This section of vulcanhammer.info is about the drivability and performance of pile driving equipment in general and Vulcan hammers in particular. It’s divided into several sections:
- Dynamic formulae: the original method of relating hammer performance to pile capacity and resistance
- Wave equation analysis: civil engineering’s first foray into computer aided design, and a key tool in the prediction of pile performance during and after driving
- Introduction to Wave Mechanics in Piling: the basics
- Isaacs and Glanville: The Beginnings of the Wave Equation for Piles
- Smith’s Wave Equation Program–the first numerical method
- Wave equation programs for free download or use (along with in-depth background information on the program being downloaded):
- Information on wave equation programs and routines developed by Vulcan or its personnel
- ZWAVE, Vulcan’s own wave equation program in the 1980’s
- Closed form solution of the wave equation for piles, the definitive work on the subject, from the 1990’s. Includes some of the background documents and derivative works.
- Differential Equations and Laplace Transforms in Soil Dynamics
- Other Monographs on the Wave Equation
- Pile dynamics and Inverse Methods: the wave equation applied in the field during test and production pile installation
- Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles: a new research project on the subject.
- Papers and monographs on pile driving and pile driving equipment
These topics are treated in detail in the Vulcanhammer.info Guide to Pile Driving Equipment, which includes a worked example.
It’s always good to hear pile driving superintendents say that Vulcan hammers are “hard driving hammers.” As edifying as that is for the salesman and equipment manufacturer, it isn’t very informative from an engineering standpoint. Estimating the drivability of a given pile with a certain hammer is an important part of the design and installation process of a driven pile. Some questions that need to be answered are as follows:
- What maximum blow count (blows per inch, foot, centimetre or metre) of penetration will be experienced during driving?
- How does this compare with the refusal criterion associated with the specific hammer?
- How high do the driving stresses–tension and compressive–rise in the piles during driving?
- How long does it take to drive the pile?
- What kind of pile load capacity: axial, lateral, allowable or ultimate–can we expect from the pile once it’s driven?
This section deals with the issue of how to answer all of these and more questions, which are related to the issue of “drivability.”
Driven piles are unique in that their driving resistance–and thus their axial capacity–can be estimated/verified by the performance of the hammer during driving. That’s why the Pile Driving Contractors Association’s motto is “A Driven Pile is a Tested Pile.” The methods for correlating the hammer performance with the pile resistance have changed over the years, and Vulcan hammers have been and are involved in almost all of the changes that take place. Although Vulcan hammers are featured in this section, most of these principles apply to any impact hammer.
The Wave Equation Page for Piling
This was the original title for the page that eventually became vulcanhammer.net. In turn this page was spun off of that one in 2007. Today its contents have been incorporated into this section of vulcanhammer.info. The original introduction, with some changes, is below:
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, knowledge 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 program. 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 meaningful 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.
Blast from the past: relive the original, GeoCities “Wave Equation Page for Piling” with the following articles directly printed from it:
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