IMPACT FORCES ON A VERTICAL PILE FROM PLUNGING BREAKING WAVES

Abstract

There is at the moment some concern and uncertainty on slamming wave forces due to plunging breaking waves on truss structures as support structures for windmills in shallow water. Some work has been done on the wave slamming forces on single vertical and inclined piles, e.g. Goda et al. (1966), Sawaragi and Nochino (1984), Tanimoto et al. (1986) or Wienke and Oumeraci (2005). The slamming force is generally written as Fs = 0.5ρwCsDcb 2ληb, where Cs is a slamming force factor, cb is the breaking wave celerity (the water particle velocity is set equal to the wave celerity at breaking), ηb is the wave crest height at breaking and λ is the curling factor which indicates how much of the wave crest is active in the slamming force. For a vertical pile the value of λ has been reported to be in the range λ = 0.2 – 0.5. The value of Cs has been reported to be in the range Cs = π - 2π, while the duration of the slamming force has been reported to be in the range τ = (0.25D/cb) – (0.5D/cb). The test results of impact forces from plunging breaking waves show a considerable scatter. This is inherent due to the nature of the issue. In order to gain some more insight in the problem it was decided to carry out another study on the issue of impact forces from plunging waves on a vertical pile, Ros (2011), with a different test set-up, different instrumentation and different analysis methods than reported before. A pile with diameter D = 0.06 m is instrumented with six ring force transducers at different elevations. All the tests were run with regular waves with frequencies around 0.5 Hz or periods around T = 2.0 s. The wave heights were varied and the highest waves were around H = 30 cm at the pile with crest heights ηb = 25 cm. One of the problems with high intensity and short duration forces is to measure the actual force. Ideally one should have an almost indefinitely stiff measuring system. But then this system would be so stiff that the necessary sensitivity is lost. Hence acompromise is made such that what is measured is the response, which is not the force, due to dynamic effects on the mass-spring system the transducer represents. The challenge is then the analysis of the response to arrive at the force. We applied the Duhamel integral, which requires some knowledge on the wave slamming force, which is the parameter we are seeking. We have in our case assumed a triangular impulse load, similar to Goda et al. (1966), but with a duration similar to Wienke and Oumeraci (2005), and some rise time. The sampling frequency during testing was 20 kHz. The natural frequencies of oscillation of the individual transducers were measured during pluck tests to be 900 Hz in the beginning of the oscillations to about 250 Hz later. This could be due to different modes of oscillations of the transducer. During the slamming force tests the added mass will be changed during the impact, hence also the natural frequency of oscillations. The procedure of analysis was then to start with an assumed value of the force, Fo, and possible rise time and adjust them by trial-and-error such that the calculated value and the time location of the first response peak corresponded to the first peak of the measured response signal.