Citation
Erosion, navigation and sediimentation imperatives at Jupiter Inlet, Florida: Recommentations for coastal engineering management: Addenda to final report: Appendices H and I

Material Information

Title:
Erosion, navigation and sediimentation imperatives at Jupiter Inlet, Florida: Recommentations for coastal engineering management: Addenda to final report: Appendices H and I
Series Title:
Miscellaneous Publication - University of Florida. Coastal and Oceanographic Engineering Program ; 93/02
Creator:
Mehta, Ashish J.
Affiliation:
University of Florida -- Gainesville -- College of Engineering -- Department of Civil and Coastal Engineering -- Coastal and Oceanographic Program
Place of Publication:
Gainesville
Publisher:
Dept. of Coastal and Oceanographic Engineering, University of Florida
Publication Date:

Subjects

Subjects / Keywords:
Coastal Engineering
Beach erosion ( LCSH )
University of Florida. ( LCSH )
Inlets -- Florida ( LCSH )
Tidal currents -- Florida ( LCSH )
Spatial Coverage:
North America -- United States of America -- Florida -- Jupiter Inlet
North America -- United States of America -- Florida -- Loxahatchee River
North America -- United States of America -- Florida

Notes

Abstract:
Sponsor: Jupiter Inlet District Commission, 400 North Delaware Boulevard, Jupiter, FL 33458
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact Digital Services (UFDC@uflib.ufl.edu) with any additional information they can provide.

Full Text



UFL/COEL/MP-93/02


EROSION, NAVIGATION AND SEDIMENTATION
IMPERATIVES AT JUPITER INLET, FLORIDA:
RECOMMENDATIONS FOR COASTAL ENGINEERING
MANAGEMENT: ADDENDA TO FINAL REPORT:
APPENDICES H AND I





by


Ashish J. Mehta


October, 1993





Sponsor:
Jupiter Inlet District Commission
400 North Delaware Boulevard
Jupiter, FL 33458





REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Iacipient 's Accessioe o.


4. Title aod Subtitle Report Date
EROSION, NAVIGATION AND SEDIMENTATION IMPERATIVES AT October, 1993
JUPITER INLET, FLORIDA: RECOMMENDATIONS FOR COASTAL
ENGINEERING MANAGEMENT: ADDENDA TO FINAL REPORT:
APPENDICES H AND I _
7. Autbor(s) 8. PerformiLn Organizatioo Report No.
Ashish J. Mehta UFL/COEL/MP-93/02

9. performing Organisation ama and Address 10. rzrject/Task/Mork Unit Mo.
Coastal and Oceanographic Engineering Department
University of Florida 11. contract or crant No.
336 Weil Hall
Gainesville, Florida 32611 13. Typ of Report
12. Sponsorinf Organiation Name and Address
Jupiter Inlet District Commission Addenda to Final Report
400 North Delaware Boulevard
Jupiter, Florida 33458
14.

15. Supplemtary Motes



16. Abstract
Appendices H and I contained herein are addenda to the following report:


Mehta A.J., Montague C.L. and Thieke R.J. (1992). Erosion, navigation and
sedimentation imperatives at Jupiter Inlet, Florida: recommendations for coastal
engineering management. Report UFL/COEL-92/002, Coastal and Oceanographic
Engineering Department, University of Florida, Gainesville, 238p.


These appendices have been written to expand the scope of the management plan to include an element
related to the stability of the interior banks of the inlet channel close to the inlet mouth, where areas prone to bottom
scour or sedimentations exist. These phenomena were examined in detail previously in the following study:


Buckingham W.T. (1984). Coastal engineering investigation at Jupiter Inlet, Florida.
Report UFL/COEL-84/004, Coastal and Oceanographic Engineering Department,
University of Florida, Gainesville, 243p.





17. Orignator's Key Vords 18. Availability Statemet
Beach erosion
Inlet management
Jupiter Inlet
Loxahatchee River
Tidal entrances
19. U. S. Security Classif. of the Report 20. U. S. Security Clasaif. of This Page 21. No. of Patge 22. Price
Unclassified Unclassified 39










UFL/COEL/MP-93/02


EROSION, NAVIGATION AND SEDIMENTATION IMPERATIVES AT JUPITER INLET, FLORIDA:
RECOMMENDATIONS FOR COASTAL ENGINEERING MANAGEMENT:
ADDENDA TO FINAL REPORT: APPENDICES H AND I




by




Ashish J. Mehta















Sponsor:


Jupiter Inlet District Commission
400 North Delaware Boulevard
Jupiter, FL 33458


October, 1993










SYNOPSIS


Appendices H and I contained herein are addenda to the following report:


Mehta A.J., Montague C.L. and Thieke R.J. (1992). Erosion, navigation and
sedimentation imperatives at Jupiter Inlet, Florida: recommendations for coastal
engineering management. Report UFL/COEL-92/002, Coastal and Oceanographic
Engineering Department, University of Florida, Gainesville, 238p.


These appendices have been written to expand the scope of the management plan to include an element
related to the stability of the interior banks of the inlet channel close to the inlet mouth, where areas prone to bottom
scour or sedimentations exist. These phenomena were examined in detail previously in the following study:


Buckingham W.T. (1984). Coastal engineering investigation at Jupiter Inlet, Florida.
Report UFL/COEL-84/004, Coastal and Oceanographic Engineering Department,
University of Florida, Gainesville, 243p.











TABLE OF CONTENTS

SYNOPSIS ............................................................ ii

LIST OF FIGURES ...................................................... iv

LIST OF TABLES ....................................................... v

APPENDIX H: MANAGEMENT CONSIDERATIONS RELATED TO IMPACTS OF RECOMMENDED
ACTIONS ON INLET CHANNEL BANKS ................................. 1


HI. Introduction .................
H2. Scope .....................
H3. Impact Assessment .............
1H Action PI ................
1.1H North Bank ...........
1) Natural Processes......
2) Boat Wakes .........
3) Trap Dredging .......
4) Bulkheads ..........
5) Other Engineering Works


1.2H South Bank ...
2HAction P2 .........
2.111 North Bank ...
2.2H South Bank ...
3H Action P3A ........
3.1H North Bank ...
3.2H South Bank .
4H Action P3B .......
4.1H North Bank ...
4.2H South Bank ...
51 Action 12.........
5.1H North Bank ...
5.2H South Bank ...
H4. Causes of Impacts .....


H5. Recommendations for Impact Management/Mitigation ....................... 15
i. Boat Wakes Plus Tidal Current ................................... 15
ii. Episodic Ocean Waves Plus Tidal Current ............................. 16
iii. Tidal Current ............................................... 16
iv. Trap Dredging ............................................. 16
v. South Jetty Modification ........................................ 20
H6. Concluding Comments ........................................... 20

APPENDIX I: BANK STABILITY RELATED CALCULATIONS AND COMMENTS .......... 22
I1. Bank Slope Stability ............................................ 22
12. Boat-Induced Waves and Bottom Scour ................................ 25
12.1 Computation of Boat-generated Waves and Associated Bed Shear Stress .......... 25
12.2 Scour In Front of Bulkhead ..................................... 28
13. Trap Expansion and Efficiency ...................................... 28
14. Bulkhead Site Visit ............................................. 30

BIBLIOGRAPHY ....................................................... 34


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


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


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


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










LIST OF FIGURES


FIGURE PAGE
H.1. Problem areas of erosion and sedimentation identified in Buckingham (1984) ............... 2

H.2. Channel bathymetry after dredging. Note the depression marked P and shoals marked Q and R.
Depths are in feet. Numbers in parentheses are depths at specific sites between contours. Dots
indicate locations where the impact of dredging on tidal current speed is predicted in Table H2 .... 4

H.3. A typical channel cross section showing the trap. The top plot is based on a distorted scale;
the bottom is undistorted. Notice the different visual impacts of the scales on slopes; the
actual slope (bottom plot) is comparatively mild. Bank slope between points M and N is assumed
to be uniform. The actual slope may be milder; however, measurements between points M and N
that are contemporaneous with the remainder of the survey are not available. Marginal "channels"
are believed to represent natural depressions. ................................... 4

H.4. Courses followed by surface drogues released from a boat during a flood event (Buckingham, 1984)
Note the manner in which the drogues "grazed" a portion of the shoreline, implying a strong
flood flow action against that portion of the bank ............................... 8

H.5. Modifications made to the southjetty in 1967 ................................. 11

H.6. Variation of boats registered in Palm Beach County with years since 1960. ............... 14

H.7. Wood sheet pile seawall with toe protection (from Collier, 1975). ................... .. 14

H.8. Plan view of proposed trap based on a drawing by Lidberg Land Surveying, Inc. The design is
based on a recommendation for trap expansion per UF3 (see Chapter 4). Sloughing allowance is
per suggestion by Applied Technology Management, Inc. (Grella, personal communication) ..... 19

I.1. Typical bulkhead .................................................... 31

1.2. Concrete sheet pile wall ............................................... 32











LIST OF TABLES


TABLE PAGE


H1 An a priori qualitative assessment of recommended actions and potential physical impacts
relative to channel banks. .............................................. 5

H2 Maximum water velocity (un) predictions near the north bank under three inlet channel
configurations. .................................................... 9

H3 Noteworthy factors influencing bank stability in decreasing order of importance. ............ 15

I1 Results of computation on transverse bank stability .................. ........... 24

12 Computation on boat-generated waves ...................................... 26


F I










APPENDIX H: MANAGEMENT CONSIDERATIONS RELATED TO IMPACTS OF RECOMMENDED
ACTIONS ON INLET CHANNEL BANKS


HI. Introduction
To date, three noteworthy studies have been carried out to assess the state of Jupiter Inlet and propose
changes, where necessary, with respect to navigational access and safety, shoreline erosion, and sedimentation in
the interior areas of the inlet. The first study, UF1 (Coastal Engineering Laboratory, 1969), was mainly concerned
with improving navigation by appropriate modifications to the jetties. The second study, UF2 (Buckingham, 1984)
was concerned with erosion along the interior shorelines or banks, and sedimentation localized in the Dubois Park
area and the adjacent public marina (which was then in use). The management goals of the third study, UF3, are
described in Chapter 4 of this report; they deal with navigation, beach erosion and sedimentation in the interior.
The purpose of this appendix (and the next) is to visit the question of the impacts of recommended actions in
Chapter 4 on the southern and northern banks of the inlet channel. Concerns for potential impacts arose after UF3
was completed in 1992. This appendix and the next thus represent an addendum that was incorporated in 1993.
While impacts within the channel can be both physical and ecological, the latter have essentially been
addressed in Appendix F. Here, in conjunction with the scope of UF2, we will deal with physical impacts of the
recommended actions on the interior shorelines examined in that study.


