This part of vulcanhammer.net is where the site got its start. In 1997, The Wave Equation Page for Piling was started to propagate (a good wave-related term) knowledge and understanding concerning the wave equation as applied to driven piles, knowedge that also extends to drilled shafts and other cast-in-situ piles when verification methods are employed.

Most treatments of the wave equation as applied to piles concern a computer program, most commonly GRLWEAP. But the topic in general predates this prgram. The use of wave theory to predict pile drivability and driving stresses was first proposed in 1931. It quickly became evident that a numerical method would be necessary to solve the problem in piling in a meanigful way. It was not until the early 1960's that real progress began in applying the theory to practice.

Today the wave equation is applied both to the capacity and drivability prediction of impact-driven piles and to the in situ monitoring of piles during installation. However, many engineers, equipment manufacturers, owners and in some cases the practitioners themselves are unaware of some of the complexities related to the application of stress wave theory to piles. This page will hopefully advance the dissemination of this knowledge and perhaps the application itself.

One thing the Wave Equation Page has done is to feature "non-WEAP" solutions to the problem. The WEAP lineage of programs (and more recently the TNO programs) have offered the deep foundations industry the following advantages:

• Convenience: In their current versions both of these programs have extensive databases of hammers, cushion materials, and pile and soil properties. They also help to compute the driving resistance of the pile and how it relates to its ultimate capacity. They save the engineer a great deal of time in having to do all of these by hand or separate program. A part of convenience rests in the fact that most Geotechnical engineers (unless they deal a lot with seismic phenomena) are not familiar with mechanical dynamics, which are at the heart of the wave equation. (It is no accident that many of the developers of wave equation programs are either structural or mechanical engineers.)
• Reputation: These programs have been around for a long time; they have been extensively tested (in their early development at least) and promoted by their developers extensively.
• Relation to Dynamic Testing: Both of the developing organizations offer dynamic testing and the equipment to perform this. This has become a standard part of pile dynamics, and adds to the credibility of the program.

But we feel that the serious study of the topic requires access to other types of solutions for the following reasons:

• As a Check: Any scientifically developed tool needs to be subject to verification. These solutions provide that kind of check.
• As Research Tools: There is nothing to prevent these being used in a research environment.
• For Progress: No technical development is immune from improvement! For example, why do we use finite difference methods only and not finite element ones, in common with so many other disciplines? There are still so many things in Geotechnical engineering we do not have adequately quantified that the need for improvement should be obvious. Wave equation programs are no exception.

We trust this this page is useful to you.

Features of the Wave Equation Page for Piling are as follows:

• Articles and Monographs
  • A Short History of the Wave Equation for Piles
  • Design and Performance of an Electro-Pneumatic Pile Hammer for Laboratory Applications
  • Efficiency and Energy Transfer in Pile Driving Systems
  • Implementación de una Solución Analítica para el Fenómeno de Propagación Unidimensional de Ondas en Pilotes y su Adaptación para la Interpretación de Resultados de la Prueba de Integridad de Pilotes (PIT) (Implementation of an Analytic Solution for the Phenomenon of One-Dimensional Propagation of Waves in Piles and its Adaptation for Result Interpretation of Pile Integrity Test (PIT))
  • Loading Rate Effects on Pile Load-Displacment Behaviour Derived from Back-Analysis of Two Load Testing Procedures
  • Mechanics of Diesel Pile Driving
  • Mechanics of Impact Pile Driving
  • Some Thoughts on Engineering and Pile Driving
• Closed Form Solution of the Wave Equation for Piling
• Wave Equation Programs
  • WEAP
  • TNOWAVE
  • TTI/Microwave
  • ZWAVE
  • TAMWAVE -- our own online wave equation program
• Differential Equations and Laplace Transforms in Soil Dynamics
• Papers by Mark Svinkin
• Bibliography of Pile Dynamics and Vibratory Pile Driving

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