1. 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 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

2. 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

3. 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 The Problem

4. 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 Failure mode: Horizontal sliding of caisson Elastic/plastic deformations of foundation and caisson disregarded Failure function: Equation of motion:

5. 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 Determination of sliding distance Sliding distance:

6. 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 Example analyses Model length scale 1:50

7. 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 Example: H m0 = 6.2 m, T p = 14 s, WL = 0.00 m, 1000 waves Necessary increase in caisson width = 20.9 m Necessary increase in caisson width = 51.8 m Conclusion: Very large influence of sampling frequency

8. 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 Simple static force analysis Effect of sampling frequency when force averaging Example: H m0 = 6.2 m, T p = 14 s, WL = 0.00 m, 1000 waves 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.

9. 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 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

10. 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

11. 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 Illustration of importance of shape of load variation Assumption: Constant impulse 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.

12. 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 demonstration of influence of width of caisson on sliding distance Example: H m0 = 6.2 m, T p = 14 s, WL = 0.00 m, 1000 waves

13. 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 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. Example: H m0 = 6.2 m, T p = 14 s, WL = 0.00 m, 1000 waves

14. 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 Dynamic force analyses Example 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. Example: H m0 = 6.2 m, T p = 14 s, WL = 0.00 m, 1000 waves

15. 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 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.

16. WAVE LOADS ON CAISSONS. DETERMINATRIOTION OF WAVE PRESSURE SAMPLING FREQUENCY IN MODEL TESTS Burcharth, Lykke Andersen & Meinert 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. 16 of 16