BED, BANK & SHORE PROTECTION

Faculty of Coastal Engineering
BED, BANK & SHORE
PROTECTION
Lecturer: Pham Thu Huong

Chapter 6
Waves - Loads
(6 class hours)

6.1 Introduction
Content
6.2 Non breaking waves
6.3 Breaking waves
6.4 Wave on the slope
6.4 Reduction of wave loads
6.5 Summary

Wave issues
Generation: H, T characteristic = f (u wind, h, fetch)
Hydrodynamics: u, p, τ = f (H,T,h)
Statistics:p(H) = f (H characteristic, distribution function)
3. Wave statistics
1. Wave generation
2. Wave hydrodynamics

Examples of wave loads
In which:
(A) - standing wave
(B) - breaking wave on a mild slope
(C) - breaking wave on a steeper slope

Wave motion in periodic,
unbroken wave

Validity of wave theories

Application of linear theory

gradient in filter under breakwater

Friction under waves

with:
friction factor and cf uˆ= ω a =
b b
u = uˆbsinω t
1 c u
2
w 2 f b
ˆ ˆ
τ = ρ
ω a
sinh kh
( ) 0.19 −
a k
⎡
⎢
− 6.0+ 5.2
⎣ b/ r
⎤
⎥⎦
f f max
a b: wave amplitude at
bottom
ω : angular frequency
in waves (=2π/T)
c = e with: c = 0.3

Shoaling
Near-shore Near shore effects

Shoaling
Refraction
Near-shore Near shore effects

Shoaling
Refraction
Diffraction
Near-shore Near shore effects

Shoaling
Refraction
Diffraction
Reflection
Near-shore Near shore effects

Shoaling
Refraction
Diffraction
Reflection
Breaking
Near-shore Near shore effects

eaking waves
⎛2π⎞ H = 0.142 L tanh h
b
⎜ ⎟
⎝ L ⎠
Hb
0.78 ( solitary wave)
h ≈
H
h
s
≈0.4 −0.5

the Iribarren number
(surf similarity parameter)
ξ =
tan
α
H L
tan α slope of the shoreline/structure
H wave height
L0 wave length at deep water
0

eaker types

eaker types
spilling ξ < 0.5
plunging 0.5 < ξ < 3
collapsing ξ = 3
surging ξ > 3
(sóng vỗ bờ)
(Sóng cuộn đổ)
(sóng đổ)
(sóng cồn,
sóng dâng)

ore and hydraulic jump

H R 2
Kr = ≈0.1ξ
H
I
reflection
Battjes, 1974
small ξ less reflection
K r = 1 seawall (standing wave)

Loads due to breaking

Breaker-depth
Breaker depth
γ b = H/h = 0.78 (solitary wave limit)
γ b = 0.88 (Miche formula)

change of distribution in
shallow water

un up

Run-up Run up calculation
Hunt’s Formula (for regular waves)
Ru
H ξ =
CUR/TAW, 1992 (for Irregular waves)
R = 1.5 γ γ γ γ H ξ ( R = 3 H )
u2% r β B f s p u 2% max s
correction factors:
• γr roughness
• γβ approach angle
• γB berm reduction
• γf foreshore reduction

Wave run-up run up irregular wave
H s = significant wave height
ξ 0 = breaker parameter based on T m-1,0
For smooth slope

γr 1.0
friction values
Type of revetment
Asphalt, concrete, smooth blocks, grass,
Sand-asphalt
Sand asphalt
0.95 Blocks in asphalt or concrete matrix,
blocks with grass
0.90 Placed block revetment
0.80 riprap penetrated with asphalt
0.70 Single layer of riprap
0.55 Double layer of riprap

Angle of attack
For long crested waves (swell)
γγ ββ = √cos cos ββ
(with minimum of 0.7)
For short crested waves (wind wave)
γγ ββ = 1 - 0.0022 (ββ in degrees)
(with with a minimum of 0.8)

SWL
H s
γ
B
berm effect
h B
B B
L B
2
⎛ ⎡ ⎤ ⎞
B B
B h
= 1− ⎜1−0.5 ⎟
L ⎜
⎢ ⎥
B H ⎟
⎝ ⎣ s⎦⎠
limits: 0.6 < γ B < 1 and -1 < d h /H s < 1
H s

Shallow foreshore
γ f = H 2% / 1.4H s

Battjes formula, 1994:
R = R 1− 0.4ξ=
d u
( )
= H 1−0.4ξ ξ
( )
run-down run down
R = −0.33
H ξ
d 2%
s p
( R =−1.5
H )
d 2% max
s

Example
A dike with concrete block revetment, slopes 1:3 and a
2 m berm at design level is attacked by perpendicular
(swell) waves with Hs = 1 m and a steepness of 0.01.
What is the wave run-up? run up?
H S = 1
Wave Slope = 0.01
1:3 Ru ?
1:3
2m

γ
B
2
⎛ ⎡ ⎤ ⎞
B B
B h
= 1− ⎜1−0.5 ⎟
L ⎜
⎢ ⎥
B H ⎟
⎝ ⎣ s⎦⎠
solution
Starting point is equation for run-up run up irregular wave R u2%. u2% .
R = 1.5 γ γ γ γ H ξ ( R = 3 H )
u2% r β B f s p u 2% max s
γγ r = 0.9
γγ ββ = 1 and γγ f = 1
hB = 0
LB = 2Hs 2Hscot
cotαα + 2 = 8 m
hence, γγ B = 0.75
The surf similarity parameter is tanαα/0.1 tan /0.1 = 3.33 > 2, hence ξ = 2. 2.
The wave run-up, run up, finally, is then: Ru2% u2% = 1.5*0.9*0.75*1*2 ≅ 2m
above the design level.