H2. Scope
As a precursor to impact examination, it will be necessary to delineate the inter-relationships between the
scopes of the three studies whose goals were commensurate with then existing needs. In UF3, navigational safety,
beach erosion and sedimentation in the interior areas were considered, and in quantitative evaluations of alternatives
for improvement, navigation and beach erosion were given equal weights, while sedimentation was weighted one-
half. This weighting was done in an effort to quantify management policy via development of a decision matrix for
the technical options (Grella, 1993).
In UF1, jetty designs were examined in a physical model for improvements in navigation, in essentially
the same manner as at several other East Coast inlets (see, e.g. Bruun et al., 1966). Since beach erosion potential
was not examined explicitly (in contrast to UF3), had any of the designs, e.g. an extended north jetty, been
implemented, a mechanical means for sand bypassing would have had to be instituted to stabilize the south beach.
(See recommended actions P3A and P3B in Chapter 4.)
UF2 was concerned with the region shown in Fig. H.1, which appears as Fig. 1.5 in Buckingham (1984).
Sites A,B,C,D,G and H highlight areas where erosion problems were examined, and sites E,F and I indicate areas
where sedimentation was a problem. In this context, differences between the goals of UF2 and UF3, the latter
outlined in Chapter 4, are noteworthy. In UF3, erosion and bank stability along the north and south banks of the
inlet channel were not examined as a part of the protocol in developing management options (recommended actions).


-L


















N


Jupiter Inlet Colony


O 100 200m
scale


Deposition Basins


XM"T\M\23 Erosion
-:'. Accretion


Figure H.1. Problem areas of erosion and sedimentation identified in Buckingham (1984).


1,\
-Z-


\ 7
CI


I I
r J

L 't EP.P..









Likewise, sedimentation in areas shown in Fig. H. 1 were not considered. Instead, the primary concern in UF3 was
for sedimentation in marinas further westward than the public marina shown in Fig. H.1, (see Fig. 2.5 for the
location of the marinas), and in the aquatic preserve west of the FECRR bridge shown in Fig. 4.14. It is therefore
evident that bank erosion (and associated bank stability) and sedimentation concerns in UF2 were not addressed in
UF3.
For the purpose of this appendix, the same regions of erosion and deposition as those shown in Fig. H. 1
will be considered, since the problems continue to remain the same qualitatively, even though quantitatively there
may have been changes in the intervening years. In part, changes in the erosion/deposition regime may have been
due to engineering works, such as the placement of additional rocks westward of point D in Fig. H. 1 to contain
erosion there. Other changes may be natural, e.g. due to continued infilling of Dubois Park lagoon. Such changes
are however not believed to have materially altered the nature of the problems since 1984, when UF2 was
completed.
At this point it is essential to make an a priori, albeit qualitative, assessment of the potentiality of any
physical impacts of the recommended actions (Table 4.2) on erosion/sedimentation and bank stability. Table HI
repeats the information in Table 4.2, and also provides the assessment. In what follows likely impacts of each action
requiring an examination are dealt with. In so doing, we have relied upon several sources of information: 1) site
visits, 2) UF1, UF2 and UF3 studies, 3) numerical computations as extensions of UF3, 4) analytic calculations
including those in Appendix I, 5) other assessments (e.g. bulkhead assessment given in Appendix I), and 6) other
relevant publications, surveys and information of a technical nature.


H3. Impact Assessment
1H Action P1
1.1H North Bank: This action proposes an expansion of the sand trap (shown with nominal dimensions in
Fig. 4.6), an increase in trap dredging frequency to once per year (at least), and a rearrangement of the sand
placement protocol on the south beach (as shown approximately in Fig. 4.5). The last will have no tangible impact
on the interior shorelines, hence is not considered further. Annual dredging of the trap has been the recent practice;
dredging at a higher frequency (e.g. twice per year) should be required only as needed, either due to excessive
shoaling of the channel, or for procuring sufficient sand when there is a substantial erosion of the south beach. In
either event, the trap bottom will remain deeper on a time-average basis than in the past, when there were periods
of biennial dredging. Thus, impact issues related to increasing the dredging frequency are, to an extent, linked to
those for the proposed trap expansion, since expansion and frequent dredging are to be carried out more or less
simultaneously to improve the sand trapping efficiency of the channel.
A contour map of the bottom in the trap area following dredging in 1993 is shown in Fig. H.2. A cross-
section of the channel starting approximately at the bulkhead of property lot 79 is shown in Fig. H.3. The trap is







































Fig. H.2. Channel bathymetry after dredging. Note the depression marked P and shoals marked Q and R. Depths
are in feet. Numbers in parentheses are depths at specific sites between contours. Dots indicate locations where the
impact of dredging on tidal current speed is predicted in Table H2.

1- M 1 vertical : 10 horizontal

o N

-1

-2- "Channel"
"Channel"
-3-J

-4-

E -5- Trap

-6-
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
Q)
"o
L-
0)
;5 1 vertical : 1 horizontal



0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
distance from North Bulkhead (m)

Fig. H.3. A typical channel cross section showing the trap. The top plot is based on a distorted scale; the bottom
is undistorted. Notice the different visual impacts of the scales on slopes; the actual slope (bottom plot) is
comparatively mild. Bank slope between points M and N is assumed to be uniform. The actual slope may be milder;
however, measurements between points M and N that are contemporaneous with the remainder of the survey are
not available. Marginal "channels" are believed to represent natural depressions.









Table HI: An a priori qualitative assessment of recommended actions and potential physical impacts relative to
channel banks.
Impact
No. Action North Bank South Bank

1 P1 (Trap dredging and sand placement protocol modification) Ra R

2 P2 (P1 + raising north and south jetty elevations and extend
south jetty) R R

3 P3A (P2 + north jetty extension and installation of beach sand
bypassing facility) R R

4 P3B (P2 + Installation of a sand fluidizer system in the channel) R R

5 II (Modification of Corps trap dredging protocol) No No

6 12 (Regulating boat speed) R R

7 13 (Placement of beacons) No No

8 14 (Dredging offshore navigation channel) No No

9 15 (Offshore dredging for sand equity) No No

10 16 (Interior trap dredging) No No

'Requires examination


identified as a depression between approximately 48 m and 143 m from a bulkhead at the north bank. An important
issue that needs to be addressed is if sand is drawn away from the bulkheads into the existing trap and, if so, what
the causes might be. This issue has a potentially significant bearing on the question of stability of the mostly
bulkheaded north bank shown in Fig. H.1, especially in view of the proposed trap expansion.
At the outset it must be recognized that no direct evidence to support or refute the possibility of sand
transport paths leading directly from the bulkhead to the trap in such a way as to cause local scour in front of the
bulkhead exists, even though local scour is indeed known to have occurred. Consequently, a clear-cut answer related
to sand transport pathways must await further studies. Here we will attempt to explore available (indirect) evidence
and identify various sand displacing causes and their qualitative effects.
A noteworthy evidence of erosion in front of the bulkheads is provided by observations of local residents.
According to one account (Etherington, personal communication), at some locations the bed at the toe of the
bulkhead has scoured by as much as 3 to 4 ft (0.9 to 1.2 m) since 1965. In that context, Snyder (1993) cites JID
records of 1960 according to which, at that time, a sandy shoreline existed along the bulkheads at low tide level.
This is the year in which trap dredging commenced formally, and for several purposes, we will conveniently select









