STADYN Wave Equation Program 11: Application of the STADYN Program to Analyze Piles Driven Into Sand —

The newest update for the STADYN research project is available: Download Application of the STADYN Program to Analyze Piles Driven Into Sand The abstract is as follows: Abstract: The STADYN program was developed for the analysis of driven piles both during installation and in axial loading. Up until now the test cases used were in […]

via STADYN Wave Equation Program 11: Application of the STADYN Program to Analyze Piles Driven Into Sand —

Picking Up Concrete Piles for Driving

One of the concepts students in geotechnical engineering courses seem to have the most trouble with is estimating stresses in concrete piles during pick-up and setting them in place to drive.  The basic problem is that it’s sometimes hard to get our heads around the analytical simplification of the actual situation.  Let’s start by looking at the operation itself.  These first photos come from a job in Delaware in 1998, using a Vulcan 530 to drive cylinder piles.

The pile starts on the ground. What we have here is “one-point pickup” where only one line is used to pick up the pile. It’s put in a certain place (more about that later) in this case using a “choker.” (Some piles have pickup lifting eyes, they are best cast into the pile at the time of manufacture.) In this position the pile is horizontal. Once the crane operator lifts the choker, the pile is supported at two points: the choker and the far end of the pile. This is the most severe case of loading during pick-up.
The pile is being lifted into position. As the pile rotates, more of the load is shifted to the choker, but that load is more and more axial in the pile and not bending.
The pile is now vertical, almost all the load is on the choker and the stresses in the pile are now axial.
The pile is set into a template (shown in previous photograph) and the hammer is set on top of it, preparing to drive it. The template keeps the pile vertical until enough of the pile is in the ground to support it.
Vulcan 530 Delaware 1998 7
The pile is nearly down to the desired elevation due to the blows of the impact hammer.

Depending upon the configuration of the pile, it’s also possible to have two- and three-point pickup, as we can see from these photos, taken at the construction of a terminal in Portsmouth, VA, in 2005-6.  The contractor is Weeks Marine, the same contractor that got Sully’s plane out of the Hudson after his famous “landing” in the river.

A two-point pickup of a cylinder pile. The pile is off the ground and horizontal; it is simply supported at the chokers. Behind the pile is Weeks Marine’s Raymond 60X hammer.
The pile is being lifted up at one end for driving. As this happens more and more of the load is shifted to the left (top) choker, just as is the case with one-point pickup. Note Weeks Marine’s large barge which they use to do this kind of work.
The pile is almost vertical, almost all of the load is on the upper choker, suspended in turn from Weeks Marine’s crane.
The pile is now vertical. Weeks Marine’s Raymond 60X is now atop the pile, ready to begin driving. Note the grips on the pile at the bottom of the photo. This is called a “pile monkey” and is very useful for pile alignment in the leaders (guides.)

So how to we solve problems like this?  Basically we assume that the pile is a horizontal beam, simply supported at the pickup points (or in the case of one-point pickup, at the pickup point and at the furthest end from the pick-up point) with the weight of the pile as the only load.  One thing that can be done is to raise the distributed load of the weight by a factor for inertial effects during handling.  An example of this is a 60′ long 12″ square concrete pile with a 50% increase for inertial effects with single point pick-up.  We used the CFRAME program from the U.S. Army Corps of Engineers to analyse the beam, although most any beam software (or in some cases tables or hand calculation) can be used for this computation.

This slideshow requires JavaScript.

In this case we are displaying the output of CFRAME which shows each section of the beam/pile (i.e., one one side of the pick-up point and the other.)

According to the Prestressed Concrete Institute’s Recommended Practice for
Design, Manufacture and Installation of Prestressed Concrete Piling (1993), the maximum permissible stress (tension) for transient loads such as handling loads is as follows

F_b = 6 \sqrt {f'_c} (US Units, psi for both variables)

For SI units, this works out to

F_b = \frac {1}{2} \sqrt {f'_c} (SI Units, MPa for both variables)

Some specifications allow the prestress of the pile f_{pc} to be added to F_b , with the same units as the other variables.  Obviously with precast concrete piles (rare in the US but used elsewhere) the prestress does not apply.

FL DOT Concrete Pile Pickup
For several sizes of concrete piles, the Florida Department of Transportation recommends these permissible configurations and pick-up point locations.  The pickup locations relative to the length are fairly standard with concrete piles.

Other piles sizes and lengths can be computed using the methods described above.

A Sea Fight in a Fog: Revisiting the ASCE Controversy about Dynamic Formulae

It’s always good for geotechnical professors and practitioners alike to think about where our industry has been and where it’s headed.  A little while back three of our most eminent people (Garland Likins, Bengt Fellenius and Robert Holtz) came together and wrote an excellent piece for the 2Q 2012 issue of the Pile Driver (the official publication of the Pile Driving Contractors Association) on “Pile Driving Formulas”.  The article is centred on the 1941-2 discussion (that’s putting it politely) in the Proceedings of the American Society of Civil Engineers on a committee report on the subject.

On this site there is a history of pile dynamics from the Sanders (not Stanton, as the PDCA article states) Formula to the present.  I considered adding a page on this particular topic, but with a website like this where the compensation is minimal, time failed me.  In a sense, the PDCA article fills an important gap in the narrative.  Having said that, I can’t help but think that the authors took some inspiration from what I had posted.  For example, the inventor of the Engineering News formula is not generally referred to as “Arthur Mellen Wellington” and the quote from his work is the same as the one I used, the more “spiritual” part excised.

In any case, the number of pile driving formulae increased in the first three decades of the last century to the point where, in 1930, the American Society of Civil Engineers appointed a committee to study the issue and recommend a formula.  The timing was interesting.  The following year, the Australian civil engineer David Victor Isaacs published his historic paper which first identified (and developed a method to analyse) wave propagation in precast concrete piles.  Later in the decade the British Building Research Board did their extensive research on wave propagation in piles.  The civil engineering world was taking its first steps to get beyond simple Newtonian impact mechanics in the dynamic analysis of driven piles.

The Committee finally released its report in 1941.  One recommendation was that static load tests be used in place of dynamic formulae.  This was definitely one way to solve the problem, but static load tests are long and expensive, and neglect the use of the pile hammer as a measuring tool.  Another proposed a refinement of existing dynamic formulae.  At this point the controversy erupted.  From September 1941 to February 1942 the discussion raged in the Society’s proceedings.  It involved many of the “greats” of geotechnical engineering: Karl Terzaghi, Ralph Peck, Arthur Casagrande, Gregory Tschebotarioff, Lazarus White and many others.  As is often the case in the earth sciences, from global warming to earthquake engineering, it sometimes got heated and emotional, with some defending the status quo while others pointing out the inadequacies of dynamic formulae.  The PDCA article does an excellent job in distilling this discussion to its basics.

While the end result—a “new” dynamic formula was not imposed on the industry—was a satisfactory one for the moment, the discussion revealed a great deal about geotechnical engineering, some of which has changed and some of which has not.

