## Introduction 
As offshore turbines get larger, their support structures become bigger and more expensive and their optimization becomes steadily more important for cost reduction. It is known that in storms large waves can induce extreme loads on bottom-fixed structures, that can become design drivers. Design standards outline fast engineering procedures to compute these loads, which usually consist in computing a time series of uni-directional (2D) linear waves where a nonlinear regular wave is embedded. However, unlike regular waves, extreme waves are rarely symmetric around their crests, which can lead to modeling inaccuracies. Furthermore, real life storms also have a directional spreading, generating multi-directional (3D) sea states. Including the directionality of the waves leads to improved load estimations, as extreme loads from 3D sea states can differ significantly from extreme loads from a corresponding 2D sea state, also depending on the slenderness of the structure with respect to the waves.To overcome these shortcomings, more complex computations are needed. Fully-nonlinear potential flow solvers allow for a higher-fidelity representation of reality. They are more computationally intensive than the engineering models, but the advent of faster computers and of precomputed datasets as the DeRisk database makes their use more feasible. This is a timely issue, as the industry is currently designing the bottom-fixed substructures for the next generation of multi MW turbines, and they need advanced tools to validate and improve their design routines.## MethodologyIn this work, we numerically reproduce a subset of the results from the DeRisk experimental campaign via the fully-nonlinear potential flow solver OceanWave3D. In the experiments, a set of 2D and 3D sea states with 10, 100 and 1000 year return period were realized at two depths, 20m and 33m, in DHI Denmark's wave tank. Experimental loads were also measured on a bottom-fixed stiff monopile foundation with a full-scale diameter of D=7.0[m]. 
We reproduce 4 storms, 2 with uni- and 2 multi-directional waves, in an equivalent numerical wave tank, and perform a statistical comparison between computations and experiments, meaning we aim to match the extreme wave statistical distributions, and not to deterministically reproduce each wave. We also re-compute the loads on the cylinder through the simulated kinematics and the Rainey load model, and compare with the experimental statistics.## Expected results and conclusionsThe first results show that OceanWave3D is able to reproduce the trends that were observed in the experiments fairly well. In particular, the extreme free surface elevation crest distribution shows that larger waves are more likely to arise in the 3D sea state rather than on the 2D sea state. For the crest distribution of the in-line force on the monopile, the contrary is true. This may be explained by the difference in the wave focusing process. In 2D sea states the focusing of wave energy happens more slowly, as it is mainly generated by frequency and amplitude dispersion of waves traveling in the same direction. 
In the 3D sea states, the focusing happens more suddenly, as it comes from the superimposition of waves traveling in different directions. Hence, steeper waves are more likely to happen in 2D sea states than in 3D sea states. These are more prone to break, leading to a lower wave crest distribution in the 2D sea state, but to a larger probability of observing large wave loads.We further aim at quantifying the goodness of the reproduction of the experimental waves by our numerical model. In particular, we extract the 30-minute experimental and numerical hourly crest and load maxima and fit a Gumbel distribution thorough them. By comparing the fitted distribution parameters and their statistical spread, we assess the accuracy of our numerical model in reproducing the experiments. In addition, we analyze the average shape of the waves inducing the 30-minute maximum loads, to gather information about their steepness and the asymmetry in their shape.

Numerical Reproduction of the Derisk Physical Model Tests on a Bottom-Fixed Foundation Exposed to Uni- and Multi-Directional Storm Sea States

Paper Proceedings: https://asmedigitalcollection.asme.org/OMAE/OMAE2021/volume/85116

OMAE 2021

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