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Closure depth considerations along the Florida shoreline

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Title:
Closure depth considerations along the Florida shoreline
Series Title:
Closure depth considerations along the Florida shoreline
Creator:
Dean, Robert G.
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Language:
English

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University of Florida
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University of Florida
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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 ..................................................1I
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 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.l1 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 Reconmmended 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.
H 2
e gT 2
in which H.e 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
Breaig

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. = 1.75 He-57.9 (-e
gT2
and stated that the following more simple equation would yield nearly equally valid estimates.
.= 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.
W S S~Lio/ 3 1975.11
WIS Stio T, 30) 1905- 1 9D9
Survey Date on Which
h., Based
30.
W Average hi.
10
Io~ ~Q- M cc M C- CO CO
'rime 4n ytear-s
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, T.. 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 ten-n 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- -4AI~:LLV'-k.
1~T

JA MA I I I TST
cc T-T ~ CL V
WP MI 12 16 20 24
h~ (Feet)

24
~20 L
16i

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

12 1. 1 -1 1




(43,60) (40,54)
(48,65)
(34,47) (25,33) (23,30) *
(18,
*USCOE WIS Stations

27) *

(14,22) *

Key West
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.
:ttA
25
Legend:
Scale: STD U i
1, iol", ~ h* in Feet 0 0 6 0
0 3oft h, in 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.




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
14 +B= v (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 14 +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) Ay vYer
(ft) (yd 3/ft) Yas (ft)
Proec AferRelative from
Construction) to MoniNative Nourish- Average toring
ment IData
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
I Closure Depth, h. (ft)
PoetBased on Monitoring Based on Based on WIS Data
JData j Figure3 _Anna Maria Key J16.9 13.5 19.0
Perdido Key 15.0 J 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 Stationf 48 1976-1995 Sre aeo hc WiS Stationlf 65 1995-1999 Sre aeo hc h. Based
40
Average b.
30
0)
0
10
Time in Years
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 ....... .. ....- ... ... G ULF O F
0
-10
-20
EROSON
+ + DEPbSmTON
-30
-40
-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
(FEET)
OFFSHORE PROFILE County. OKALOOSA
11JAN90 BUREAU Or BEACHES I R-36
... -17NOV95 & COASTAL SYSEMS MON. ESTAB.: OCT. 1995
FLA. DE.PT. OF em:So=o'w(re
MM96ENVIRONMENTAL PRO'TECT10lOj
__ .....MAR1996 FADFO BADG i 0 UG)
Figure 7. Sand Transported to in Excess of the 3o 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 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.1l1, 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, 16t' 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-98-0 1, 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 2.28He- 68.5(-) gT 2
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
h, = 1.75He -57.9(-_)

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