Impact of wave load-related model choices on structural failure probabilities

Abstract

In 2022, the Eastern Scheldt barrier was assessed regarding its compliance with the requirements in the Environment and Planning Act. The result of this assessment, mentioned in HKV et al. (2022), was that the barrier barely met the standards in failure probability: a value of 1/13.057 years while the minimum requirement is 1/10.000 years and the signal value is 1/30.000 years. This leaves a margin of a factor 1.3 increase for the current failure probability. The upper trusses of gates Scharen 13 (S13) untill Scharen 16 (S16) proved to be the weakest link in the barrier and contributed most to the total failure probability. This study only focuses on the upper truss of gate S13, and the results are assumed to be a rough indication of how the barrier responds as a whole.

This research investigates the usage of alternative wave load related model choices and their effect on the structural failure probability of the upper truss of gate S13. Combining these two aspects provides an estimate of the uncertainty in the estimated 1/13.057 years. Four areas within the current wave load related framework were considered.

- Dynamic wave pressure model. This aspect considers how the waves translate to dynamic pressures on the gates. Sainflou, quasi-regular linear wave theory (LWT), New Wave LWT η_recalculated and a spectral LWT are considered suitable alternatives compared to SainflouOSK, which is the currently used method. The linear models, especially the spectral variants, have the most complete representation of the physical processes. The spectral methods need the complete wave spectra as input, which is not yet accurately reproduced by the wave propagation model. New Wave LWT η_recalculated is particularly recommended because it provides a spectral calculation that accounts for the effects of steep waves. Sainflou corresponds best with a small, but high quality dataset of average pressures during regular waves. The linear theories perform best with a larger, but lower quality dataset of pressures during six hours in one storm. However, as no wave conditions were measured during this specific storm, wave propagation model output was used to employ this dataset. It is advised to solve the inconsistency between the data sources by performing scale model tests or SWASH simulations. Especially the performance under steep regular waves and bimodal spectra is crucial, as this study shows that these are the conditions that prevail during relevant storms. The structural failure probability changes significantly when these other dynamic wave pressure models are employed. Sainflou results in a factor 10 increase in failure probability for the upper truss of gate S13 and spectral LWT in a factor 100 decrease.

- Wave height distribution. This distribution is applied to move from a significant wave height to a maximum wave height within a storm. Two alternative distributions were considered, the Rayleigh distribution and the Battjes-Groenendijk distribution. The Rayleigh distribution, which is currently used in the assessment, is demonstrated to be conservative compared to six hours of wave pressure measurements in one storm. The Battjes-Groenendijk distribution could be an alternative, even though not validated in this study, leading to a factor five decrease in failure probability for the upper truss of S13. Given the significant impact on the failure probability and the indication of room for improvement, it is advised to perform further research in which wave height distribution is most suitable. SWASH simulations could be used to validate an alternative distribution. 

- Wave propagation model. Wave propagation is computed with SWAN considering wind-induced wave generation, whitecapping, depth-induced breaking, bottom friction, triad wave-wave interactions and quadruplet wave-wave interactions. From these source terms, adjustments to the formulations of wind-induced wave generation, whitecapping, depth-induced breaking and triad wave-wave interactions are considered. Modifying the CDS2 KOMEN whitecapping parameter within the current SWAN settings, which increases the whitecapping dissipation, improved the bias correction for both the wave height and period. However, this SWAN setting is not considered a better alternative. This is due to the lack of physical substantiation and its inability to reproduce measured spectral characteristics, especially during high water levels in storm conditions. The DCTA triad wave-wave interaction formulation showed most promising results in reproducing the bimodal spectra measured during severe storms. Additional research to improve the calibration of the DCTA formulation is recommended over employment of the adjusted CDS2 parameter. Using four other variations in SWAN settings with their corresponding bias corrections resulted in a spread of failure probabilities for the upper truss of S13 ranging from a factor 1.2 decrease to a factor five increase. 

- Wave load-related uncertainties and biases. This concept relates to the methodology of how uncertainties in parameters (probabilistic or deterministic) and models (bias corrections) are taken into account. Using energy interpolation over wave height interpolation between SWAN outcomes is considered an improvement for estimating the bias corrections. It leads to a factor 1.1 reduction in failure probability for the upper truss of gate S13. Similarly, bias estimation of the wave height and period by using measurements with an additional restriction on the water levels resulted in a factor 1.1 decrease. However, incorporating the entire distribution of wave heights, not only the mode of the chosen distribution, is considered an advancement that increases the failure probability by a factor two.

When combining the evaluations of alternative wave load related models and their effect on the structural failure probability of the upper truss of gate S13, it can be concluded that there is a large scatter around the 1/13.057 years. This uncertainty is a consequence of the inability to draw definite conclusions on which SWAN setting, dynamic wave pressure theory and wave height distribution to choose. There are well evaluated choices that decrease the failure probability below the signal value, but also other interesting options that increase it beyond the minimal requirement. Further research and data collection is necessary to determine which of these two scenarios is most likely. This study illustrates the starting point and direction for these next steps, while also providing the motivation and urgency to take them.