that date as the "base" year. Contemporary aerial photographs of the inlet (stage of tide unknown), and also later
ones from the late Sixties, tend to support this documentation, i.e. the presence of more sand on the bank beaches
than at present. Note that the seeming time-lag between the beginning date of trap dredging and the eventual loss
of sand suggests that irrespective of the causes) of sand loss, the rate of loss was perhaps steady but certainly very
slow.
Snyder (1993) estimates that the total amount of sand lost over the past 33 years is approximately 3,000 m3
(about 4,000 yd3). This erosion has occurred over an approximately 410 m of shoreline. Thus, assuming a 3 m
shore-normal distance of the beach in question, the rate of erosion has been (3000)/(410)(3)(33) = 0.074 m3 per
square meter of bottom per year. While this rate is very small for an inlet bank such as at Jupiter, it is a matter of
considerable concern to the residents, since sand loss has created the potential possibility of eventual toe failure at
the bulkheads.
There appear to be five principal causes of scour at this site: 1) natural processes including waves and
currents, 2) boat wakes, 3) trap dredging, 4) presence of the bulkheads, and 5) other engineering works. These are
described briefly in the sequel.
1) Natural Processes: UF2 identified tidal current and, to an extent, the impingement of refracting oceanic
waves in the area of concern, (a part of which does not readily receive oceanic sand due to the natural,
cove-like configuration of the region,) as two of the significant causes of erosion. These causes are still
effective, and there is no reason to believe that their role has diminished in the absolute sense. They were
also present 33 years ago. Assuming at first that the primary agent is the tidal current, simple calculations
presented in Appendix I can be taken as a rough guide. The effect of bank slope on scour is included in
these calculations. Results in Table I1 suggest that the fluid stress due to current at the bottom in the
vicinity of the bulkheads causes a winnowing effect, whereby finer sand grains (of diameters smaller that
around 0.36 mm and having critical stresses lower than the fluid stress) are "washed away", leaving the
larger ones (with critical stresses greater than the fluid stress) in place. Grain size data reported in UF2
do suggest the occurrence of an armoring effect and, based on the relatively low rate of erosion reported
in the area it can be inferred that armoring of the bottom by the larger grain tends to impart a degree of
stability to the bottom. Given this observation and the fact that ocean waves, which have mainly episodic
impacts, occurred even in earlier times when the banks were fronted by more robust beaches suggests that
other causes of erosion in recent years must also be explored. (Note, however, that before 1967 wave
intrusion was possibly less severe; see later.)
2) Boat Wakes: UF2 qualitatively identified boat wakes as a significant potential cause of bulkhead
damage, and in our opinion this observation is even more important now then in 1984, when UF2 was
completed. According to recent survey data provided by JID (Grella, personal communication) the majority
of the boats are 16 ft (4.9 m) to 30 ft (9.1 m) in size. Usage is heavy during weekends, but week days are










by no means excluded. Thus, boat wakes are ubiquitous in this area, and their action on the shorelines in
the inlet area is visually quite evident.
Here we may consider the simple calculations presented in Appendix I as an approximate guide.
These calculations indicate that typical boat-induced waves may nearly double the fluid stress at the bottom,
in the vicinity of the bulkheads. This increase is sufficient to mobilize all sizes of sand grains present there.
Furthermore, these waves potentially cause a local bottom scour depth on the order of a foot (the actual
calculated value is 35 cm) immediately in front the bulkheads, in areas where a sandy bank does not front
the bulkhead. When a bank is present, wake-induced local scour can lead to a general scour (bed elevation
lowering) as the material is gradually winnowed away, thus in turn inducing further local scour. Eventually
the entire bank can be lowered by this process to result in an elevation lower than the low tide level.
Presently such a situation exists at numerous segments of the bulkheaded shoreline.
3) Trap Dredging: Trap dredging is an anthropogenic action which unquestionably influences the physical
regime of Jupiter Inlet. The extent to which it causes toe erosion at the bulkheads remains unresolved.
However, we would like to offer the following comments.
The numerical hydrodynamic model for tidal flow in the inlet region used in UF3 was used to
calculate the tidal prism for this inlet, which is 6.34x10m3. When the trap is dredged, the mean water
velocity over the channel cross-section in the trap area is generally reduced, given that the tidal prism does
not increase measurably, because the channel cross-section east of the trap does not change (see calculations
presented by Applied Technology Management, Inc. in Snyder, 1993). This reduction (see Table H2) is
in fact the primary reason for the sand-catching ability of the trap. More regular dredging of the trap, as
proposed would mean lower velocities over longer periods than in the past. Lower mean velocities do not,
however, in themselves imply that the trap does not draw sand directly by way of grain rolling over the
slopes in the vicinity of the bulkhead. We therefore need to examine the stability of the bank slopes in the
area.
With regard to bank slopes, the angles are generally in the range of 50 to 260 (see comments in
the caption to Fig. H.2), while the critical angle for failure is 300 to 310 (Table II, Appendix I). Thus in
some spots the actual slope is close to that for failure, but the evidence for failure by gravity slide does
not appear to be clearly present. If so, where do the fines (less than around 0.36 mm) that are winnowed
away end up? There is no evidence to refute the possibility that at least some end up in the trap itself. On
the other hand, water motion studies in UF2 (see, e.g. Fig. 2.9 in Buckingham, 1984, reported as Fig. H.4
here) clearly show that there is a strong flood flow pathway that leads towards Jupiter/Hobe Sound due
north, and the ICWW "trap" (Fig. 2.4). Sedimentological investigation in UF3 shows that fine sand does
deposit in the area within and surrounding the Corps trap (Map 5, p. 125). Finer fractions are further
carried into the aquatic preserve, as evidenced by the (very) slow growth of the shoals there. (Calculations



















































0 75 150m
cole


Fig. H.4. Courses followed by surface drogues released from a boat during a flood event (Buckingham, 1984).
Note the manner in which the drogues "grazed" a portion of the shoreline, implying a strong flood flow action
against that portion of the bank.


J


OCEAN


ROUTE DIST4m) TIME(s) VELimn/)
BOAT-013 232 160 1.45
BOAT-CS3 286 220 1.30
BOAT-W13 345 280 1.23
013-014 150 175 086
013-014 15 ITS 065
W13-W14 177 175 1.00
014- 016 10 10 1.00
014.-16 91 160 0.51*
W 14-W6 189 180 1.05
016 -017 110 95 1.15
WI6 -WIT 70 95 0.74
017 .018 76 90 0.85
W17 .WIS 70 90 076
018 .019 76 100 076
W16 -W9I 46 100 046
019 -020 107 155 069
W19 -W20 110 55 0.71
020 -022 61 310 0.20
W20 -W22 1001 310 0.335
* DROGUE PICKED UP AT THIS POINT






Table H2: Maximum water velocity (u) predictions near the north bank under three inlet channel configurations.

Configuration Location um (flood) um (ebb)
(m/s) (m/s)
Existing without dredged trap Westa 0.94 0.99
Central 0.80 0.79
Easta 0.73 0.61
Existing with dredged trap West 0.93 0.96
Central 0.64 0.67
East 0.50 0.57
South jetty extension plus enlarged trapb West 0.94 0.89
Central 0.65 0.64
East 0.49 0.54

aApproximately 50 ft (15 m) off the bank. See Fig. H.2 for locations.
blmpact is mainly attributed to trap expansion as opposed to jetty extension.


indicate that the annual influx of sand which moves westward past the FECRR bridge ranges from 1,000
to 2,400 yd3, or 800 to 1,800 m3; see p. 57).
Notice in the cross-section of Fig. H.3 a distinct trough or depression (or a marginal "channel")
between the bulkhead and the trap. This depression appears to represent a secondary flow channel in the
neighborhood of the bulkhead as seen in Fig. H.2. This figure shows the secondary channel to be flanked
by the bulkheads on one side and shoals Q and R on the other. Note also the depression marked P within
the channel. Drogue studies (e.g. Fig. H.4) seemingly corroborate the flow diverting role of the channel
towards the bulkhead. In turn, this channel is likely to be the main conduit for the upstream transport of
grains, including those derived from the bank in front of the bulkheads.
4) Bulkheads: The role of the bulkheads in scour was qualitatively examined in UF2, and the fact that
scour inherently results when waves impinge upon them was noted earlier. A recent assessment (Appendix
I) of their state and their role in causing scour does not materially change the observations made in 1984,
although, apparently, in the intervening years some of them have been replaced and/or strengthened by rock
revetments or otherwise. There is however concern on the part of the local residents that, among other
effects, toe scour causes protective measures such as rock revetment to be undermined in due course, thus
requiring additional riprap protection or other measures to prevent bottom bulkhead failure.
The need for continued measures to protect residential land from loss by marine forces, especially
boat wakes and also, to an extent, episodic waves was clearly established in UF2, and that need
unquestionably exists at present. Interestingly enough, the bulkheads (thus far at least) have consistently
withstood toe scour, and have not failed from that mode scour (Appendix I). Instead, where failure appears
potentially imminent, it is believed to be due to inadequate anchorage provided by the tie-bars (Appendix
I). For a general description of the types of bulkhead failures encountered in Florida, see Collier (1975).






5) Other Engineering Works: Of the engineering works other than trap dredging carried out since 1960,
south jetty modifications in 1967 is noteworthy. As shown in Fig. H.5 (reproduced from Mehta et al. 1990,
Part II, Fig. 3.4), an angular sheet pile and cap extension of the jetty was essentially removed, and the jetty
extended linearly seaward by approximately 100 ft (30 m). Removal of the angular extension is likely to
have been a comparatively much greater perturbation to channel hydraulics than the seaward jetty
extension, simply because this removal increased the inlet throat cross-section, hence the tidal prism. It also
increased the admittance of ocean waves. Although no estimates of the increase in the prism are available,
a simple calculation based on the relationship between the throat area and prism (Bruun, 1978) suggests
that the increase was probably on the order of 10%. Thus, while the removal of the angular extension was
meant to benefit navigation, a likely added benefit was the enhancement of tidal flushing of the inlet due
to increased water flow, hence water quality. The degree to which this action caused sand loss (as a result
of a higher strength of flow due to the increased prism, and also due to wave action) cannot be easily
determined at this late date. However, it should be noted that changes such as these to the inlet mouth can
cause a measurable readjustment of channel morphology over the subsequent years (Bruun, 1978). We
consider this effect to be noteworthy, but do not assign it a high grade as the causative factor in sand loss,
even while recognizing that historically it may not have been altogether negligible.


