditions as those for muddy

profiles showed behaviors characteristic of sandy profiles.

The above observations suggest that for a muddy profile to prograde, suitably low

waves, and most importantly, a source of sediment that is not necessarily within the active

profile length may be required. This source can be alongshore, or from land drainage, or

from a distal offshore site. Also, the erosional and accretionary cycles of muddy shores

appear to be related to the concavity and convexity of the shore profiles, respectively. If this

observation is borne out by further studies, it will require the development of a new

methodology for calculating the rates of recession of muddy shoreline, e.g., due to sea level

rise.

xvii

CHAPTER I
INTRODUCTION

1.1 Problem Statement

Since a relatively large fraction of the world's growing population resides in the

coastal zone (Graff, 1991; Yuwono, 1993), the task of coastal engineers to deal with

problems related to the intensive use of zones bordering the seas and the oceans demands a

better understanding of shoreline erosion and accretionary processes. The fight against

shoreline retreat is a worldwide issue that requires knowledge of the behavior of beach

profiles responding to natural forces, such as water waves, storms and sea level rise, as a

fundamental step toward problem solving.

The study of profile dynamics has been a matter of considerable interest in engineering

practice, and has led to the development of many theories and formulas that describe two-

dimensional cross-shore sediment transport and beach profile geometry. However, most of

the applications of such formulas have been confined to coarse-grained, e.g. sandy, profiles,

even while many of the coastal areas are composed of fine-grained (silt and clay) sediments.

It is also the case that in the coastal zone the sedimentary environment often comprises of

mixtures of sand and mud (Torfs, 1995). Thus, with respect to the assessment of profile

characteristics, a better knowledge of the nature of mud profile geometries should provide

a more rational basis for assessing shoreline changes than at present.

2

Field and laboratory evidence supports the conclusion that the nature and dynamics

of beach profiles composed of mud are different from those of coarse-grained profiles such

as those composed of sand. A sandy profile can be largely characterized by the variation of

sediment size across the profile length, whereas muddy profiles are more difficult to deal with

due to the complex properties and transport behavior of fine-grained material. As a result,

the task of analyzing the characteristics of mud profiles is considerably more complicated than

that of sandy profiles.

A common feature of sandy profiles is the seasonal profile change according to the

weather cycle, i.e., fair and severe sea conditions. During fair sea conditions with relatively

low wave heights and long periods that typically occur during summer, shoreward sediment

movement prevails and produces an accretionary profile. Summer shore profiles are generally

marked with gentle nearshore sand bars and relatively flat foreshore. During severe sea

conditions in winter, storm waves cause offshore sediment movement, thus eroding the

shore. The nearshore sandbars move offshore and, along with the material deposited

offshore, form one or more relatively larger bars in deeper waters. At the same time, the

foreshore becomes steeper and narrower than in summer.

The seasonal profiles can be considered to be in dynamic equilibrium when averaged

over some suitable time-scale over which wave forcing can be assumed to remain reasonably

unchanged. Based on the findings by, among others, Bruun (1954), Dean (1977), and

Kaihatu (1990), it is observed that the equilibrium shape of sandy profiles is typically

concave-upward. Furthermore, for some applications it is found reasonable to assume that

the profiles do not change their shape in response to a rise in sea level due to storm

3

conditions, eustatic change, or subsidence, and that cross-shore sediment transport is the

prevalent profile changing mechanism. As a result, the sand volume over the active profile

is also considered to be conserved. Thus, for example, according to the well known Bruun

Rule (Bruun, 1962; Bruun, 1983) for predicting the rate of shoreline recession due to an

increase in sea level, the profile is to be shifted upward (by a height equal to the sea level

rise) and then landward (so that the volume of material eroded from the foreshore equals that

deposited offshore, up to the depth of closure) by the distance equal to the shoreline retreat.

Normal profile

Storm profile

Figure 1.1: Typical normal and storm profiles along a sandy shoreline

Field observations suggest that when a mud shore erodes under high waves, the

eroded material does not necessarily deposit in sufficient proximity to be potentially available

to rebuild the profile naturally under low waves. This behavior thus contrasts with that

characteristic to a sandy profile, for which beach mass balance can be represented

geometrically in terms of the equal areas associated with "normal" and "storm" profiles as

4

shown in Figure 1.1. In the mud environment, the equal area description does not always

apply because an offshore bar within the active profile zone containing the entire mass of

resuspended eroded sediment does not necessarily form. There are two reasons for this: 1)

the settling velocity of resuspended material being very low, it is carried to alongshore or

offshore sites that are considerably remote from the profile, and 2) when the eroded material,

that is transported as suspended load settles, a bar-like undulation does not necessarily

develop due to the natural tendency of sediment to deposit in a relatively uniform manner.

-9 Western Site
Profile in 1984
- Profile in 1980
-12
-100 0 100

200 300 400 500 600
offshore distance from baseline (m)

Figure 1.2: Long-term profile change along a glacial till profile at Grimsby, Lake Ontario,
Canada (after Coakley et al., 1988)

In fact, at mud shores all the eroded sediment may be "lost," as shown by the example

in Figure 1.2 ofprofile changes in a highly consolidated glacial till profile along Lake Ontario.

700 800 900

5

When the till erodes, it can not reconstitute itself and the fine material is transported to distal

sites (Bishop et al., 1992). Figure 1.3 plots elevation changes with distance along a mud

profile near Cheniere au Tigre in southwestern Louisiana, based on two surveys (Kemp,

1986) of the profile over a five month period in 1981 ranging from winter (i.e., storm

conditions in February) to summer (i.e., normal conditions in July). Note the lack of full

recovery, as indicated by the unequal areas below and above the zero change line. Erosion

outweighed accretion most probably because of a lack of sediment supply, despite the

occurrence of conditions conducive to deposition and accretion during the summer months.

05

0.4

03
shoreward saward
02
U

0.0

-0 1

-0.3

-0.4 -denotes erosion
+ denotes accretion Period From 2/13/81 (Profile No. LK71) to 7/29/81 (Profile No. LK73)
-0.5 ,
-60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240

Offshore Distance, y (m)

Figure 1.3: Spatial changes between periodic surveys for a mud profile along the
southwestern Louisiana chenier plain (after Lee, 1995)

6

Results from tests in laboratory flumes can be interpreted to demonstrate trends akin

to those in the field. As shown by the profiles obtained at different times in Figure 1.4, when

a beach composed of a mixture of attapulgite and kaolinite clays and of an initially uniform

slope eroded, the material was transported beyond the active profile in deeper zone (Lee,

1995). As a result, a substantial sedimentary imbalance occurred. In contrast, a test carried

out under the same conditions of initial beach slope, water depth (h), wave height (Ho) and

wave period (7) using a cohesionless loess showed a considerably closer balance, as observed

in Figure 1.5.

01 00i i
-- t=0.7hr Run I (AK mud)
0.00 T = 1.3 s
St 4.6hr Ho 12cm
0.060 -- t=21.9 h=0.6m
shorewrd seaward
040 t=44.3hr

g 0.020
CL
oIooo v -
o 000

S-0.020
"-- -0,040

-0.060

-0 080 denotes erosion
+ denotes accretion
-0.100 I I I I I I I I l l i I
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Distance along Flume (m)

Figure 1.4: Spatial changes between periodic surveys for a clayey mud profile in a
laboratory flume (after Lee, 1995)

0.100 1 I I .II I I I I
St=- 07hr Run 1 (Loess
0.080 t-46hr H12

0060 t=21.9hr s ewad seward h-0.6m
U -- t-=44.3hr
S 0.040

0 0040
0.020

denotes erosion
-0.080
+ denotes accretion
-0.100 I I I .II Ii I i A
0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23
Distance along Flume (m)

Figure 1.5: Spatial changes between periodic surveys of a profile composed of a
loess in a laboratory flume (after Lee, 1995)

While the above test results neither comprehensively nor unequivocally demonstrate

the characteristic behavior of mud profiles under wave action, they do make a point that since

the sediment transported away during erosion may not be "recoverable" as it can be in the

case of a sandy profile, one or more sources of suspended sediment external to the active

profile may be required to build up the mud profile.

1.2 Objective and Scope

Based on the above observations, the goal set for this study is to examine different

features of mud profiles and their dynamics in relation to characteristic features of sandy

profiles and their response to wave forcing. The most important aspect is related to profile

8

shape and cross-shore sediment budget as would be required, e.g., for the application of the

Bruun Rule. Specifically, the two following issues are studied: 1) the shape of mud profiles

and their response to wave forcing, and 2) role of sediment supply in governing profile

erosion/accretion. To examine these issues, field data from three different coastal areas are

first examined. Then, laboratory experiments are conducted to test the influence of waves

and sediment supply, so that the behavior of the profile changes in time toward either erosion

or deposition can be recorded and analyzed. Finally, conclusions concerning the applicability

of Bruun Rule for mud shores are given.

1.3 Outline of Presentation

Chapter 2 describes the selected coastal locations and information on the

hydrodynamic and sedimentary environments of the areas. Chapter 3 reviews profile

equations used in this study. Results of profile fitting and a discussion of the characteristics

of field profiles are then presented. Chapter 4 deals with laboratory experiments. The

characteristics of measured profile changes are discussed in detail, and differences between

mud and sand profiles are further examined. Chapter 5 presents and discusses the findings

of this study in terms of erosional and accretionary cycles at muddy coasts, and the

applicability of Bruun Rule is reviewed. This chapter ends with concluding remarks and

recommendations for future studies.

CHAPTER 2
FIELD INFORMATION

2.1 Site Descriptions

Three beach sites were selected for the purpose of obtaining field information: 1)

Pantai Madura, i.e., Madura coast, 2) Pantai Surabaya, and 3) Teluk Waru, i.e., Gulf of Waru.

These beaches are located on the south coast of eastern Madura, north coast of eastern Java,

and west coast of Lombok, respectively. They were chosen because they are characterized

by different hydrodynamic and sedimentary environments, and also due to the availability of

data from the sites.

SOUTH CHINA SEA PACIFIC OCEAN

k P, KAPANT|I O
s ao. I DI N OC AN I
RAL 0

A = LOCATIONS OF PANTAIMADURA AND SURABAYA
B = LOCATION OF TELUK WARU
A LOCATIONS OF PANTAIMADURA AND SURABAYA

Figure 2.1: Map of Indonesia. Locations of Pantai Madura, Surabaya, and Teluk Waru are
indicated by the letters A and B with arrows pointing to the areas.

