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Design - Overview
• introduction
• design wave height
• wave runup & overtopping
• wave forces
- piles
- caisson; non-breaking waves
- caisson; breaking waves
- revetments
Design Wave Height
• H1/3 (Hs) = average of highest 1/3 of all waves
• H10 = 1.27Hs = average of highest 10% of all waves
• H5 = 1.37Hs = average of highest 5% of all waves
• H1 = 1.67Hs = average of highest 1% of all waves
Design Wave Height
Rigid structure: H1
Semi-rigid structure: H10 – H1
Flexible structure: Hs – H5
Factors Determining Selection of Design Wave Height (flexible structure)
• permissible damage and associated repair costs
• access to construction material
• quality and extent of input wave data
Breaking or Non-Breaking Waves
(4.0 9.25 )p bx m H Fig 7-1
Breaker travel distance:
Non-breaking Breaking Non-breaking
Breaker Height and Depth Index
Fig 7-3 (2-72)
Fig 7-2 (~2-73)
Most Dangerous Breaking Wave at Structure
Implicit expression Iteration (Fig. 7-4)
(7-5)s sb
pbp
b b
d dH xdm mH H
ds
min( )s b p b b p b pd d x m H mH H m
Determining Most Dangerous Breaking Wave at Structure
Fig 7-5 Ho’
Fig 7-4 Largest possible Hbagainst the structure
Most Dangerous Incident Wave Angle
Table 7-1
L6-12
Wave Forces on Structures
Wave Forces
Classification of wave force problems:
Fig 7-66
Wave Forces Against Piles
Important Parameters for Piles2
2
HgT
dgT
DL
D
HDT
wave steepness
dimensionless water depth
pile diameter to wavelength
relative pile roughness
pile Reynolds’ number
Vertical Cylindrical Pile and Non-Breaking Waves
2 14 2
0.05
i D M D
A
D duf f f C C Du udt
DL
Fig 7-67
(7-20)
(7-21)
Calculation of Forces and Moments
2cos2H t
T
cosh 2 ( ) / 2cos2 cosh(2 / )
z d LH gT tuL d L T
cosh 2 ( ) / 2sincosh(2 / )
z d Ldu g H tdt L d L T
Water surface profile:
Water particle velocity:
Water particle acceleration:
(7-22)
(7-23)
(7-24)
2 14 2i D M DD duf f f C C Du u
dt
Combining these expressions
2 cosh 2 ( ) / 2sin4 cosh(2 / )i M
z d LD tf C g HL d L T
Inertia force:
Drag force:
222
2
cosh 2 ( ) /1 2 2cos cos2 4 cosh(2 / )D D
z d LgT t tf C gDHL d L T T
(7-25)
(7-26)
2 14 2i D M DD duf f f C C Du u
dt
Relative Wavelength and Pressure Factor
Fig 7-68
2 cosh 2 ( ) / 2sin4 cosh(2 / )i M
z d LD tf C g HL d L T
222
2
cosh 2 ( ) /1 2 2cos cos2 4 cosh(2 / )D D
z d LgT t tf C gDHL d L T T
( )( 0)
i
i
f z dKf z
2 ( )( 0)
D
D
f z dKf z
1cosh(2 / )
Kd L
0
LL
0
and LKL
2
dgT
Ratio of Crest Elevation to Wave Height
Fig 7-69
Wavelength Correction Factor
2 cosh 2 ( ) / 2sin4 cosh(2 / )i M
z d LD tf C g HL d L T
222
2
cosh 2 ( ) /1 2 2cos cos2 4 cosh(2 / )D D
z d LgT t tf C gDHL d L T T
Fig 7-70
6-08
Total Force and Moment on a Pile
i D i Dd d
F f dz f dz F F
Force:
Moment (around the bottom of the pile):
( ) ( )i D i Dd d
M z d f dz z d f dz M M
(7-27)
(7-28)
2 cosh 2 ( ) / 2sin4 cosh(2 / )i M
z d LD tf C g HL d L T
222
2
cosh 2 ( ) /1 2 2cos cos2 4 cosh(2 / )D D
z d LgT t tf C gDHL d L T T
●
●
F
M
Maximum Values of the Components
2
4im M imDF C g HK
212Dm D DmF C gDH K
Inertia force
Drag force
im im imM F d S
Dm Dm DmM F d S
Moment due to inertia force
Moment due to drag force
Note! Maximum values are not attained simultaneously.
(assuming uniform pile & Integration from –d SWL)
(7-37)
(7-38)
(7-39)
(7-40)
Force and Moment Coefficients
Fig. 7-71
Kim, KDm, Sim, and SDm (Figs. 7-71, 7-72, 7-73, 7-74)
Kim
Hb= ?