The first problem was that, for all of their erudition and well-deserved reputation for expertise in the field, many of the commenters were not, for want of a better term, well versed in the ins and outs of things moving, especially as rapidly as takes place during wave propagation in piles.  It is to their credit that the pioneers of this profession were able to transform a profession from a strongly empirical one to one subject to engineering analysis and quantification, and doing so in an environment of complexity and unpredictability as the earth itself.  But the skill set required to do that didn’t always lend itself to the understanding of the phenomena seen in driven piles during driving.  In that respect, the controversy resembled one description of the Trinitarian controversies of the fourth century: a “sea fight in a fog”.  While the shortcomings of the dynamic formulae were clear to those who spent time the jobsite time that these men did, the solution for the problem would have to come from somewhere else.

The second problem was that the computational power needed to analyse the problem was lacking at the time, especially to the practitioners in the field.  Isaacs solved this problem by using a graphical method, a solution seen elsewhere in the profession, but making his method general practice would have involved some kind of instrumentation to verify the results.  On the other hand the BBRB came up with the instrumentation, but their analytical method—a type of d’Alembert solution of the wave equation—was far too complex for practical implementation at the time.  Neither of these methods, even if they had been combined, adequately addressed the soil response to impact, especially along the shaft of the pile.  But in any case the Committee’s inclusion of these methods was not a significant part of their work product, and World War II put a stop to the research.  It’s tempting to think that, without that great and destructive conflict, a workable solution could have been proposed a decade earlier than it was.

The third problem was the frequently unhelpful role of building codes and standard specifications.  Codes enable owners to insure that their work is done properly.  One way they do this is by specifying methods of verification that are both easy and repeatable to evaluate.  What’s “easy” depends upon the tools of the time, but one of the reasons it has been so difficult to displace the dynamic formulae from geotechnical practice is because they—and especially the Engineering News formula—became deeply embedded in the codes and specifications by which many structures were built.  To take these away required their replacement, and risk averse owners of all kinds were reluctant to do this.

As the PDCA article rightly notes, the most prescient commenter was Raymond Concrete Pile’s A.E. Cummings, who noted the existence of Isaacs’ and the BBRB’s work on wave propagation in piles.  This is no accident.  Raymond was involved in every aspect of the installation of driven piles, from the design and manufacture of the driving equipment to the load testing of the piles.  They had a more comprehensive view of the issues involved and, being a large organization, had the means to tackle the problem.  Combined with the advent of digital computers, Cummings’ Raymond colleague E.A.L. Smith was able to write the first code suitable for the analysis of piles during impact driving, and the rest, as they say, is history.

Today of course the analysis of wave propagation in piles, both predictively and inversely, is at the core of pile dynamics.  It’s worth noting, however, that, although there have been many refinements in the methodology and advances in the software used, the basic theory in use is ostensibly the same as it was in the 1970’s.  It’s also worth noting that the use of pile dynamics is still a very specialized business, not only because they involve deep foundations, but also because, as was the case seventy years ago, most geotechnical engineers (except those in research) are not specialists in dynamics or numerical methods, both of which are at the heart of the analysis of piles (and other deep foundations) during impact driving.  Finally, although it’s been a long process to displace the dynamic formulae with wave related methods of analysis in building codes and specifications, it’s unreasonable to say that newer methods will not come along to displace or upgrade them, even in this conservative industry.

One of these days, significant breaks with current practice will appear to be considered.  Hopefully we won’t go through another “sea fight in a fog” as we did in the 1940’s and make the transition to newer, vetted methods smooth and efficient, for the benefit of both our profession and for those who use the structures we design and build.

Partying Like It’s 1987: Running WEAP87 and SPILE (and other programs) on DOSBox

It’s been a long time since many computers ran DOS or even Windows 3.1.  Given the changes in hardware, it would be difficult to get most any recent PC to run one or both.  Yet every time we have a major software upgrade, we lose some of the capabilities we had in the past.  It’s something we don’t think about in the advance of computer power, but it’s a fact.

That’s more true in two fields than any other: business and scientific/engineering software.  Ever wonder why businesses and medical establishments, for example, still run Windows XP or 7 so often?  With engineering software, it’s even worse: there are still DOS programs which do things that more recent software either does not do or does very expensively (the “per seat” cost of programs like AutoCad and most commercial finite element software, would shock most people outside of the field).

This article concentrates on two venerable pieces of DOS software: WEAP87, the wave equation program to analyse driven piles during installation, and SPILE, which estimates axial driven pile capacity.  As long as XP “ruled the roost” and was capable of running 16-bit software, it was certainly possible to run both and other DOS and Windows 3.1 packages.  With the creeping advance of Windows 7 and 8 (Vista wasn’t an advance) and 64-bit software, it’s become impossible to run these programs.  So we’re stuck with two choices: either forget about using them or purchase expensive wave equation software.  The latter option is OK if you use it all the time, but for occasional use (and when WEAP87 was perfectly adequate for your needs) it doesn’t make sense.  But what is to be done?

The solution to the problem for this and other DOS program requirements is DOSBox, an x86 emulator that runs DOS on a variety of platforms, including 32-bit Windows, Mac OS X and Linux.  The purpose of this article is to give an overview of DOSBox, some tips about its installation, how to set up WEAP87 and SPILE on DOSBox, and a quick look into Windows 3.1 on DOSBox.

About DOSBox

DOSBox is first an emulator for DOS games.  That may look like an odd platform for running a scientific/engineering application with WEAP87, but it actually works well.  Games have been a driving force in pushing local computer power forward.  Behind the graphics and interaction are some very complex mathematics, and running those in “real-time” has been a challenge of gaming computers from the very start.

DOS gaming for its part is the classic example of taking lemons and making lemonade.  Most DOS applications were text-based running on poor graphic standards such as CGA and EGA; it wasn’t until 800 x 600 VGA (or the venerable B&W Hercules standard) when graphics really began to look realistic.  The operating system itself came with few integral interfaces other than the screen and keyboard; no common graphical interface like the Mac, no mouse or joystick drivers in the early versions, and the math coprocessor was optional until the “486” processors.  It forced DOS gamers to write the visual output directly to the screen.  They took up the challenge with zeal and DOS games squeezed every bit of output from the computer it was capable of.

With the advent of Windows 3.0/3.1/3.11 and certainly of 95, many of the routines that had to be written for the software specifically became part of the operating system.  Unfortunately that, combined with the system overhead of the OS, slowed down games, which meant that Windows games lagged for a while until the hardware caught up with them.  (The system overhead of Windows is still significant, something that anyone who has ventured outside of the Windows world will attest).  Thus DOS gaming was something of a “golden age” and DOSBox was designed to recapture that golden age on computers that were no longer capable of running them.

Running Non-Gaming Applications on DOSBox

That having been said, DOSBox’s developers have traditionally discouraged non-gaming applications from DOSBox.  For one thing, DOSBox lacks many of the facilities that non-gaming applications often need, such as printing (not an issue with either one of these programs, as they put out text files) and many of the DOS features (which are missing because of patent and copyright issues in many cases).  There’s also the issue of emulation; no two computers do digital calculations the same, and that especially applies to an “operating system” which was primarily designed for gaming.