Samphire Hoe,
United Kingdom
overtopping
Ostia, Italy

Overtoping in Jaade Siel, Germany
22-12-1954

Measured overtopping (breaking)

Measured overtopping
(non-breaking)
(non breaking)

Seaward slope seadike Haiphong

Sea dike near Haiphong

After Durian (2005)

TAW formula, 2000:
wave impacts on slope
pmax 50% ≈ 8ρw gHs
tanα
pmax 0.1% ≈16
ρw gHs
tanα

Waves
Load reduction
transmission
Coastal line
reflection
absorption
Costs Effectiveness

Linear wave theory

definitions and behaviour of
hyperbolic functions

standing wave

Relative depth
Wave Celerity
Wave Length
Group
Shallow Water
h 1
<
L 20
c =
L
= gh
c =
L
=
T
T
L = T g h
Velocity c = c = g h
g
Energy Flux
1
2
(per m width) F = E c = ga g h
Particle
velocity
Horizontal
Vertical
Particle
displacement
Horizontal
Vertical
Subsurface
pressure
g
Transitional water depth
L
=
1 h 1
< <
20
L
2
Deep Water
h 1
>
gT
L
tanh kh
c = c = =
0
2 π
T
2
gT
gT
tanh kh
L = L =
0
2 π
2 π
L
NM
O
QP
1 2 kh
c
g
= n c =
2
1 +
sinh 2 kh
∗ c
L
2
gT
2 π
1 gT
c
g
= c
0
2
=
4 π
1
T
2
ρ F = E c = ρ ga n c
F = ρ g a
g
2
2
8 π
u = a
g
h
sin θ
e j cos
z
w = ω a 1 + θ
h
a g
ξ = − cos θ
ω h
( )
cosh k h + z
u = ω a
sin θ
sinh kh
( )
sinh k h + z
w = ω a
cos θ
sinh kh
( )
cosh k h + z
ξ = − a
cos θ
sinh kh
( )
sinh k h + z
ζ = a
sin θ
sinh kh
( )
cosh k h + z
p = − ρ g z + ρ g a sin θ
p = − ρ g z + ρ g a
cosh kh
sin θ
a
H
2 π 2 π
= ω = k = θ = ω t − k x
2
T
L
2
2 2
u a e kz
= ω sin θ
w a e kz
= ω sin θ
ξ = − ae θ
kz
cos
ζ = ae θ
kz
sin
p g z g a e kz
= − ρ + ρ sin θ
linear wave
theory
basic equations

parameters
in linear
wave theory

definition of H and T

wave definitions and wave height
distribution

Rayleigh distribution
2 2
⎡ ⎤ ⎡ ⎤
⎛ H ⎞ ⎛ H ⎞
P{ H > H}
= exp ⎢− ⎜ ⎟ ⎥ = exp ⎢−2⎜ ⎟ ⎥
⎢ Hrms H
⎣ ⎝ ⎠ ⎥⎦ ⎢⎣ ⎝ s ⎠ ⎥⎦
H ≡ H ≡ H ≡ H ≡ H ≈4m
s visual 1/3 13.5% m0
0

wave height and wave period

wave registration in the North Sea
Spectral moments: m 0 = surface of energy density spectrum
m -1 = first negative moment of spectrum
T m-1,0 = m -1 /m 0 = spectral wave period ≈ 0.9

spectrum types

two types of spectra

wave spectra across shallow bar

wave generation
Deep water (no limitations of depth and fetch):
gH s gTs
= 0.283 and = 1.2
2
u 2π
u
w w
Shallow water (limitations of depth and fetch) :
⎡ 0.42 ⎤
⎢ ⎛ gF ⎞
0.75 0.0125
⎥
2
gH ⎡ ⎜ ⎟
⎛ s
gh ⎞ ⎤ ⎢ u ⎥
w
= 0.283tanh ⎢0.578 tanh
⎝ ⎠
2 ⎜ 2 ⎟ ⎥ ⎢ ⎥
0.75
uw u ⎡ w
gh ⎤
⎣
⎢ ⎝ ⎠ ⎦
⎥ ⎢ ⎛ ⎞ ⎥
⎢tanh ⎢0.578⎜ ⎥ 2 ⎟ ⎥
⎢ ⎢ uw
⎥
⎣ ⎣ ⎝ ⎠ ⎦ ⎥⎦
⎡ 0.25 ⎤
⎢ ⎛ gF ⎞
0.375 0.077
⎥
2
gT ⎡ ⎜ ⎟
⎛ s
gh ⎞ ⎤ ⎢ u ⎥
w
= 1.20 tanh ⎢0.833 tanh
⎝ ⎠
⎜ 2 ⎟ ⎥ ⎢ ⎥
0.375
2π
uw ⎢ u
⎣ ⎝ w ⎠ ⎥
⎦
⎢ ⎡ ⎛ gh ⎞ ⎤ ⎥
⎢tanh ⎢0.833⎜ ⎥ 2 ⎟ ⎥
⎢ ⎢ uw
⎥
⎣ ⎣ ⎝ ⎠ ⎦ ⎥⎦

wave height as function of wind,
depth and fetch

wave period as function of wind,
depth and fetch