9

10

Figure 2.1 shows the Indonesian archipelago, which consists of approximately 13,800

large and small islands. The combined shoreline of the islands stretches to about 81,000 km

in length. Although most of the islands are small and sparsely populated, 75% of Indonesia's

cities, which contain more than 100 million people, lie in coastal areas (Yuwono, 1993). Java,

Madura, and Lombok, where the selected coastal sites are located, are comparatively large

and densely populated. Overall, the present coastline of these islands became established

about 6,000 years ago, at the end of the major phase of Holocene marine transgression

(Hoekstra, 1993).

Figure 2.2 : Locations ofPantai Madura and Surabaya. Both are in the vicinity of an area
(enclosed by the rectangle) designated for a proposed bridge connecting the two islands.
Pantai Madura is on the Madura side of the area, while Pantai Surabaya is on the Surabaya
side.

11

The areas of Pantai Madura and Surabaya (Figure 2.2) examined are situated

approximately 3 to 5 km across from each other with Madura Strait in between. A 1991

Indonesian government plan purposed building a bridge for Madura-Surabaya transportation

across Madura Strait. Following the plan, geologic, hydrographic, and oceanographic

investigations were executed from April 1991 to end of June 1991 as a part of the feasibility

study of the area. The area, located about 70 10' to 70 13/ northern latitude and 1120 46'

to 1120 47' eastern longitude, is approximately 20 km2. Bathymetric, sedimentary and

hydrodynamic information used in the present study is based on reports of these investigations

(BPP Teknologi and Pusat Pengembangan Geologi Kelautan, 1991; BPP Teknologi and

Lembaga Penelitian Institut Teknologi Bandung, 1993). Figures 2.3 and 2.4 show the

respective beach sites.

...... .........

^ >ts ." i'' '* i, '- .' _,

Figure 2.3: Photograph of the study site in Madura taken on August 13, 1994. The shoreline
is in Kecamatan (village) Labang of Kabupaten (county) Bangkalan-Madura.

12

-F-

Figure 2.4: Photograph of the study site in Surabaya taken on August 13, 1994. The
shoreline is in Kecamatan (village) Kenjeran of Kabupaten (county) Surabaya.

Pantai Teluk Waru (Figure 2.5) is located in a western embayment of Lombok Island,

east of the famous Bali Island. Due to its strategic location for supporting marine (shipping)

transportation in the eastern part of Indonesia, this site was proposed as a location for

dockyards. A hydro-oceanographic survey was conducted from May 13, 1993 to June 5,

1993. The surveyed area, located in the vicinity of 80 45' southern latitude and 1160 04'

eastern longitude, was about 1 km2. Information used in the present study is based on the

survey report (BPPT Survey Team, 1993; Anantasena et al., 1994). Figure 2.6 is a site

photograph of Teluk Waru.

Figure 2.5: Teluk Waru site (Amsari, 1994). This site is located about 50 km south of
Mataram, the capital city ofNusa Tenggara Barat Province. Lembar, a small natural harbor
just north of Teluk Waru, can be reached easily by boat from Bali. The rectangular area
indicates the region surveyed.

Figure 2.6: Photograph of the study site in Teluk Waru taken on May 19, 1993. The
shoreline is in Desa (village) Teluk Waru of Kabupaten (county) Labuhan Tereng Lombok
Barat.

2.2 Hydrodynamic Information

Wave characteristics in Pantai Madura and Surabaya were predicted from wind

conditions available for these areas using the well known empirical method of Svedrup,

Munk, and Bretschneider (BPP Teknologi and Lembaga Penelitian Institut Teknologi

Bandung, 1994). Based on 10-year statistics of wind data, the maximum wave height was

shown to reach up to 2.1 m with a period of 8 seconds. The dominant wave height (with

probability greater than 50%) was in the range of 0.2 to 0.8 m with a period of 3 to 6

seconds.

15

Unlike Madura and Surabaya, wind data are not available for Teluk Waru, and

probably due to the typically low wave heights (less than 0.2 m), no wave measurements

have been conducted. The comparatively calm wave conditions coupled with a relatively

steep sea bottom slope toward offshore contours (from 3 m up to 15 m deep) may explain

why this site was the preferred location for dockyards. However, in Lombok Strait, severe

wave conditions do occur during the wet monsoon. If these severe waves are taken into

consideration, and if they do enter the embayment, maximum wave heights may possibly reach

2 m.

The tidal regimes in the coastal waters of Madura and Surabaya are similar to those

in the embayed waters of Teluk Waru. The tides have a mixed character with predominant

semidiurnal constituents. It can be seen from Figure 2.2 that the geometry of Madura Strait

resembles an open bay with the head on the western side. The incoming tidal wave (from east

to west), which originates from a typically predominant diurnal type of tide, may experience

superposition due to the reflection of tidal energy. This would result in a forced standing

oscillation increasing the contributions of semidiurnal constituents. Hoekstra (1993) found

that the amplitudes of the semidiurnal constituents (M2 and S2) exhibit an increase towards

the head of the bay by more than 100%, and concluded that the bay of Madura Strait acts as

a quarter-wave resonator for semidiurnal tides.

The spring tidal range for both coastal areas of Madura and Surabaya is 2.4 m and

based on 15-days of tidal measurements (BPP Teknologi and Pusat Pengembangan Geologi

Kelautan, 1991). Current measurements showed that the tidal current in the Surabaya area

varies from 0 to 0.7 m/s during spring tide, and a maximum current with magnitude of 1.0

16

m/s was measured during neap tide. In the Madura area the tidal current varies from 0 to 0.8

m/s with no significant differences between spring and neap tide. In Teluk Waru, based also

on the same 15-days of tidal measurements, it was found that the spring tidal range is 1.6 m

(BPPT Survey Team, 1993; Amsar, 1994). Tidal current in this coastal area varies between

0 to 0.10 m/s during spring tide and 0 to 0.06 m/s during neap tide.

From their geographical positions, it can be seen that the selected beaches are not on

open coasts. Due to their protected state, they are not subjected to large waves from open

seas, such as the South China Sea or the Indian Ocean. On the other hand, large rivers from

the hinterland, such as B. Solo and Brantas as shown in Figure 2.2, flow toward the north

coast of eastern Java. In Teluk Waru, S. Bagong and S. Sekotong empty into the embayed

coastal waters as shown in Figure 2.5. Hence, tidal and estuarine processes coupled with

seasonal wind generated waves appear to be the significant hydrodynamic factors at the three

sites. Table 2.1 summarizes information collected on the hydrodynamic characteristics of the

locations.

Table 2.1: Hydrodynamic Characteristics of Pantai Madura, Surabaya, and Teluk Waru.

Location Spring Tidal Maximum Wave Wave Period Tidal Current
Range (m) Heiht (m) (second) (m/s)
Pantai Madura 2.4 1.7 2.1 5 8 0.0 0.8

Pantai Surabaya 2.4 1.7 2.1 5 8 0.0 1.0

Pantai Teluk Waru 1.6 2 8 0.0 0.1

2.3 Sedimentary Characteristics

The surficial sedimentary material covering the Madura and Surabaya sites ranges

from about 80% clay to 100% sand. The textural classification for sediment samples from

Madura and Surabaya is shown in Figure 2.7 and is based on grain size analysis of beach

sediment samples taken at 21 different sampling stations (see Tables Al and A3 in Appendix

A). Fifteen samples were from the Surabaya side and six from the Madura side. The data

points seem to fall into two distinct clusters: 1) a large cluster featuring mixed sand-silt-clay

sediment with predominant clay fraction, and 2) a small cluster of sand dominated sediment.

In fact, it was stated in the report of the feasibility study (BPP Teknologi and Pusat

Pengembangan Geologi Kelautan, 1991) that the sediments in the Madura and Surabaya

coastal waters consist of silty mud and poorly graded sand.

The lithology of the deposits in the Surabaya area can be categorized into 5 different

classes: 1) flood plain deposits, 2) recent-Holocene nearshore deposits, 3) beach ridge

deposits, 4) old river deposits, and 5) marine deposits (BPP Teknologi and Pusat

Pengembangan Geologi Kelautan, 1991). Flood plain deposits are characterized by soft and

moist clay. The thickness of this type of deposits is on the order of 1 m. Recent-Holocene

nearshore deposits are characterized by a variation between soft clay and sandy clay (with a

range of fine to medium sand) accompanied by high contents of minerals and mollusks. This

class covers the upper layer of sediment with about 10 to 19 m thickness. Beach ridge

deposits are characterized by medium to coarse sands with a high content of minerals and

mollusks. These deposits are 2 to 3 m thick below the recent-Holocene nearshore deposits.

18

Old river deposits and marine deposits are found at more than 10 m depths. They are

characterized by a higher solidity compared to that of the other three deposits.

Hoekstra (1993) noted that the northern shoreline of Java has changed considerably

in the last 5,000 6,000 years, since its establishment. He found that in many places along

the coast significant coastal progradation has occurred as a result of sediment flux from the

hinterland. The layer of 1 m of flood plain deposits found in the Surabaya side is an indication

of coastal progradation due to these deposits.

No such classification is available for the Madura coastal area, although clayey and

sandy materials with contents of mollusk are found there. The submerged lithology in

Madura is distinguished by a high content of rock layers. Clayey, silty and sandy rocks that

are frequently composed of limestone are typically found below the upper layer sediments.

Also, the composition of rocks in some locations indicates the presence of a fault.

Similar to the Madura and Surabaya areas, the textural classification ofTeluk Waru

profile sediments is depicted in Figure 2.8, also based on a grain size analysis of surficial

samples taken at 19 different sampling stations (see Tables A2 and A3 in Appendix A). As

a result of the grain size analysis, it was reported (Anantasena et al., 1994) that fine-grained

sediment, with a grain size of 7.53 to 8.20 phi (0.0034 to 0.0054 mm), covers 80% of the

surveyed area. However, the sediment distribution has two distinct clusters. As shown in

Figure 2.8, the larger cluster featuring a mixture of sand, silt and clay is skewed toward the

fine-grained size range.