The reason programs like WEAP87 and SPILE can be considered for DOSBox is because they’re batch mode programs.  You put data in, you process the data, you get a result out, that’s it.  Programs which need long-term interaction with the data may not do so hot in DOSBox.  I would also avoid running the programs on non-x86 platforms because of math coprocessor issues.

What You’ll Need

To run WEAP87 and SPILE on DOSBox, you’ll need the following:

  1. WEAP87 and SPILE themselves, which can be found here.
  2. The printed manual for WEAP87.  Programs in the 1980’s came with printed manuals; online help wasn’t an option except for very basic commands.
  3. SPILE doesn’t have a printed manual available, but the second volume of the FHWA Soils and Foundations Manual has a good description of the underlying theory behind SPILE and its Windows successor, Driven.
  4. MCF, a TSR to aid in file management and program running.  Especially useful with WEAP87 as you run one program to input/preprocess the data and another to actually run the analysis.  Unlike many TSR programs designed for this purpose, MCF is very light on system resources.
  5. DOSBox, for whatever operating system you’re using.

Basic Setup

Setting up DOSBox (the first step) is pretty simple.  Open-source packages are notoriously deficient in understandable documentation, but DOSBox has been around for a long time, and seems better than average.  I would strongly urge you to check out their wiki for the information you need on installation and running.

One thing you definitely need to do is to set up a “C” drive.  DOSBox starts out with a “Z” drive with its basic programs to run.  The process is described here.  One big advantage of this over, say, a virtual machine is that you’re using the same file system for the emulator as you are for the host computer.  This means that you can open the data results in either a text editor or do a screen grab of the graphics.

Once you’ve done that, the easiest way to get the programs going is to do the following:

  1. Unpack MCF and put it in the root directory of the C drive (c:\).
  2. Create a directory c:\WEAP87 and put the WEAP 87 files in it.
  3. Create a director c:\SPILE and put the SPILE files in it.  It’s better to use two separate directories to avoid file name conflicts.

And that’s it.

Running SPILE and WEAP87

If you’ve run these programs on, say, Windows XP, running them on DOSBox–either directly from the command line or from MCF–is a familiar experence.  If you used either or both in the DOS era, it’s a trip down memory lane–down to the pace the computer runs the programs.  That’s because DOSBox deliberately slows down the pace of execution to simulate a DOS-era computer, and thus (for games where it’s critical) the timing of the game isn’t thrown off by faster execution speeds.  For either of these programs, it isn’t a big deal, and in any case DOSBox will “pick up the pace” for really processor intensive programs.  But after watching the output of WEAP87 in particular whiz by, seeing it going more slowly brings back memories.


SPILE is pretty straightforward, since there’s only one executable file.  The one thing you need to watch for is not to print out the output; just save it to a file.  If using the output for WEAP87, many engineers prefer to estimate the pile capacity using a spreadsheet and other methods.


WEAP87 is a little more complicated because the preprocessing file and the file that actually executes the wave equation analysis are different.  But other than that there is little difference between using it in DOSBox and elsewhere.  The governing data files can be edited either with MCF or with another text editor, and the text output can be done likewise.  One thing that comes back in DOSBox is shown above: the graphical bearing graph, in all of its CGA glory.  I’m not sure you want to put it into a report, but it’s good to have in any case.

Other DOS Programs

I’ve also tried other DOS engineering programs in DOSBox with success, including finite element analysis.  The ability to preserve the graphics using a screen grab program is a big plus (see below.)  These programs, however, like WEAP87 put their output in a text file, which can then be edited by either a text editor or a word processor.  Again a big advantage of DOSBox is that the file system for the program is accessible by the host operating system, which means that you can keep files generated by DOS programs and other data (such as soil boring data, for example, with SPILE and WEAP87) together.

A screen shot from DesignCAD 4 for DOS, showing the hydraulic schematic for the Vulcan 2800 vibratory hammer. Given the limitations of DOS and the computers they ran on, the results that DesignCAD produced were amazing. Additionally DesignCAD did fine with just a keyboard, a mouse and a standard graphics card, obviating the need for additional hardware such as digitising pads.

Another interesting program in DosBOX is CFRAME, the Corps of Engineers’ structural finite element analysis program.  It was used in preparing the book Sheet Pile Design by Pile Buck.  Here are some screen shots showing its graphical output:

This slideshow requires JavaScript.

Windows 3.1


Since Windows 3.1 was basically run on top of DOS, and 16-bit software (including software written for 3.1) is becoming out of bounds for newer Windows machines, the obvious question is, “Can DOSBox run Windows 3.1”?  Having a legal copy of Windows 3.11 for Workgroups, I gave it a shot, with tremendous help from this post in DOSBox’s forum

Although I haven’t spent much time with it, the short answer is “to some extent”.  DOSBox allocates enough extended and expanded memory to run it.  There are some obstacles, however, not the least of which is that DOSBox doesn’t contain a full copy of DOS, but simulates DOS 5.0.  It thus lacks the key file for full Windows functionality: SHARE.EXE.  If you can get this file and get it running, that will probably change.  But I’ve gotten further with this approach than, say, setting up a virtual machine.  (Any virtual machine I’ve seen for DOS or Windows 3.1 is challenged in accessing files outside of the virtual machine).

Since I’ve spent time on SPILE, I’ll mention that the version of Driven (the Windows successor to SPILE) I offer for download is a 32-bit version and thus won’t run on Windows 3.1 without the 32-bit upgrade (which, in turn, requires SHARE.EXE).  A 16-bit version was developed but at this point I don’t have it available.

The Wrap

DOSBox is a tremendous help in using DOS (and to a lesser extent Windows 3.1) programs on current machines and operating systems.  I would strongly urge anyone who wants to try this to “test drive” some of these programs to make sure the results are good.

As West Point professor J. Ledlie Klosky noted about geotechnical knowledge in general, “In this modern information age, it is hard to believe that important knowledge could simply vanish through disuse, but the sad fact is that it happens.”  That applies to software too; DOSBox is yet another weapon in our arsenal to prevent the loss of knowledge and once again fight “the creep of ignorance.”

Vulcan Hammers and the Gates Formula

For many years, Vulcan included Engineering News Formula charts and data in its literature.  Vulcan dropped the EN formula out of its literature in the 1970’s, for two reasons: the wave equation was in the ascendancy, and endorsement of the EN formula was an implied endorsement of the “bearing power” of the piles they drove, an endorsement which Vulcan was justifiably reluctant to make.

Nevertheless, the use of dynamic formulae persists for smaller projects and is embedded in many specifications.  For this purpose, the FHWA favours the Modified Gates Formula, and this is discussed in the latest edition of their Design and Construction of Driven Pile Foundations.  The section on the Modified Gates Formula is reproduced below:

FHWA Gates Formula Section

Gates Formula tables can be found for many Vulcan hammers can be found at the Vulcan Foundation website.

Copies of the FHWA Design and Construction of Driven Pile Foundations can be obtained by clicking on the cover images to the right.

