Single wave overtopping volumes
and their travel distance
Coastal Structures 2007, Venice
Lykke Andersen, T., Aalborg University, Denmark
Burcharth, H. F., Aalborg University, Denmark
Gironella, X., UPC, Barcelona, Spain
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
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Introduction
• The critical overtopping is typically given as an average
discharge and not as single wave overtopping volume and
velocity, which are expected to be more directly associated to
hazards.
• The landward distribution of overtopping
in combination with the single wave
overtopping volume can be used to give
an idea of the damage/forces exerted on a
structure.
Qpass / Qtot
1
x
• The landward distance the overtopping
water travel put restrictions to the use of
these areas and their drainage.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
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Methodology
Methodology for single wave overtopping estimations:
1. Estimate mean overtopping discharge (e.g. CLASH
Neural Network or conventional overtopping
formulae)
2. Estimate number of overtopping waves
3. Estimate maximum single wave overtopping
volume (use results from 1 and 2)
4. Estimate travel distance of maximum single wave
overtopping volume
The present work deals with step 2, 3 and 4 for
rubble mound breakwaters.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
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Experimental set-up (main
tests)
OVERTOPPING
Lykke Andersen, 2006 (PhD thesis - includes both large and small scale data)
TANK
Landward
Seeward
Water levels
1:2
1:1
.5
Cross Section 1 - Low wall
1:2
Cross Section 2 - Normal wall
Cross Section 3 - High wall
Cross Section 4 - High wall with recurved face
1 :1
• Chambers more narrow at the .5
CORE bottom for good accuracy also for
small overtopping discharges.
• Chambers equipped with surface
elevation gauges and pumps
configured to start and stop
automatically during tests.
• Wave steepness s0p: 0.02 – 0.045
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
4 of 17
Experimental set-up (additional tests)
Burcharth et. al, 2007 (Puerto de la Cruiz, small scale tests)
Long waves (s0p = 0.01)
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
5 of 17
Data analysis
• Controlling of pumps in
overtopping chambers from
data acquisition software
(e.g. WaveLab2 software
package from Aalborg
University).
• Select water levels for start
and stop of each pump.
• Measure levels in chambers
and state of pumps.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
6 of 17
Methodology
Methodology for single wave overtopping estimations:
1. Estimate mean overtopping discharge (e.g. CLASH
Neural Network or conventional overtopping
formulae)
2. Estimate number of overtopping waves
3. Estimate maximum single wave overtopping
volume (use results from 1 and 2)
4. Estimate travel distance of maximum single wave
overtopping volume
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
7 of 17
Number of overtopping waves
Formula by Van der Meer & Janssen (1995)
Non-breaking waves:
  R / H 2 
N ow
s
 exp   c
 
Nw
  c  
c  1.62  h  f  
•
•
f = 0.4 used
Armour crest freeboard
used (Ac) for all four crosssections
Burchart et. al, 2007
(f = 0.55)
Gives in most cases values in
the correct order of magnitude.
Large difference between the
two data sets.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
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Number of overtopping waves
Formula by Besley (1999)
Number of overtopping waves
related to the dimensionless
overtopping discharge:
Q 
q
Tm  g  H s
N ow
 55.4  Q0.634 for Q   8  10  4
Nw
N ow
 2.50  Q0.199 for 8  10 4  Q   1  10  2
Nw
N ow
1
Nw
for Q   1  10  2
Gives a very good estimate for
all tested cases!
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
9 of 17
Methodology
Methodology for single wave overtopping estimations:
1. Estimate mean overtopping discharge (e.g. CLASH
Neural Network or conventional overtopping
formulae)
2. Estimate number of overtopping waves
3. Estimate maximum single wave overtopping
volume (use results from 1 and 2)
4. Estimate travel distance of maximum single wave
overtopping volume
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
10 of 17
Single wave overtopping volume
Franco et al. (1994), Van der Meer and Janssen (1995):
 V /V
F V   1  exp  
  A





B



A = 0.84, B = 0.75
Weibulls plotting position formula is used:
F Vi   1 
i
N ow  1
Combining the two equations leads to:



i

 A   Ln
V

 N ow  1 
Vi
i = 1 =>
1/ B
 A  Ln N ow  1  Lni 
1/ B
Vmax
 A  LnNow  11/ B
V
Vmax
A

 LnN ow  11 / B
Vtotal N ow


V
V  total 
N ow 

Similar to the equation used by Franco et al. (1994) and van der Meer and
Janssen (1995) except that they used Now instead of Now +1 in the logarithm.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
11 of 17
Single wave overtopping volume
Vmax
A

 LnN ow  11 / B
Vtotal N ow
Upper envelope: A = 1.63, B = 0.75
Lower envelope: A = 0.60, B = 0.75
Central:
A = 1.12, B = 0.75
Franco + VdM:
A = 0.84, B = 0.75
Large Now: Franco + VdM is close to a
central estimate
Small Now: Franco + VdM is close to a
lower limit (unsafe prediction of Vmax)
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
12 of 17
Methodology
Methodology for single wave overtopping estimations:
1. Estimate mean overtopping discharge (e.g. CLASH
Neural Network or conventional overtopping
formulae)
2. Estimate number of overtopping waves
3. Estimate maximum single wave overtopping
volume (use results from 1 and 2)
4. Estimate travel distance of maximum single wave
overtopping volume
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
13 of 17
Landward distribution of mean discharge
Formula by Lykke Andersen & Burcharth, 2006
Ratio of overtopping passing travel distance x at splash down level hlevel:
q passing x
q total

0.15



max
x
/
cos

2.7

h

s
0p , 0
level
- 1.05
= exp - 1.1  s0p


L0 p

where  is the angle of incidence



More than 1000 tests
x(hlevel=0)
H
hlevel
x(hlevel=H)
x
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
14 of 17
Landward distribution of
max single wave overtopping volume
Application of formula for distribution of mean discharge on
max single wave overtopping volume.
Vmax,passing x
Vmax,total

0.15



max
x
/
cos

2.7

h

s
level
0p , 0
-1.05

= exp - 1.1 s 0p 

L0 p




Distribution of large single wave
overtopping volumes seems not to
be very different from the
distribution of the mean discharge
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
15 of 17
Influence of wind & scale effects
• In the EU-CLASH project differences between prototype and
small scale overtopping results have been observed.
• The differences might be due to model effects (e.g. wind) or
scale effects.
• Wind and scale effects are expected to be most pronounced
for relatively small overtopping discharges (q < 1 l/sm).
• The presented formula for landward distribution of
overtopping is limited to green water overtopping and
cannot predict travel distance of wind carried spray.
• The influence of scale effects on the landward distribution is
expected to be quite small as indicated by the test results in
large and small scale.
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
16 of 17
Conclusions
• Experimental results on overtopping of individual waves
have been analysed.
• A calculation procedure for calculating single wave
overtopping volumes and their travel distance has been
presented.
• The formula by Besley (1999) estimate the number of
waves overtopping with great accuracy in all of the
tested cases.
• The existing formula for single wave overtopping volume
has been slightly modified to account for cases with few
overtopping waves. Upper and lower envelope curves has
been given for single wave overtopping volume.
• The travel distance of maximum single wave overtopping
volumes is quite similar to that found for the mean
discharge.
Thank you for your attention!
SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCE
Lykke Andersen, Burcharth & Gironella
Coastal Structures 2007, Venice, July, 2007
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