Wave Loads on Caissons
Determination of Wave Pressure Sampling Frequency in Model Tests
COPEDEC 7, Dubai
Burcharth, H. F., Aalborg University, Denmark
Lykke Andersen, T., Aalborg University, Denmark
Meinert, P., Aalborg University, Denmark
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
1 of 16
The Problem
Fw,horizontal
Fw,uplift
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
2 of 16
The Problem
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
3 of 16
Failure mode: Horizontal sliding of caisson
x
G
Fw,horizontal
h
friction factor f = 0.6
Fw,uplift
Elastic/plastic deformations of foundation and caisson disregarded
Failure function:
G  F
w , uplift
 0 , no sliding

g


w , horizontal
 0 , sliding
f  F
d2x
Equation of motion: Ft   Fw ,horizontal  G  Fw ,uplift  f  M caisson  M added  2
dt
d2x
Ft   g  M caisson  M added  2
dt
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
4 of 16
Determination of sliding distance
F(t) = Fw,horizontal + f·Fw,uplift -Gf = -g
acceleration phase (g<0)
deceleration
time
0
t1
t2
t1
t2
velocity, x t 2   0
t
2
1
x t 2  
 g dt  0
M caisson  M added t1
t2 t
Sliding distance: xt 2   xt1     M
t1 t1
1
 Ft  dt dt

M
caisson
added
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
5 of 16
Example analyses
+10.50
Model length scale 1:50
Head-on waves
Hm0 = 6.2 m
Tp = 14 s
+0.00
1.70
JONSWAP spectrum
 = 3.3
13.70
Mcaisson = 463 t
Madded = 162 t
-10.00
-12.00
-14.50
22.0
1:100
6.00
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
6 of 16
Simple static force analysis
Effect of sampling frequency
Sampling 7.1 Hz (50 Hz in model)
No averaging
min. g = -1901 kN/m
6000
Horizontal force per metre [kN/m]
Horizontal force per metre [kN/m]
Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
Sampling 141.4 Hz (1000 Hz in model)
No averaging
min. g = -4703 kN/m
6000
5000
4000
3000
2000
1000
0
0
Down-crossing wave height [m]
Necessary increase in caisson width = 20.9 m
2
4
6
8
10
12
Down-crossing wave height [m]
Necessary increase in caisson width = 51.8 m
Conclusion: Very large influence of sampling frequency
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
7 of 16
Simple static force analysis
Effect of sampling frequency when force averaging
6000
Sampling 7.1 Hz (50 Hz in model)
Averaging over 0.71 s (0.1 s in model)
min. g = -312 kN/m
Horizontal force per metre [kN/m]
Horizontal force per metre [kN/m]
Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
Sampling 141 Hz (1000 Hz in model)
Averaging over 0.71 s (0.1 s in model)
min. g = -226 kN/m
6000
5000
4000
3000
2000
1000
0
0
Down-crossing wave height [m]
Necessary increase in caisson width = 3.4 m
2
4
6
8
10
12
Down-crossing wave height [m]
Necessary increase in caisson width = 2.5 m
Conclusion: In this case no significant influence of sampling frequency when averaging.
However, in general large influence of averaging time interval. The choice of time interval
depends on the simultaneous distribution of pressures over the caisson front.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
8 of 16
Dynamic force analyses
If some sliding of the caisson is allowed then the sensitivity to
sampling frequency and time averaging is reduced significantly.
As an example the design conditions could be:
• Serviceability Limit State: 0.2 m sliding
• Repairable Limit State: 0.5 m sliding
• Ultimate Limit State: 2.0 m sliding
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
9 of 16
Dynamic force analyses
Illustration of importance of shape of load variation
Assumption: Constant impulse Ft  dt for gt   0

F(t) = -g
area A
area A
area A
area A
t
0
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
10 of 16
Dynamic force analyses
Illustration of importance of shape of load variation
Assumption: Constant impulse Ft  dt for gt   0

Conclusion: The total load histories of a wave impacts – not only the load peaks – are of
importance for the sliding distance. Actually the short duration peaks might have little
influence compared to the pulsating part of loading.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
11 of 16
Dynamic force analyses
Example demonstration of influence of width of caisson on sliding distance
Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
12 of 16
Dynamic force analyses
Example of influence of sampling frequency and
width of caisson on sliding distance
Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves
Conclusion: If more than app. 50-100 samples within Tp is used, then the influence of
sampling frequency is minimal.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
13 of 16
Dynamic force analyses
Example of influence of time averaging of force buoyancy
reduced weight and width of caisson on sliding distance
Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves
Conclusion: If the time interval for averaging is app. 0.01·Tp or less, then the influence of
averaging is marginal.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
14 of 16
Overall conclusions related to sampling and
analyses of wave loads on caissons
• If no horizontal sliding of caissons is allowed then the caisson must be
designed for largest recorded wave load which increases a lot with the
force sampling frequency due to the narrow peaks in the loadings.
• However, the impulse (momentum) of the load peaks will often be too
small to move the caisson and might be disregarded in a stability
analysis.
• Only a dynamic analysis based on high frequency recorded load time
series can tell which peaks can be disregarded.
• Example analysis indicates that if the local sampling frequency is higher
than 50-100 samples within a Tp-period then the influence on calculated
caisson displacements is marginal.
• The same holds for time averaging of the loads if time intervals of less
than 1%·Tp are used.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
15 of 16
Overall conclusions related to sampling and
analyses of wave loads on caissons
• Example analyses showed that if, for a middle size breakwater caisson,
a sliding of approximately 2 cm is allowed, then the width can be reduced
by approximately 30% compared to a non-sliding caisson.
• The analyses also indicate that elastic/plastic deformations of the
foundation – which is often in the order of 1 cm – are of importance in
reducing the effect of very peaky loadings and should therefore be
included in the analysis.
• The dynamic analysis must be based on high frequency sampling of the
wave loads because a low frequency sampling will often give too large
impulses (and too large calculated displacements) when a peak or part of
a peak are accidentally recorded and multiplied by the relative large time
intervals between samples.
High frequency sampling must in any case be applied in order to give
correct forces for the design of the structure itself.
WAVE LOADS ON CAISSONS.
DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS
Burcharth, Lykke Andersen & Meinert
COPEDEC 7, Dubai, Feb, 2008
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