Force and Moment Coefficients
Kim, KDm, Sim, and SDm
Hb
Figs. 7-71, 7-72, 7-73, 7-74
Fig 7-75
Ex: F = Fi + FD = 1683 sinθ + 1260 cosθ |cosθ|
0 90 180 270 360Phase Angle (deg)
-2000
-1000
0
1000
2000
Forc
e (N
)
FFi
FD
2 cosh 2 ( ) / 2sin4 cosh(2 / )i M
z d LD tf C g HL d L T
222
2
cosh 2 ( ) /1 2 2cos cos2 4 cosh(2 / )D D
z d LgT t tf C gDHL d L T T
Fim
FDm
Fm
Fm = Fim + FDml=
i D i Dd d
F f dz f dz F F
Maximum Value for Inertia and Drag Combined
Maximum force:
2m m DF g C H D
Maximum moment:
2m m DM g C H D d
(7-42)
(7-43)
(In your book )g w
_
_
Figs. 7-76 – 7-83
M
D
C DWC H
(7-41)
Isolines of m and m versus H and d (different Wvalues)
gT2 gT2
2H
gT
2d
gT
2d
gT
2H
gT
2
0.05
mm
D
FwC H D
W
2
0.1
mm
D
FwC H D
W
Force Coefficients CD
maxo
A
LHuT L
Fig 7-85
(7-47)
maxe
u DR
DC
Fig 7-68
Fig 7-85
maxo
A
LHuT L
(7-47)
maxe
u DR
DC
Force Coefficients CM
CM=2.0 when Re < 2.5 · 105
CM=2.5 - Re ·5 ·10-5 when 2.5 ·105 < Re < 5 ·105
CM=1.5 when 5 ·105 < Re
(7-53)
Transversal Forces
21cos 2 cos 22L Lm L DmF F C g D H K
(7-44)
FL
Fig. 7-84
H/gT2 < 0.0075
H/gT2 > 0.0075
FL
L
D
CC
Horizontal pipe
fxifxD
fzifzD
221 kN /m
4 2z zi zD M z LDf f f C a C D u
2 1 | | k N /m4 2x x i x D M x DDf f f C a C D u u (7-20)
L7-2012
dz
Changed!
ax = f(sin), u = f(cos), az = f(cos) => fxi & fxD not simultaneous max, fzi & fzD have simultaneous max
Wave Forces on Breakwaters
Non-breaking waves against a wall (caisson)
AA
A = AFig 7-88
Pressure Distribution for Non-Breaking Waves
11
2 cosh(2 / )igHpd L
Fig 7-89
(7-75)
Clapotis Orbit Center
Fig. 7-90
Total Force
212total s wave waveF F F g d F
Fig. 7-91
(7-76)
2waveFgd
Fs
Fwav
e
Total Moment
313 6total s wave s wave wavedM M M F M gd M
3waveM
gd
A:
Fig. 7-92
Fs
Fwav
e
SWL F Sliding
SWL F Overturning
Caisson Failure Modes
Forces and Moments on a Caisson Non-Breaking Waves
BG
ho
di
zHoutside
ds
Hin/2
p1
Fwave
FsoFsi
yc
B/3
RHU1
U2
pipo
RV R
Stability of a Caisson, Non-Breaking Waves
Overturning A:
Sliding:
1 22
2 2 3 3o I VB B B BM M G U U R
0.75 Heff eff
V
RR
1 2,H wave so si VR F F F R G U U
Rock foundation, non-breaking waves
BG
ho
di
zHoutside
ds
Hin/2
p1
Fwave
Fso Fsi
yc
B/3
RH
U1U2
pipo
RV R
A
Caisson on Rubble Foundation
''
''
''
'' '' ''
1
1
1 1
f
m
B m f
B A
F r F
M r M
M r M b r F
M M bF
Fig. 7-98
(7-82)
(7-83)
(7-84)
Fig. 7-97
Breaking Waves on Caisson – Minikin Method
Rm
Rs
Fig. 7-99
dsD
Breaking Waves on Caisson: Theory
101 b sm s
D
H dp g D dL D
3
3
s d
m bm
m b sm m s
D d L mp HR
p H dM R d
2
3
1 / 22
1 / 26
t m s m s b
t m s m s b
R R R R g d H
M M M M g d H
(7-85)
(7-86)
(7-87)
(7-89)
(7-90)
Fig. 7-99
(7-88)
Ld LD
m
D
Rm
Rs
●
●
Dimensionless Minikin Wave Pressure and Force
Fig. 7-100
Stability of a Caisson, Breaking Waves
BG
di
zHb/2
ds
po pI
Rso
Rsi
U1U2
Rm
B/6 RH
RRV
Hin/2
Stability of a Caisson, Breaking Waves
Overturning A:
Sliding:
1 25
2 2 3 6o I VB B B BM M G U U R
0.9 Heff eff
V
RR
Rock foundation, breaking waves
BG
di
zHb/2
ds
Hin/2
po pI
Rso
Rsi
U1U2
Rm
B/6 RH
RRV
A
Caisson on Rubble Foundation
Rs
Fig. 7-101
Rm
Influence of a Low Wall
'm m mR r R
Force and moment reduction
(7-91)
Fig. 7-102
Parameter in Moment Reduction, Low Wall
Fig. 7-103
'
'
( )(1 )
( )m s m s m m
