Run-up on vertical piles due to regular waves: Small-scale model tests and prediction formulae

In wave-structure interaction, one of the most important phenomena clearly identified is wave run-up on offshore structures. In this study, wave run-up on a slender pile due to non-breaking regular waves is investigated by means of small-scale experiments performed in the 2 m-wide wave flume of Leichtweiss-Institute for Hydraulic Engineering and Water Resources (LWI) in Braunschweig, Germany. The test programme is designed to generate a comprehensive data set covering a broader range of wave conditions including not only deep and intermediate water conditions but also nearly shallow and shallow water conditions, which are missing in the available laboratory studies on wave run-up on piles. The relative wave height (H/h), relative water depth (h/L) and slenderness of pile (D/L) are identified as the key parameters governing the relative wave run-up (Ru/H). Based on these parameters, new formulae covering the range of tested conditions (0.028 ≤ H/h ≤ 0.593, 0.042 ≤ h/L ≤ 0.861, 0.003 ≤ D/L ≤ 0.206) are developed to predict regular non-breaking wave run-up on single piles using a combination of the M5 model tree and nonlinear regression techniques. Using statistical accuracy metrics such as agreement index Ia, squared correlation coefficient R2 and scatter index SI, the performance of the developed formulae is evaluated. It is shown that the new formulae outperform the current formulae in predicting regular wave run-up on single piles. This success is in part due to the explicit account for the water depth in the new experiments and formulae. The proposed model is valid for a wider range of wave conditions and, therefore, more appealing for engineering practice compared to those available for the estimation of regular wave run-up.