TAMWAVE: Cavity Expansion Theory and Soil Set-Up

One of the things that was attempted in the TAMWAVE project is the use of cavity expansion theory to estimate soil set-up in cohesive soils. Doing this, however, brought some complications that need some explanation. Cavity expansion theory is basically the study of what happens when one body expands inside of another. When this takes […]

via TAMWAVE: Cavity Expansion Theory and Soil Set-Up —

Relating Hyperbolic and Elasto-Plastic Soil Stress-Strain Models

It is routine in soil mechanics to attempt to use continuum mechanics/theory of elasticity methods to analyse the stresses and strains/deflections in soil. We always do this with the caveat that soils are really not linear in their response to stress, be that stress axial, shear or a combination of the two. In the course […]

via Relating Hyperbolic and Elasto-Plastic Soil Stress-Strain Models —

TAMWAVE: Pile Toe Resistance, and Some More on Pile Shaft Resistance —

With this post we begin to discuss our “other” project: the TAMWAVE project. It’s been around a long time but is now being revised. The concept is to afford students a method of getting acquainted with several aspects of computer-aided driven pile design, including the following: Estimating axial capacity of the pile; Estimating the axial […]

via TAMWAVE: Pile Toe Resistance, and Some More on Pile Shaft Resistance —

Drivability of Vulcan Hammers and Other Pile Driving Equipment

This section of is about the drivability and performance of pile driving equipment in general and Vulcan hammers in particular. It’s divided into several sections:

These topics are treated in detail in the 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 In turn this page was spun off of that one in 2007. Today its contents have been incorporated into this section of 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:

Papers and Documents on Pile Driving and Driven Piles

The papers and monographs below are of general interest. We also offer the following topical pages as well:

Detailed information on pile dynamics and the wave equation is here.

Analysis of the Pile Load Test Program at the Lock and Dam 26 Replacement Project

Jean-Louis Briaud
Larry M. Tucker
Texas A&M University

U.S. Army Corps of Engineers
Miscellaneous Paper GL-88-11
June 1988

Prior to performing twenty-eight axial and two lateral load tests on piles at the Mississippi River Lock and Dam 26 project in Alton, IL, an in situ test program was conducted. The program consisted of four cone penetration tests , twelve pressuremeter test borings, and four standard penetration test borings. Comparisons of pile capacity predictions were made for each of the in situ test methods. The initial study generated four reports and voluminous test data.

Assessment of Axially-Loaded Pile Dynamic Design Methods and Review of INDOT Axially-Loaded Pile Design Procedure

Dimitrios Loukidis, Rodrigo Salgado, and Grace Abou-Jaoude

October 2008

The general aim of the present research is to identify areas of improvement and propose changes in the current methodologies followed by INDOT for design of axially loaded piles, with special focus on the dynamic analysis of pile driving. Interviews with INDOT geotechnical engineers and private geotechnical consultants frequently involved in INDOT’s deep foundation projects provided information on the methods and software currently employed. It was found that geotechnical engineers rely on static unit soil resistance equations that were developed over twenty years ago and that have a relatively large degree of empiricism. Updated and improved static design equations recently proposed in the literature have not yet been implemented in practice. Pile design relies predominantly on SPT data; cone penetration testing is performed only occasionally. Dynamic analysis of pile driving in standard practice is performed using Smith-type soil reaction models. A comprehensive review of existing soil reaction models for 1-dimensional dynamic pile analysis is presented. This review allowed an assessment of the validity of existing models and identification of their limitations. New shaft and base reaction models are developed that overcome shortcomings of existing models and that are consistent with the physics and mechanics of pile driving. The proposed shaft reaction model consists of a soil disk representing the near field soil surrounding the pile shaft, a plastic slider-viscous dashpot system representing the thin shear band forming at the soil-pile interface located at the inner boundary of the soil disk, and farfield- consistent boundaries placed at the outer boundary of the soil disk. The soil in the disk is assumed to follow a hyperbolic stress-strain law. The base reaction model consists of a nonlinear spring and a radiation dashpot connected in parallel. The nonlinear spring is formulated in a way that reproduces realistically the base load-settlement response under static conditions. The initial spring stiffness and the radiation dashpot take into account the effect of the high base embedment. Both shaft and base reaction models capture effectively soil nonlinearity, hysteretic damping, viscous damping, and radiation damping. The input parameters of the models consist of standard geotechnical parameters, thus reducing the level of empiricism in calculations to a minimum. Data collected during the driving of full-scale piles in the field and model piles in the laboratory are used for validating the proposed models.

Assessment of the Feasibility of the Application of Threaded Connections in Offshore Platform Caissons

M. Q. Smith
T. S. Rennick
C. J. Waldhart
C. D. Redding
Southwest Research Institute

Minerals Management Service
SwRI Project No. 06-8955
September 1998

This document summarizes the findings for phase one of a two-phase study assessing the feasibility of applying threaded connections in offshore platform caissons. Please note that the report is not structured in accordance with the work task breakdown defined in the program scope of work. Rather, existing caisson and threaded connection design practices are addressed independently of each other in two separate sections, while a third section integrates these into a discussion of their application to threaded connection designs for caisson structures. Following this discussion, recommendations are made for development of a general guideline, and an accompanying scope of work is outlined for the second phase of the feasibility study.

Behavior of Fiber-Reinforced Polymer (FRP) Composite Piles Under Vertical Loads

August 2006

Composite piles have been used primarily for fender piles, waterfront barriers, and bearing piles for light structures. In 1998, the Empire State Development Corporation (ESDC) undertook a waterfront rehabilitation project known as Hudson River Park. The project is expected to involve replacing up to 100,000 bearing piles for lightweight structures. The corrosion of steel, deterioration of concrete, and vulnerability of timber piles has led ESDC to consider composite materials, such as fiber-reinforced polymers (FRP), as a replacement for piling made of timber, concrete, or steel. Concurrently, the Federal Highway Administration (FHWA) initiated a research project on the use of FRP composite piles as vertical load-bearing piles.