2.4 Beach Profiles

Beach profiles were taken from the bathymetric maps of the study areas surveyed

under supervision of Badan Pengkajian dan Penerapan Teknologi (BPP Teknologi). BPP

Teknologi, the Subproject of Study Tri Nusa Bima Sakti covered the Madura-Surabaya area,

and BPP Teknologi, Directorate of Technology of Natural Resources Inventory, covered the

Teluk Waru area. The bathymetric maps were digitized from the shoreline to selected

offshore contours for determining the profiles. Linear interpolation was made between

contours whenever necessary. For most profiles, the deepest offshore depth selected was 5

m. For Pantai Madura, 21 profiles were chosen approximately 150 m apart and designated

as M1-00, MI-01 to M1-09, and M7-10, M7-11 to M7-20. With the same spacing, 20

profiles were chosen for Pantai Surabaya, designated as S1-01 to S1-09, and S4-10 to S4-20.

For Teluk Waru, 10 profiles approximately 250 m apart were designated as TW-01, TW-02

to TW10. All the profiles are presented in Appendix C. Figures 2.9 and 2.10 sketch the area

maps with numbered profiles for the Madura-Surabaya area and the Teluk Waru area,

respectively.

In general, the bottom topographic contours at all the three areas have a tendency to

be parallel to the shoreline, and most of the profiles taken have mild slopes and convex-

upward profiles. However, in the Madura area, the irregularity of the bottom topography is

marked, most likely due to the presence of a rocky substrate. Also, on the Surabaya side of

Madura Strait the slope of the profiles markedly increases toward the west (the head of the

bay of Madura Strait). While in Teluk Waru, an increase in slope of the mud profiles is due

to the increasing fraction of sand. A more detailed discussion regarding the profiles is given

in Chapter 3.

100% clay

100% sand

100% silt

Figure 2.7: Textural classification of sediment for beach profiles from Madura and Surabaya.
Data points represent median particle size. Circles are for samples from Surabaya, and
rectangular points are from Madura. Data points for both areas are clustered by open ovals,
indicating that the sediment can be classified in two dominant size ranges.

100% clay

100% sand

100% silt

Figure 2.8 : Textural classification of sediment for beach profiles from Teluk Waru. Circles
represent the median particle size. Two open ovals cluster the data points into two
dominant size ranges.

Pantai Madura

M7-20
M1-06 M7-18
M1-00 M1-0OM7-10 M7-14M7"16
M1-02 M1-04 M7-12

0 sOm Madura Strait t

S4-0

i-i"
L''.

S4-01

S4-03

S4-07 Madura
Q +Ir ;+

, LI ,L I,
S4-09

S4- 1

"$5- -17

Pantai Surabaya

0 500 m

Figures 2.9: Sketch showing beach profile lines at Madura and Surabaya. Dashed lines from
the shoreline toward offshore represent profiles. Lengths of profiles depicted do not reflect
the actual lengths digitized. Numbers 1 and 7 following letter M for Madura profiles, and
4 and 5 following letter S for Surabaya profiles are associated with the sheet numbers of the
bathymetric maps.

,/,

Figure 2.10: Sketch showing Teluk Waru profile lines. Dashed lines from shoreline toward
offshore represent the profiles. Lengths of profiles do not in general reflect their actual
lengths digitized.

CHAPTER 3
PROFILE ANALYSIS

3.1 Introduction

The understanding of the dynamics of natural beach profile fluctuations suffers from

the complexity of the interaction between sedimentary materials constituting the profiles and

the forces acting on them. Nevertheless, the concept of an equilibrium beach profile has been

proven to be a useful tool in examining profile changes due to wave action. Under the

premise of a balance of the forces acting on the profile, it is considered that an equilibrium

shape of the profile will be achieved. Since in nature the profile responds continuously to the

changing nearshore forces, the equilibrium profile should be considered to be a dynamic

quantity (Dean and Dalrymple, 1995).

-, y

(0,
h(y)

(h, y,)

(ho, Yo)

Figure 3.1: Two-dimensional beach profile showing the coordinates adopted. Point (0,0) is
the shoreline position, and (h,, y1) is a profile point denoting an arbitrary position with depth
hand distance y, from the shoreline. Point (h, yo) is the offshore terminus beyond which the
profile does not change significantly.

As far as the study of equilibrium beach profiles is concerned, natural profiles may

be classified as: 1) coarse-grained profiles and 2) fine-grained profiles. Coarse grained profiles

are typically sand (cohesionless) dominated, with size of sand ranging from fine to coarse

sand. On the other hand, fine-grained profiles are typically mud dominated in size, ranging

from silt to clay. The two types of profiles can be disthinguised not only from their different

sedimentary characteristics, but also from their mechanics of sediment transport, which result

in different profile responses to the prevailing hydrodynamic forces.

The shore-normal beach profile depicted in Figure 3.1 can be expressed as

h = h(y) (3.1)

where h is the water depth and y is the offshore distance from the shoreline. Intuitively, if

h(y) in Equation 3.1 is a representative model of the profile geometry of the actual profile,

it should involve one (or more) physical parameters) that represent the physical processes

which mold the profile. Many investigators have proposed various expressions of profile

models, ranging from the most simplistic linear relationship to complicated empirical and/or

theoretical relationships; some of them are mentioned by Bodge (1992). Lee (1995) tabulated

many of the profile equations in terms of the forms of the equations (power, exponential and

logarithmic), sediment size (sand and rock), the development basis (theoretical, laboratory

and field), and the investigators.

26

3.2 Coarse-Grained Profile Equation

A well known coarse-grained profile equation was proposed by Bruun (1954) and

Dean (1977), and has the power form

h = A y (3.2)

where A is a profile scale parameter and n is an empirical exponent. Bruun (1954) examined

beach profiles from the Danish North Sea coast and from Monterey Bay in California, and

found that n has a central value of 2/3. Dean (1977) applied Equation 3.2 to 504 beach

profiles collected by Hayden et al. (1975) along the U.S. east coast and the Gulf of Mexico,

and also concluded that n is centered at 2/3. Most recently, Charles (1994) investigated

Equation 3.2 using 207 profiles from Florida's east coast, and found that n = 0.67 is a good

representative value for the profiles.

Dean (1977) further found that Equation 3.2 would result from considering the

equilibrium state of (constructive and destructive) forces through a uniform wave energy

dissipation argument. In fact, the central value ofn = 2/3 is in agreement with the equilibrium

beach profile resulting from uniform wave energy dissipation per unit volume Dq expressed

as

df
Deq- dy (3.3)

where F is the wave energy flux. It is important to note that the concept behind this

development is based on the assumption that the turbulence in the surf zone created by

breaking waves is responsible for the wave energy dissipation. Using shallow water linear

27

wave theory (Dean and Dalrymple, 1984) for energy flux, i.e., F = pgH2'vgh, and
8
assuming a spilling breaker in terms of wave height H and breaking index K, i.e., H = K h, it

can be shown that Equation 3.3 is simplified to:

h = A y2/3 (3.4)

where A is given by

A=( 24 e)3/2 (3.5)
5pg3/2K2

with g and p representing gravitational acceleration and the density of the water, respectively.

Furthermore, De has the form

D,,q = [ 3/22] h 1/2 (3.6)
16 dy

which indicates that wave energy dissipation is related to the slope of the profile dh/dy, which

thereby indirectly relates to the grain size of the beach profile. Dean (1990) postulated that

Dq represents wave energy dissipation rate per unit water volume under which a sediment

particle of a given size is stable. Therefore A can be expected to be related to the grain size.

In this respect, Moore (1982) developed an empirical relationship between A and grain size.

As a consequence, Equation 3.4 can be considered to mean that for a beach profile composed

of a given sediment size there should be a corresponding A, and that the water depth should

be proportional to the distance offshore to the two-thirds power, thus forming a concave-

upward curve.

28

For the purpose of examining the relationship between the shape of field profiles and

the sedimentary environment described in Chapter 2, Equation 3.2 is used instead of Equation

3.4. Whether field profiles have concavity characteristic of sandy shores is a matter of interest

here. Note that the profile shape exhibited by Equation 3.2 can be concave upward when n

< 1, convex upward when n > 1, and linear when n = 1.

Two methods of profile fitting based on the least squares principle are used in this

study in order to determine the n and A parameters that provide the best approximations to

the measured profiles. The first method, which may be called the log-log method, is

performed by first linearizing Equation 3.2, i.e., taking the logarithm of each side of the

Equation 3.2:

Inh = InA + n Iny (3.7)

Substituting X = Inh, B = InA and Y = Iny, Equation 3.7 can be rewritten as a linear

equation

X = nY + B (3.8)

Applying the least squares method, i.e., minimizing the objective error Eob given by

Eob = (X, nY B)2 (3.9)

the best (least squares) fit of n and B can be established from

Zr,Y -(Y)(LX)
N
n = (3.10)

N

B = X nY (3.11)

where N= number of data points, X = -X,, and Y = lY. The scale parameter A
N N '
is then obtained from Equation 3.11, i.e.,

A = eB (3.12)

It is necessary to note that the expression of the summation of the square errors e for

Equation 3.2 is different from the objective error Eob expressed in Equation 3.9. The

quantity E is given by

E = (h, A y,")2 (3.13)

where hi denotes the measured water depth at the position y,.

The second method, which may be called the iteration method, is similar to the

Newton-Raphson method for calculating the roots of equations. Using Taylor Series

expansion, Equation 3.2. can be rewritten as

6h 9h
h = A y" + AA +- An (3.14)
9A on

30

Similar to Equation 3.9, the objective error Eob is given by

eOh ch.
ob = (h, A y" AA - An)2 (3.15)
dA an

9h,
Applying the least squares method, i.e., minimizing eob, and substituting = yin and
BA
9h
h, Iny leads to
an

aEb = (-h, + Ay,") y," + AA O(yn)2 + An y y (h, Iny) = 0 (3.16A)
aAA

= (-h, + Ay,") y,n + AA (h, Iny,) + An (y,2= 0 (3. 16B)
aAn

which are linear, and solvable for the two unknowns AnandAA with given initial values of

n and A. Equations 3.16A and 3.16B are then iterated with improved values of A and n which

can be expressed as

Ak+1 = Ak + AA k (3.17A)

nk1 =n k + An (3.17B)

where superscripts k and k+1 denote values at the kth iteration and (k+J)th iteration,

respectively. This iterative procedure will converge to a minimum value of e given by

Equation 3.13, at which the best fit values of A and n are obtained.

