wave loads on caissons determination of wave pressure sampling frequency in model tests

WAVE LOADS ON CAISSONS.DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS

Burcharth, Lykke Andersen & Meinert

COPEDEC 7, Dubai, Feb, 20081 of 16

Wave Loads on CaissonsDetermination 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




The Problem

Fw,horizontal

Fw,uplift




The Problem




Failure mode: Horizontal sliding of caisson

Elastic/plastic deformations of foundation and caisson disregarded

Failure function:

Equation of motion:

2

2

addedcaisson

2

2

addedcaissonuplift,whorizontal,w

dt

xdMMgtF

dt

xdMMfFGFtF

sliding , 0

sliding no , 0gFfFG horizontal,wuplift,w

Fw,horizontal

x

G

Fw,uplift

friction factor f = 0.6

h




Determination of sliding distance

Sliding distance:

0dtgMM

1tx

2

1

t

taddedcaisson2

0tx velocity, 2

dtdttFMM

1txtx

2

1 1

t

t

t

t addedcaisson12

F(t) = F + f·F -Gf = -gw,horizontal w,uplift

time

t1 t1t2 t2

0

acceleration phase (g<0)

deceleration




Example analyses

1.70

Head-on waves

Hm0 = 6.2 m

Tp = 14 s

JONSWAP spectrum

= 3.3Mcaisson = 463 t

Madded = 162 t

6.0022.0

1:100

+10.50

+0.00

-12.00

-10.00

-14.50

13.7

0

Model length scale 1:50




Simple static force analysisEffect of sampling frequency

Example: Hm0 = 6.2 m, Tp = 14 s, WL = 0.00 m, 1000 waves

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12

Hor

izon

tal f

orce

per

met

re [k

N/m

]

Down-crossing wave height [m]

Sampling 7.1 Hz (50 Hz in model)No averaging

min. g = -1901 kN/m

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12

Hor

izon

tal f

orce

per

met

re [k

N/m

]


Sampling 141.4 Hz (1000 Hz in model)No averaging

min. g = -4703 kN/m

Necessary increase in caisson width = 20.9 m Necessary increase in caisson width = 51.8 m

Conclusion: Very large influence of sampling frequency




Simple static force analysisEffect of sampling frequency when force averaging


Necessary increase in caisson width = 3.4 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.

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12

Hor

izon

tal f

orce

per

met

re [k

N/m

]


Sampling 7.1 Hz (50 Hz in model)Averaging over 0.71 s (0.1 s in model)

min. g = -312 kN/m

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12

Hor

izon

tal f

orce

per

met

re [k

N/m

]


Sampling 141 Hz (1000 Hz in model)Averaging over 0.71 s (0.1 s in model)

min. g = -226 kN/m




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




Dynamic force analysesIllustration of importance of shape of load variation

Assumption: Constant impulse 0tgfor dttF F(t) = -g

t0

area Aarea A

area Aarea A




Dynamic force analysesIllustration of importance of shape of load variation

Assumption: Constant impulse 0tgfor dttF

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.




Dynamic force analysesExample demonstration of influence of width of caisson on sliding distance





Dynamic force analysesExample of influence of sampling frequency and

width of caisson on sliding distance

Conclusion: If more than app. 50-100 samples within Tp is used, then the influence of sampling frequency is minimal.





Dynamic force analysesExample of influence of time averaging of force buoyancy reduced weight and width of caisson on sliding distance

Conclusion: If the time interval for averaging is app. 0.01·Tp or less, then the influence of averaging is marginal.





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.



COPEDEC 7, Dubai, Feb, 2008

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.

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wave loads on caissons determination of wave pressure sampling frequency in model tests

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