A full-scale experiment, including dynamic and static load tests (SLT) on FRP piles was conducted at a site provided by the Port Authority of New York and New Jersey (PANY&NJ) at its Port of Elizabeth facility in New Jersey, with the cooperation and support of its engineering department and the New York State Department of Transportation (NYSDOT). The engineering use of FRP-bearing piles required field performance assessment and development and evaluation of reliable testing procedures and design methods to assess short-term composite material properties, load-settlement response and axial-bearing capacity, drivability and constructability of composite piling, soil-pile interaction and load transfer along the installed piling, and creep behavior of FRP composite piles under vertical loads. This project includes:

  • Development and experimental evaluation of an engineering analysis approach to establish the equivalent mechanical properties of the composite material. The properties include elastic modulus for the initial loading quasilinear phase, axial compression strength, inertia moment, and critical buckling load. The composite material used in this study consisted of recycled plastic reinforced by fiberglass rebar (SEAPILETM composite marine piles), recycled plastic reinforced by steel bars, and recycled plastic reinforced with randomly distributed fiberglass (Trimax), manufactured respectively by Seaward International Inc., Plastic Piling, Inc., and U.S. Plastic Lumber.
  • Static load tests on instrumented FRP piles. The instrumentation schemes were specifically designed for strain measurements. The experimental results were compared with current design codes as well as with the methods commonly used for evaluating the ultimate capacity, end bearing capacity, and shaft frictional resistance along the piles. As a result, preliminary recommendations for the design of FRP piles are proposed.
  • Analysis of Pile Driving Analyzer® (PDA) and Pile Integrity Tester (PIT) test results using the Case Pile Wave Analysis Program (CAPWAP)(1) and the GRL Wave Equation Analysis of Piles program GRLWEAP(2) to establish the dynamic properties of the FRP piles. The PDA also was used to evaluate the feasibility of installing FRP piles using standard pile driving equipment. Pile bearing capacities were assessed using the CAPWAP program with the dynamic data measured by the PDA, and the calculated pile capacities were compared to the results of static load tests performed on the four FRP piles.

The dynamic and static loading test on instrumented FRP piles conducted in this project demonstrated that these piles can be used as an alternative engineering solution for deep foundations. The engineering analysis of the laboratory and field test results provided initial data basis for evaluating testing methods to establish the dynamic properties of FRP piles and evaluating their integrity and drivability. Design criteria for allowable compression and tension stresses in the FRP piles were developed considering the equation of the axial force equilibrium for the composite material and assuming no delamination between its basic components. However, the widespread engineering use of FRP piles will require further site testing and full-scale experiment to establish a relevant performance database for the development and evaluation of reliable testing procedure and design methods.

Check List for Design of Pile Foundations

Ralph B. Peck

The design of a pile foundation cannot be carried out by cookbook procedures. Nevertheless, the design can proceed in a rational matter such that no important points are overlooked. This checklist is undoubtedly oversimplified, but it may prove useful.

Deep Foundations–Specifications

Gay D. Jones, Jr., Howard, Needles, Tammer and Bergendoff

An overview of specifications for deep foundations, from various sources.

Design and Performance Verification of UHPC Piles for Deep Foundations (Final report of project entitled Use of Ultra-High Performance Concrete in Geotechnical and Substructure Applications)

T. Vande Voort, M. Suleiman, S. Sritharan
Iowa State University
IHRB Project TR-558
November 2008

The strategic plan for bridge engineering issued by AASHTO in 2005 identified extending the service life and optimizing structural systems of bridges in the United States as two grand challenges in bridge engineering, with the objective of producing safer bridges that have a minimum service life of 75 years and reduced maintenance cost. Material deterioration was identified as one of the primary challenges to achieving the objective of extended life. In substructural applications (e.g., deep foundations), construction materials such as timber, steel, and concrete are subjected to deterioration due to environmental impacts. Using innovative and new materials for foundation applications makes the AASHTO objective of 75 years service life achievable. Ultra High Performance Concrete (UHPC) with compressive strength of 180 MPa (26,000 psi) and excellent durability has been used in superstructure applications but not in geotechnical and foundation applications. This study explores the use of precast, prestressed UHPC piles in future foundations of bridges and other structures. An H-shaped UHPC section, which is 10-in. (250-mm) deep with weight similar to that of an HP10×57 steel pile, was designed to improve constructability and reduce cost. In this project, instrumented UHPC piles were cast and laboratory and field tests were conducted. Laboratory tests were used to verify the moment-curvature response of UHPC pile section. In the field, two UHPC piles have been successfully driven in glacial till clay soil and load tested under vertical and lateral loads. This report provides a complete set of results for the field investigation conducted on UHPC H-shaped piles. Test results, durability, drivability, and other material advantages over normal concrete and steel indicate that UHPC piles are a viable alternative to achieve the goals of AASHTO strategic plan.

Dynamic Behavior of Pile Groups

Arnir M. Kaynia and Eduardo Kausel, Massachusetts Institute of Technology

The objective of this paper is to present solutions to determine the dynamic behavior of pile groups using finite element methods.

Driven Pile Manual Volume 1a
Driven Pile Manual 1b
Driven Pile Manual 2

Design and Construction of Driven Pile Foundations

Federal Highway Administration
FHWA-NHI-16-009, FHWA-NHI-16-010 and FHWA-NHI-16-064 (NHI Courses 132021 and 132022)
September 2016

The purpose of this manual is to provide updated, state-of-the-practice information for the design and construction of driven pile foundations in accordance with the Load and Resistance Factor Design (LRFD) platform. Engineers and contractors have been designing and installing pile foundations for many years. During the past three decades, the industry has experienced several major improvements including newer and more accurate methods of predicting and measuring geotechnical resistance, vast improvements in design software, highly specialized and sophisticated equipment for pile driving, and improved methods of construction control. Previous editions of the FHWA Design and Construction of Driven Pile Foundations manual were published 1985, 1996, and 2006 and chronicle the many changes in design and construction practice over the past 30 years. This two volume edition, GEC-12, serves as the FHWA reference document for highway projects involving driven pile foundations.

Volume I, FHWA-NHI-16-009, covers the foundation selection process, site characterization, geotechnical design parameters and reporting, selection of pile type, geotechnical aspects of limit state design, and structural aspects of limits state design. Volume II, FHWA-NHI-16-010, addresses static load tests, dynamic testing and signal matching, rapid load testing, wave equation analysis, dynamic formulas, contract documents, pile driving equipment, pile accessories, driving criteria, and construction monitoring. Comprehensive design examples are presented in publication FHWA-NHI-16-064.

Throughout this manual, numerous references will be made to the names of software or technology that are proprietary to a specific manufacturer or vendor. Please note that the FHWA does not endorse or approve commercially available products, and is very sensitive to the perceptions of endorsement or preferred approval of commercially available products used in transportation applications. Our goal with this development is to provide recommended technical guidance for the safe design and construction of driven pile foundations that reflects the current state of practice and provides information on advances and innovations in the industry. To accomplish this, it is necessary to illustrate methods and procedures for design and construction of driven pile foundations. Where proprietary products are described in text or figures, it is only for this purpose.

The primary audience for this document is: agency and consulting engineers specialized in geotechnical and structural design of highway structures; engineering geologists and consulting engineers providing technical reviews, or who are engaged in the design, procurement, and construction of driven pile foundations This document is also intended for management, specification and contracting specialists, as well as for construction engineers interested in design and contracting aspects of driven pile systems.

We also have the two previous versions of this document:

Design and Construction of Driven Pile Foundations — Lessons Learned on the Central Artery/Tunnel Project

June 2006

Five contracts from the Central Artery/Tunnel (CA/T) project in Boston, MA, were reviewed to document issues related to design and construction of driven pile foundations. Given the soft and compressible marine clays in the Boston area, driven pile foundations were selected to support specific structures, including retaining walls, abutments, roadway slabs, transition structures, and ramps. This report presents the results of a study to assess the lessons learned from pile driving on the CA/T. This study focused on an evaluation of static and dynamic load test data and a case study of significant movement of an adjacent building during pile driving. The load test results showed that the piles have more capacity than what they were designed for. At the site of significant movement of an adjacent building, installation of wick drains and preaugering to mitigate additional movement proved to be ineffective. Detailed settlement, inclinometer, and piezometer data are presented.