31

3.3 Fine-Grained Profile Equation

As mentioned earlier in this chapter, fine-grained profile response to hydrodynamic

forces is different from that of coarse-grained profiles. There have been few systematic

studies examining the behavior of natural fine-grained profiles. In fact, the manner in which

fine-grained profiles respond to wave forcing is not well understood, and is just beginning to

be dealt with in analytic terms (Lee and Mehta, 1996). In the present study, the mud profile

geometry due to Lee (1995) is used as the counterpart of the power form (Equation 3.2) for

sandy profiles.

Lee (1995) argued that wave breaking is not always the primary energy sink within

the surf zone for mud profiles, and postulated that instead it is the viscous effects in mud that

mainly dissipate the wave energy. Hence, he developed a mud profile geometry by first

stating wave energy dissipation in terms of the well known exponential decay law for wave

height due to viscous effects as

H(y) = Ho e -k'0 y) (3.18)

where Ho is the incident wave height at y = yo, kI is the wave attenuation coefficient and yo

is the seaward end of the active profile length (Figure 3.1). Next, similar to the development

of Equation 3.4, this decay law is substituted into the expression for uniform wave energy

dissipation per unit area Eeq (as opposed to unit volume)

dJF
Eeq (3.19)
dy

leading to

pgl3/2H2 d -2k(yo Y)h 1/2) = Eeq
8 dy

or

d -2k(ily-h 1/2 8Eeq
ay pg3/2HO2

Integration of Equation 3.21 yields

S-20-k,0 Y) h 8Eeq
pg3/2H2

(3.20)

(3.21)

(3.22)

Lee (1995) pointed out that k, may vary withy across the profile, and defined a representative

average value k1, corresponding to the equilibrium value of energy dissipation. Equation 3.22

can then be rewritten as

e-2(yo h 1/2] 8Eeq
pg 3/2HO2

(3.23)

At the offshore terminus (ho, yo), Equation 3.23 can be expressed as

H02 8Eeq Y
Spg 3/2h/2

(3.24)

33

Eliminating H02 between Equation 3.24 and Equation 3.23 yields the profile geometry

h = h ) (3.25)

which can be conveniently non-dimensionalized according to

h = e4K(1-) 92 (3.26)

where y = ylyo, h = h/ho, and K = ki yo is a non-dimensional wave attenuation parameter,

which scales k1 by the length of the profile, yo.

Lee (1995) found that Equation 3.25 did not fit field data well in the nearshore portion

of profiles, and indicated that wave dissipation mechanisms other than those arising from

wave energy absorption by mud, e.g., turbulence due to wave breaking, were responsible for

the discrepancy. To cope with this problem, Lee (1995) added an empirical nearshore depth

correction term, CN

C = Fye (3.27)

to Equation 3.25 resulting in a modified profile geometry

h = Fye -y + ho e 4(y-o (3.28)

where F = the bottom slope at the shoreline and P= the offshore extent of the combined

influences of the slope at the shoreline and scour due to wave breaking. Ultimately, in order

34

to consistently retain the boundary condition at offshore terminus, i.e., h = ho at y =yo, Lee

(1995) obtained the final form of the mud profile geometry

h =Fye + (h Fye -) e 4( )( (3.29)

He concluded that this geometry still retains the analytic nature of the model expressed by

Equation 3.25.

The least squares method can be used to obtain the best-fit parameter values of P, k,

and F. If hi denotes the measured water depth at the position y,, and h(y) denotes the

predicted depth at the same position y,, then the summation of the squares of errors, e, is

E = [ h, h(y) ]2 (3.30)

which is identical to Equation 3.13, except that here the predicted depth h(y) is given by

h(y) = Fy,e -" + (ho Fye PY) e 4y -Y i)(Y2 (3.31)

Due to the difficulty in linearizing Equation 3.31 to obtain analytic expressions for the best-fit

parameters, a trial and error method is used. The method involves the computation of the

sum of the square errors in the P, kI, and F values, and then locates the minimum value of

E at which the three parameters provide the best-fit for the profile data.

The root-mean-square error, ers, for each profile fitted is determined by

erms = ,i 1 (3.32)

where e is given by Equation 3.13 with respect to the power form of Equation 3.2 for sandy

profiles, or Equation 3.30 for the mud profile geometry given by Equation 3.29.

It is necessary to note that for the purpose of profile fitting, not all of the data points

digitized in a particular profile line are used. The end of the offshore point should be taken

as the offshore terminus beyond which there are no significant temporal profile changes.

Judgement is required in selecting the terminal depth ho of the profiles examined. Often this

terminal depth is selected at the point where a sudden change in a profile occurs. This is

illustrated in Figure 3.2, which shows a profile from Pantai Madura. As seen the total number

of data points in the profile designated as M7-14 is 38, but the number of data points used

for profile fitting is only 16, because the terminal depth is located (3.50 m, 400 m) where an

abrupt change in the profile curve begins to occurs and forms a mound before sinking into

greater depths offshore. This bar-like formation, which can also be found in the other profiles

in the east part of the study area (M7-13 to M7-21), is possibly due to the presence of a rocky

substrate in Pantai Madura.

Plotting of Field Profile
Pantai Madura, M7-14

I Offshore terminus
0 50 100 150 200 250 0 00 350 400 450 500 550 600 50 700 750 00 650 900 950 100
Offshore Distance (m)

Figure 3.2: Plot of profile M7-14 from Pantai Madura, showing the selected location of the
offshore terminus. All the field profiles from the three areas are given in Appendix C.

37

3.4 Field Profile Analysis

Fifty one field profiles were examined in the present study. They are 21 profiles from

Pantai Madura, 20 profiles from Pantai Surabaya, and 10 profiles from Teluk Waru, as

described in Section 2.4. Equations 3.2 and 3.29 were fitted to all of the profiles to inspect

the ranges of the values of the respective parameters involved in the equations, and to assist

in the interpretation of the nature of the profiles. Examples of the best-fit from each location

are shown in Figures 3.3, 3.4, and 3.5. Results for all the profiles are given in Tables B.1

through B.6 in Appendix B, while the distributions ofA and n values of Equation 3.2 for each

location are given as histograms in Figures 3.6, 3.7, 3.8, and in Figure 3.9 for all profiles

from the three areas.

Figure 3.6 shows the n and A histograms for the Madura profiles. It is seen that the

n and A have average values of 0.98 and 1.87 x 10-2, respectively, while n ranges from 0.50

to 1.55 and A from 1.50 x 10-4 to 1.13 x 10-1. Although not quite distinct, the n

distribution has a tendency toward a bell-shape, consistent with what is normally found by

others (e.g., Lee, 1995; Dean, 1977). This distribution is roughly centered at n = 1, more or

less demarcating the distributions of n >1 and n < 1. On the other hand, the highest frequency

of occurrence of A is found at A < 0.01. It is observed that higher values ofn (>0.80) are

typically accompanied by smaller values A (<0.02), and when n > 1 the profile (see Figure 3.3,

3.4, and 3.5) is notably convex, suggesting stable, accretionary fine-grained dominated

beaches (Lee, 1995). In addition, it is noted that the overall slope of the profiles from

Madura tends to increase slightly in the westerly direction (toward the head of the bay of

Madura Strait).

............. ........ .............. ...

-IM7-I II1

o0 200 300 4 0 so 7o 0 90m omo0 11 m
Ofthsro DiOtance (m)

S --- Log --I....... Mud

Log-log Method: A = 2.54 x 10', n = 0.71 e = 0.28 m
Iteration method: A= 4.69xl0-2, n = 0.53, e, = 0.98 m
MudProfileEq.:K=1.10x10"'m-1' F=0.007, P=0.001, e =0.17m

0 0 10 150 200 2 300 350 4W 450 00 S 600
Offhor Ditance (m)

I d-- L ....... Mud

Log-log Method: A = 4.80x10- n = 0.98 e,=0.26 m
Iteration Method: A= 3.31x10 n =1.31 e,,= 0.91 m
Mud Profile Eq.:t=3.31x10'm -1, F=0.009, P=0.011, e ,0.13m

Figure 3.3: Two examples of fitting Equation 3.2 and Equation 3.29 to Madura profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed line is for the
iteration method. The log-log method is found to fit the profiles better than the iteration
method for all Madura profiles. Equation 3.29 is shown by a dotted line.

-3. 5 J T --__

a deI-La It
0 2 4 8 8g 10 1 114 8 18 0 22 24 26 28 20 32 34 1 40 42
Offhor Dietsnc. (meter)

Log-log Method: A 4.61x 10' n= 1.22, e,, = 0.10 m
Iteration method: A= 2.79x10" n= 1.37, e,, = 0.20 m
MudProfile Eq.:;=3.07x10"4m ,F=0.080, p=0.041, e =0.03m

0 0 10 1 00 0 -i iam ma00 200 am u 700 m
Offhor. Distance (meter)

| dat-L0og--i -- A

Log-log Method : A = 7.70x10 n =1.19, e,,=0.08 m
Iteration Method: A= 2.70x10 n= 0.78, e,,,=0.91 m
MudProfileEq.: =5.70x10-4m -, F=0.008, P=0.031, e,=0.16m

Figure 3.4: Two examples of fitting Equation 3.2 and Equation 3.29 to Surabaya profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed line is for the
iteration method. For profile S4-0, the log-log method gives a better fit, but not for profile
S5-20. However, most of the Surabaya profiles are better fitted by log-log method than by
the iteration method. Equation 3.29 (mud profile equation) is shown by a dotted line.

.. ... ............. .... ..

I-. .. ......................................

-5 . ... ..... ................ .......................... ..... ..... ............. .. .. ............... .. .-

0 5 10 5 20 25 30 35 40 45 50 5 60 65 70 I
OffWhoretDence (me) 0 5 10o 1 20 2 30 35 40o 4s so s5 so 70 75 sO 85
Offshore Dtnce (meter)
a-- t dat- Log --t kJ

Log-log Method: A = 4.61x 10' n= 1.22, e, = 0.20 m Log-log Method : A = 7.70x10-4, n =1.19, e,,,,= 0.11 m
Iteration method: A= 2.79x10-, n=1.37, e,, = 0.14 m Iteration Method : A= 2.70x10-3, n=0.78, e,,,,,=0.10 m
MudProfile Eq.:K=1.7610-'m1 ,' F=0.169, P=0.031, e,=0.08m MudProfile Eq.:K=1.01x10-'3m -, F=0.053, P=0.021, e,,=0.09m

Figure 3.5: Two examples of fitting Equation 3.2 and Equation 3.29 to Waru profiles.
Solid line represents Equation 3.2 using the log-log method, while the dashed line is for the
iteration method. Unlike for the other two areas, the iteration method fits all of the Waru
profiles better than the log-log method does. Fitting of Equation 3.29 (mud profile equation)
is presented by dotted line.

