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