Mathematical Problems in Engineering

Volume 2017, Article ID 6849658, 10 pages

https://doi.org/10.1155/2017/6849658

## A Numerical Simulation of Base Shear Forces and Moments Exerted by Waves on Large Diameter Pile

School of Energy Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, China

Correspondence should be addressed to Zhan-pu Xue; moc.361@321upnahzeux

Received 29 December 2016; Revised 17 March 2017; Accepted 11 June 2017; Published 2 August 2017

Academic Editor: Stefan Balint

Copyright © 2017 You-liang Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To solve the problem of the dynamic variation of wave force diameter of pile foundation for offshore wind turbines, wave force and moment of large diameter pile foundation can be calculated. In this paper, simulation technique is used to calculate the wave force and moment of different large diameter pile foundation, and the base shear force and moment of the interval 20-degree phase angle are obtained by the base line of the pile. Under the action of a certain load, the complete stress variation of the pile foundation is obtained. According to the basic principle of diffraction theory, the process curve of large diameter pile, and analysis of wave force, diffraction force changes in a certain period of time interval. The results show that the wave after the large diameter pile formed around the vortex, large diameter pile base shear, and moment dynamic change is nonlinear in a complete cycle, the diameter of the pile increases by 0.5 m, and the wave force increases by about 5%, the results show that it provides certain reference value for the offshore pile foundation pile with large diameter primary site. Some significant results for practical application are discussed.

#### 1. Introduction

The wave response of large diameter piles is one of the most important problems of offshore wind power pile foundation. Researchers have paid much attention on the problem of the large diameter pile surface waves. Ong et al. [1] provided a practical stochastic method based on assuming the waves to be a stationary narrowband random process and compared it with the Sumer and Freds data for 2D random waves plus current. Liu et al. [2] gave a review of the two-dimensional Reynolds-Averaged Navier–Stokes (RANS) equations with a Shear-Stress Transport (SST) turbulence closure to establish a two-dimensional numerical model. The roles of local scour around submarine pipelines induced by the orbital fluid motion under surface water waves were discussed. The results that Si et al. [3] used the generalized KdV model (GKdV model for short) to calculate ISWs on a supposed rigid pile are of benefit to revealing the mechanism of destructive power exerted by large-amplitude ISWs on a pile. It is essential to make reliable assessments of the wave and current loads on the structure, as well as of the scour around the base of the foundation at the seabed. For example, by means of an analytical model subjected to vertical loading from the superstructures and lateral loading due to wind or wave actions, the interaction effects of vertical loads on the lateral responses of piles applied in such cases were further investigated numerically by Liang et al. [4]. Studies on the solitary wave-induced loads on a submerged plate were very limited. Combining with the shift of polar coordinates, Liu et al. [5] examined the Bragg reflection of water waves by multiple submerged semicircular breakwaters. Experimental tests were carried out and the analytical results are in reasonable agreement with the experimental data. Li et al. [6] found that the extreme waves in deep waters are better reproduced than those in shallow waters, which is partly attributed to the limitations of the wave model used. In addition to the results and laboratory tests, various numerical models presented in this paper had also been developed to study the effect of wind data resolution on the simulation of long-term waves. Hayatdavoodi and Cengiz Ertekin [7, 8] also conducted wave loads due to nonlinear waves of solitary and cnoidal type propagating over a submerged, horizontal, and thin plate to compare the results that they obtained with the available laboratory data and with linear solutions of the problems. Accordingly, a new higher order boundary element method for the main diagonal elements was obtained. The proposed model can be used to simulate nonbreaking waves propagating on uneven bottoms or wave passing through surface-piercing structures, governing equations, and boundary conditions in the transformed plane which are first presented in [9–11]. Lian et al. [12] based on the diffraction theory show that the analytical solution of the wave pressure and the wave force on the composite bucket foundation is accurately derived by assigning reasonable boundary conditions.

In this paper, different wave forces are calculated by using the numerical simulation method. The base shear forces and moments on changes of linear wave which goes through large diameter piles are obtained; wave force time history curves and stress changes can be defined as the pile foundation of offshore wind power to provide reference.

#### 2. Numerical Approach

##### 2.1. Theoretical Background

On the ratio of the wavelength and the diameter of large diameter pile more than 0.2, the wave diffraction theory assumes that the fluid is homogeneous, incompressible, and powerful, nonviscous ideal fluid. The velocity potential of any point in the wave field is thatwhere is the position parallel to the horizontal direction of wave motion, is the position perpendicular to the direction of wave motion, is the depth from the bottom of the sea, is the velocity potential of undisturbed incident wave, is the velocity potential of scattered wave, and is the total velocity potential of any point in the wave fieldwhere is total velocity potential after separation of time variable, is the velocity potential of undisturbed incident wave after separation of time variable, and is the velocity potential of scattered wave after separation of time variable.

The random function of wave force acting on the large diameter pile is thatwhere is the total wave force random function, is the wave density, is the wave number, is the water depth, is the wave amplitude, and is Bessel function of the first kind. is Bessel function of the second kind, and is the displacement wave relative to the static water.

The wave force spectrum of playing a role in large diameter pile is thatwhere is the circular frequency, is the total wave force spectrum, and is the spectral density function. is the wave density, is the wave number, is the water depth, is the wave amplitude, and is Bessel function of the first kind. is Bessel function of the second kind.

The governing equation of the surface wave after the pile foundation [2] can be written aswhere and are the horizontal and vertical coordinates, respectively, is the fluid velocity in the -direction, is the velocity of moving grid in the -direction, is the time, is the pressure, is the wave density, is the kinematic viscosity of the fluid, denotes the gravitational acceleration, and is the mean strain rate tensor with . The stress term in (6) reads , where is the turbulent eddy viscosity, is the turbulence kinetic energy, and is the Kronecker operator.

##### 2.2. Numerical Model

In the change process of studying wave force on the large diameter pile foundation of offshore wind power, the large diameter pile foundation structure is regarded as a dynamical system, and effect of wave and other loads is called system input, structural stress, deformation, and movement, known as the output of the system. The wave spectrum and the response spectrum of the large diameter pile foundation are connected through the transfer function which is a function of frequency about the ratio of stress amplitude and cyclic wave. Airy wave theory is derived from the waveform which is a sine curve, and the other wave theory is derived from the wave which is not pure sine wave. They can be reasonably used to generate the transfer function.

As shown in Figure 1 of wave force decomposition diagram, the wave force is decomposed into two parts of water power and water static; hydrodynamics is divided into coupling wave force and diffraction wave force, considering the influence of structure on the wave force; static wave force included the influence of gravity and stages of wave force change and finally comes down to wave positive response, namely, the wave force in direction.