Design Criteria for Driven Piles in Permafrost

Dennis Nottingham
Alan B. Christopherson
Peratrovich, Nottingham & Drage, Inc.
January 1983

Past placement of structural foundation support piles in frozen soils generally has been performed using drilled and slurry backfill techniques. The early success of specially modified H-pile structural shapes driven into permafrost, and the promise of more economical and faster methods of pipe pile placement, has fostered development of refined pile driving techniques on the North Slope of Alaska. The proposed criteria presented in this paper are primarily addressed to the practicing design engineer, including design and construction considerations for driven piles in permafrost. A s more research and experience accumulate, factors in this report may change. The reader is cautioned to use the findings in this paper with discretion, and only after thorough confirmation of actual site conditions.

Design of Deep Foundations

D. Michael Holloway
Deep Foundations Institute, Annual Meeting, 8-9 October 1980, La Jolla, CA

An outline overview of the essential elements of the successful design of deep foundations. The meeting venue where this was presented had its liquor license suspended during the conference, so this is probably the most sober document available on the subject.

Design of Pile Foundations

EM 1110-2-2906
15 January 1991

This manual provides information, foundation exploration and testing procedures, load test methods, analysis techniques, allowable criteria, design procedures, and construction consideration for the selection, design, and installation of pile foundations. The guidance is based on the present state of the technology for pile-soil-structure-foundation interaction behavior. This manual provides design guidance intended specifically for the geotechnical and structural engineer but also provides essential information for others interested in pile foundations such as the construction engineer in understanding construction techniques related to pile behavior during installation. Since the understanding of the physical causes of pile foundation behavior is actively expanding by better definition through ongoing research, prototype, model pile, and pile group testing and development of more refined analytical models, this manual is intended to provide examples and procedures of what has been proven successful. This is not the last nor final word on the state of the art for this technology. We expect, as further practical design and installation procedures are developed from the expansion of this technology, that these updates will be issued as changes to this manual.

Effect of Pile-Driving Induced Vibrations on Nearby Structures and Other Assets

Adda Athanasopoulos-Zekkos, Richard D. Woods and Athena Grizi
University of Michigan
RC-1600, ORBP Number OR10-046
November 2013

The work described here represents an attempt to understand the mechanisms of energy transfer from steel H-piles driven with diesel hammers to the surrounding soil and the energy attenuation through the soil by measuring ground motion vibrations in the near vicinity of the pile. Attenuation rates of vibration decay with radial distance from the driven pile were calculated. A spreadsheet tool was developed to estimate distances from the pile at which the threshold settlement vibrations may be exceeded.

Efficiency and Energy Transfer in Pile Driving Systems

A description of the basic principles of energy transfer and efficiency ratings as they apply to pile driving equipment and the piles they drive.

Experimental Evaluation and Design of Unfilled and Concrete- Filled FRP Composite Piles
Task 3 – FRP Composite Pile Flexural Testing

Dale Lawrence, Roberto Lopez-Anido, Thomas Sandford, Keenan Goslin and Xenia Rofes
University of Maine
AEWC Report Number 15-2-1199, ME 15-08
June 2014

The overall goal of this project is the experimental evaluation and design of unfilled and concrete-filled FRP composite piles for load-bearing in bridges. This report covers Task 3, FRP Composite Pile Flexural Testing. Hollow and concrete filled fiber reinforced polymer (FRP) piles were tested in four point bending to examine degradation in stiffness, ultimate strength, and loss of concrete‐FRP composite action due to pile driving and cyclic loading. Testing showed a high level of variability in the ultimate strength of the piles, but all driven and load-cycled samples broke within the upper and lower bounds of the control piles. This series of tests showed no degradation in stiffness during static tests in the piles due to driving or cyclic loading. However, driving and cyclic loading appear to affect composite action between the FRP shell and concrete.

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))

Víctor Hugo Restrepo Botero
Pontifica Universidad Javeriana, Bogotá

We feature this paper because it references extensively our own Closed Form Solution of the Wave Equation for Piles, and because it takes the solution a step further with the use of Fast Fourier Transforms. In Spanish. We have this in two versions:

Investigation of the Resistance of Pile Caps to Lateral Loading

Robert L. Mokwa
Virginia Polytechnic Institute
September 1999

Bridges and buildings are often supported on deep foundations. These foundations consist of groups of piles coupled together by concrete pile caps. These pile caps, which are often massive and deeply buried, would be expected to provide significant resistance to lateral loads. However, practical procedures for computing the resistance of pile caps to lateral loads have not been developed, and, for this reason, cap resistance is usually ignored. Neglecting cap resistance results in estimates of pile group deflections and bending moments under load that may exceed the actual deflections and bending moments by 100 % or more.

Advances could be realized in the design of economical pile-supported foundations, and their behavior more accurately predicted, if the cap resistance can be accurately assessed. This research provides a means of assessing and quantifying many important aspects of pile group and pile cap behavior under lateral loads.

The program of work performed in this study includes developing a full-scale field test facility, conducting approximately 30 lateral load tests on pile groups and pile caps, performing laboratory geotechnical tests on natural soils obtained from the site and on imported backfill iii materials, and performing analytical studies. A detailed literature review was also conducted to assess the current state of practice in the area of laterally loaded pile groups.

A method called the “group-equivalent pile” approach (abbreviated GEP) was developed for creating analytical models of pile groups and pile caps that are compatible with established approaches for analyzing single laterally loaded piles. A method for calculating pile cap resistance-deflection curves (p-y curves) was developed during this study, and has been programmed in the spreadsheet called PYCAP. A practical, rational, and systematic procedure was developed for assessing and quantifying the lateral resistance that pile caps provide to pile groups.

Comparisons between measured and calculated load-deflection responses indicate that the analytical approach developed in this study is conservative, reasonably accurate, and suitable for use in design. The results of this research are expected to improve the current state of knowledge and practice regarding pile group and pile cap behavior.

Lateral Motion of Piles During Driving

T.J. Poskitt, Queen Mary College, University of London

Using an energy method, the lateral response of an initially curved raked pile to an axial blow from a piling hammer is derived. By treating the blow as an impulsive force, a considerable simplification results which enables a closed form solution to be obtained. The solution is in general terms and enables all boundary conditions of practical interest to be studied. The cases of cantilever and a propped cantilever pile are presented as being of most practical interest. Propping corresponds to supporting the hammer in leaders and results in lower bending stresses. The most critical case is the raked cantilever pile. This can experience signifcant bending stresses.

Loading Rate Effects on Pile Load-Displacment Behaviour Derived from Back-Analysis of Two Load Testing Procedures

We feature this thesis for several principal reasons.

First, it is unusual in that it deals with both soil dynamics and wave propagation in piles in the same place. These two subjects are obviously related but are not tied together as often as one would like.