Figure 3.7 shows n and A distributions for the Surabaya profiles. It appears that the

distributions are wider than those for Madura profiles. The range value ofn is 0.13 to 1.60

with average n = 0.97, while the range value ofA is 4.88 x 10-4 to 3.83 x 10-1 with an

average A = 6.89 x 10-2. Unlike the Madura data, the n-distribution does not seem to have

a bell-shaped tendency, and is skewed toward higher values ofn (>0.80). This implies that

the majority of the profiles are convex, indicated by n approaching (or greater) than 1, and

accompanied by relatively low values ofA (<0.02). It should be noted that two profiles (S5-

10 and S5-12) gave unusually small values of n, accompanied by unusual large values ofA.

This anomaly probably reflects the complexity of the sedimentary environment and of the

bottom topography of the study area.

40

0.25

Average n = 0.98
o

O

' 0.1 . ............ ....... ...... .................................

0.7

Average A = 1.87 x 10-'
0
&
1 -

0.2

0.1 ....... .....
0.35 0.15 0.25 0.5 0.05 0.05 0.0 007 0.085 0.95 0 5 1.35 0.105 .515 0.125
n (for Madura)
Average A = 1.87 x 10~2

0.005 0.015 0.025 0.035 0.045 0.055 0.065 0.075 0.0865 0.095 0.105 0.115 0.125
A (for Madura)

Figure 3.6: Histograms of parameters A and n for Madura profiles

0.4

0.35

U
C 0.3

0.25
0

0.15

O 0.42
t
. -

a
bs.35
0-

0.5-
0.45-

a
o.35 -

0.1

S0.05

0.05

i

I Average n = 0.97

-

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 1.45 1.55 1.5
n (for Surabaya)

MN aMiS M e. s L* mis; LUS *.48 LISS LUS ,u s & i LaS &I U M S U .3s .3S LMU S 4LMS

A (for Surabaya)

Figure 3.7: Histograms of parameters A and n for Surabaya profiles

Average A = 6.89 x 10-
.......I........ + ,+""' ""..... """'""".. ""... I.." ""....

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' ' . . .' . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..' ' . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' ' . . . . . '

. I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' ' ' ' '

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..' ' ' ' '

................ I .........................................................................' ' ' ' '
..................................... i ............ I ..' '' '' '' '' '' '' '' '' ''

n

Ah

"'

42

0.35

Average n = 0.90
0.3........................................
o0

0 0.2 .......................................................................

0.55 0.85 0.75 0.85 0.95 1.05 1.15 1.25 1.35
n (for Waru)

0.35

Average A = 8.42 x 10-2

0.02 0.04 0.0 0.08 0 0. 0.12 0.14 0.16 0.18 0.2 0.22 0.24
A (for Waru)

Figure 3.8: Histograms of parameters A and n for Teluk Wa35 profiles
Average A = 8.42x 102

C)

0.05 ...

0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
A (for Waru)

Figure 3.8: Histograms of parameters A and n for Teluk Waru profiles

43

It is observed that Surabaya profiles have a noteworthy tendency of increasing overall

slope in the westerly direction. At the eastern end of the study area, the overall slope is very

mild, on the order of 0.002, while at the west end area it rises to the order of 0.1. This rise

in slope is indicated by higher values of A, and is most likely due to the higher current along

the narrower width of Madura Strait toward the head of the bay.

Figure 3.8 shows n and A distributions for Teluk Waru profiles. These profiles have

the narrowest distributions ofn and A of the three. The range ofn is between 0.63 to 1.20

with an average n = 0.90, while the range ofA is between 2.52 x 10-2 and 1.10 x 10.' with

an average A = 8.42 x 102. It should be pointed out that these narrow distributions are likely

to be reflective of the narrow sediment size distribution covering the profiles and of the

relatively less complex bottom topography of the area. From the distributions of n and A and

the sedimentary properties, it is deemed that Teluk Waru profiles exhibit the characteristics

of mildly convex, fine-grain dominated profiles with a tendency toward accretion. In addition,

unlike the profiles from Madura and Surabaya, the iteration method for A and n for least

squares fit gives better results than the log-log method for all Teluk Waru profiles, in terms

of giving the smallest root-mean-square errors.

The average values of n for the three areas do not fall into the range normally found

for sandy profiles. The values are higher than 2/3 as indicated by Equation 3.4, and also

higher than 0.82 found by Kaihatu (1990) and 0.83 by Kotvojs and Fried (1991) for

dissipative beaches, respectively. This indicates that in general the shape of profiles examined

are characteristically different from the common shapes of sandy profiles.

44

0.3

Average n = 0.96
0.25 6
e

3 0.2
o
o

0
0.15 .......................

0.05 0.15 0.25 0.35 A 0. 0.66 0.76 05 0.65 1.05 1.15 1.26 1.35 1.45 1.55 1.66 1.75
n (for all profiles)

0.4
0

0.005 0.025 0.045 00 5 0.085 0.105 0.126 0.145 0.165 f.185 0.205 0.225 0.245 0625 0.215 0.305 0.325 0.345 0.35 0305
A (for all profiles)

Figure 3.9: Histogram of parameters A and n for all profiles
S0.

0~~

Figure 3.9: Histogram of parameters A and nfor all profies

45

The combined distributions ofA and n for all of the profiles fitted are shown in Figure

3.9. Average values of n and A are 0.96 and 5.12 x 10-2, respectively. These values are

consistent with the fact that the majority of the profiles have mild slopes and are linear to

convex. From these distributions, it is tentatively concluded that the profiles are relatively

stable and have a tendency toward accretion rather than erosion. Lee (1995) observed that

convex profiles (n >1) do occur on both coarse-grained and muddy shorelines; however his

average values of n for mud profiles were in the range of 0.5 0.6 (with a mean of 0.54).

This lower value ofn may represent the eroding profiles he fitted, e.g., from the western

Louisiana coast, and from the western coast of peninsular Malaysia.

The average values ofA and n for each location and for all profiles are quite different

from the 2/3 value in Equation 3.4. It is not possible from the present study to determine

whether this difference is due to profile disequilibrium, or due to failure of Equation 3.4 in

describing the profiles. Nevertheless, some rational arguments can be advanced as follows:

a) The majority of the profiles fitted have convex-upward shapes. In contrast, a basic feature

of beach profiles on which Equation 3.2 is originally based is that the profiles tend to be

concave-upward (Dean and Charles, 1994).

b) The sedimentary environment and bottom topography of the study sites (Pantai Madura

and Surabaya) are very complex, with fine-grained material dominating the sediment

distribution. On the other hand, most applications and evaluations of Equation 3.4 have been

for sandy profiles by considering a single representative sediment size across the profiles.

Although attempts have been made to include the natural, cross-shore variation in sediment

size along the profile (e.g., Larson, 1991; Work and Dean, 1991; Dean et al., 1993), it is not

46

feasible in the present study to consider such sediment variations due to the limited data

available.

c) The profiles examined feature very gentle slopes upward from a moderate depth (3 to 5 m)

to the shoreline so that there is a high probability that most of the time the wave energy

approaching the shoreline dissipates gradually (most likely due to viscous effect), and that

waves disappear without any significant breaking (Keulegan and Krumbein, 1949).

Moreover, the relatively protected situations of the coastal waters make the areas rarely

subject to large waves. On the other hand, Equation 3.4 is valid for the breaking wave

regime.

d) The simple equilibrium beach profile used here is not sufficient to represent the complex

nearshore hydrography of the selected coastal areas. As mentioned in Section 2.2, tidal and

estuarine processes play a significant role in the coastal dynamics of the study sites. Dean and

Charles (1994) noted that the equilibrium beach profile concept (represented by Equation 3.4)

is not applicable to three-dimensional situations or where extraneous influences occur, such

as near inlets where other agents (beside waves) are operative or where rock outcrops and

reefs are present.

e) The method of profile data collection by digitizing bathymetric maps probably does not

give an accurate picture of the actual profiles, because some details of profile shape may have

been overlooked by the interpolation method used to estimate depths between contour lines

(or points).

f) As observed by Lee (1995), the settling velocity, w, of the fine-grained material is so low

that it is beyond the range of the empirical relationship parameter A versus w,, formulated by

Dean (1987) as

A = 0.067 0.44

(3.33)

Figure 3.10 based on the overall range of average A-values found in this study illustrates the

relationship ofA and w, It is observed that this relationship is not unequivocal, and therefore

is not predictable by Equation 3.33.

n n'f

0.01

1.00 10.00 100.00
Sediment Settling Velocity, w, (cm/s)

1000.00

Figure 3.10: Profile scale parameter, A, as a function of sediment settling velocity, w,. Box
shows the domain of values obtained for field mud profiles analyzed by Lee (1995) and of
mean values in the present study.

0 Data compiled by Dean (1987)
SEquation 3.33

0

7d

0/

S f 0 ! ! ! ! ! ! HII i i i

6-

.d
XT

~Bi
,

.... I

48

From Figures 3.3, 3.4 and 3.5, it is evident that Equation 3.29 fits the profiles better

than Equation 3.2. In fact, the root mean square error (er,,) given by fitting of Equation 3.29

yields a smaller values than Equation 3.2, for most of the profiles fitted. Hence, it is

concluded that Equation 3.29 better represents the profiles examined in this study, and this

appears to be consistent with the sedimentary environment, which is dominated by fine-

grained material.

