Study On Longitudinal Vibration Of Pile Considering 3D Wave Effect Of Soil And Its Application

Modeling soil as a three-dimensional axisymmetric continuum and taking its 3D wave effect into account, longitudinal vibration of pile and its application is systematically investigated. The main original work is as the followings:1. Longitudinal vibration of an integral pile in an uniform soil with end bearing boundary or elastic bottom boundary undergoing vertical harmonic load is theoretically investigated. The pile is assumed to be vertical, elastic and of uniform cross-section, and the soil is regarded as a linear visco-elastic layer with hysteretic damping. With the aid of two potentials, the displacement of soil layer is decomposed and then the dynamic equilibrium equation of it is uncoupled and solved first. Thus the resistance factor and vibration modes of the soil layer are obtained and used to analysis the pile response. By considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at the interface of soil layer and pile, the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded, which is used to define complex stiffness and mobility at the level of the pile head. Based on the convolution theorem and inverse Fourier transform, a semi-analytical solution of velocity response in time-domain subjected to a semi-sine exciting force is given. A parametric study of the effect of these governing dimensionless parameters is conducted to illustrate the behavior of soil-pile interaction.2. Longitudinal vibration of pile with variable impedance(variable sections or modulus) in layered soil undergoing arbitrary load is theoretically investigated. The pile is assumed to be vertical, elastic and of variable impedance, and the soil is layered and with viscous damping. With Laplace transforms, the question can be solved in Laplace domain. With the aid of impedance transmit functions, an analytical solution for the impedance function in Laplace domain is yielded, so is the corresponding analytical solution for the impedance function in frequency domain, semi-analytical solution of velocity response in time-domain subjected to a semi-sine exciting force and mobility at the level of the pile head. Based on the solutions proposed herein, the Longitudinal vibration properties of an integral pile in a uniform soil or layered soil, a pile with variable sections or variable modulus in a uniform soil are discussed respectively. The influence on the curves of complex stiffness, mobility and reflection wave of pile caused by soil modulus, the degree of pile defects, and the length and location of pile defects are emphatically discussed.3. A comparison is made with available simplified theories such as that corresponding to plane strain model. The comparison involves many aspects such as the soil resistance factor, the soil complex local stiffness and the pile complex stiffness at the level of the pile head. The applicability of the other two models is analyzed and checked. It is proved that when frequency is low, there can be significant discrepancies between them, with frequency increasing, the simplified solutions converge to the new more rigorous one.4. With visco-elastic boundary of soil considered, the eigenvalue equation in frequency domain of soil dynamic equilibrium equation falls into a complex transcendental equation. In course of seeking its solution, Based on argument principle and contour integral, with the aid of MATLAB, two numerical algorithm combined with the corresponding procedures for solving transcendental equations in a complex plane is developed by the author. In the first algorithm, a solution to transcendental equations is converted into a solution to roots of a monic polynomial, and the latter can be fulfilled easily by using functions ROOTS or SOLVE in MATLAB. In the second algorithm, taking advantage of the property that thedistance between solves in a circular domain and the center of the circle is less than that of solves out...