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

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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)

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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

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