m m m s
M d R d a r R
M R r d a a
(7-92)
(7-93)
Broken Waves, Caisson in the Water
21 12 2
0.7812
/ 2
m b b
c b
m m c b c
m m s c
p C gd C d g
h H
R p h gd h
M R d h
Rs
Rm
Fig. 7-104
(7-94)
(7-95)
(7-96)
(7-97)
2
3
( )1 ( )2
1 1( ) ( )3 6
s s c
s s c
s s s c s c
t m s
t m s
p g d h
R g d h
M R d h g d h
R R RM M M
Total Force and Moment on Caisson in Water
Rs
Rm
(7-98)
(7-99)
(7-100)
(7-101)
(7-102)
Broken Waves, Caisson on Land
1 1
2 2
1
2
' 1 1
' 1
b
c
x xv C gdx x
xh hx
(7-103)
(7-104)
221
2
3
1
2
42 1
2
22 2 1
2
33 1
2
' 1 12 2
1' 12
' 1 12 4
1 1' 12 2
' 1 13 6
m b
m m b c
m m b c
s c
s s c
v xp g gdg x
xR p h gd hx
h xM R gd hx
xR gh ghx
h xM R ghx
t m s
t m s
R R RM M M
Total Force and Moment on Caisson on Land
Rs
Rm
Eqs. (7-105) – (7-111)
Effect of Angle of Wave Approach
2
sin '
' / sin
n
n
R R
R R W R
R’ = Dyn force per unit length of wall
Fig. 7-106
The reduction is not applicable to rubble structures!
Rs
Rm
Fs
Fwave
Non-Breaking
Breaking
Broken
MODES OF WAVE FORCES AGAINST A WALL
Rm
Rs
Rm
Rs
Rubble Mound Breakwaters
Rubble Mound Breakwaters
3
3( 1) cotr
D r
w HWK s
Hudson’s formula
W = weight of individual armour unit (kg)
wr = unit weight of armour unit (kg/m3)
Sr = wr/ww
KD = stability coefficient
Cover Layer/Armour LayerUnder Layers
Suggested KD-Values for Determining Armor Unit Weight
Selection of KD-Value
Value includes:
• shape of the blocks
• number of layers
• placement of the blocks
• roughness
• type of wave (breaking/non-breaking)
• incident wave angle
• breakwater shape (height above water level, width etc)
• scale effects
Breakwater Armor Units
Xbloc
A-Jacks
Tetrapod
Dolos
AccropodeQuarrystone
Core Loc
Submar
Concrete cubes?? concrete blocks
Antifer concrete blocks
Tri Bar
Nikken stone blocksNikken Sanren
Nikken GraspNikken Rakuna IV
Typical Breakwater Designs
Recommended Three-Layer Section
Fig. 7-116. Non-breaking waves and one exposed side.
Typical Breakwater Designs
Fig. 7-117. Breaking waves or two exposed sides.
Breakwater Design Elements
* Still water level(s) (depending on co-variation with waves)
Breakwater Design Elements
* Design wave height Hs
Breakwater Design Elements
* Run-up level Ru2%
Ru2%
→ crest elevation
Breakwater Design Elements
* crest width
1/3
r
WB nkw
( 3)n Table 7-13
Ru2%
= B
Breakwater Design Elements
* side slopes (~ 1:1.5 – 1:3)
Ru2%
= B
θinθout
1/3
r
Wr nkw
Breakwater Design Elements
- Layer thickness (W)
- Rock units (W/10)
1/3
50
0.3m
( /10) max2.0
r
r W Ww
Ru2%
= B
2 thickness = 2r(W)n
50 /10W W
1/3
50
max
0.3
( /10) max 2.0
1.25
r
r
m
Wr Ww
Ww
(7-123)
Ru2%
= B
Breakwater Design Elements
- bottom elevation of cover layer
- toe berm W/10
- under layers
- filter layer or geotextile
15,cover 85,underD D
15,filter 85,undergroundD D
for 1.5to bottom for 1.5
s
s
H d Hd H
2 for 2to bottom for 2
s
s
H d Hd H
1/3
503 3r
Wr kw
1/3
502 2r
Wr kw
50where /10W W
> 1.5 m2r > 3 m
2r2r
Non-breaking waves and one exposed side.Breaking waves or two exposed sides.
STABILITY OF RUBBLE FOUNDATION AND TOE PROTECTION
Fig 7-120
MAIN ITEMS
- Understand most dangerous (biggest) breaking wave
- Calculate run-up & overtopping
- Understand & calculate wave forces
L9 -11
