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Some Things I Would Say if Giving the E.A.L. Smith Award Lecture for the Pile Driving Contractors Association

I found it intriguing that the Pile Driving Contractors Association has instituted the E.A.L. Smith Award with lecture following.  It looks like I’ve already made a contribution to the effort: the graphic they used for the LinkedIn announcement probably comes from my piece on E.A.L. Smith and his contribution.

I don’t anticipate actually doing this, but that’s the result of some choices I’ve made along the way.

To begin with, I allowed my technical membership in PDCA to lapse many years ago, although the organisation I work for certainly is a member.  As the musicians say, you can’t sing the blues if you don’t pay your dues, and that’s as true in deep foundations as it is in jazz music.

Beyond that, most people who have been in the driven pile industry for a while know that Vulcan Iron Works passed from the Warrington family in 1996, and that things really didn’t get better for some time thereafter.  My years in the equipment business convinced me that equipment people could not remain uninvolved in the whole business of pile dynamics, which led me to start this site twenty years ago.  Unfortunately that involvement was not accompanied by a sponsoring organisation or budget, so I had to use the emerging internet to do what I felt needed to be done: furnish information on pile dynamics and driven piles, and ultimately geotechnical and marine engineering in general, without paywall or restriction.  That effort has been successful; the award for it is in geotechnical engineers who can get their work done in a better way, students who can learn about this part of the profession, and those in countries which lack the resources to purchase materials.  If I’ve helped them, I’ve succeeded, and that’s award enough.

In any case part of that effort was my piece on E.A.L. Smith and his development of the wave equation program, and I think my piece has been just about the only one on the subject for a long time.  In looking back at the piece and the whole effort behind it, I’d like to make some observations that hopefully with shed some light on Smith’s effort.

The first is that Smith was Raymond’s Chief Mechanical Engineer.  Raymond was an organisation that defined vertical integration: they not only drove the piles, but made or modified the equipment that did the work.  Smith worked during an era when geotechnical engineering was coming into maturity as a science; Terzaghi and Peck’s Soil Mechanics in Engineering Practice was published in 1947.  Nevertheless it took a mechanical engineer to crack the forward problem in pile dynamics.  That’s because civil engineers in general and geotechnical engineers in particular don’t really like or understand things that move, but moving things (like pile driving equipment) are the centrepiece of a mechanical engineer’s work.  That simple fact invited the interdisciplinary approach to the problem that Smith took, but it also has made pile dynamics a “black box” to many of the civil engineers who work with the problem, and that in turn has guided the way the solution of the problem has been implemented.

The second is that the physics of Smith’s wave equation program is a classically mechanical engineer’s solution to a problem.  Spring-dashpot-mass systems are the core building blocks of any vibrating system; Smith basically took this, made the springs elasto-plastic, and strung them together into the system he developed.  It is a tribute to Smith’s ability to see the big picture of the system to relate the parameters of the system to the soil he was driving into, and not permit himself to get lost in the soil mechanics of his geotechnical peers.

The third is that Smith developed his numerical method at a time when numerical simulation of physical systems was itself in its infancy.  He had the feedback of the likes of W.E. Milne and the collaboration of crosstown IBM’s computers and expertise in the development.  It’s also worth noting that civil engineering, although it has pushed forward finite element modeling with people such as T.J.R. Hughes and D. Vaughn Griffiths, is still content with using “classical” methods for many of its designs, especially in the transportation field.  The singularity of Smith’s achievement needs to be seen in the context of both the situation at the time and afterwards.

The fourth is that Smith’s wave equation program was the result of an extended effort that lasted at least a decade and probably more.  That was facilitated by Raymond itself, a large organisation with considerable resources and the ability to test the model with its own work.  It was done at a time when U.S. corporations were more inclined to engage in long-term research projects and to share those results.  The government’s involvement only entered in the wake of Smith’s seminal ASCE paper, and that too was an extended effort.

So Smith’s effort is certainly worthy of celebration and commemoration, and to learn some lessons from it.  Smith’s basic model of the pile has endured to this day, finding application in both forward and inverse solutions of the wave equation for piles.  But is Smith’s model the last word on the subject?  Probably the best answer came from Smith himself.  In his ASCE paper he noted the following, in his discussion of soil mechanics:

When future investigators develop new facts, the mathematical method explained herein can be modified readily to take account of them…

It’s unreasonable to expect that Smith’s model cannot be improved on beyond tweaking the parameters.  And there are fundamental problems: Smith, wise to initially bypass much conventional soil mechanics, developed a model where the relationship between the parameters he used and the properties of the soil he was driving into is not clear.  Solving that problem might, for example, reduce the importance of the sensitivity issue of soil damping on the results of the wave equation.  Efforts have been made to solve the model-soil properties issues but they are neither as widely perfected or implemented as one would like.