1.2H South Bank: In this case the main concern is the potential impact of expanding the trap on the stability of
the bank along Dubois Park. The southern edge of the trap will be closer (by about 50 ft or 15 m) to the shoreline
between points D and G in Fig. H. 1. Much of this shoreline is protected by riprap or concrete, while the remainder
is sandy. Trap expansion will indeed not increase the stability of the shoreline, but at the same time our expectation
is that adverse effects of the expansion will not be "felt" measurably (Table H2). If however visual and other means
of monitoring over, say, two years after expansion of the trap can unequivocally demonstrate detrimental effects,
then the benefits of trap expansion versus the cost of decreased stability of the shoreline will have to evaluated for
further actions, including possibly the abandonment of the expansion project, implementation of some of the
proposed actions for this stretch of the shoreline in UF2, or others. In the last context we note that the proposed
stabilization of the promontory near point H in Fig. H.1 according to Palm Beach County's plan [per permit
application no. 199300768(IP-EJ) to the U.S. Army Corps of Engineers, Jacksonville District] appears to be in line
with the proposed action for the region in UF2 or, at the least, is meant to accomplish essentially the same purpose,
i.e. enhancement of bank stability.


2H Action P2
2.1H North Bank: Here we must address the impact of raising the seaward sections of the north jetty and the
south jetty by about 1 m (3 ft), and extending the south jetty by 53 m (175 ft) on interior shoreline stability. The


10



























0
-I \
0.
0b


rt SLne jupiter Inlet
-- t~R\ Ln


BID ITEM A -----
Remove Existing Sheet Pile and Cap to
Elevation -10.00 ft, Within These Limits ,
~-~~--J


BID ITEM B
Construct Approximately 100 Linear Feet -
of Steel Sheet Pile and Granite Jetty


0 10 200 South L
0 100 200 ft
I I 1


Fig. H.5. Modifications made to the south jetty in 1967.


11










purpose of raising the jetties is to reduce episodic influx of sand. [This action will not reduce the tidal prism,
however. Likewise, numerical hydrodynamic computations carried out in UF3 suggest that extending the south jetty
will not have any substantial change in the tidal prism, because : 1) the inlet throat section will not be altered, and
2) jetty extension will not increase flow dissipation in the channel itself in any measurable way.] Even though the
north bank is apparently starved of sand, the anticipated 11,500 m3 (15,000 yd3) reduction in sand supply on an
annual basis is unlikely to impact the shoreline measurably. Such will be the case because the supply of littoral sand
to the north bank appears to be mainly limited by its natural concave configuration (see Buckingham, 1984), and
considerably less so by the rate of supply via transport of sand around and over the north jetty (or the south jetty).
UF2 showed that sand that is transported around and over the north jetty moves mainly through (more or
less) the northern half of the channel, while sand which enters around and over the south jetty moves mainly over
the southern half. Given these approximate "compartmentalized" sand transport pathways, modifications to the
jetties, as proposed, are unlikely to decrease the stability of the northern bank in a measurable way, although no
increase in stability can be expected either.


2.2H South Bank: Following arguments presented in Section 2.1H above, raising the north jetty is unlikely to
impact the stability of the south bank. Extending and raising the south jetty is meant to reduce the influx of sediment
by around 9,200 m3 (12,000 yd3) per year. However, given the natural concave shape of the Dubois Park
shoreline, we anticipate that the main impact of reduced littoral sand transport into the channel will be in terms of
reduced deposition of sand in the trap, and reduced westward transport past the trap. The main causes of erosion
at points D and G (Fig. H.1) have been identified in UF2 (Buckingham, 1984), and solution options were
investigated in that study. We continue to recommend the then proposed protective structures for the Dubois Park
beach area in the vicinity of point G. As for point D and vicinity, the placement of large rocks via a westward
extension of the south jetty since 1984 does not seem to have arrested the erosion problem, although it may be less
severe than before rock placement. Unfortunately, as a result, the riprap revetment design proposed in UF2 may
no longer be suitable, since that design was meant for the bank which was not covered by the large rocks placed
there as mentioned. Nevertheless, it should be feasible to design a suitable revetment for that region without much
additional studies, should further protection become essential. As for the promontory in the vicinity of point H, see
comments under Section 1.2H.


3H Action P3A
3.1H North Bank: In this case, the proposed extension of the north jetty is a matter of considerably greater
consequence as far as impact is concerned, than the concurrent beach sand bypassing facility. As mentioned in
Section 10, p. 43, the purpose of north jetty extension would be to improve navigation by virtue of a measurable
reduction in wave heights within the channel. Thus the proposed extension would reduce episodic wave action










against the bulkheads, thereby prolonging their life and reducing toe scour potential. This action may, on the other
hand, increase boat wake-induced scour, if improved accessibility leads to a greater boat traffic. Given the
considered dominance of boat wakes on bulkhead stability, there may be no overall benefit of this action on the
northern shoreline.
The bypassing plant will reduce the influx of sand; however, for reasons cited under Section 2.1H, a
significant negative impact of plant installation and operation on bank stability is unlikely.

3.2H South Bank: Impacts in this case will be similar to those at the north bank.

4H Action P3B
4.1H North Bank: The impact of north jetty extension is noted in Section 3.1H. In this case, however, the sand
bypassing system would be located in the trap. This arrangement is to ensure a continuous, or "as needed basis",
dredging of the trap to -19 ft (-5.8 m), with a consistently deeper bottom than in the case of annual hydraulic
dredging. Given a tenuous linkage between the trap and bank stability however, the presence of a deeper trap would
imply lower scour potential in the vicinity of the bank due to reduced current velocities. In any event, the stability
of the bank is unlikely to be undermined.


4.2H South Bank: See Section 3.2H. Note, however, that pumping and associated facilities will have to be based
in the Dubois Park area. This requirement, although in no way connected with bank stability, is a factor that must
be evaluated in conjunction with the placement of the fluidization system.


5H Action 12
5.1H North Bank: In agreement with the observational findings of UF2, we consider boat wakes to be the most
important cause of toe erosion (see 1.1H), as well as damage to the bulkheads by direct onslaught of impinging
waves. In Fig. H.6, an approximate relationship between the number of boats registered in Palm Beach County and
years since 1960 is plotted. On the basis of this plot, it is evident that there has been a substantial increase in
registered vessels over the past 33 years. While it is not certain if this trend will continue (note the recent decline),
a noteworthy, albeit rather indirect, inference is that wakes have been an increasing problem since 1960 in the inlet
area, assuming that boating trends in this area correspond with those of the county as a whole. Boat speeds must
be regulated for insuring bank stability.


5.2H South Bank: Here as well boat wakes do impact the shoreline, but overall the effects are likely to be less
significant than those along the north bank because: 1) a significant section of the shoreline is protected by concrete
and riprap, and 2) the normal navigational route for vessels is slightly more distant than from the north bank.
Reducing boat speeds should help in the retention of any placed sand in the cove-like beach area of Dubois Park,


i











40000


LLJ
W L

s. 30000-


U *
Cn

5 20000- *
0
u Mean Trend
0
n-
w 10000 -





1960 1970 1980 1990

YEAR

Fig. H.6. Variation of boats registered in Palm Beach County with years since 1960.


Fig. H.7. Wood sheet pile seawall with toe protection (from Collier, 1975).


14


_ ____









but otherwise speed control doe not appear to be wholly essential. Note that erosion in the vicinity of point D is
believed to be largely episodic, induced by ocean waves and associated storm surges.


H4. Causes of Impacts
Given the large number of marine and anthropogenic factors that actually influence bank stability, and the
variability in the degree of dominance of each, it is difficult to identify any one particular factor as being uniquely
responsible for negative impacts to the banks. In our judgement, the following noteworthy factors have influenced
bank stability since 1960; in Table H3 they are arranged in qualitatively decreasing order of importance. Since their
general significance has already been noted, it remains to examine ways to manage or mitigate the impacts.


Table H3: Noteworthy factors influencing bank stability in decreasing order of importance.