Second, it is an extensive treatment on the subject of loading rate in pile load testing. The significance of loading rate in testing is important both for the proper interpretation of the results and in relating the determined load to actual loads on piles, all of which have some kind of load rate.

Third, the background section of the thesis deals with many of the same soil models that were used in our own thesis. The soil modelling described in that work was heavily influenced by the work of Alain Holeyman, who supervised Charue’s thesis. The thesis also cites our own paper on the development of the ZWAVE wave equation analysis program, which used soil models that were a departure from Smith.

Nicolas Charue
Catholic University of Louvain, Belgium

Soils, like several other materials, exhibit strong time-dependent behaviour which can be evidenced in terms of creep or strain-rate effects. The degree of this rheological behaviour varies with the type of soil, its structure, and with the stress history. This effect is exacerbated in pile load testing where the procedure duration tends to be shortened under increasing time pressures. The modelling needed to interpret the results therefore becomes more and more complex, including soil viscosity, wave radiation into the soil and other significant phenomena.

Within this framework, it would be interesting to study the influence of the loading rate on the load-displacement behaviour of the pile through the results of two testing procedures loading piles with variable duration (Static Loading Test (SLT) used as reference and Dynamic Load Test (DLT)). Based on these data issued from two national research programs organised by the Belgian Building Research Institute (BBRI), the objective of the research reported herein is to refine the rheological parameters characterizing the influence of the loading rate within the framework of a relevant pile/soil interaction model fed with dynamic measurements acquired during pile Dynamic Load Tests. The final goal is to predict and simulate the quasi-static pile load settlement curve.

After an overview of the loading rate effects in the literature through the experimental and modelling aspects, the dynamic data measured on field are analysed. It has been observed that some relationships exist between maximum quantities such as: energy transmitted to the pile, pile head velocity and force and the settlements (maximum and permanent) measured after a sequence of blows during a DLT event. These relationships are similar for the sandy and clayey sites and repeatable in time. It has been found that there are some critical quantities (correlated with the hammer drop height) from which a significant settlement of the pile is possible while the pile does not settle if these quantities are not exceeded.

The pile/soil interaction system is described by a non-linear mass/spring/dashpot system supposed to represent the pile and the soil, with constitutive relationships existing within and between them. These relationships account for the static and the dynamic or rheologic behaviour. A back-analysis process based on a matching procedure between measured and computed curves (force and velocity) allows one to describe the pile/soil interaction in terms of constitutive and rheologic parameters based on the dynamic measurements. After optimisation of the matching procedure, the parameters obtained are used to simulate the “static” load-settlement curve. The matching procedure is based on an automatic multi dimensional parameter perturbation analysis. Since the parameters influence the system response with a relative weight, they are sorted in order to optimise all the parameters by successively retrieving the most influential ones and working on the remaining ones.

A Laboratory and Field Study of Composite Piles for Bridge Substructures

Miguel A. Pando, Carl D. Ealy, George M. Filz, J.J. Lesko, and E.J. Hoppe

March 2006

The most commonly used pile materials are steel, concrete, and wood. These materials can degrade, and the degradation rate can be relatively rapid in harsh marine environments. It has been estimated that the U.S. spends over $1 billion annually for repair and replacement of waterfront piling systems. This high cost has spurred interest in alternative composite pile materials such as fiber-reinforced polymers (FRPs), recycled plastics, and hybrid materials. Because only minimal performance data have been collected for composite piles, a research project was undertaken to investigate (1) soil-pile interface behavior of composite piles, (2) the long-term durability of concrete-filled FRP shell composite piles, and (3) the driveability and axial and lateral load response of concrete-filled FRP composite piles and steel-reinforced recycled plastic piles by means of field tests and analyses. In addition, a long-term monitoring program was implemented at a bridge over the Hampton River in Virginia.

According to laboratory rest results, values of residual interface friction angle between three pile surfaces and a subrounded to rounded sand were 27, 25, and 28 degrees for a FRP composite pile, the recycled plastic pile, and the prestressed concrete pile respectively, while the values of residual interface friction angle between these piles and a subangular to angular sand were 29, 29, and 28 degrees for the FRP composite pile, the recycled plastic pile, and the prestressed concrete pile, respectively. Regarding durability of FRP composite piles, it was found that moisture absorption caused degradation of strength and stiffness of the FRP shells, but that freeze-thaw cycles had little effect. Analyses indicate that FRP degradation due to moisture absorption should have minimal impact on axial capacity of the FRP composite piles because most of the axial capacity is provided by the concrete infill; however, FRP degradation has a larger effect on lateral capacity because the FRP shell provides the capacity on the tension side of the pile. The field tests demonstrated that there were not major differences in driveability of the FRP composite pile, the recycled pile, and the prestressed concrete pile. In static load tests, the FRP composite pile and prestressed concrete pile exhibited similar axial and lateral stiffness, and the plastic pile was significantly less stiff. Conventional static analyses of axial load capacity, axial load versus settlement, and lateral load versus deflection provided reasonable predictions for the composite piles, at least to the levels of accuracy that can be achieved for more common pile materials. The long-term monitoring program has been implemented for an FRP composite pile and a prestressed concrete pile so that their load-transfer performance can be compared over time. The long-term monitoring is being done by Virginia DOT.

Mechanics of Diesel Pile Driving

Dave Rempe (1937-2010) was an eminent researcher and practicioner in the field of driven piles and the wave equation, having both worked in the field for Raymond, produced academic works such as this one, and consulted on numerous pile driving projects. You can see the tribute to his life here. In addition, he was a devoted family man and a great friend. His pastor noted that “Dave came to faith as an adult, and he studied diligently. His dog-eared Bible showed that he expended the same effort in his spiritual life that he did towards both work and family. I always appreciated his questions, as challenging as they might be.”

David Maher Rempe
University of Illinois

Research was conducted into the mechanics of pile driving with diesel hammers. The first step consisted of an investigation of the mechanical and operational details of diesel pile hammers. Then, a mathematical simulation of diesel hammer operation was developed for purposes of wave equation analysis, which is an analytical method for prediction of pile load capacity and driving stress on the basis of driving resistance (pile penetration per hammer-blow). Finally, the performance characteristics of diesel pile hammers and the factors affecting performance were studied. The details of diesel hammer design and operation are described. Differences in design and operation among the various types of diesel hammer are discussed as they relate to pile-driving effectiveness. Design features related to inclined operation and soft-ground operation are discussed. The mathematical model of the diesel hammer is described in detail, with emphasis on the simulation of diesel combustion, steel-on-steel impact, and interaction of hammer operation with the dynamic response of pile and soil. In wave equation analysis of diesel pile driving, the mathematical hammer model is combined with models of the pile and soil to produce a total simulation of the hammer-pile-soil system.

Mechanics of Impact Pile Driving

Jerry F. Parola
University of Illinois

Impact pile driving was studied by utilizing longitudinal wave propagation theory as ananalytical tool . Field data from pile driving jobs was used to establish the validity and usefulness of the analytical techniques developed herein.