Geometrically, it can be observed that the difficulty of fitting Equation 3.2 to profiles

is primarily due to the inability of this equation in simulating the nearshore part of the profile,

which tends to be irregular. Dean (1990) applied a correction for this problem by

reconfiguring Equation 3.3 with an added gravity term leading to

Deq dh dF
+ D (3.34)
Fs dy h dy eq

where Fs is the beach slope. Equation 3.34 can be integrated to yield

Sh 1 h 3/2
y =- + ----- (3.35)
Fs A 3/2 (3.35)

Referring to Equation 3.2 as the basic form of the beach profile, Equation 3.35 by analogy

is

h 1
Y + -h (3.36)
Fs A"

49

Equation 3.36 seems to be comparable with Equation 3.29 because it has three

parameters to be fitted. However, unlike Equation 3.29, Equation 3.36 does not satisfy the

boundary condition at the offshore terminus. Thus, comparing Equations 3.2, 3.29, and 3.36,

Equation 3.29 has the advantage in fitting the profiles because it has the nearshore depth

correction and also satisfies the offshore terminus condition. Furthermore, Equation 3.29

is physically based on the concept of wave energy absorption by mud, which is realistic for

the present case.

Table 3.1 gives the average values of the three parameters including in Equation 3.29.

Lee (1995) reported that convex and accretionary profiles are observed in the range of0

< K < 0.2, and concave and erosional profiles in the range of 0.3 < K < 0.5. In the range 0.2

mean values of K in Table 3.1 are in the transition range. These values are consistent

compared with n-values of Equation 3.2, as discussed earlier in this section. The smallest

K found in Pantai Surabaya imply that the majority of Surabaya profiles are convex, as

discussed earlier. Also, consistent with the transition range, it was reported (BPP Teknologi

and Pusat Pengembangan Geologi Kelautan, 1991) that some parts of the shorelines in

Madura and Surabaya have been observed to retreat, and that dikes and sea walls have been

built to prevent further erosion at some locations.

0.7

0.6
0

0

0.5
0.1

0

0.0003 00009 0.0015 0.00 00027 0.00 0.003 0.0045 0. 0057 0.863 0.00 00075 000

k, (for all profiles)

0.5

0

0

L-

0.1

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.65 0.95 1.65 1.15
K (for all profiles)

Figure 3.11: Histograms of k, and K for all field profiles examined

0.4

1-
U

0.2

0

IUS Lef5 #Ls AOM .6aS U4s Ua uS L S &lfS LUS MIfS i tis &Si &US61 .liU .17S5
F (for all profiles)

0.3

0.2

O

01 ^ -

oi06 o 0o025 0.035 0.046 0. 0.06 0.075 05 0.o6 0.O06 0.56 0.1.26
Beta (for all profiles)

Figure 3.12: Histograms of F and P for all field profiles examined

Table 3.1: Mean values of the three parameters in Equation 3.29 for each study area

Mean Mean Mean Mean Mean
I rI k, (1/m) K F P em, (m)
Pantai Madura 4.12 x 104 0.22 0.010 0.016 0.21

Pantai Surabaya 1.07 x 10-3 0.20 0.058 0.041 0.13
Teluk Waru 2.00 x 103 0.26 0.073 0.037 0.05

Figure 3.11 shows the distributions of k and K, and Figure 3.12 shows the

distributions ofF and P, for all profiles. For each area, the histograms of the parameters are

given in Figure B.1 through Figure B.6 in Appendix B. The histograms in Figure 3.11 and

Figure 3.12 are skewed toward smaller values. This feature is probably reflective of the

mildly convex shapes of the profiles. It is noted that thirty-two profiles are scattered over the

convex to transition ranges (K < 30). However, if the distributions are split into two

categories by K = 0.15, as done by Lee (1995), i.e., accretionary profiles for K < 0.15 and

erosional profiles for K > 0.15, then twenty four profiles are in the accretionary state, and

twenty-seven in erosional state. Table 3.2 summarizes this division in terms of the mean and

standard deviations of the parameters in Equation 3.29. For comparison, Table 3.3 shows

the results of Lee (1995) using 96 field profiles from six different coastal areas.

53

Table 3.2: Values of parameters in Equation 3.29 for erosional and accretionary profile
configurations using K = 0.15 as the demarcation value

Profile F P K k (K/m)
State
Stae Mean Std. dev. Mean Std. dev. Mean Std. dev. Mean Std. dev.
Accretionary
(24) 0.059 0.055 0.026 0.028 0.04 0.04 0.00034 0.00047

Erosional
(27) 0.025 0.023 0.034 0.032 0.39 0.19 0.0016 0.0019

a Numbers in parentheses denote number of profiles.

Table 3.3: Results of profile divisions into erosional and accretionary configurations (after
Lee, 1995) using K= 0.15 as the demarcating value

Profile F P K
State"
Stata Mean Std. dev. Mean Std. dev. Mean Std. dev.

Accretionary
(15) 0.026 0.019 0.015 0.008 0.02 0.03

Erosional
(81) 0.059 0.083 0.046 0.054 0.42 0.13

aNumbers in parentheses denote number of profiles.

It should be be noted that, in general, F and P (in addition to k1) play important

roles in characterizing the profile. In other words, changing the values of F or P for a

constant k, can change the profile shape significantly, or at least modify the profile from the

original shape. The effects ofF and P become more apparent when the length of the profile

54

is relatively short. However, it is difficult to extract general characteristics of F and p

associated with concave and convex profiles, because a concave profile may have a range of

values of F and p. At the same time, an increase in F can be identified by a decrease in

profile length. From Table 3.1 it is seen that an increase in the (mean) value of F from

Madura to Waru may be explained by a decrease in profile length from Madura to Waru.

Also, the decreasing length of Surabaya profiles in the westerly direction is matched by

increasing values of F. This effect ofF can be explained as the result of the significance of

F as accounting for the influence of bottom scour due to wave breaking in the nearshore

portion of the profile. Hence, the longer the profile the smaller the relative contribution of

F.

Some of the tendencies characteristic of these parameters in shaping a profile are

outlined in the following:

a) A larger k1 is associated with a more concave-upward profile. Conversely, lower k is

associated with a more convex-upward profile. A concave-upward profile is identified by a

steep slope over the nearshore part of the profile, indicating an erosional situation due to a

larger wave height that is reduced by dissipation due to fluid mud generated by erosion, and

reflected by a comparatively high k The opposite is the case for a convex-upward profile.

b) A larger p tends to raise the nearshore part of the profile, while a smaller P tends to lower

it. The effect of this parameter seems to be in opposition to that ofF.

c) A larger F corresponds to an increase in the nearshore slope of the profile, while a smaller

F decreases it.

CHAPTER 4
LABORATORY EXPERIMENTS

4.1 Introduction

To further assess the characteristics of profile response to wave action, and the role

of sediment supply in accreting the profile, laboratory experiments were conducted using sand

and mud as sediment. The experiments were intended to give detailed information on : 1)

time-dependent profile change, 2) wave attenuation coefficient obtained from wave

measurements, 3) differences in profile changes, if any, between muddy and sandy profiles,

and 4) the effect of covering the mud profile with a layer of fluid mud. Based on this

information, the temporal behavior of the profiles and the characteristics of the equations used

to fit the field profiles were further examined.

The experiments were conducted in a wave flume in the Coastal Engineering

Laboratory at the University of Florida. This flume has been divided into four subflumes.

The same flume was used by Lee (1995) previously, except that in the present study only two

of the four subflumes were used. In these subflumes sand and mud profiles were formed.

Fluid mud was poured over the mud profile to magnify the viscous effect of wave energy

dissipation, and to study the role of external sediment supply in changing profile geometry.

56

The equipment and procedures for data acquisition, in general, followed those used

by Lee (1995). The experimental equipment, procedure, test conditions, results and

discussions are given in the following sections.

4.2 Equipment

The experimental equipment included: 1) wave Flume, 2) measuring carriage, 3)

sediment coring device, and 4) other apparatuses.

Wave Flume

The wave flume was 3.1 m wide, 0.9 m deep, and 33.5 m long and was divided into

four subflumes (see Figures 4.1 and 4.2). Each subflume, partitioned by concrete brickwalls,

had a width of 0.16 m and spanned about 3/4 length of the main flume (from the end of the

shore portion of the main flume at 0.00 m to the end of the subflume partitions at 23 m). The

two subflumes used are indicated by letters A and B in Figure 4.1.

At the offshore end of the main flume, a wave board actuated by a piston driven by

a 7-HP motor generated monochromatic waves. Wave conditions could be adjusted by

changing the wave stroke position (for wave height) and the periodicity of the stroke (for

wave period).

Measuring Carriage

The measuring carriage was a moving conveyance made of steel, and could carry

wave gages and point gages so that measurements of profile changes and wave height

57

envelope along the subflumes could be made. With a wheel base, the carriage was moveable

on iron rails placed atop both sides of the main flume walls. Two capacitance-type wave

gages were fixed on the wave-generator side of the carriage, and two point gages on the

opposite side, one pair (wave gage and point gage) for each subflume (see Figure 4.1).

Top View

35 m

Piston type
wave maker
-4 -

Plan View

0.91 m
Sediment

1

Not drawn to scale

Figure 4.1 : Schematic of the flume. The two subflumes used were A and B.

A B

Figure 4.2: Photograph of the flume with the wavemaker at the end of seaward portion of
subflumes A and B

~r~ ~c~ --~a~
,a

~k

59

The point gages were equipped with graduated scales with verniers capable of

measuring height changes to the nearest 0.1 mm. Bottom profile measurement was carried

out under muddy water conditions when visual observation of the profile bottom was not

possible. Therefore, to help determine the bottom elevation, the point gages were equipped

with expanded tips made of 2 cm by 8 cm steel strips that augmented the "feel" of profile

bottom during measurement.

Surface waves were measured by capacitance-type wave gages. The wave signals

produced were then recorded and digitized by an integrated data acquisition system

comprising a signal amplifier, a digitizing interface card and a personal computer with Global

Lab software. The wave gages were calibrated by changing the vertical position of the gages

at fixed water levels in the flume. Given digitized data sets consisting of voltage outputs

corresponding to known water levels, the calibration constant was easily determined using

linear regression.

Sediment Coring Device

For density measurement, the sediment coring device consisted of two 76 cm long

concentric tubes: the inner tube of a 1.5 cm diameter made of metal and open at both bottom

and top, and the outer cylinder of 8 cm diameter made of PVC. These two tubes formed an

annular space between them which was closed at the bottom and open at the top (see Figure

4.3).

During measurement, a plastic tube of 1.30 cm diameter was enclosed in the inner

cylinder and embedded in the soft mud bottom for about 15 minutes, while the annular space

60

was filled with a mixture of dry ice and denatured alcohol to freeze the soft mud contained

in the plastic tube. The density of the sediment core retrieved from the plastic tube was then

determined as the weight of the core divided by the volume occupied by it in the plastic tube.