Factor Comment

Boat wakes plus tidal current Increasingly important since 1960
Episodic ocean waves plus tidal current Have always been operative
Tidal current Has always been present
Trap dredging Since 1960; however, dredging of channel actually
began in the late Forties
South jetty modification In 1967; effect probably became negligible -10
years later



H5. Recommendations for Impact Management/Mitigation
i. Boat Wakes Plus Tidal Current
Given the likelihood that it will be difficult to legislate and enforce boat speeds in the inlet area, adequately
defending the shoreline against boat wakes in the presence of tidal current is perhaps the only realistic option. With
regard to the state of the existing bulkheads, comments in UF2 and in Appendix I are noteworthy. For a
bulkhead/concrete sheet pile wall that is robust, protection by riprap, as already afforded at some sections, is
recommended, although specific designs are beyond the scope of this study. It appears (Snyder, personal
communication) that at some sites bottom instability at the toe has possibly led to some undermining of the placed
rock, thus requiring a form of toe protection wherever such is an issue. Although the actual design of an appropriate
structure will be site specific and beyond the present scope, Fig. H.7 shows an example using wood (Collier, 1975).
At Jupiter Inlet the material will probably have to be steel or reinforced concrete sheet pile.
A degree of uncertainty in the above approach is related to the fact that the structure of the bottom in the
bulkhead area remains unknown; thus, if and where hard rock is present, it may be difficult to drive a sheet pile
toe wall. In this case, an alternative would be to drive a pre-stressed concrete batter pile into the bottom at a suitable









angle to support the bulkhead, if necessary. In most cases, however, the bulkheads, assuming they are in a
structurally robust condition or are repaired to make them as such, can be protected by rock riprap over a filter cloth
base. In a few cases this arrangement can be supplemented by a batter pile support. An important consideration in
all cases will be the need to carefully inspect the bulkheads, and develop site-specific solutions that assure pre-
established design standards for performance.


ii. Episodic Ocean Waves Plus Tidal Current
"Episodic" is emphasized here since significant wave action is not a daily occurrence along the banks, other
than that due to boats. Unfortunately, no measurements of the distributions of wave heights and periods have been
made. We believe that presently the overall effect of ocean waves is decidedly lower than that of boats; yet the same
type of protection as that for boat-induced waves is required.


iii. Tidal Current
In places tidal current appears to be a noteworthy agent in washing away fine sand. For that reason, the
elevation of toe protection must be as low as possible for the retention of riprap, since a submerged wall that is too
high may channelize a strong current (especially flood flow) between the wall and the bulkhead, and cause bed
erosion and undermining of the riprap.


iv. Trap Dredging
The precise role of trap dredging since 1960 on bank stability, especially the north bank, remains unclear;
our calculations suggest that gravity slide of particles in the absence of waves (boat wakes and ocean waves) is not
a significant factor in transporting sand from the toe of the bulkhead into the trap, although there is no basis to state
that it has no role what so ever to play in perturbing the flow and sedimentary regimes in the vicinity of the trap.
To the best of our knowledge, the majority of fine sand particles near the bulkheads that are winnowed by tides and
wave seemingly end up in the area of a bend in the ICWW near the lighthouse and beyond, into the aquatic
preserve. The occurrence of a "natural" secondary or marginal channel (it does not appear to be an artifact of the
dredging practice, although the latter may have had some influence on its course) between the bulkheads and the
trap apparently facilitates this transport pathway.
Trap dredging is of paramount significance to navigation and water quality in the Loxahatchee River. It
is almost certain that without a dredging protocol the inlet will close or become so shallow as to be practically
unnavigable, with concurrent degradation of interior water quality due to a lack of adequate flushing. The inlet had
shoaled most recently during the 1942-1947 period, and historic records show that it was closed as far back as 1765.
Furthermore, the creation of St. Lucie Inlet and Lake Worth (Palm Beach) Inlet has diverted the flow to those inlets
to such an extent that retention of a navigable entrance without dredging in out of the question. As noted elsewhere
(Snyder, personal communication), Jupiter Inlet is really the ocean end of an estuary. In an estuary, river runoff









dilutes seawater, and plays a role in maintaining entrance stability. Assuming an average yearly maximum runoff
of 2,000 cfs (57 m3/s), Escoffier and Walton (1979) showed, through an analytic approach, that this entrance is
unstable and prone to closure. [We believe that over the past few decades, due to the use of fresh water for
agricultural and other purposes, Loxahatchee River receives lower runoff than, say, a century ago. This possibility,
combined with the diversion of waters to the neighboring inlets has most probably made the entrance to this river
almost entirely dependent on intervention via dredging. Unfortunately, historic runoff data for this estuary are very
limited; see, e.g. Mehta et al. (1990)]. The comparatively small runoff does not seem to play any significant role
in keeping the entrance open.
The trap location, in terms of the distance of its eastern edge from the seaward tips of the jetties, has been
appropriately selected (for sand trapping purposes) to be roughly at the beginning of the channel where it begins
to widen westward. Furthermore, in terms of length, width and depth, experience shows that the trap dimensions
have been reasonably chosen to insure catchment of sand required for south beach nourishment and for keeping the
river open for navigation. The proposed expansion of the trap is to provide an adequate amount of sand to the south
beach at regular (annual) intervals, and to reduce the transport of finer sand to the marinas and the aquatic preserve
which lie west of the trap. Overall, trap expansion has been proposed to meet the State of Florida's requirements
to make the inlet "invisible" to the beaches, as far as littoral sand transport in concerned. A recent survey of sand
management at inlets on the southeast coast of Florida indicates that, over the past decades, Jupiter Inlet has very
nearly (96%) met the State of Florida's goal of bypassing all littoral sand (100%), and that at a very low unit cost
(Dombrowski and Mehta, 1993; Bruun, 1993).
The management objective in UF3 in terms of reducing the influx of sediment in areas upstream of the trap
is by no means perfunctory, considering the fact that while the annual supply of sand into the aquatic preserve is
minor, the management goal is based on a long term (a decade) perspective in terms of accumulation of sand to the
interior and associated navigational problems that are likely to develop as a result. On the other hand, it is certain
that trap expansion will increase the perturbation to the system. Thus, if an unequivocal relationship between
expanded trap dredging and bank stability is demonstrated, the cost of bank stability must be weighed against the
benefits that accrue from the expanded trap, for an assessment of future action with regard to continued dredging
in the trap in its expanded form. In our qualitative assessment, any likely perturbation to the interior shorelines
caused by the present trap or even the expanded trap is significantly "masked" by the onslaught of boat wakes in
the presence of tidal current at the bulkheads.
In UF3, implicit quantitative goals for sand transport reduction were: 1) increasing the efficiency of the
JID trap by a about third, and 2) reducing the influx of sediment past FECRR bridge by about one-half. These goals
have been met approximately by way of the recommended actions. In Appendix I, we have explored the possibility
of replacing the proposed width-wise and length-wise expanded trap with one that is expanded only length-wise,
given the same increase in the trapping efficiency (28%). The calculations show that without widening the trap, its
length would have to increased by 128 m (420 ft). This change in the plan area would mean that the trap would be









more distant from the south bank than otherwise, but would intrude further into the river. This intrusion would be
considerable, and in our opinion would amount to a rather significant (albeit presently unquantified) perturbation
to the system, which may be unacceptable ecologically or otherwise. It is not the preferred choice and we do not
recommend it from that perspective, despite the marginal benefit it could accrue to the southern bank. It should also
be noted that extending the trap beyond the presently proposed design (Fig. H.8) may not adversely affect the
stability of the northern bank (Table H2 actually indicates a potential reduction in the ebb current speed near the
bulkhead, although not flood), yet no advantage in terms of stability would be gained, and adverse impact cannot
be ruled out entirely.
According to the proposed design in Fig. H.7 the trap, with allowance for sloughing, will be dredged such
that the closest distance of the northern edge of the trap will be about 105 ft (32 m) from the north bank. It is
conceivable that the northern edge of the trap borders a rock formation (see Appendix I), so that the danger of
dredging closer than designed may not actually occur. Note however that no suitable geotechnical data are available
to ascertain the nature or the extent of the rock formation. Yet we note the somewhat curious presence of shoals
Q and R in Fig. H.2. Their presence is also suggested qualitatively in an earlier survey (Buckingham, 1984). The
nature of the bottom in that area requires an examination. For that purpose, an earlier investigation (Jammal &
Associates, 1993) involving core boring and grain size analysis must be extended, partly because, in our opinion,
additional coring is required in the areas of the proposed expansion of the trap to ascertain the nature of the bottom.
Also, such an investigation will shed light on the occurrence of any "bank-protecting" rock formation separating
the trap from the secondary flow channel. Depending on the nature of the bottom, the dimensions of the expanded
trap may have to be modified, albeit in a minor way. Specifically, if shoals Q and R are rock formations, they must
be largely left undisturbed.
In UF2 a plan to establish a feeder beach, possibly with one or more groins to control the rate of sand
feeding of the beach west of the feeder beach, was recommended as a measure against toe erosion along the north
bank in the vicinity of Jupiter Inlet Colony clubhouse property (see Section 7.2.1 in Buckingham, 1984). Sand for
the feeder beach was to be derived from the trap, when dredged. It was suggested that groins would not be required
if the beach stayed in place for a period of two years, corresponding to the then dredging frequency. Note, however,
the following: 1) It is believed that some of the owners of properties where the feeder beach would have occurred
were apparently not enthusiastic (in 1983-84) about the creation of an effective public beach between their lots and
water. 2) Since the UF3 study had reduction of sand transport west of the trap as a goal, any action that does not
meet that requirement must be carefully weighed in terms of the advantage gained for shoreline stability against an
increase in the rate of sand accumulation in the aquatic preserve. 4) Boat wake action has increased measurably
since 1984. 3) The retention time of any sand placed in front of the bulkheads is still not known.
Given the above issues we suggest the option of constructing a toe protection wall where necessary, and
placing a riprap (rock) prism between the bulkhead and the toe structure. Such a measure must only be taken after
assuring the structural integrity of the bulkhead. We also recommend a sand placement and tracing study










































Edge of Bottom of
Limit of Dredge Cutterhead Activity in the
Predicted Outer Perimeter (Top) of -
4** 7*?


