Closed form solution of the wave equation for piles

This thesis details the research into the one-dimensional wave equation as applied to piles used in the support of structures for civil works and driven using impact equipment. Since the 1950's, numerical methods, both finite difference and finite element, have been used extensively for the analysis of piles during driving and are the most accepted method of analysis for the determination of driving stresses, dynamic and static resistance of piles. In this thesis the wave equation is solved in a relatively simple closed form without recourse to numerical methods. A review of past efforts to solve the wave equation in closed form is included. Problems that appear in previous related works are discussed and derived again, including the Prescott-Laura problem of the cable system stopped at one end and the solution of a hammer/cushion/cap/pile system for a semi-infinite pile. The latter is used to assist in the determination of a pile top force-time function that can be used to simulate the impact of the hammer on the pile. The basic equations, initial and boundary conditions are detailed, with the parameters adjusted to match actual soil dynamic behaviour while at the same time being a form convenient for closed form solution. To avoid difficulties due to spectral elements in the boundary conditions, a strain-based model of the radiation dampening in the pile toe was developed. The solution technique uses a Laplace transform of the semi-infinite pile problem for 0 < t < L/c (or for a time duration 0 < t < δ, where δ < L/c) and a Fourier series solution of the Sturm-Liouville problem thereafter. This solution is applied both to undamped and damped wave equations. The work includes comparison with existing numerical methods such as WEAP87, ANSYS, and Newmark’s method using Maple V.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Warrington, Don C

Contributors dc:contributor

• Wynn, R. H. (Robert Hugh), 1938-
• Belinskiy, Boris; Foster Jr., Edwin P.; Gurley, William Q.
• College of Engineering and Computer Science

• Laplace transformation
• Piling (Civil engineering)--Mathematical Models
• Soil mechanics
• Wave equation

Licence

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English, eng

Identifier

LB2369.2 .W377 1997

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2211