A vast amount of flood defence structures contribute to the safety and water regulation in coastal areas. Gates form essential parts of flood defence systems as they regulate the discharge between bodies of water (Erdbrink, 2014). During storm conditions these structures are often subjected to high water levels and waves. When breaking waves impact on a gate, this generally involves high peak pressures of short durations in the order of a few milliseconds (Bagnold, 1939; Hofland, Kaminski, & Wolters, 2011; Ramkema, 1978). Such impulsive loads lead to vibrations of the structure, potentially amplifying internal stresses compared to the static situation.
Due to the two-way interaction between the structure and fluid, detailed prediction of these dynamic interactions can become very complex. Advanced numerical methods exist, but are still too computationally costly to test a wide variation of boundary conditions. For this reason, in present engineering practice generally a simplified quasi-static approach is taken, in which an amplification factor is applied to the time-varying load to account for vibrations (Kolkman & Jongeling, 2007a, 2007b, 2007c). However, such an approach lacks far behind in accuracy compared to design standards in other fields, and gives little insight in the actual behaviour of the structure. Not knowing the exact dynamic behaviour of the gate requires conservative design assumptions leading to suboptimal design.
For this reason, a semi-analytical model using fundamental theory of dynamics of continuous systems was developed by the author that fulfils these requirements. In the present study, this model is applied to the reference design of the sluice gates in the Afsluitdijk. Results are compared to a standard, simplified quasi-static design approach, showing the benefits of more accurately predicting the dynamic behaviour of gates.
The discharge sluices of the Afsluitdijk contain double sets of gates, of which the closest to the Waddensea will act as flood gates in the future situation. During storm conditions, these gates will have to withstand the loads resulting from the water level difference and incoming waves corresponding to 1/10,000 return period conditions. Due to the presence of the overhanging monumental defence beam, breaking waves were expected to result in high impact pressures. This was confirmed in physical scale experiments performed in the Deltares Scheldegoot (Hofland, 2015), where peak pressures were measured corresponding to 32 times the significant wave height Hm0. Since the duration of the measured integrated peak impact force was of the same order as the first dry natural frequency of the existing gate reference design, the maximum amplification factor for impulsive impacts was applied to obtain the design load. This results in such a large required strength of the gate and the related lifting mechanism and towers, that the decision was made to remove the monumental defence beam in order to reduce the impact pressures.
The analysis based on the semi-analytic model approach is more detailed on several aspects. First of all, the interaction with the surrounding fluid is taken into account. The hydrodynamic mass and stiffness are expected to have a substantial effect on the natural frequency of the designed gate, leading to a different response and potentially lower amplification. Secondly, the effect of the temporal and spatial distribution of the measured wave impact signal on the gate’s response and required strength is studied. Finally, multiple gate vibration modes are included in the analysis. The combination of these effects is expected to result in a more efficient design than the existing one, which has benefits for the surrounding structures as well. More generally, it shows that the developed semi-analytical model approach efficiently predicts vibrations of flood gates with more accuracy than existing design methods, leading to more economic designs. (Further) validation of the model is still required, so small scale model tests are discussed to obtain this validation.
References
Bagnold, R. A. (1939). Interim Report on Wave-Pressure Research. (Includes Plates and Photographs). Journal of the Institution of Civil Engineers (Vol. 12). https://doi.org/10.1680/ijoti.1939.14539
Erdbrink, C. D. (2014). Modelling flow-induced vibrations of gates in hydraulic structures.
Hofland, B. (2015). Modeltesten golfkrachten spuisluizen Afsluitdijk.
Hofland, B., Kaminski, M., & Wolters, G. (2011). Large Scale Wave Impacts on a Vertical Wall. Coastal Engineering Proceedings, 1(32), 15. https://doi.org/10.9753/icce.v32.structures.15
Kolkman, P. A., & Jongeling, T. H. G. (2007a). Dynamic behaviour of hydraulic structures - Part A. Delft Hydraulics, 304. Retrieved from http://repository.tudelft.nl/view/hydro/uuid:057be929-11e8-4da0-93cd-7df8c59d1d4d/
Kolkman, P. A., & Jongeling, T. H. G. (2007b). Dynamic behaviour of hydraulic structures - Part B. Retrieved from http://repository.tudelft.nl/view/hydro/uuid:057be929-11e8-4da0-93cd-7df8c59d1d4d/
Kolkman, P. A., & Jongeling, T. H. G. (2007c). Dynamic behaviour of hydraulic structures - Part C. Delft Hydraulics, 304. Retrieved from http://repository.tudelft.nl/view/hydro/uuid:057be929-11e8-4da0-93cd-7df8c59d1d4d/
Ramkema, C. (1978). A model law for wave impacts on coastal structures. Coastal Engineering Proceedings, 16(Figure 7), 2308–2327.