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Title: Closure depth considerations along the Florida shoreline
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Title: Closure depth considerations along the Florida shoreline
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Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Table of Contents
        Page i
        Page ii
    Main
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    Reference
        Page 14
    Example calculations with three closure depth equations
        Page A-0
        Page A-1
        Page A-2
    Examples illustrating closure depth recommendations
        Page B-0
        Page B-1
        Page B-2
Full Text




UFL/COEL-2002/009


CLOSURE DEPTH CONSIDERATIONS ALONG THE FLORIDA
SHORELINE








by



Robert G. Dean
and
Subarna B. Malakar



Submitted to:

Bureau of Beaches and Wetland Resources
Department of Environmental Protection
Tallahassee, FL 32399


2002












CLOSURE DEPTH CONSIDERATIONS
ALONG THE FLORIDA SHORELINE











June 26, 2002









Submitted to:

Bureau of Beaches and Wetland Resources
Department of Environmental Protection
Tallahassee, FL 32399








Submitted by:

Robert G. Dean and Subarna B. Malakar
Department of Civil and Coastal Engineering
University of Florida
Gainesville, FL 32611








TABLE OF CONTENTS


EXECUTIVE SUMMARY ...................................................... 1

1.0 INTRODUCTION ......................... ........................................ 2

2.0 GENERAL DISCUSSION ................................................ 2

3.0 BASES FOR DETERMINING CLOSURE DEPTH ........................ ... 5
3.1 Previous Estimates ................................................... 5
3.2 Wave Hindcasts ...................................................... 5

4.0 RESULTS ............................................................... 8

5.0 DISCUSSION ........................................................... 9
5.1 G general ...... ..................................................... 9
5.2 Method .................... .......... ................... ......... 9
5.2 Anna Maria Key Project .............................................. 10
5.3 Perdido Key Project .................................................. 11
5.4 Considerations in Closure Depth Specifications ............................ 11

6.0 RECOMMENDED GUIDELINES AND FUTURE EFFORTS ...................... 13
6.1 Siting of Borrow Pits ............. .... ....... ....... .................. 13
6.2 Application to Beach Nourishment Design ....................................... 13
6.3 Exceptions to Application of Guidelines .................................. 13
6.4 Future Efforts to Refine Closure Depth Estimates .......................... 13

7.0 REFERENCES .......................................................... 14

APPENDIX A: EXAMPLE CALCULATIONS WITH THREE CLOSURE DEPTH
EQUATIONS ....................................................... A- 1
A. 1 Introduction ......................... ................ .......... A 1
A.2 Equations Compared ..................... ....................... A- 1
A.2.1 Hallermeier Equation ..................................... A- 1
A.2.2 Full Birkemeier Equation .................... ............... A- 1
A.2.2 Simplified Birkemeier Equation ........................... A-2
A.3 Comparison of Calculated Closure Depths ............................. A-2

APPENDIX B: EXAMPLES ILLUSTRATING CLOSURE DEPTH
RECOMMENDATIONS .............................................. B 1
B.1 Introduction .... .................................................. B 1
B.2 Siting of Borrow Pits ............... ..............................B 1
B.3 Application to Beach Nourishment Design .......................... B 2












LIST OF FIGURES

Figure 1. Schematic of Sediment Transport Activity Across the Nearshore ................. 3

Figure 2. Calculated Annual Closure Depths in the Vicinity of Anna Maria Key, FL ......... 4

Figure 3. Closure Depths Recommended by Dean and Grant (1989) ...................... 6

Figure 4. Wave Information Study (WIS) Stations used in This Report .................... 7

Figure 5. Closure Depth Values Determined in This Report (Solid Lines) Compared With Those
Determined by Dean and Grant in 1989 (Dashed Lines). The Vertical Bars Represent
One Standard Deviation About the Averages of the Closure Depth Values ........ .8

Figure 6. Calculated Annual Closure Depth Values in the Vicinity of Perdido Key, FL ...... 11

Figure 7. Sand Transported to in Excess of the 30 foot Depth Contour by Hurricane Opal
(Leadon, et al 1998) .................................................... 12