Innertube 8cm

Outer tube Plastic tube

T ---- Metal cylinder

76 cm

15
1.5cm

- -- PVC cylinder

Annular space
filled with mixture
of dry ice and
denatured alcohol

Sediment core

Not drawn to scale

Figure 4.3: Schematic of sediment coring device

Other Apparatuses

Other apparatuses were those required to facilitate the operation of the equipment

described and running the experiments. Examples are a water pump, a wooden board, 40-

gallon plastic containers, etc.

4.3 Sediments

The selected sediments for subflumes A and B were an artificial clay mixture and a

fine sand, respectively. The clay mixture was an equal proportion (by weight) of an

attapulgite and a kaolinite. The atapulgite was obtained from Floridian Company, in Quincy,

FL, and the kaolinite from Feldspar Corporation, in Edgar, FL. The median sizes of

attapulgite and kaolinite were approximately 1.5 jim. The clay mixture was prepared by

mixing the dry mixture with well water, resulting in a cohesive mud with density ranging from

1,350 kg/m3 to 1,450 kg/m3, which could be sustained in a sloping configuration. Detailed

information on the physical and the chemical properties of this mixture can be found in Feng

(1992), Jiang (1993) and Lee (1995). The fine sand consisted of quartz from WHIBCO, Inc.,

in New York, NY. Its median size was around 85 pm.

4.4 Test Conditions

Five runs with different combinations of initial profile slope, wave height, wave

period, and test duration were conducted. Table 4.1 summarizes the test conditions for each

run. The test number sequence is in chronological order. For each run, wave period was

measured by timing the passage of a given number of waves passing a mark on the side of

the flume before the waves entered the subflumes.

Table 4.1: Summary of test conditions

Incident Wave
Initial Slope Wave Height (cm) Water Test
un Period Depth Duration Notes for Mud Profiles
No. Mud Sand (s) Mud Sand (cm) (hr)
Profiles Profiles Profile Profile
1 0.010 0.019 1.4 9 9 20 48 fluid mud
2 0.017 0.015 1.2 14 14 30 53 fluid mud
3 0.017 0.015 1.2 6 14 30 72 wave damper & fluid mud
4 0.008 0.014 1.2 5 13 24 94 wave damper
5 0.007 0.016 1.2 5 13 24 64 wave damper & fluid mud

For mud profiles two features were included: 1) a fluid mud blanket, and 2) a wave

damper. Fluid mud (density 1,120 kg/m3) was prepared in 40-gallon plastic containers and

poured over the pre-placed mud profile of higher density, with the objective of enhancing

wave absorption and determining whether fluid mud would be retained or eroded under given

incident wave conditions. This method of fluid mud placement had to be adopted because

fluid mud could not be generated rapidly enough in-situ, due to limitations of flume size, wave

action and design test durations. The wave damper was a floating wooden board that was

1.5 m long, 0.5 m wide and 3 cm thick. It was placed on the water surface at the seaward

end of the mud profile (Figure 4.1). Its purpose was to reduce the incident wave height for

63

the mud profile. As a result, the effective incident wave height acting on the mud profile was

smaller than that for the sand profile.

For subflume A containing mud, the initial profiles of Runs 1 through 3 were shaped

with an approximately uniform slope. The initial profile of Run 4 was the continuation of the

final profile of Run 3, with a lower water depth. The initial profile of Run 5 was the

continuation of the final profile of Run 4, with fluid mud added. Table 4.1 gives the initial

mean slope values for all the tests.

4.5 Experimental Procedure

The experimental procedure can be described in five categories: 1) profile preparation,

2) fluid mud preparation, 3) wave measurement, 4) profile measurement and 5) density

measurement, as follows.

Profile preparation

Profile preparation (for Runs 1, 2 and 3) was done by first draining out water from

the main flume using a water pump. Then, building of the profiles was done iteratively using

a spade to obtain the desired slope. Point gages were used to help measure the slopes. It was

difficult to achieve a truly uniform slope, especially for the mud profile, because the subflumes

were narrow, and the muddy bottom was so soft that it was difficult to define the exact depth

at a particular position. In any event, after profile preparation, water was pumped to the

desired level to submerge the profiles, which were then left undisturbed for at least 24 hours

before a particular run was initiated.

Fluid mud preparation

Like the bottom sediment used for the mud profile, the fluid mud was an equal

proportion of attapulgite and kaolinite clays. The required amounts of attapulgite and

kaolonite were first dry-mixed in 40 gallon plastic containers. Well water was then added to

achieve the required fluid mud density, pf, which was 1,120 kg/m3 based on the following

formula:

Pf -P (P, P,) + P (4.1)
PS

where pm = fluid mud density, p,= sediment granular density (2,650 kg/m3), p,= density of

water (1,000 kg/m3) and Pd = dry density of the slurry determined from the known weight

of dry sediment used and the total volume of the slurry in the container. The slurry was

mechanically agitated by a rod with vanes. The resulting density was checked by a density

meter (PAAR DMA35). The amount of fluid mud prepared was sufficient to cover the entire

profile with an approximate thickness of 3 cm.

Profile Measurement

Profile depth was measured along the center line of each subflume at 0.3 m intervals.

The depth measurement was conducted by lowering the point gage until its expanded tip just

touched the bottom. Using the moving carriage, profile measurement commenced from the

profile end toward the wave generator, so that one sequence of measurements resulted in a

snapshot of the profile at each selected time. Wave (envelope) measurements were performed

immediately after profile measurement so that the two sets of measurements could be

considered to correspond with each other.

Wave Measurement

Wave height was measured by the (capacitance-type) wave gages affixed to the

carriage which moved longitudinally on rails. Wave height was determined at different

locations at intervals of 0.6 m. At each location, a time series of elevation of about 20 s

duration was obtained. The measurements were conducted along the center line of each

subflume. During measurement, wave breaking locations were identified for later analysis.

The arithmetic mean wave height at each location was taken to represent the wave height at

that location, and a longitudinal distribution of wave envelope was developed by joining wave

heights at different locations along the subflumes.

Density Measurement

In-situ mud density for the mud profile was measured using the coring apparatus

described earlier. As noted, a transparent plastic tube of a 1.30 cm inner diameter was inserted

into the inner cylinder, while the annular space was filled with dry ice pieces. The PVC

canister, including the plastic tube and dry ice, was then pressed into the mud bottom. Since

the depth of mud was less than 20 cm everywhere, the depth of penetration was typically 15

cm or less. Once embedded, the annular space was the filled with commercial grade

denatured alcohol to accelerate the freezing process. In about 15 minutes the PVC canister

was withdrawn along with the frozen core within the plastic tube.

The canister was then cleared of dry ice using tap water, and the plastic tube was

taken out of the inner tube. The plastic tube was then refrozen by placing it into another

similar apparatus 15 cm high, previously used by Parchure (1980). After refreezing, the

plastic tube was laid horizontally and was ready to be cut into segments using a hack-saw.

Each cut segment was weighed and the plastic piece alone was weighed again after the sample

was removed. The difference in the two weights gave the weight of the sample. The density

of each segment was then determined as the weight of the sediment divided by the volume of

the sample.

Results of density measurement are given in Table 4.2. They describe the trend in

mud density change due to mud fluidization or consolidation. It is observed that the density

of mud bottom in Run 2 tended to decrease slightly, as a result of mud fluidization due to

profile erosion in this test. On the other hand, as observed in Run 5, the typically low mud

density at test initiation (due to the poured fluid mud) tended to increase toward the end of

the test. This consolidation corresponded with mud deposition as shown by mud profile

change in Figure 4.11.

However, caution must be exercised with respect to the accuracy of this simple

method due to: a) the tendency of the sediment sample to increase in length in the tube while

being frozen, b) the difficulty of making an even cut by the saw resulting in errors in

volumetric determination, and c) the tendency for some mass loss during retrieval and

67

sawing. Because of these reasons, Table 4.2 should be regarded as providing a qualitative

description of density variation with time and depth.

Table 4.2 : Results of mud density measurement

Run No. 1 2 3 5

(@ 12 hrs @ 29 hrs @, test initiation
1,310 @ 1.5 cm 1,320 @ 1.5 cm 1,140 @ 1.5 cm
1,390 @ 4.5 cm 1,490 @ 4.5 cm 1,370 @ 4.5 cm
Mud density 1,400 @ 7.0 cm 1,520 @ 7.0 cm 1,380 @ 7.5 cm
(kg/m3) 1,700 @ 10.5cm

@ Depth (end of test ( 45 hrs @end of test
below 1,230 @ 1.5 cm 1,300 @ 1.5 cm 1,330 @ 1.5 cm
profile surface 1,360 @ 4.5 cm 1,320 @ 4.5 cm 1,510 @ 4.5 cm
1,480 @ 7.5 cm 1,460 @ 7.0 cm 1,500 @ 7.5 cm
1,700 @ 10.5cm 1,520 @ 10.5cm 1,700 @ 10.5cm

4.6 Corrections for Wave Data

The raw wave height data were subjected to corrections for side-wall friction and

shoaling as described next.

Correction for Side-Wall Friction

The common criterion used for determining the presence of various oscillatory

boundary layer structures, i.e., laminar (viscous), transitional and turbulent, is the wave

Reynolds number defined as

68

Re (4.2)
w

where U, = maximum orbital velocity just outside the boundary layer, a, = orbital amplitude

just outside the boundary layer, and v, = kinematic viscosity of water. From linear wave

theory U, and a, can be defined as

U8 = ao (4.3)

H
a 2sinhkh (4.4)

where h = water depth, H= wave height, a = wave frequency, k, = wave number obtained

from linear dispersion relation. Then Re, can be rewritten as

w H2o
4v sinh2kh (4.5)

The wave Reynolds numbers for the test conditions given in Table 4.1 were in the

range of 2.9x103 to 1.4x104, which is considered to be within the limit of the existence of a

viscous boundary layer (Collins, 1963; Kamphuis, 1975). Therefore, the approach of Hunt

(1959) was considered adequate for calculating the correction for flume side-wall friction.