Fig. H.8. Plan view of proposed trap based on a drawing by Lidberg Land Surveying, Inc. The design is based
on a recommendation for trap expansion per UF3 (see Chapter 4). Sloughing allowance is per suggestion by
Applied Technology Management, Inc. (Grella, personal communication).


19









immediately following trap expansion, to ascertain the retention time of sand and its transport path. Relatively small
sand prisms may be constructed (by pumping sand) against the bulkheaded shoreline at two selected locations at the
time of trap dredging, and their fate monitored subsequently. Given a practically high retention time, e.g. a one year
period (and thus corresponding to the proposed dredging frequency), the soundness of a plan to place sand on an
annual basis must be evaluated against the need to reduce the influx of sand in the upriver areas. On the other hand,
if the placed sand is not retained effectively, then, given the need to contain sand transport to the interior, and no
real likelihood of controlling boat speeds, an option may be to construct two or three short experimental (sand bag)
groins such as those suggested in UF2 to increase the retention time of sand. Note, however, that we consider it
highly unlikely that such groins, in the presence of an otherwise scour-prone bank and the absence of a feeder
beach, will be able to function effectively. Note also that we tentatively recommend against feeder beach
construction, given the need to reduce upriver transport of sand, unless the proposed experiments reveal the beach
to be adequately stable. In the area of concern, groins in the absence of a feeder beach can only enhance the stability
of a generally stable or even perhaps a marginally stable beach, but they cannot reverse the trend, i.e. make a
measurably scour-prone beach stable. In other words, if the retention time of placed sand is found to be low, groins
will be unable to materially increase retention.


v. South Jetty Modification
We postulate that the effects of this action in 1967 on water motion and bank morphology was historically
not negligible. Yet, and on the other hand, we do not consider this factor to have any bearing on the future
management plan for the inlet.


H6. Concluding Comments
Our essentially qualitative assessment of the impacts of proposed actions P1, P2, P3A, P3B and 12 (per
Table H1) on the stability of the north and south banks of the inlet channel leads us to the conclusion that actions
P1 (trap dredging and sand placement protocol modification) and 12 (regulating boat speed) especially require
management considerations with regard to the northern bank (identified in Fig. H. 1) in particular.
The sand bed in the vicinity of the bulkheaded shoreline is thought to be marginally stable even in the
absence of: 1) boat wakes, 2) ocean waves or 3) trap dredging. Strong flood currents are believed to be the main
cause of this low degree of stability. Among the factors that have imparted further instability, we consider boat
wakes (which occur regularly) to be most significant, and ocean waves (which are episodic) to a lesser extent. Sand
trap dredging is believed to be the least important of the three. Historically the order of importance may have been
different. For instance, when comparatively very few boats plied the waters, and the channel was dredged (on an
"as needed" basis), ocean waves and trap dredging may have been two important causes perturbing the system.
The proposed expansion of the trap will not in any way improve bank stability; however, its role in
decreasing the stability is difficult to define at this stage. We assert that boat wakes together with flood current will










continue to remain the dominant causes of scour in front of the bulkheads. Given that assertion, we are of the
opinion that: 1) bulkheads must be maintained in a robust state via inspections and repair, 2) a protective wall
against toe scour together with rock riprap placement between the wall and the bulkhead must be examined as design
features against wave attack and scour, 3) trap expansion must be carried out after an additional geotechnical
investigation, and 4) the placement of dredged sand in front of the bulkheads must be explored. The last action must
be instituted only after conducting an exploratory investigation meant to unequivocally demonstrate that a practically
stable beach can be made to exist in front of the bulkheads.
The inclusion of interior shoreline stability as a management goal to the UF3 study (which only examined
the impacts of proposed actions on navigational access and safety, open coast beach erosion and sedimentation in
the interior areas) is a decidedly forward step in the overall management plan for Jupiter Inlet. Shoreline stability
consideration is timely in that sense, especially since it was examined in an earlier study (Buckingham, 1984). In
that study, however, the need for a reduction in the rate of sedimentation in the interior areas, a important long term
issue in managing the Loxahatchee river estuary, was not considered. The effort presented in this appendix is meant
to integrate bank stability concerns without compromising the goals of the overall management plan. A question that
naturally arises is: how does the incorporation of the bank stability element affect the overall decision matrix
presented in Table 4.3? For all practical purposes here we only need consider the impact of action P1. This action
should reduce sedimentation in the interior areas, provide a more consistently dredged channel for navigation, and
better stabilize the eroded south beach. The inclusion of bank stability as an additional management issue should
not measurably reduce the benefits to be derived from action P1, provided the suggested recommendations with
regard to bank stability are implemented.









APPENDIX I: BANK STABILITY RELATED CALCULATIONS AND COMMENTS

I1. Bank Slope Stability
This section presents an analysis of bank slope stability fronting the bulkheads along the northern bank of
Jupiter Inlet channel in the vicinity of the JID sediment trap. The analysis is based on the bank correction factor
for the critical shear stress for incipient motion on cohesionless channel bank introduced by Christensen (1972).
However, here the lift coefficient used in computing the time-mean lift/shear stress ratio, l/r,, is modified from
that based on the experimental results of Einstein and El-Samni (1949), which in turn was based on pressure
difference, to that based on 3-dimensional potential flow theory for a spherical grain (Christensen, 1992).
In addition, the analysis follows a probabilistic approach whereby the critical bed shear stress for channel
bank, Fcr.b.p., is defined as the time-mean value of the fluctuating shear stress when the probability of exceeding
the instantaneous failure shear stress (To.max) is p. Usually the exceedance probability is taken as 0.001, which

corresponds to n = u,'/ou = 3.09 based on the Gaussian distribution 4(n)=(1/27r)exp(-n2/2), where

u( = u1 + ut', 0, = and IT and u' are the mean and fluctuating components of the velocity, respectively.
The suite of analytic expressions involved is as listed below:

Tcr.b.p. = Kb7r.h.p. = KbEh.p. (Ys-)d^ (I.1)

where

(s'-cot'4)- +cot))
Kb = o 1 (1.2)
s-+ s2-cot2( +- cot4
To ( To



= 0.809 In' 1+ 6.475 2 (13)
TOJ LI r J

For the loosest state: Eh.1-3 = 0.237
0.809 In 1+ 6.475 +cot
I I r J










0.2735
For the densest state: Eh.lO-3 = 0.27
6.47511
0.809 In + 6.475 +cot<4
I I r

and r = kide, Kb = bank correction factor, Eh.. = dimensionless entrainment function, -y = unit weight of
sediment grain, y = unit weight of water, de = effective grain size defined as the grain size of uniform material
in equivalent bed that behaves in the same way as the natural heterogeneous bed, s = inverse bank slope ( = cotO
where 0 is the acute angle the bank makes with the horizontal), 0 = angle of repose, and k is the equivalent sand
roughness. Also, the loosest state refers to a square pattern of grain arrangement and the densest state refers to a
hexagonal pattern and Su = o,/ u, = 0.164 has been assumed in arriving at the above expressions.

The required input parameters are 0, 0, de and k. The value of 0 was computed from the available cross-
section survey within a transverse region of 5 m width from the bulkhead along the portion of channel bank that
fronts the JID trap. In this respect, three cross-sections were selected, two bracketing the range of 0 values and
the third one being intermediate.
k can be computed from the Manning-Strickler equation (Henderson, 1966) in the fully rough range,

f = 0.113(k/h)113, where is the friction factor given byf = 8(u ./)2, and u. is the friction velocity and u the

depth-mean velocity over the water depth, h. The computation of k proceeded as follows.
The value of u. /u was first computed as the average of the u. /u values reported in Fig. 3.3 and 3.4

in Buckingham (1984) for section C1 (at inlet mouth), which yielded values of u. /u = 0.127 andf = 0.129,
respectively. Thisfvalue is assumed constant in computing k, which varies with h. The water depth, h, was
computed based on a uniform bank slope at a distance 5 m from the bank.

de can be computed from de/ds.so% = (2CulnCu)/(C2-1) where ds.0% is the median grain size and Cu

( = ds.60%/ds.lo) is the uniformity coefficient. For well-graded sediments, which was the case here, de can be
approximated by the mean grain size. The only available sediment textural information is for the sample station
between the trap and the bulkhead (Sample # 31 in Table 3.4 of Buckingham, 1984) where dJo = 0.36 mm.
However, two other sizes of 0.2 mm and 0.5 mm, which are the sediment sizes used in the numerical modelling
study in Mehta et al. (1991) are also included for analysis. Lastly, the value of 4 was estimated from Table 2.11
in Garde and Ranga Raju (1977) as the average of the very angular and very rounded categories.
The values of the critical shear stress thus computed are compared with the fluid-induced bottom shear
stress, Tb, which was computed in the following manner. The value of u was first estimated from Fig. 3.5 in
Buckingham (1984) for Section C-2, which is about 140 m upstream of the upstream edge of the JID trap, at a
distance of 5 m from the bank, and equalled 0.4 m/s. It must be borne in mind that this value of u is based on
measurement at section C2, which is narrower than the section cutting through the JID trap (about 190 m width)









and about half the area of the latter (450 m2 versus 810 m2). Hence, the velocity and, therefore the shear stress
exerted on the bank would be smaller in the latter based on continuity consideration. Accounting for this difference

in area results in i = 0.22 m/s. Next the ratio of u. u computed previously was used to compute the value of

u. here, which yielded u, = 0.028 m/s. rb was then computed from Tb = pu2 giving Tb = 0.8 N/m2.