LIST OF TABLES

Table 1. Project Characteristics Employed in "Ground Truthing" Closure Depth
Determination ................ .................................... 10

Table 2. Comparison of Closure Depth Values Based on Monitoring Data and The Two Other
Bases ...... ........................................ ...................... 10


Table A.1. Comparison of Calculated Closure Depths ............................... A.2









EXECUTIVE SUMMARY

Calculations of closure depth were carried out around the sandy beach shorelines of the
Florida peninsula based on the most recent wave hindcasts and compared with closure depths
recommended in 1989 based on less complete information. Present calculations were based on
the Hallermeier (1978) formulation. The closure depths calculated in the present effort were
substantially greater than those developed earlier. At some locations, the new results were
twice the earlier results and, on average, the new results were a factor of 57% greater.

To evaluate which of the two representations is more appropriate, profiles were examined for
the Anna Maria Key and Perdido Key beach nourishment projects. It was found that the
earlier closure depth recommendations are generally more consistent with the monitoring data
from these projects.

Advantages and disadvantages exist for locating the borrow pits farther seaward. A significant
advantage is less potential adverse interaction with the shoreline. Primary disadvantages
include cost and the possible designation of good quality sand resources off limits for beach
nourishment.

It is recommended that, until it can be demonstrated that the earlier estimates of closure depth
(presented in Figure 3) require modification, these estimates continue to be used. Clearly, the
estimates based on the wave hindcasts as calculated in this report are too large. It is further
recommended, as a basis for the siting of borrow pits, that the depth be 25% greater than that
in Figure 3 or at a distance of 25% greater than the depth on the profile of interest
corresponding to Figure 3, whichever is greater. For beach nourishment design, it is also
recommended that the results in Figure 3 be applied. Finally, it is recognized that each
situation is unique and that extenuating circumstances and judgment may provide a rational
basis for deviating from these recommended guidelines.









CLOSURE DEPTH CONSIDERATIONS
ALONG THE FLORIDA SHORELINE



1.0 INTRODUCTION

Closure depth is central to many coastal engineering and coastal management activities. This
quantity represents an estimate of the average annual depth limit to which sediment motion is
active to a significant degree. Thus, this depth provides an approximate limit to which nourished
beach profiles will equilibrate and a limit, shallower than which, sediment will tend to be active
in the vicinity of a borrow pit. Since the equilibrated dry beach width is inversely related to the
closure depth, this quantity is significant to beach nourishment design and performance.
Additionally, closure depth provides an obvious inshore limit for the siting of borrow pits since if
the sediment transport activity is significant in the vicinity of the borrow pit, some of the sand
placed in the nourishment project will be "short circuited" back into the borrow pit and thus lost
to the nourishment project.

This report provides the results of a reexamination of the closure depths along the Florida
shoreline based on the most recent wave hindcasts, compares these results with estimates
developed more than a decade ago and presents recommendations for future engineering and
management applications.

2.0 GENERAL DISCUSSION

Sediment activity is greatly enhanced by wave breaking and the associated generation of
turbulence, which mobilizes bottom sediments. The sediment "activity" thus decreases with
increasing water depth outside the breaker zone, and probably decreases inside the breaker zone
toward the shoreline as shown qualitatively in Figure 1. Hallermeier (1978) was the first to
quantify closure depth. Based on considerations of the bottom water particle velocities associated
with water waves and the Shields Curve for the initiation of sediment motion, and calibration
with limited data, Hallermeier formalized the following relationship for the closure depth, h.
H2
h, = 2.28H 68.5 (--) (1)
S gT2


in which HI is the significant wave height that is exceeded twelve hours per year, T, is the
associated wave period and g is gravity. It is somewhat surprising that sediment characteristics
do not appear in Eq. (1).

