Statistical description of wave-induced inertial forces and mudline moments on a monopile in finite-depth, directionally-spread, irregular seas

We develop a theoretical stochastic framework for a monopile in irregular, directionally spread, finite-depth seas. This framework predicts the probability density functions of wave-induced, depth-integrated inertial forces and mudline moments. The formulation is based on linear wave theory coupled with the inertial component of the Morison equation and is applicable with arbitrary combinations of wave spectra and separable directional spreading functions. Apart from requiring numerical integration of their respective spectra to determine the force and moment variances, the framework is fully explicit. It is shown that, while their horizontal components are Gaussian, the resultant horizontal force and mudline moment follow a Hoyt distribution. This reduces to a Rayleigh distribution in the limit of uniform directional spreading and to a half-normal distribution in the unidirectional limit. The theory is validated against results from a fully-nonlinear wave model. A practical example demonstrates determination of design loads corresponding to a desired exceedance probability based directly on the stochastic description. The framework gives new theoretical insight into the statistical distribution of resultant loads in directionally-spread, finite-depth seas, and is well suited to determining preliminary design loads for monopiles in the inertia-dominated regime (low Keulegan-Carpenter number), without requiring Monte Carlo simulations.