The theoretical treatment of the dynamics of impact pile driving included an analysis of both the force generated at the head of the pile and the response of the pile tip to a generated force pulse. A model consisting of a hammer system operating on the head of an infinitely long pile was used to determine both the pile force pulse and the transmitted energy. The model was used to make a dimensionless parameter study of the factors influencing force and energy. The driver system consisted of concentrated masses for both the ram and the drivehead and an energy absorbing spring (both linear and nonlinear) for the hammer cushion.

Soil and pile responses were investigated with respect to an arbitrary force pulse in order to assess the variables controlling pile penetration and load capacity. Special emphasis is placed on soil and pile response a t the pile tip; the soil model includes viscous damping, mass and an elastic-plastic spring.

Characteristics of the hammer-pile-soil system as a whole are summarized. Theoretical results using wave propagation theory are compared with both case histories and commonly used dynamic formulas. Correlation of wave analyses and field case histories are used to support the conclusion that wave propagation theory is the proper theoretical tool for pile driving analysis.

Modeling Embankment Induced Lateral Loads on Deep Foundations

(Slide Show Technical Presentation)

Dr. Siva Kesavan, URS Corporation
Professor Rajah Anandarajah, Johns Hopkins University

The problem analyzed in this presentation is inspired by a real-world problem where the construction of a landfill at a rate too fast caused damage to an adjacent bridge. Without presenting actual names, the problem is described and analyzed using an elasto-plastic finite element computer code (HOPDYNE) to illustrate how an advanced numerical procedure can help develop an understanding of the failure mechanism, and reveal the true cause of the failure in a complex problem like this, where loading and consolidation take place simultaneously. The problem involves soil-structure interaction. The geometry is too complex, raising questions concerning the validity of one-dimensional assumptions used in Terzaghi’s one-dimensional consolidation theory. The clayey soil in the foundation is too soft and is certain to behave highly plastically, raising questions about the validity of using elastic theories to calculate the stresses in the foundation caused by the weight of the landfill. In other words, the problem is too complex, pointing to the need for a method like the finite element method for not only verifying the validity of the conventional methods normally used in analyses, but also to explain the true cause of failure.

Static and dynamic analysis of an offshore mono-pile windmill foundation

L. Kellezi and P. B. Hansen
GEO – Danish Geotechnical Institute, Lyngby, Denmark

Different foundation concepts have been presented and applied to offshore windmill turbines designed and constructed all over the world. The advantages and disadvantages of different concepts are already outlined and research from universities and private companies continues with this respect. The choice of the foundation concept for an offshore windmill turbine is governed by several factors, which include soil conditions, the water depth at the location, the scour and erosion, the capacity of the turbines, the foundation cost etc. It is investigated that for offshore windmill turbines the foundation costs are approximately 25% of the total cost [1].

There are basically three types of foundations applied to different windmill parks. These are: gravity based, skirted and piled foundations. Piled foundations are the most common foundations for offshore structures. Driving the piles into the seabed is the standard method of installation [2]. Considering the soil conditions and other factors the mono-pile foundation concept was chosen for the windmill park at Horns Rev, Denmark. Such concept is also applied at Utgrunden and Bockstigen in Sweden and other places.

Large diameter mono-piles are generally used for offshore windmill turbines placed at shallow water. A lot of progress has been made in the last decades towards the development of engineering methods for the static and dynamic analysis of the pile foundations. Different approaches can be adopted in solving the problem. The p-y approach or Winkler model, [3-5] has been widely used to design piles subjected to lateral static or dynamic loading. Based on this approach the lateral soil-structure interaction can be modeled using empirically derived nonlinear springs and dashpots.

More rigorous finite element methods (FEM), which allow application of soil constitutive modeling and soil-pile nonlinear interaction, have been developed lately. Some representative FEM applications regarding pile foundation design are given by [6-9] where a series of 3D FEM studies were conducted on the behavior of piles under static loads. For dynamic loads the problem can be considered as viscous-dynamic with material damping included, [10-11], or nonlinear-dynamic depending on the current situation.

A structure resting on pile foundations and subjected to dynamic vibrations with small amplitudes can be analyzed as a viscous-dynamic problem. However piles under earthquake excitations or pile driving analysis, which is associated with large amplitudes of vibrations and penetration, should be considered as a strongly nonlinear-dynamic problem, [12-13]. The mono-pile windmill foundation at Horns Rev is analyzed here for maximum static and dynamic loads. 3D nonlinear FEM design is carried out for static loads employing ABAQUS program. 3D axisymmetric viscous-dynamic analysis is carried out for dynamic loads as small vibration amplitudes are expected for a windmill turbine foundation structure. Self developed FEM programs are used in this case.

Static Testing of Deep Foundations
(pdf format)

Federal Highway Administration
February 1992

A majority of the bridges in the United States are supported on deep foundations. The economical design and construction of a pile foundation depends on the use of rational procedures to determine pile load capacity. Additional, unwarranted costs can result from either inadequate or overly conservative design and from construction claims related to pile driving difficulties.

A static load test is conducted to measure the response of a pile under applied load. Conventional static load test types include axial compressive, axial tensile and lateral load testing. The cost and engineering time associated with a load testing program should be justified by a thorough engineering analysis and foundation investigation. An adequate pile foundation design requires detailed subsurface exploration, appropriate soil testing, subsurface profile development, static pile analyses and selection of optimum pile type(s).

Static load tests provide the best means of determining pile capacity and, if properly designed, implemented and evaluated, should pay for themselves on most projects. Depending on availability of time and on cost considerations, the load testing program may be included either in the design or in the construction phase. Dynamic load tests, performed in conjunction with static load tests, greatly increase the cost-effectiveness of a pile load test program and should be specified whenever piles installed by impact driving are load-tested.

Many different procedures have been proposed for conducting pile load tests. The main differences are in the selection of loading systems, instrumentation requirements, magnitude and duration of load increments, and interpretation of results.

The objective of this manual is to present a comprehensive, easy-to-follow guide describing the steps required in planning, conducting and interpreting the results of static load tests on driven piles and drilled shafts. It is intended to serve as a reference for experienced engineers and as a learning aid for those not experienced in pile load testing. Types of testing covered include axial compressive, axial tensile and lateral load tests. A brief description of dynamic pile load testing is included in the Appendix.

Theoretical Manual for Pile Foundations

Reed L. Mosher and William P. Dawkins

U.S. Army Corps of Engineers Information Technology Laboratory

The purpose of this manual is to provide a detailed discussion of techniques used for the design/analysis of pile foundations. Several of the procedures have been implemented. Theoretical development of these engineering procedures and discussions of the limitations of each method are presented.

The purpose of a pile foundation is to transmit the loads of a superstructure to the underlying soil while preventing excessive structural deformations. The capacity of the pile foundation is dependent on the material and geometry of each individual pile, the pile spacing (pile group effect), the strength and type of the surrounding soil, the method of pile installation, and the direction of applied loading (axial tension or compression, lateral shear and moment, or combinations). Except in unusual conditions, the effects of axial and lateral loads may be treated independently.