Based on the preceding discussions and Eq. (1), it is clear that the concept of closure depth is
intended as an aid in dealing approximately with the complex nearshore sediment transport

















Range of Dominant

Brea ing


Figure 1. Schematic of Sediment Transport Activity Across the Nearshore.

characteristics for engineering purposes. Referring to Eq. (1), it is seen that the single most
significant variable is the wave height, whereas the wave period plays a secondary role with the
closure depth decreasing with increasing wave period as expected. After the development of Eq.
(1) by Hallermeier, Birkemeier (1985) examined more accurate profile data from Duck, NC
based on surveys carried out with the CRAB (Coastal Research Amphibious Buggy), and
proposed the following equation which differs from Eq. (1) only by modified coefficients
H2
h, = 1.75He 57.9(-)
gT2




and stated that the following more simple equation would yield nearly equally valid estimates.
h = 1.57H, (



Many studies have been conducted to modify or improve on Eq. (1); however, this equation is in









widespread use today and no equation has been proven superior for engineering purposes.
Sample calculations of the three closure depth equations above are presented in Appendix A.

The above equations suggest that an appropriate interpretation of the closure depth would be one
in which the closure depth increases with time. Figure 2 presents the annual calculated closure
depths in the vicinity of Anna Maria Key, FL.


:l. I'J Il '.l


Nurny Date on \Which
h. Based


.1 J. 1 .l-L- 1 1,
r ,7 ."3. .' '


IIIr, in Years


Figure 2. Calculated Annual Closure Depths in the Vicinity of Anna Maria Key, FL.

It is seen that the largest closure annual closure depth in Figure 2 is more than 35 feet; however,
it is doubtful that sand transported and deposited offshore during such a major event would
remain offshore. Stated differently, should the closure depth increase monotonically with time or
would the closure depth be "reset" during longer periods of more normal wave conditions? Also,
what is the "effective closure depth"? To investigate this question, Nichols, et al (1996)
examined 13 years of high quality profile measurements from Duck, NC in which the profiles
were nominally surveyed every two weeks and the closure depths were established as the depth
at which the standard deviations of the profile changes about the mean ceased to decrease in the
seaward direction. These data were obtained from a natural beach and thus may not be entirely








representative of nourishment projects. The somewhat surprising result was found that the
profile did seem to "reset" to some degree, that is, at the end of the 13 year period considered, the
depth of net profile disturbance was less than the maximum based on the individual years. This
finding is a result of the weak onshore forces which are exerted by the waves on the sediment
particles causing the reestablishment of the equilibrium profile following an event which
transports the sediment seaward and deposits it in deeper water, thereby resulting in a profile
which is out of equilibrium. This weak onshore sediment transport results in considerably longer
time scales than those associated with the seaward transport during storms. Additionally, it was
found that Eq. (1) tended to over predict, by approximately 24%, closure depths based on profile
changes. The explanation for two closure depth estimates for the Year 1995 in Figure 2 will be
explained later.

The above discussion has established that the closure depth will vary from year to year, but that
over a long period, the depth to which a profile will equilibrate is expected to be approximately
(or perhaps slightly less than) than associated with the average closure depths based on Eq. (1).
Thus, in the application of this methodology over several years, it should be expected that during
some years, sand motion (whether on a nourished or natural profile or in the vicinity of a borrow
pit) will be mobilized to depths greater than the average of closure depths predicted based on Eq.
(1) and using the average annual effective wave height, He and associated wave period, Te.
Possible consequences of varying annual closure depths will be discussed later.

The above discussion has illustrated that, rather than being a precise value, the "closure depth" is
a concept which is necessary for engineering design purposes and that although in some years,
the annual closure depth will be significantly greater than the average of a series of annual
closure depths, the average can be considered appropriate for design.

3.0 BASES FOR DETERMINING CLOSURE DEPTH

3.1 Previous Estimates

Previous estimates of the closure depths around the sandy beaches of the Florida peninsula have
been developed by Dean and Grant (1989) under contract with the then Division of Beaches and
Shores. These results are presented in Figure 3 and were based on a blend of data from the
reasonably long term wave gages maintained by the Department of Coastal and Oceanographic
Engineering of the University of Florida and results from monitoring of beach nourishment
projects. Wave gages were located at a total of the nine stations shown in Figure 3 around the
sandy shoreline portion of the State of Florida over a period of several decades.