This correction was applied between two adjacent measurement locations based on the

expression:

H = H+( -e -k-Ay H,1 (4.6)

where kis the wave attenuation coefficient due to side-wall friction and is expressed by

2k vw )1/2 sinh2kh (
S b 2a 2krh + sinh2k (4.7)
r r

Note that, the indices i-1 and i denote adjacent spatial locations increasing in the wave

propagation direction, superscript c denotes the corrected value, Ay = distance between two

adjacent locations of wave measurement, b = width of subflume, and h = average water depth

between two measurement locations. See Lee (1995) for further details.

Correction for Shoaling

The wave height corrected for side-wall friction was further corrected for shoaling

based on the linear wave theory. This correction was applied between two adjacent

measurement locations using the expression:

Hjc = Hj, (k 1)Hj- (4.8)

with k, is the shoaling coefficient given by

1/2
k (2(kh)_1 + sinh2(kh)i_,) cosh2(krh)j (
S(2( +inh2(k)) coshkh)

70

Similar to index i in Equation 4.6, index increases in the direction of wave propagation. See

Lee (1995) for further details.

4.7 Profile Change Data and Discussion

As examples of time-evolving profiles, Figures 4.4 and 4.5 show mud and sand

profiles at different times for Run 1. For further analysis, only the initial and final profiles

were considered.

Figures 4.6 to 4.11 (except Figure 4.9) show initial and final configurations of sand

and mud profiles for Runs 1 through 5. Two major features of sand profiles that are

identifiable from these figures and not found in mud profiles are bar and trough formations.

Bars were typically found in the vicinity of the subflume ends, and shoreward of that region

noteworthy changes in the sand profile took place. On the other hand, trough formation was

typically found in the nearshore part of the profiles in the proximity of the swash zone. The

presence of two bars close to each other in the sand profiles, as shown in Figures 4.7 and 4.8,

is an interesting phenomenon which is also found in natural profiles (see Figure 4.9). Dolan

and Dean (1985) indicated that multiple bar formation they observed was related to the

multiple wave break-point mechanism. In the present study, it was also observed that the

positions of these major features (bar and trough) were at the localities of wave breaking.

The locations of the two bars in the Figures 4.7 and 4.8 was related to two positions of

waves breaking (almost simultaneously).

A characteristic behavior associated with sandy profiles is their tendency of

maintaining a volumetric sedimentary balance over the length of the active profile. Bottom

71

scour yields sediment resulting in trough formation in some part of the profile, and the eroded

sediment is deposited seaward resulting in bar formation over that portion of the profile. Thus

in Runs 4 and 5 (Figures 4.10 and 4.11, respectively), the breaker positions and the resulting

bars migrated offshore beyond the end of the subflume.

Unfortunately, a volumetric balance could not be fully established in the experiments.

Two major factors that significantly affected the results were: 1) the length of the active

profile spanned beyond the sandy subflume, so that the profile measured could not include the

entire active profile, and 2) some sediment mixing occurred between the subflumes, as

evidenced from the top layer of the sand profile becoming soft and slurry-like due to mud that

entered the sand subflume from the other subflume via the common flume region located

beyond the subflumes.

The mud profiles did not exhibit any trend toward a volumetric balance, but in fact

demonstrated the contrary trend, i.e., a volume imbalance in profile change between erosion

and deposition, as can be seen from the spatial profile changes shown in Figures 4.12 and

4.13. The eroded mud was suspended and most likely spread throughout the entire flume,

as observed from the uniformly muddy and turbid water all over the flumes during

experiments. The common flume area beyond the ends of partitioned walls of the subflumes

was where the eroded material was stored. Lee (1995) also found in his experiments that

significant differences between the erosion and deposition volumes occurred for fine sediment

profiles.

0.05

0.03-

S0.01 --
%@_70.01 water level

to

50o.0 1
C0.07

0.11

-0.13
-0.15

5 7 8 9 10 11 12 13 14 15 16

Distance along Flume (m)

-- initial 2 hrs 8 hrs 21 hrs
27 hrs -e- 34 hrs 43 hrs final (48 hrs)

Figure 4.4: Time-evolving profiles for mud bottom of Run 1

0.05
0.03
0.01 -. water level

-0.01

-0.17 -
-0.0719

-0.52
-0.17
-0.19

9 10 11 12 13 14 15 18 17 18 19 20 21 22 23
Distance along Flume (m)

Figure 4.5: Time-evolving profiles for sand bottom of Run 1

initial 2 hrs 8 hrs 21 hrs
- 27 hrs 34 hrs 43 hrs final (48 hrs)

74

Mud Profile Change
Initial and Final Profiles for Run-1

0.03

01 "-- ,.- -.... ,. .l d-
10.01.

10.03
.006.

-0.07

0.11
-0.13
0.15

5 6 7 8 9 10 11 12 13 14 16 16
Distance along Flume (m)

SiniMsl .... flud mud --final Ed profile kvel unbown

Sand Profile Change
Initial and Final Profiles for Run 1

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Distance along Flume (m)

I- Initial final

Figure 4.6: Initial and final profiles of mud and sand bottoms of Run 1

Mud Profile Change
Initial and Final Profiles for Run-2

2 3 4 5 6 7 8 8 10 11 12 13 14 15 16
Distance along Flume (m)

-- initial .. fluid mud final

Sand Profile Change
Initial and Final Profiles for Run-2

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Distance along Flume (m)

initial final

19 20 21 22 23 24

Figure 4.7: Initial and final profiles of mud and sand bottoms of Run 2

Mud Profile Change
Initial and Final Profiles for Run-3

0.04-
0.02
0-

C.0.04
a.o.os -
So.oa-
-EO.-
-i.o2
S-0.1
Q-0.12-
-0.14 -
E~-
90.16-
10.18-
-0.2-
40.22-
-0.24-
-0.26-
A-
-0.28-
-0.3

wCte leve

'- a..

2 3 5 7 8 9 1 11 2 1

2 3 4 5 6 7 8 9 10 11 12 13
Distance along Flume (m)

-initial fluid mud -final

14 15

Sand Profile Change
Initial and Final Profiles for Run-3

0.04
0.02
0- 0

12

&0.14
rO.02

S -0.2
-0.142 W

-0.24
-0.2-

-0.23 -

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Distance along Flume (m)

I- initial final

Figure 4.8: Initial and final profiles of mud and sand bottoms of Run 3

-r

FS______ VERY FESS ----F--- N
ISorophium... . --- Arenicola-- - - - - .- - Lanice .-.
or igh iSMal

0 I--~
i Tangue and mud l

Fine or very ine sand () Cherrue La Saline Section
Medium sand La Chapelle Ste Anne Section
Ca Coarse and medium sand

Figure 4.9: Schematic section showing the sedimentary formations of multiple bars of sandy
banks and of the flatness of mud deposits in the western part of the Bay of Mont-Saint-Michel
(after Caline, 1994)

78

Mud Profile Change
Initial and Final Profiles for Run-4

6 7 8 9 10 f11 12 13 14 15
Distance along Flume (m)

initial -final

Sand Profile Change
Initial and Final Profiles for Run-4

0.08
0.02
0
O.02
o0.04
a 06-,

-0.1
ULO.12

1-0.18
-0.22

-0.26
-0.28

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Distance along Flume (m)

-E- initial final

19 20 21 22 23

Figure 4.10: Initial and final profiles of mud and sand bottoms of Run 4

79

Mud Profile Change
Initial and Final Profiles for Run-5

Distance along Flume (m)

I initial fluid mud -final

Sand Profile Change
Initial and Final Profiles for Run-5

o0.06
0.04
S_.02 water level
0.02

50.14
`0.18
-0.12

0.22
-0.2
0.16
-0.18--

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Distance along Flume (m)

initial fna

Figure 4.11: Initial and final profiles of mud and sand bottoms of Run 5

0.05

0.04

o
&0 02

to0.02

4.02
-0.03

-0.04

5 6 7 8 9 10 11 12 13 14 15 16
Distance along Flume (m)

--5hrs 27 hrs 48 hrs

&0.01
-0-

I.oo
I0.0-

?o.oe

-0.07-
-0.08 -
-o0.9. Run1-Sand Bottom

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Distance along Flume (m)

I-5hrs -- 27hrs -48hrs

Figure 4.12: Spatial changes between surveys, for mud and sand profiles of Run 1

81

0.05
Erosion
0.04 + Accretion Run 2 M

0.03-
%O.02-

00.01
o0.0o -

-0.03

-0.04 -

-0.05 I I : I I I : I i I M
2 3 4 5 6 7 8 9 10 11 12 13
Distance along Flume (m)

-- hrs .25hrs -53hrs

0.08
Erosion
0.0 + Accretion

.0.04

0.02

02"

Run 2 -Sand
.os0
2 3 4 5 6 7 8 9 10 11 12 1314 15 16 17 18 19
Distance along Flume (m)

2 hrs .25 hrs 53 hrs

14 15 16

Bottom

20 21 22 23

Figure 4.13: Spatial changes between surveys, for mud and sand profiles of Run 2

In Figure 4.14, the total change in sediment mass with time calculated from successive

profile measurements is plotted. This mass was obtained from the total area of the spatial

profile change, the width of the flume and the density of profile bed (1,300 kg/m3 for mud

and 1,500 kg/m3 for sand). It is seen that for mud bottom, overall erosion was exhibited

only in Run 2. In this run, the initially poured fluid mud did not remain there due to the

relatively large wave height. In Run 4, although no fluid mud was added at the beginning of

the run, the wave conditions were favorable for consolidation. Hence, fluid mud, which had

not hardened from the previous experiments, coupled with some shoreward transport of

sediment from the pool of mixed (mud and sand) sediment from the common area of the

flume settled down and accumulated over the active profile, thus forming a new bed. It

should be noted that the amount of fluid mud poured at the beginning of each run (except Run

4) was approximately 350 kg. If this amount is compared with the weight gained at the end

of Runs 1, 3, and 5, it is realized that there still was some fluid mud loss, corresponding to

the mass not retained through consolidation. This lost fluid mud either remained in

suspension over the mud profile, spread out over the entire flume, or deposited in the

common flume. Therefore, it is evident that profile development toward an accretionary state

was a result of sediment supply (fluid mud) from poured fluid mud and, to a much lesser

extent, from the "offshore" source, as described earlier.

A noteworthy feature in Figure 4.11 is the "exponential" trend in volume change with

time. As observed, significant profile changes typically occurred within the first 24 hours.

Later changes were relatively smaller, indicating an approach to equilibrium. The final

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