Table II summarizes the results of computation as outlined above. Computation showed that the value of
k is larger than the corresponding h in all cases due to the high value off = 0.129. Hence, invariably r > 100.
The disposition of Kb is such that for r > 100, Kb tends to a constant value. Hence, the computation is based on

r = 100 as shown in Table II. A revised computation using a similar expression, k/h = 3.15x10(u, u)6, led

to similar results. A point of note is that r = 10 would correspond to a sand surface with some shells and
irregularities in the field, while r = 100 corresponds to a highly irregular surface such as one with a rocky
protuberance or other local irregularities.


Table I1: Results of computation on transverse bank stability.

0 (0) r (0) de (mm) Kb Tr.b.3 (N/m) T7b (N/m2)

4.5 100 30.2 0.20 0.99 0.47 0.80
8.3 100 30.2 0.20 0.96 0.46 0.80
25.8 100 30.2 0.20 0.50 0.24 0.80
4.5 100 30.4 0.36 0.99 0.86 0.80
8.3 100 30.4 0.36 0.96 0.83 0.80
25.8 100 30.4 0.36 0.51 0.44 0.80
4.5 100 30.5 0.50 0.99 1.20 0.80
8.3 100 30.5 0.50 0.96 1.16 0.80
25.8 100 30.5 0.50 0.51 0.62 0.80




From Table II, all the bank slopes are stable except for the smallest grain size and those associated with
the steepest slope. Hence, it may be concluded that the existing bank slope fronting the bulkhead are at least
marginally stable under the influence of channel flow, and hence, channel flow due to tides and river discharges
by itself is unlikely to be the primary cause of bank erosion.










12. Boat-Induced Waves and Bottom Scour
This section consists of two parts. The first part is concerned with estimating the magnitude of bottom
shear stress in the vicinity of the north bulkhead induced by boat-generated waves, while the second part attempts
to estimate the scour that may occur in front of the bulkhead due to wave reflection-generated vertical velocity there.


12.1 Computation of Boat-generated Waves and Associated Bed Shear Stress
The analysis here is based on the interim ship-generated wave predictor model advanced by Sorensen and
Weggel (1984). The empirical expressions are developed from field data that include wave height data from seven
different ships having displacements ranging from 3 to 18,800 tons, lengths from 23 to 504ft and drafts from 1.7
ft to 28ft. They caution that the interim model should not be used much beyond the range of the data from which
it was derived.
In the present case, two representative boat sizes of 16ft and 30ft in length (L) are selected based on the
Boating Survey Data Results supplied by JID. Since no other information relating to boat geometry is available,
the other relevant quantities were estimated using published empirical relations as follows. One such empirical
expression relates the boat weight, WB, to L (California Department of Boating and Waterway, 1980) where WB
= 25 L2 for commercial crafts and WB = 12 L2 for recreational crafts. For L = 16ft and using an inverse water
density of k = 39.2ft3/ton, the corresponding values for Vare 100ft3 (WB = 3.2 ton) and 48ft3 (WB = 1.54 ton).
The corresponding values for L = 30ft are 352ft3 (WB = 11.25 ton) and 169ft3 (Wg = 5.4 ton), respectively.
For the present purpose, an intermediate expression based on the algebraic average of the two coefficients, i.e., WB
= 18.5 L2, has been employed in the subsequent analysis. The resulting boat displacements are 2.4 tons (V = 92.8
ft3) and 8.3 tons (V = 326.3ft3), which are within the range of data valid for the empirical relations of Sorensen
and Weggel (1984), except for the smaller size, which however, is deemed close enough for the same method to
be approximately applicable.
A cruising speed, Vs, of 10 knots has been suggested as typical of the boats plying the waters via Jupiter
Inlet (Michael Dombrowski, personal communication). However, since lighter boats can usually cruise at a higher
speed, two speeds of 9 knots (for L = 16 ft) and 11 knots (for L = 30ft) are adopted for the two boat sizes,
respectively.
The interim model is expressed as:

H* =c (y*)n (1.4)

an assumed exponential form from the theoretical result of Havelock (1908) that the wave height decreases as the
1/3 power of the distance from the sailing line where:


log a = a + b logh + c (logh *)2











n = Pf(h )


and H* = H/V1/, y* = y/V"3' h* = h/V13, and y = transverse distance from sailing line and V13 =

characteristic length dimension of the ship. (, 6, a, b and c are empirical constants that are functions of the Froude

Number, F = Vs/ gi .

Usually, a boat moves in the middle of a channel. However, it is likely that two-way traffic is common
here and the position of two passing boats can be estimated to be at the one-third point of the channel width from
the nearer bank for each boat. Hence, y is taken to be 200ft for the 190 m width (average) channel. For the sailing
line aligned along the one-third point, the boats are still traversing over, but close to the edge, of the JID trap.

Hence, h = 19ft. The remaining empirical expressions are:


a = -0.6 Fr", b = 0.75 Fr-'125, c = 2.6531 Fr 1.95
= = -0.225 Fr-0.699; 0.20 S Fr < 0.55

3 = -0.342 ; 0.55 : Fr 5 0.80
6 = -0.118 Fr-o.356; 0.20 : Fr 0.55
6 = -0.146 ; 0.55 Fr 0.80


Table 12 summarizes the results of computation. It is noted that a smaller boat traveling at a higher speed generates
a higher wave height as observed in the field.


Table 12: Computation of boat-generated waves.

Boat Size, L (ft)
Parameters
16 30
WB (ton) 2.4 8.3
V13 (ft) 3.61 8.74
F 0.75 0.61
n -0.28 -0.30
a 0.73 0.34
H (y = 200f) (ft) 1.15 0.87
T (s) 2.0 2.0


As a check, the H values are compared with ship waves measured in the Oakland Estuary by Sorensen (1967) using
a wave gage installed at the end of the Market Street Pier at various sailing line distances. For a pleasure craft of









25ft long travelling at a speed of 10.2 knots with a sailing line distance of 600ft, the measured maximum wave
height and wave half-period, T1, were 0.5ft and 1 s, respectively. For a cabin cruiser with V-bottom hull (L
= 23ft, Wg = 3 tons), the corresponding values for the case of Vs = 9.8 knots and y = 100ft are 1.lft and 1.0
s, respectively, while those for V, = 9.2 knots and y = 300ft are 0.8ft and 0.9 s, respectively. It is seen that for
boats of comparable size, the wave height estimated here would correspond to the maximum wave height measured
elsewhere. The bottom elevations of the Oakland Estuary are not available. However, from the statement that the
critical speed there is generally in the order of 17 to 21 knots, the depth can be estimated from the critical Froude
Number of unity to yield a depth of 30ft to 45ft. The F value for the Oakland Estuary for a boat of comparative
size is smaller by about 25%. Therefore, the trend of higher wave height here over that at Oakland Estuary is also
consistent with the empirical evidence that a large Froude Number that approaches unity leads to a higher wave
height. Hence, H = 1.15 ft is accordingly adopted here. Correspondingly, based on the finding of Johnson (1958)
that the half-period is independent of distance from the sailing line, the wave period is taken to be 2 s for analysis.
Next the wave-induced bottom shear stress is computed using linear wave theory for the wave kinematics.
First, the water depth of interest was estimated at a distance of 5 m from the bulkhead using a bank slope of 10P,
which yielded a local depth of 0.9 m. Based on linear wave theory, the magnitude of the bottom wave-induced
orbital velocity, Iubl, can be computed from:

1ib = Ha (1.5)
2 sinhkh

where a = 2/TT and k is the wave length, which can be solved from the linear dispersion relation:

o2 = gk tanhkh (1.6)

and g is the gravitational acceleration. Finally, the maximum wave-induced bottom shear stress, w.6m, is

computed from:


w.b.max. (1.7)


where p = fluid density andfis the friction factor usually taken to be 0.01. Plugging in H = 0.35 m (1.15ft),
T = 2 s, h = 0.9 m led to k = 1.245 m'1, kh = 1.121, |iub = 0.40 m/s, and hence, w.b.max = 0.80 N/m2.
In the above computation, the effects of shoaling and refraction on the wave height have been assumed small since
the waves do not really feel the bottom until almost near the point of concern and they approach the bank at near
normal incidence.
Recalling that the depth-mean current velocity, u, at the same location has been computed earlier to be 0.22
m/s, the magnitude of the vectorial sum of the combined velocity, assuming the current velocity and orbital velocity










vectors are normal to each other, can be computed as (| ub 2 + u2)1/2 = 0.46 m/s. The induced combined bottom

shear stress then becomes 1.06 N/m2. Hence, boat-generated waves have the potential both to mobilize bottom
sediments and induce bank instability in conjunction with current flow.