3.2 Wave Hindcasts

The Waterways Experiment Station has produced hindcasts of wave conditions around the
United States shorelines including the Great Lakes. These results are the product of a long term
effort termed the "Wave Information Study" and are referred to as WIS data. The WIS data are








-- -- I-f-f-I-- -~
--- -I-I-I- -I-
- -- -1-4-4- -4-
AI~:LLV'-k.
1~T


JA


MA
ST


cc
CL
VB


VE WP


MI
12 16 20 24
h* (Feet)


24

1 20
U.
S16


Figure 3. Closure Depths Recommended by Dean and Grant (1989).


the results of complex and detailed modeling of the meteorology, the transfer of wind energy to
waves, and the propagation of these waves to the nearshore areas. These data are stored at three
locations in the cross-shore direction with the shallowest storage depth being approximately 30
feet which are the data that will be used for purposes of calculating closure depths in this report.
Figure 4 presents the locations of the fourteen shallow water stations selected for purposes of
calculating closure depths based on the WIS data. These data are available for two different time
periods (1976 to 1995 and 1995 to 1999) and the two numbers in parentheses adjacent to each of
the stations selected denote the identification number for each of these stations and for each of
these periods. Although the stations at which the data were stored for the periods 1975 to 1995
and 1995 to 1999 were not at exactly the same locations, the stations for the two periods were
selected to be co-located as nearly as possible. The WIS data are tabulated every three hours for
the period 1976 1995 and are designated with the first Identification Number (ID) shown in
Figure 4. For the second period (1995 1999), the data are tabulated every hour and the second
ID number in Figure 4 applies. For example, the most northern station off the east coast of
Florida is designated as ID Number 26 for the period 1976 to 1995 and ID Number 147 for the
period 1995 to 1999.


h. (Feet)
12 16 20 24


12l I I I I 1


D


-













S(43,60) (40,54)
(48,65)

(34,47)


(25,33) *

(23,30) *



(18,



*USCOE WIS Stations


27)*


(14,22)* -#


Key West 6 "

Figure 4. Wave Information Study (WIS) Stations Used in This Report.


,147)


*(19,158)


14,164)


174)








4.0 RESULTS


Closure depths were calculated for each of the stations and each of the years for which hindcast
data were available. In addition, for each station, the standard deviations of the closure depths
about their averages were calculated. These results are plotted in Figure 5 where the standard
deviations are shown as vertical bars. Note that these standard deviations have a different scale
than that for the closure depths. Figure 5 also contains the earlier (1989) results. It is seen that for
all locations, the closure depths calculated as part of the present study are substantially greater
than the estimates developed earlier. At some locations on the east coast, the present results are
twice those developed earlier and, for all 14 locations, the average of the present results is 57%
greater than those recommended earlier.



















Legend:
h4-














hin Feet o ,- a a
0 3ft 4 4hin Feet


Figure 5. Closure Depth Values Determined in This Report (Solid Lines) Compared With Those
Determined by Dean and Grant in 1989 (Dashed Lines). The Vertical Bars Represent One
Standard Deviation About the Averages of the Closure Depth Values.
Standard Deviation About the Averages of the Closure Depth Values.








5.0 DISCUSSION


5.1 General

As shown in Figure 5 and discussed previously, the closure depths calculated for this report
based on the WIS data are considerably larger than determined in the earlier study by Dean and
Grant in 1989. At some locations on the east coast, these estimates differ by a factor of two with
an average difference of 57%.

A basis for determining which of the two representations is more correct is to compare with high
quality "ground truth" monitoring results from beach nourishment projects. For this purpose, the
monitoring results for the Anna Maria Key (Manatee County) and the Perdido Key beach
nourishment projects have been selected due primarily to the quality of the monitoring data.

