1
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
2
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
3
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
xdmm
H 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 Hb
against the structure
4
Most Dangerous Incident Wave Angle
Table 7-1
L6-12
Wave Forces on Structures
Wave Forces
Classification of wave force problems:
Fig 7-66
5
Wave Forces Against Piles
Important Parameters for Piles2
2
H
gT
d
gT
D
L
D
HD
T
wave steepness
dimensionless water depth
pile diameter to wavelength
relative pile roughness
pile Reynolds’ number
Vertical Cylindrical Pile and Non-Breaking Waves
2 1
4 2
0.05
i D M D
A
D duf f f C C Du u
dtD
L
Fig 7-67
(7-20)
(7-21)
6
Calculation of Forces and Moments
2cos
2
H t
T
cosh 2 ( ) / 2cos
2 cosh(2 / )
z d LH gT tu
L d L T
cosh 2 ( ) / 2sin
cosh(2 / )
z d Ldu g H t
dt L d L T
Water surface profile:
Water particle velocity:
Water particle acceleration:
(7-22)
(7-23)
(7-24)
2 1
4 2i D M D
D duf f f C C Du u
dt
Combining these expressions
2 cosh 2 ( ) / 2sin
4 cosh(2 / )i M
z d LD tf C g H
L d L T
Inertia force:
Drag force:
22
22
cosh 2 ( ) /1 2 2cos cos
2 4 cosh(2 / )D D
z d LgT t tf C gDH
L d L T T
(7-25)
(7-26)
2 1
4 2i D M D
D duf f f C C Du u
dt
Relative Wavelength and Pressure Factor
Fig 7-68
2 cosh 2 ( ) / 2sin
4 cosh(2 / )i M
z d LD tf C g H
L d L T
222
2
cosh 2 ( ) /1 2 2cos cos
2 4 cosh(2 / )D D
z d LgT t tf C gDH
L d L T T
( )
( 0)i
i
f z dK
f z
2 ( )
( 0)D
D
f z dK
f z
1
cosh(2 / )K
d L0
L
L
0
andL
KL
2
d
gT
7
Ratio of Crest Elevation to Wave Height
Fig 7-69
Wavelength Correction Factor
2 cosh 2 ( ) / 2sin
4 cosh(2 / )i M
z d LD tf C g H
L d L T
222
2
cosh 2 ( ) /1 2 2cos cos
2 4 cosh(2 / )D D
z d LgT t tf C gDH
L d L T T
Fig 7-70
6-08
Total Force and Moment on a Pile
i D i D
d d
F f dz f dz F F
Force:
Moment (around the bottom of the pile):
( ) ( )i D i D
d d
M z d f dz z d f dz M M
(7-27)
(7-28)
2 cosh 2 ( ) / 2sin
4 cosh(2 / )i M
z d LD tf C g H
L d L T
222
2
cosh 2 ( ) /1 2 2cos cos
2 4 cosh(2 / )D D
z d LgT t tf C gDH
L d L T T
●
●
F
M
8
Maximum Values of the Components
2
4im M im
DF C g HK
21
2Dm 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
9
Ex: F = Fi + FD = 1683 sinθ + 1260 cosθ |cosθ|
0 90 180 270 360
Phase Angle (deg)
-2000
-1000
0
1000
2000F
orc
e (
N)
F
Fi
FD
2 cosh 2 ( ) / 2sin
4 cosh(2 / )i M
z d LD tf C g H
L d L T
222
2
cosh 2 ( ) /1 2 2cos cos
2 4 cosh(2 / )D D
z d LgT t tf C gDH
L d L T T
Fim
FDm
Fm
Fm = Fim + FDml=
i D i D
d 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 DW
C H (7-41)
Isolines of m and m versus H and d (different Wvalues)
gT2 gT2
2
H
gT
2
d
gT
2
d
gT
2
H
gT
2
0.05
mm
D
F
wC H D
W
2
0.1
mm
D
F
wC H D
W
10
Force Coefficients CD
maxo
A
LHu
T L
Fig 7-85
(7-47)
maxe
u DR
DC
Fig 7-68
Fig 7-85
maxo
A
LHu
T 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)
11
Transversal Forces
21cos 2 cos 2
2L 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
C
C
Horizontal pipe
fxifxD
fzifzD
221
k N /m4 2z zi zD M z LD
f f f C a C D u
2 1| | k N /m
4 2x x i xD M x DD
f 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
12
Non-breaking waves against a wall (caisson)
AA
A = A
Fig 7-88
Pressure Distribution for Non-Breaking Waves
1
1
2 cosh(2 / )igH
pd L
Fig 7-89
(7-75)
Clapotis Orbit Center
Fig. 7-90
13
Total Force
21
2total s wave waveF F F g d F
Fig. 7-91
(7-76)
2waveF
gd
Fs
Fwav
e
Total Moment
31
3 6total s wave s wave wave
dM M M F M gd M
3waveM
gd
A:
Fig. 7-92
Fs
Fwav
e
SWL F Sliding
SWL F Overturning
Caisson Failure Modes
14
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 2
2
2 2 3 3o I V
B B B BM M G U U R
0.75 Heff eff
V
R
R
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)
15
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 d
L D
3
3
s d
m bm
m b sm m s
D d L m
p HR
p H dM R d
2
3
1/ 2
21
/ 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
●
●
16
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 2
5
2 2 3 6o I V
B B B BM M G U U R
0.9 Heff eff
V
R
R
Rock foundation, breaking waves
BG
di
zHb/2
ds
Hin/2
po pI
Rso
Rsi
U1U2
Rm
B/6 RH
RRV
A
17
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)
18
Broken Waves, Caisson in the Water
21 1
2 20.78
1
2/ 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( )
21 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 R
M 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 gd
x x
xh h
x
(7-103)
(7-104)
19
221
2
3
1
2
4
2 1
2
2
2 2 1
2
3
3 1
2
' 11
2 2
1' 1
2
' 11
2 4
1 1' 1
2 2
' 11
3 6
m b
m m b c
m m b c
s c
s s c
v xp g gd
g x
xR p h gd h
x
h xM R gd h
x
xR gh gh
x
h xM R gh
x
t m s
t m s
R R R
M 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
20
Rubble Mound Breakwaters
Rubble Mound Breakwaters
3
3( 1) cotr
D r
w HW
K 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
21
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
22
AccropodeQuarrystone
Core Loc
Submar
Concrete cubes?? concrete blocks
Antifer concrete blocks
Tri Bar
Nikken stone blocksNikken Sanren
Nikken GraspNikken Rakuna IV
23
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)
24
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 nk
w
( 3)n Table 7-13
Ru2%
= B
25
Breakwater Design Elements
* side slopes (~ 1:1.5 – 1:3)
Ru2%
= B
θinθout
1/3
r
Wr nk
w
Breakwater Design Elements
- Layer thickness (W)
- Rock units (W/10)
1/3
50
0.3m
( /10) max2.0
r
r W W
w
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 W
w
W
w
(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 1.5
to bottom for 1.5s
s
H d H
d H
2 for 2
to bottom for 2s
s
H d H
d H
26
1/3
503 3r
Wr k
w
1/3
502 2r
Wr k
w
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