That’s a special problem when he consider the inverse implementation of the wave equation for piling.  Use of Smith’s model brings with it uniqueness issues (and there are enough of those with problems involving plasticity like this one) that need to be addressed.

Numerical methods and computer power have both vastly improved since Smith’s day.  So is it possible to see another paradigm shift in the way we perform forward and inverse pile dynamics?  The answer is “yes,” but there are two main obstacles to seeing that dream become a reality.

The first is the nature of our research system.  As noted above, Smith’s achievement was done in a large organisation with considerable resources and the means to make them a reality.  It was also a long-term effort.  Today the piecemeal nature of our research grant system and the organisational disconnect among between universities, contractors and owners incentivises tweaking existing technology and techniques rather than taking bolder, riskier steps with the possible consequence of a dead-end result and a disappointed grant source.

The second is the nature of our standard, code and legal system.  Getting the wave equation accepted in the transportation building community, for example, was an extended process that took longer than developing the program in the first place.  Geotechnical engineering is a traditionally conservative branch of the profession.  Its conservatism is buttressed by our code and standard system (which is also slow-moving) and the punishment meted out by our legal system when things go wrong, even when the mistake was well-intentioned.  Getting a replacement will doubtless be a similar extended process.  And of course we should consider having been “written into the specs.”  Vulcan was certainly the beneficiary of that phenomenon, although the process was driven more by the ubiquity of the product than an effort by the company.    That last point is certainly not the case here; general acceptance would have never taken place had it been so.

However, we need to face the reality that, sooner or later, the ball will move down the field and newer techniques will be developed.  The question in front of us is whether it will be done on these shores, as was the case with Smith, or somewhere else.  As I like to say, it’s our move: we need to make it.

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STADYN Wave Equation Program 4: Eta Limiting, and More on Norm Matching

In our last post we broached the subject of different norm matching methods for the actual and computed velocity-time histories at the pile top. In this post we will go into \eta limiting, while at the same time running both norms to get a better feel for the differences in the results.

Before we begin, one clarification is in order: CAPWAP’s Match Quality and the use of the 1-norm in STADYN are similar in mathematical concept but different in execution. That’s because the Match Quality weights different part of the force-time history (in their case) differently, whereas STADYN goes for a simple minimum sum difference.

One characteristic of the inverse case both in the original study and in the modifications shown in the last post are very large absolute values of \eta . These are products of the search routine, but they are not very realistic in terms of characterising the soil around the pile. To illustrate, we bring back up one of the results from the last post, showing the optimisation track using the 2-norm and phi-based Poisson’s Ratio (which will now be the program standard):


Note that the #8 track (\eta for the lowest shaft layer) has a value approaching -30; this is obviously very unrealistic.

In principle, as with \xi , the absolute value of \eta should not exceed unity; however, unlike \xi there is no formal reason why this should be the case. But how much should we vary \eta ? To answer this question, and to continue our investigation of the norm issue, we will examine a matrix of cases as follows:

  1. \eta will be run for values of 1, 2, 3 and unlimited (the last has already been done.)
  2. Each of these will be run for both the 1-norm and 2-norm matching.

A summary of the results are shown below

Changed Parameter


Static Load, kN

Average Shaft \xi

Toe \xi

Toe \eta












|\eta | < 1











|\eta | < 2











|\eta | < 3











Unrestricted \eta











\nu = f(\xi,\eta)











To see how this actually looks, consider the runs where |\eta | < 3.  We will use the 2-norm results.

Velocity-Time Output
Impedance*Velocity Comparison, 2-norm, eta limiting = 3.
Optimization Track
Optimisation Track, 2-norm, eta limiting = 3

The results indicate the following:

  1. The average shaft values of \xi tend to be negative.  This is contrary to the cohesive nature of the soils.  The interface issue needs to be revisited.
  2. The toe values do not exhibit a consistent pattern.  This is probably due to the fact that they are compensating for changes in values along the shaft.
  3. As values of |\eta | are allowed to increase, with the 2-norm the result of the simulated static load test become fairly consistent.  This is not the case with the 1-norm.  Although limiting |\eta | to unity is too restrictive, it is possible to achieve consistent results without removing all limits on \eta .
  4. The velocity (actually impedance*velocity) history matching is similar to what we have seen before with the unlimited eta case.
  5. The optimisation track starts by exploring the limits of \eta , but then “pulls back” to values away from the limits.  This indicates that, while limiting values “within the box,” i.e., the absolute values of \eta < 1, is too restrictive, reasonable results can be obtained with some \eta limiting.

Based on these results, \eta limiting will be incorporated into the program.  The next topic to be considered are changes in the soil properties along the surface of the pile, as was discussed in the last post.