5.2 Method

The basis for the determination of the closure depth, h., from the monitoring data is the so-called
"profile translation method", corrected for the differences in native and nourishment sediment
sizes. If the native and nourishment sands are compatible, the profile translation method can be
written as



h +B=-- (4)
Ay
in which B is the berm height and can be determined from the profiles, v is the average
nourishment volume density (volume per unit length remaining in the project area), and Ay is the
average additional beach width within the project area. In cases in which the nourishment sand
size is greater or less than the native sand size, the term h, +B will be less and greater than given
by Eq. (4), respectively and it is necessary to correct for this difference. One additional
consideration in the evaluation of the appropriateness of the two methods for calculating closure
depths is whether the calculated annual closure depths during the previous few years had been
greater or less than the average. As noted earlier, the time required for onshore sediment
transport and profile recovery are long following a storm event and thus the closure depth
determined from the data at a particular time could be influenced by preceding storm events. The
data employed from the two projects are presented in Table 1.








Table 1


Project Characteristics Employed in "Ground Truthing" Closure Depth Determinations

Median Sediment Previous h.
Date (Years Size (mm) Years (ft)
Project After Relative from
Construction) to Moni-
Native Nourish- Average touring
ment Data


Anna 1999 (6.0) 0.36 0.30 76 75 Stormy 16.9
Maria Key

Perdido 1997 (7.8) 0.35 0.35 157 122 Average 15.0
Key _______


5.2 Anna Maria Key Project

This project was nourished in 1993 and, as noted in Table 1, the survey on which the closure
depth was based occurred approximately six years after construction. The bars over the Ay and v
variables signify project averages. The closure depth determined from the surveys and Eq. (4),
but accounting for the difference in native and nourishment sediment sizes was 16.9 feet versus
13.5 feet determined earlier as presented in Figure 3 and 19 feet based on the WIS data.
Additionally, examination of Figure 2 documents that the few years prior to the survey were
relatively stormy as indicated by the greater than average calculated closure depths. The
explanation for two closure depths for the Year 1995 in Figures 2 and 6 (presented later) is that
the two WIS data bases overlap and each includes results for 1995. Thus, closure depths for the
two 1995 representations were included in the figures.

Table 2

Comparison of Closure Depth Values Based on Monitoring Data and The Two Other Bases

Closure Depth, h. (ft)
Project
Based on Monitoring Based on Based on WIS Data
Data Figure 3

Anna Maria Key 16.9 13.5 19.0

Perdido Key 15.0 17.0 22.5









5.3 Perdido Key Project

The Perdido Key nourishment project commenced in Fall 1989 and was completed in Spring
1990. As noted in Table 1, the survey on which the closure depth was based was almost eight
years after construction. The closure depth determined from the monitoring data was 15.0 feet
versus 17.0 feet determined earlier as presented in Figure 3 and 22.5 feet based on the WIS data.
Additionally, examination of Figure 6 documents that the wave conditions for the few years prior
to the survey were approximately average.



50
WIS Station 48 1976-1995Wh
WIS Station# 65 1995-1999 Survey Date on Which
h. Based

40 -

Average h.

30



c 20 -












Figure 6. Calculated Annual Closure Depth Values for the Vicinity of
Perdido Key, FL.


5.4 Considerations in Closure Depth Specifications

It is evident that if an average closure depth is adopted for use in beach nourishment design
and/or siting of borrow areas, there will be some years when the closure depth exceeds that
adopted. For example, Leadon, et al (1998) have documented that pre- and post-Hurricane Opal
(October 1995) profiles establish that this hurricane transported sediment to water depths
exceeding 30 feet, see Figure 7. As discussed previously, assuming that the pre-Opal profiles
were in equilibrium, it is expected that the long-term onshore forces will result in the landward











10 -V--'. ..... . .......-. .. GULF OF.^'
MEXICO
0


-20oo .






-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
(FEET)
OFFSHORE PROFILE Count OKALOOSA Rang R
11JAN90 BUREAU OF BEACHES
--- 17NOV95 & COASTALSYSTEMS MON. ESTAB.: OCT.1995
EROM1996 ENVIRONMENTAL PROT BEAR: Si W (
i ..i .. .. M R1








Figure 7. Sand Transported to in Excess of the 30 foot Depth Contour by Hurricane Opal
(Leadon, et al 1998).

