Post on 19-Jun-2015
description
Vermelding onderdeel organisatie
February 1, 2012
1
Chapter 5: use of theory
ct5308 Breakwaters and Closure Dams
H.J. Verhagen
Faculty of Civil Engineering and Geosciences Section Hydraulic Engineering
February 1, 2012 2
Theoretical background needed
• waterlevels (tides)
• flow trough gaps
• stability of floating objects
• waves
• basics
• refraction, shoaling, breaking, diffraction, reflection
• wave statistics
• short term statistics (Rayleigh)
• long term statistics
• Geotechnics
• sliding
• squeeze
• liquefaction
February 1, 2012 3
Initial tidal wave by the moon and the sun
February 1, 2012 4
Adding semi-diurnal constants resulting in spring and neap tide
February 1, 2012 5
Adding diurnal to semi-diurnal constant
February 1, 2012 6
Amphidromy in the North Sea
February 1, 2012 7
typical tides
February 1, 2012 8
adding the fortnightly constant
February 1, 2012 9
flow pattern in a gap
February 1, 2012 10
Flow over a sill
subcritical flow
critical flow
2 ( )Q mBh g H h
2 ( )Q h
u m g H hB a a
1Q = m B a 2 g H
3
( ) ( ) and ( )2 1 1
Q m B H 2 g H u m 2 g H3 3 3
( ) ( ) and ( )2 1 1
Q m B H 2 g H u m 2 g H3 3 3
February 1, 2012 11
modelling
x
Q H+ = 0B
x t
0x2
g Q QQ ( Q u) Hg A W
t x x A RC
Solving these equation by:
•physical model
•mathematical model
•2 d model
•1 d model
•storage area approach
February 1, 2012 12
Physical model
February 1, 2012 13
two dimensional model
Korea, Gaduk port, Mike21, DHI Oosterscheldewerken, Waqua, Rijkswaterstaat/WL
February 1, 2012 14
one-dimensional model
February 1, 2012 15
storage/area approach
x
Q H+ = 0B
x t
February 1, 2012 16
validity of storage/area approach
length of tidal wave: L= c*T = gh * T
= 10*10 *12*3600
= 432 km
basin < 0.05 L = 20 km
February 1, 2012 17
equations for storage/area approach
31 2
2 3 3 1
2 1 3 1
2 ( ) ( )
2
3
2 2
3 3
g R
dhA g H h B Q t
dt
h h for h H
h H for h H
Ag and B can be combined to one input parameter
February 1, 2012 18
parameters needed
• water level in the sea
• river discharge
• ratio between storage area and width of closure gap
• sill height
• discharge coefficient of the gap
Assume for the time being that the river discharge is zero and that the tide is always semi-diurnal
Set the discharge coefficient of the gap to 1
Remaining parameters:
• tidal difference
• ratio storage area/gap width
• sill height
February 1, 2012 19
design graph for the velocity
February 1, 2012 20
example of the use of a design graph
February 1, 2012 21
velocity as a function of the closure
February 1, 2012 22
Stability of a submerged object
February 1, 2012 23
Stability of a floating object
.5 2 3
.5
1
12
b
b
IMC
V
I yx dx LB
GV
g
February 1, 2012 24
Definition of a regular wave
H
H wave height
T wave period
L wave length
2 2cos
2
x tHL T
2tanh
2
gL hc
L
2
2
0 1.562
gTL T
c gh
February 1, 2012 25
validity for wave theories
February 1, 2012 26
breaking
by steepness H/L< 0.14
by depth H/h < 0.78 but…………….
February 1, 2012 27
Irregular wave
February 1, 2012 28
Rayleigh graph paper
2
2
( )s
H
H
P H H e
February 1, 2012 29
characteristic wave heights
Name Notation H/m0 H/Hs
Standard deviation free surface =m0 1 0.250
RMS height Hrms 22 0.706
Mean Height H = H1 2ln 2 0.588
Significant Height Hs= H1/3 4.005 1
Average of 1/10 highest waves H1/10 5.091 1.271
Average of 1/100 highest waves H1/100 6.672 1.666
Wave height exceeded by 2% H2% 1.4
February 1, 2012 30
characteristic wave periods
Name Notation Relation to spectral
moment
T/Tp
Peak period Tp 1/fp 1
Mean period Tm (m0/m2) 0.75 to 0.85
Significant period Ts 0.9 to 0.95
February 1, 2012 31
typical types of wave statistics patterns
February 1, 2012 32
H/T-diagram
February 1, 2012 33
waves in shallow water
shoaling
refraction
breaking
diffraction
reflection
0
1 1
4 /tanh 2 /1
sinh 4 /
sh
Hk
h LH h L
h L
February 1, 2012 34
the iribarren number (surf similarity parameter)
0
tan
H L
tan slope of the shoreline/structure
H wave height
L0 wave length at deep water