12.2 Scour In Front of Bulkhead
The most important effect arising from the reflection of incident wave energy from a bulkhead, or related
structure, is scour of the material in front of, or close to the structure. While considerable efforts have been
expended to predict the onset and extent of structure-induced scour, they are primarily based on small scale
experimental work that suffer from scale or modelling effects (Allsop, 1986). One such empirical expression is that
derived by Herbich et al. (1984), which applies to partially reflecting structure:



I-= d- (1-Kr)IubI 0.75CDp ) (.8)


where S = scour depth, a = Hincident + Hreflected Kr = reflection coefficient, CD = sand particle drag coefficient,
0 = angle of repose, p = water density, 7, = unit weight of sediment grain, y = unit weight of water and dso =
mean grain size. Assuming Kr = 0.7, dS = 0.35 mm, CD 1.0, and the values of H and d as above, S =
0.38 m. As a comparison, Shore Protection Manual (Coastal Engineering Research Center, 1984) recommends
that in the absence of scour protection measures, a scour depth equal to the maximum unbroken wave height (in
this case H = 0.35 m) that could be sustained by the original water depth at the structure toe should be allowed for.
Hence, a scour depth of about 0.35 m may be expected due to boat-generated waves at the toe of the bulkhead.


13. Trap Expansion and Efficiency
This section presents the comparison of relative trapping efficiency for the JID sediment trap between
lengthening it as opposed to widening it using the Removal Ratio approach. Sarikaya (1973) has presented a plot
for this purpose based on numerical solution to the following governing differential equation from mass
conservation:

uc c 0a [ ac (1.9)
ax 3"y -y y j

The assumptions involved include:


a) Reynolds analogy that expresses equivalence between momentum and fluid mass transfer is valid.
b) The turbulent diffusion coefficient is the same for suspended matter and fluid particles.


L










c) The flow field is two-dimensional, and uniform.
d) Longitudinal dispersive transport is negligible.
e) The condition is steady.
f) Vertical fluid velocity distribution is logarithmic:

u-U, =1f[ +1 (I.10)


g) The distribution of turbulent diffusion coefficient in the vertical is parabolic:

c = ku.y[1-Y (1.11)


h) The sediments are discrete with uniform fall velocity.
i) The sediment concentration is uniformly distributed at the inlet.
j) There is no re-entrainment of sediments from the bottom.


In using the plot for the removal ratio, r, the input parameters are h, ws, L, Uo and u. (or ). Uo was
computed from the measured cross-sectionally-averaged value in Fig. 7.18 of Mehta et al (1990) (@ Cl) by
adjusting for the flow cross-section (area @ Cl/area @ trap = 448.6 m2/809.5 m2 = 0.55) and averaging over the
flood period (multiplication factor of 2/7r) to yield a value of Uo = 0.74 m/s. w, was computed from

ws = [g(.s-T)ly]0.7dd1/6 P0.4 (CERC, 1984), which yielded 0.046 m/s for dSo = 0.35 mm. L = 275 m was scaled

off from the survey chart. Similarly, ht = 5.8 m where the subscript t denotes trap, and h = 3 m were read off
from the same chart. While the value of u. was documented, it was decided to leave it as a calibrating parameter
to replicate the dredged sediment rate in the trap.
Based on sediment budget calculation, the net longshore transport rate is 177,000 m3/yr, of which 26%
enters into the Jupiter Inlet. Hence, the sediment discharge into the inlet, Qi, is about 46,000 m3/yr. 19% of the
net longshore transport rate was dredged from the trap, and this dredged (or deposited) amount of Qd = 34,000
m1/yr was then used to calibrate for u. as follows.
The width of the trap, B, = 66 m while the width of flow section, B = 190 m. Hence, r = QdBthtl/QBh,

which yields r = 0.49. It was then found that with the value of w, computed above, the curves all lie above r =
0.49. It was then decided to calibrate for ws instead by using the computed value of u. = 0.17 m/s (Fig. 7.15 of
Mehta et al., 1990). By trial and error, the value of ws = 0.011 m/s was obtained.
These input values (ws = 0.011 m/s, Uo = 0.74 m/s, h = 5.8 m) were then used to calculate the required
L for a percentage increase in trapping efficiency of 28%. The corresponding r = 0.64. Hence, with7.5wl/u


L










= 0.49 and r = 0.64, wsL/Uoh = 1.03, thereby giving L = 402 m. The additional length of trap required is

127 m.


14. Bulkhead Site Visit
This is a letter report from our field trip June 29, 1993. We traveled by boat to the Jupiter Inlet and
observed from the inlet the bulkheads on properties in Jupiter Inlet Beach Colony that face the inlet.
These walls are all constructed of concrete and are of different types, one type is the conventional king pile
and panel bulkhead with a dead man type anchor. The other type appears to be precast or prestressed concrete sheet
piles with a concrete cap and a dead man anchor. The condition of these walls vary from poor to good condition.
The wall on lot 80 was in particularly poor condition. Some of the concrete piling are spalled and many of the
concrete panels are cracked. The wall is also leaning out towards the inlet. This is an indication of either the tie rod
failure or the dead man anchor not being large enough to resist the pressure from the earth adjacent to the bulkhead.
Attached with this letter are some exhibits (Figs. I.1 and 1.2) that show the typical types of bulkheads that I have
referred to in this paragraph.
The bulkheads along this north shore of the inlet all appear to not be suffering from any failure due to
erosion at the toe. This type of failure is one in which the soil either due to erosion or its weak nature fails at the
bottom of the wall such that the king pile or sheet actually moves outward at the bottom. This results in a wall that
is angled towards the property. There is no evidence of this type of failure occurring. The other typical failure that
one encounters with bulkheads is the failure of the anchorage systems; this is obvious in the condition of the wall
on lot 80. This is caused most frequently by the corrosion of the anchor rod which is attached to the dead man
anchor. These anchor rods are constructed normally of steel and frequently due to salt water corrosion, corrode
through near the bulkhead resulting in a failure of this rod.
These types of bulkhead generally have an economic life of approximately twenty-five years. At the end
of twenty-five years it has been my experience that these bulkheads require either extensive reconstruction or
replacement. The anchor rods frequently fail before the concrete portions of the bulkhead. These anchor rods should
be examined and/or replaced every ten years or so. The rods frequently corrode within a few feet of the bulkhead
in ten to fifteen years. When corrosion has reduced the cross sectional area of the anchor rod to a critical area it
simply pulls apart.
The matter of erosion in front of these walls was discussed during our meeting and visit to the site. Jupiter
Inlet is a very dynamic site and the elevation of the bottom does change. I have observed and made measurements
from time to time before dredging and after dredging at certain locations along bulkheads along the north side of
the inlet. The information that I obtained was simply making a measurement from the top of the wall to the bottom



'Prepared by Ron Dixon of Dixon and Associates Engineers, Inc., West Palm Beach, Florida 33409.



















CONCRETE CAP







ANCHOR ROD


-1 -CONCRETE PANEL


KING PILE


Fig. I.1. Typical bulkhead.


31


ANCHOR


V


I .























CONCRETE CAP


DEAD MAN ANCHOR


PRECAST CONCRETE SHEET


Fig. 1.2. Concrete sheet pile wall.


32


7











before and after dredging. It has been my experience that little if any change occurred and if it did the land actually

accreted in front of the walls after dredging rather than erode as some individuals have speculated.

There exists a rock formation along the north central portion of the sand trap of the Jupiter Inlet. This

offers a measure of protection to these bulkheads in that the slope of the bottom in front of these bulkheads will

always be fairly gentle.


33


__










BIBLIOGRAPHY


Bruun, P. (1993). An update on sand bypassing procedures and costs. Journal of Coastal Research, SI 18, 277-284.

Bruun P. (Co-authors A.J. Mehta and I.G. Jonsson) (1978). Stability of Tidal Inlets: Theory and Engineering,
Elsevier, Amsterdam, 537p.

Bruun P.M., Battjes J.A., Chiu T.Y. and Purpura J.A. (1966). Coastal engineering model studies of three Florida
inlets. Engineering Progress at the University of Florida, XX(6), 72p.

Buckingham W.T. (1984). Coastal engineering investigation at Jupiter Inlet, Florida. UFL/COEL-84/004, Coastal
and Oceanographic Engineering Department, University of Florida, Gainesville, FL.

Coastal Engineering Laboratory (1969). Coastal engineering study at Jupiter Inlet, Palm Beach County, Florida.
UFL/COEL-69/009, Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL.

Collier C.A. (1975). Seawall and revetment effectiveness, cost and construction. Report No. 6, Florida Sea Grant
Program, 74p.

Dombrowski M.R. and Mehta A.J. (1993). Inlets and management practices: southeast coast of Florida. Journal
of Coastal Research, SI 18, 29-57.

Escoffier F.F. and Walton T.L. (1979). Inlet stability solutions for tributary inflow. Journal of the Waterway,
Port, Coastal and Ocean Division, ASCE, 341-355.

Grella, M.J. (1993). Development of management policy at Jupiter Inlet, Florida: an integration of technical
analyses and policy constraints. Journal of Coastal Research, SI 18, 239-256.

Jammal & Associates (1993). Geotechnical Services, Sand Trap Expansion, Jupiter Inlet District, Jupiter, Florida.
Report, Professional Services Industries, Inc., West Palm Beach, Florida.

Mehta A.J., Montague C.L. and Parchure T.M. (1990). Tidal inlet management at Jupiter Inlet, Florida: first
progress report. UFL/COEL-90/005, Coastal and Oceanographic Engineering Department, University of Florida,
Gainesville, FL.

Snyder R.M. (1993). Shoreline condition report, Jupiter Inlet Colony, SEC. 31 TWP. 40 RNG. 43, Palm Beach
County. unpublished report, Snyder Oceanographic Services, Inc., Jupiter, Florida, variously paginated.


34