transport of this sediment and the reestablishment of the equilibrium (pre-Opal) beach profiles.
However, with the presence of borrow pits sited on the basis of the average closure depth,
onshore transport will be intercepted by any borrow pits located landward. Thus the presence of
.40 -1----------------- ---- *- -- ----












these borrow pits will prevent the sand from reaching shore. However, this shoreward transport is
slow and the net effect of the beach recovering slowly probably outweighs the effect of the pits
intercepting the onshore sediment transport. Also considering future storms with the borrow pits
present, the sand will be transported seaward (as in Hurricane Opal), and will be intercepted by
and deposited in the borrow pits from which it can be dredged and transported a shorter distance
to the beach.
There are advantages and disadvantages to siting borrow areas in deeper water. The advantages
include less potential for the pit to interact adversely with the sediment transport regime,
including destabilizing the profile and causing sand to be short-circuited back into the pit and
intercepting sand which is being transported slowly onshore during mild weather or seaward
during storm periods. Also, for pits located farther seaward, there is more distance for the waves
to approach uniformity as they propagate toward shore and the potential for any related erosional
hot spots would be less. The main disadvantages of requiring pits to be located farther seaward
include increased dredging costs and the possibility of good quality sand in the nearshore waters
being designated off limits for beach nourishment.








In summary, there is not an obvious single best representation for the location of a borrow pit.
For example, if the borrow pit is located well outside the region landward of the average closure
depth, considerable good quality sand resources will be placed off limits for little benefit.
However, if the borrow pits are located in too shallow a water depth, they will induce sediment
flows from the beach, thus reducing beach stability and with greater potential for wave
modification that may cause erosion hot spots.

6.0 RECOMMENDED GUIDELINES AND FUTURE EFFORTS

The following are recommended as interim guidelines for closure depth applications.

6.1 Siting of Borrow Pits

It is recommended that borrow pits be sited in water depths which are 25% deeper than the
closure depths in Figure 3 or at a seaward distance that is 25% greater than the distance to the
closure depth contour, whichever is greater. An example is presented in Appendix B illustrating
these recommendations for an actual situation. It is expected that, in almost all cases, the depth
limit will govern.

6.2 Application to Beach Nourishment Design

It is recommended that the closure depths provided in Figure 3 continue to be adopted for design
until monitoring data indicate the appropriateness for modification. Clearly, the results based on
the WIS data are inappropriate based on monitoring data from the Anna Maria Key and Perdido
Key beach nourishment projects and general knowledge of closure depths in Florida.

6.3 Exceptions to Application of Guidelines

Finally, it is recognized that each situation in the siting of borrow pits and selection of closure
depths for beach nourishment design is unique and that extenuating circumstances and/or
judgment may form a valid basis for deviating from the guidelines recommended here.

6.4 Future Efforts to Refine Closure Depth Estimates

It is recommended that efforts be continued to analyze high quality profile data from beach
nourishment projects to provide an expanded basis for the evaluation and improvement of
closure depth representations for beach nourishment design and borrow pit establishment.
Certainly, the need for modifications of the closure depth results presented in Figure 3 will
become apparent with the availability and analysis of more high quality data.








7.0 REFERENCES


Birkemeier, W. A. (1985) "Field Data on Seaward Limit of Profile Change", Journal of
Waterways, Ports, Coastal and Ocean Engineering, American Society of Civil Engineers,
Vol. 11, No. 3, pp. 598 602.

Dean, R. G. and J. Grant (1989) "Development of Methodology for Thirty-Year Shoreline
Projections in the Vicinity of Beach Nourishment Projects", UFL/COEL-89/026, Coastal and
Oceanographic Engineering, University of Florida, Gainesville.

Hallermeier, R. J. (1978) "Uses for a Calculated Limit Depth to Beach Erosion", Proceedings,
16th International Conference on Coastal Engineering, American Society of Civil Engineers, pp.
3874- 3887.

Leadon, M. L., N. T. Nguyen, and R. R. Clark (1998) "Hurricane Opal: Beach and Dune Erosion
and Structural Damage Along the Panhandle Coast of Florida", Report No. BCS-98-01, Bureau
of Beaches and Coastal Systems, Department of Environmental Protection, State of Florida.

