Dimension-reduction of stochastic wave forces and probability density evolution analysis of wave-excited pile foundation

Abstract

This paper discusses the reasonable description and simulation of the continuous stochastic wave force field at probabilistic level. Firstly, in order to overcome the challenge of high-dimensional random variables inherent in the conventional Monte Carlo sampling (MCS), the dimension-reduction (DR) simulations of stochastic processes are addressed based on both the non-deterministic spectral amplitude (NSA) method and the deterministic spectral amplitude (DSA) method. In the proposed method, merely one or two elementary random variables are required to describe the continuous stochastic wave force field at the level of probability density. Simultaneously, the simulation efficiency of the proposed scheme is significantly enhanced by employing the Fast Fourier Transform (FFT) algorithm. In addition, the DR simulations for continuous stochastic wave force field are conducted in accordance with the linear Morison's equation (LME) and the nonlinear Morison's equation (NLME). Finally, the stochastic wave force field acting on a single pile foundation is generated by the proposed method, followed by the refined linear dynamic analysis and reliability assessment of the employed single pile foundation combining the probability density evolution method (PDEM). The effectiveness, accuracy and engineering practicability of the DR methods are sufficiently illustrated by comparison with the MCS methods thereafter. The analysis results also show that the DR methods are of significance robustness in reliability assessment of offshore engineering structures.