February 1, 2012 35
breaker types (2)
spilling < 0.5
plunging 0.5 < < 3
collapsing = 3
surging > 3
February 1, 2012 36
breaking waves
20.142 tanhbH L h
L
0.78 ( )bHsolitarywave
h
0.4 0.5sH
h
February 1, 2012 37
change of distribution in shallow water
February 1, 2012 38
Battjes Jansen method
2
1
1
3.6
2
2
( ) 1 exp
Pr
1 exp
tr
tr
HF H H H
HH H
HF H H H
H
February 1, 2012 39
Influence of shallow water on the wave height
February 1, 2012 40
Wave refraction
22 1
1
sin sinc
c
2 1
1 2
H b
H b
February 1, 2012 41
Diffraction behind a detached breakwater
February 1, 2012 42
reflection
20.1Rr
I
HK
H
tot i r 2 2 2 21 cos *cos 1 sin *sin
2 2
i iH Hx t x tr rL T L T
February 1, 2012 43
Example with Cress
run demo Cress
refraction
shoaling, etc
diffraction
x(50-200;4)
y (-200,200)
February 1, 2012 44
The effect of shoaling on wave parameters
February 1, 2012 45
Typical wave record of the North Sea
212 iS a
cos 2i i it a f t
0 13.5%4sH m H
Vermelding onderdeel organisatie
February 1, 2012
46
Spectral wave periods
The use of different wave parameters to obtain better results for wave structure interaction
ct5308 Breakwaters and closure dams
H.J. Verhagen
Faculty of Civil Engineering and Geosciences Section Hydraulic Engineering
0
n
nm f S f df
February 1, 2012 47
Example wave record
28 waves, Hs = "13% wave", Hs= wave nr 4, Hs ≈ 3.8 28 waves in 150 seconds, so Tm = 5.3 s
February 1, 2012 48
composition of the record
H1 = 0.63 m T1= 4 sec
H2 = 1.80 m T2 = 5 sec
H3 = 1.55 m T3 = 6.67 sec
H4 = 0.90 m T4 = 10 sec Tm = 5.3 sec
February 1, 2012 49
Spectrum discretised spectrum
0
1
2
3
4
5
6
7
0,1 0,15 0,2 0,25
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
energy density spectrum
0
1
2
3
4
5
6
7
0 0,1 0,2 0,3 0,4
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
21
2a S f
2 221.55
8 6 [ ]8 8 0.05
HH S f S m s
f
February 1, 2012 50
Calculation of m0
0.05*2 0.10
0.05*6 0.30
0.05*3 0.15
0.05*1 0.05
0.60 04 3.1m m
discretised spectrum
0
1
2
3
4
5
6
7
0,1 0,15 0,2 0,25
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
0
n
nm f S f df
February 1, 2012 51
Calculation of m1
dist * Sf
0.10*0.10 0.010
0.15*0.30 0.045
0.20*0.15 0.030
0.25*0.05 0.013
0.098
discretised spectrum
0
1
2
3
4
5
6
7
0,1 0,15 0,2 0,25
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
0
n
nm f S f df
February 1, 2012 52
Calculation of m2 discretised spectrum
0
1
2
3
4
5
6
7
0,1 0,15 0,2 0,25
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
dist2 * Sf
0.102*0.10 1.00 10-3
0.152*0.30 6.75 10-3
0.202*0.15 6.00 10-3
0.252*0.05 3.12 10-3
1.69 10-3
0
2
0.6010 5.69sec
1.69
mT
m
0
n
nm f S f df
February 1, 2012 53
Calculation of m-1 discretised spectrum
0
1
2
3
4
5
6
7
0,1 0,15 0,2 0,25
frequency (Hz)
en
erg
y d
en
sit
y (
m2s)
1/dist * Sf
1/0.10*0.10 1.0
1/0.15*0.30 2.0
1/0.20*0.15 0.75
1/0.25*0.05 0.20
3.95
11,0
0
3.956.58 sec
0.60m
mT
m
0
n
nm f S f df
February 1, 2012 54
Overview
•Hm0 = 3.1 m (1.55+1.10+0.90+0.63=4.18)
•Tm0 = 5.69 sec
•Tm-1,0 = 6.58 sec
•Tpeak = 6.67 sec
•
•Tm = 5.35 sec
•
1,0
0
6.581.16
5.69
m
m
T
T
For standard spectra:
Goda: Tp=1.1 T1/3
PM: Tp=1.15 T1/3
Jonswap: Tp=1.07 T1/3
TAW (vdMeer): Tp=1.1Tm-1,0
Old Test (vdMeer): Tp=1.04 Tm-1,0
Also: Tm-1,0=1.064T1/3
0 5.691.06
5.35m
m
T
T
Usual assumptions: Tm0 = Tp T1/3 = Tm
February 1, 2012 55
Overview to determine shallow water wave condition
• Determine deep water wave condition, this gives wave height, peak period and spectrum shape type (e.g. Jonswap)
• Calculate shallow water condition using spectral model (e.g. with SWAN), this gives Hm0, Tm0 and Tm-1,0
• Use Battjes-Jansen method to determine H2%
February 1, 2012 56
Why these parameters ?
0.2
0.250.182%1,0
50
cotpl m
n
H Sc P s for plunging waves
d N
0.2
0.25 0.50.132%1,0 1,0
50
P
s m s
n
H Sc P s for surging waves
d N
February 1, 2012 57
stress relations determined by soil testing
February 1, 2012 58
Dam profile after the slide
February 1, 2012 59
Squeeze
February 1, 2012 60
Liquefied sand