Nichols, R. J., W. A. Birkemeier, and R. J. Hallermeier (1996) "Application of the Depth of
Closure Concept", Proceedings, 25th International Conference on Coastal Engineering, American
Society of Civil Engineers, pp. 1493-1512.








APPENDIX A

EXAMPLE CALCULATIONS WITH
THREE CLOSURE DEPTH EQUATIONS








APPENDIX A


EXAMPLE CALCULATIONS WITH
THREE CLOSURE DEPTH EQUATIONS


A.1 Introduction

This appendix presents a brief review of the three closure depth equations that have been
presented in the main body of this report. It is emphasized that the Hallermeier relationship
presented here as Eq. (1) is the most universally applied. For each of the equations, the closure
depth will be calculated for the following wave conditions: He = 7.5 feet and Te = 7 seconds
which results in a closure depth, h. = 14.7 feet based on the Hallermeier equation (Eq. (1)). This
depth is approximately that for the Delray Beach area (h. = 14.5 feet) as determined from Figure
3, thus adding realism to this comparison.

A.2 Equations Compared

A.2.1 Hallermeier Equation

This equation has been introduced earlier as

H2
h =2.28H 68.5( )
gT2




A.2.2 Full Birkemeier Equation

The full form of the Birkemeier equation was introduced as Eq. (2) and is repeated here for
reference purposes

H2
Hh
h = 1.75H, -57.9( g )
gT2


A-i










A.2.2 Simplified Birkemeier Equation


The simplified form of the Birkemeier equation was introduced as Eq. (2) and is repeated here
for reference purposes

h = 1.57He


A.3 Comparison of Calculated Closure Depths

For the wave characteristics described, Table A.1 summarizes the results of the closure depth
calculations based on the various equations.


Table A. 1

Comparison of Calculated Closure Depths


Equation Closure Depth, h. (feet)

Hallermeier (Eq. 1) 14.7

Birkemeier (Eq. 2) 11.1

Birkemeier (Eq. 3) 11.8

It is seen that for the wave conditions considered here, the Hallermeier equation predicts
significantly greater closure depths than the two Birkemeier equations.


A-2


(A.3)









APPENDIX B

EXAMPLES ILLUSTRATING

CLOSURE DEPTH RECOMMENDATIONS








APPENDIX B


EXAMPLES ILLUSTRATING

CLOSURE DEPTH RECOMMENDATIONS


B.1 Introduction

This appendix presents examples of the recommended closure depth guidelines for the siting of
borrow pits and beach nourishment design.

B.2 Siting of Borrow Pits

Suppose it is desired to nourish in the vicinity of northern Martin County and good quality sand
resources have been located in water depths between 30 and 40 feet. A profile is presented in
Figure B.1. Would this depth and location be consistent with the recommendations presented in
this report?


Distance from Monument (ft)
Figure B.1. Profile Near the North Limit of Martin County, FL, Showing the Closure Depth
From Figure 3.


Referring to Figure 3, it is seen that the recommended closure depth in this area is 15.5 feet. This
depth is located approximately 960 feet from the shoreline. Thus, the minimum recommended
depth and distance from the shoreline are 19.4 ft (1.25 x 15.5 feet = 19.4 feet) and 1,200 feet
(1.25 x 960 = 1,200), respectively. Comparing the results with the profile in Figure B.1, it is seen
that the extraction of the good quality sand resources identified is consistent with the guidelines
presented here.


B-1








B.3 Application to Beach Nourishment Design


For this example, we will consider the same area as in previous example such that the
recommended closure depth is 15.5 feet. Suppose the sand is compatible with the native sand and
it is desired to apply a sufficient volume density such that the equilibrated dry beach width, Ay,
will be equal to 100 feet. The berm elevation, B is 6 feet. The so-called "profile translation
method" which relates volume density added, v, to equilibrated dry beach width, Ay, for
compatible sands is

v=Ay(h.+B)=100(15.5+6)= 2,150ft3 / ft (B.1)

Thus, for an equilibrated dry beach width equal to 100 feet, the required volume density, v is
2,150 ft3/ft or 79.6 yd3/ft.


B-2




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