Committee Chair

Wynn, R. H. (Robert Hugh), 1938-

Committee Member

Belinskiy, Boris; Foster Jr., Edwin P.; Gurley, William Q.

Department

Dept. of Civil and Chemical Engineering

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

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.

Acknowledgments

Such a work as this would be impossible without the help of others. My first thanks are to the Thesis Committee: Dr. Robert H. Wynn (Chairman), Drs. Boris P. Belinskiy, Edwin P. Foster, Jr., and William Q. Gurley. Their assistance and support throughout this project were invaluable. Unlike most research projects that pertain to public works, this one was unfunded; however, I owe a special debt of gratitude to Dr. Edward B. Perry and the U. S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS, for their assistance in the background research for this thesis. Without this help this thesis could not have been completed as it was done. Others to whom I must express my appreciation to for furnishing material important to the completion of this thesis include Drs. G.A. Leonards and Richard Deschamps of Purdue University and Dr. Andrew J. Deeks of the University of Western Australia, and Mr. Alla H. Abdelhalim of the University of Tennessee at Chattanooga. Also thanks must go to the Church of God Department of Lay Ministries for their help in the printing of this thesis. Finally I must save my special thanks for my wife Judy, whose patience and support throughout the entire pursuit of the degree and the writing of this thesis has been unfailing, and who, as a music teacher and church musician, employs the wave equation in its most beautiful form.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-1997

Subject

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

Keyword

wave equation; driven piles; closed form solution; Laplace transform; Sturm-Liouville problem

Discipline

Geotechnical Engineering

Document Type

Masters theses

DCMI Type

Text

Extent

xv, 233 leaves

Language

English

Call Number

LB2369.2 .W377 1997

Rights

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

License

http://creativecommons.org/licenses/by/4.0/

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