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Celebrating Twenty Years of

It’s official: twenty years ago today, this website had its beginning.  That’s a long time on the internet, and there have been many changes.

Ten years ago I commemorated that anniversary starting with this:

Ten years ago today, I went online, logged onto my new GeoCities site, and uploaded the first page and images of “The Wave Equation Page for Piling,” my first website.  That website—which is still a part of the companion site—was the beginning of a long odyssey which led to the site as it is today.

You can read about the site’s first decade in that post.  The purpose of the site is unchanged, so it’s time to bring you up to date on our progress.

The first big change took place a few months after that post when was split off from  The basic idea was to give the Vulcan Iron Works material its own site.  Later the driven pile material was moved there also, to feature it separately.  Perhaps that site’s history can be featured later.

The second was the growth of our printed materials at  This site has always been about free stuff and continues to offer everything that way.  But many want printed books for one reason or another, and so many of the publications offered on this and the companion sites are now available at  The most popular of these have been NAVFAC DM 7.01 and 7.02; putting these back into print and make them available to the geotechnical engineering community has been well received and popular.  For a while we also offered CD-ROM compilations of our documents, but these fell out of favour with increasing bandwith; by the time our publisher discontinued offering optical media, they had stopped selling.  Even with this, the revenue from these sales continues to underwrite the hosting and domain expenses of this site.

That brings us into the early years of this decade.  Although updates and additions to the material available on this site have been ongoing, in 2011 I began the pursuit of my PhD and, to be frank, the site’s progress stalled a bit during those years.  But my MS pursuit was part of the genesis of this site, and the spinoff from the latest effort can be seen, from the page on finite element analysis in geotechnical engineering to the ongoing series on the STADYN wave equation program.  But not all slowed down: I continued to teach at the University of Tennessee at Chattanooga, which meant that the course materials section of the site continued to grow with each semester.

And that leads us to the most recent major change in the site: in January of this year the site was moved to the WordPress platform. The reasons for this are discussed here (along with the change in the marine documents) in the inaugural post.  The result has been a site with interactivity, both on the site and with social media (the Facebook group is still active.)  It is also secure (as has been the case with Positive Infinity for a long time) and adaptive to mobile devices, both of which enhance the site’s search engine draw.  And finally there is evidence that the documents on the site download more quickly, which is the whole point of the site.

It’s easy to say that this site has pretty much accomplished what it set out to do: to provide geotechnical information in an affordable format to those which many not have the resources to purchase them, both in our universities (which keep getting more expensive) and in countries around the world.  It is true that now there are many sites that offer information such as this, including obviously the U.S. government sites where most of this information came from to start with (although its presence there comes and goes.)  But we still claim to offer it with the fewest strings attached, and that’s saying something.

So once again we thank you for your visiting this site and your support, and may God richly bless you.

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Tribute to Harry M. Coyle

It is with sadness that we report the death of Dr. Harry M. Coyle, professor of civil engineering at Texas A&M University from 1964 to 1987, back in January.  You can read the entire obituary here.

For those of us involved in deep foundations, his name is a familiar one, and his monographs have graced this site and its companion,, for many years.  Among other things he is known for the Coyle and Castello method for estimating pile capacity in sand, the Coyle and Gibson method for determining damping for pile dynamics analysis, and the co-developer of the PX4C3 routine for axial load-settlement estimation, which we feature on this site, and which is the ancestor of many of those in use today.  He was deeply involved in the development of the TTI wave equation program, and some of his work relating to that is here.

Our continued condolences and prayers go to his family, and, as the obituary states, “Having loved his friends and family well, Harry Coyle will be missed by all until we are reunited with him in Glory. “

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My Perspective on Driven Pile Drivability Studies

This post originally appeared in 2013 on my companion site.

Recently I had a round of correspondence with a county official in Washington state re pile drivability studies and their place in the contract process.  (If you’re looking for some explanation of this, you can find it here).  His question was as follows:

During the bidding process, is the contractor’s sole basis for anticipating the size of the hammer needed the WEAP analysis? Does a contractor rely solely on design pile capacities or does the contractor combine geotechnical boring logs and cross-sections with his expertise? Who will be ultimately responsible that a large enough hammer is considered in the bid and brought to the site, the contractor or the preparer of the design package?

My response was as follows:

First, at this time the WEAP analysis is the best way for contractor and owner alike to determine the size of a hammer (both to make sure it isn’t too small with premature refusal, or too large and excessive pile stresses) necessary to install a certain pile into a certain soil.

It is a common specification requirement for a contractor to furnish a wave equation analysis showing that a given hammer can drive a pile into a given soil profile.  As far as what soil profile is used, that’s a sticky issue in drivability studies.  Personally I always attempt to estimate the ultimate axial pile capacity in preparation of a wave equation analysis.  There are two important issues here.

The first is whether the piles are to be driven to a “tip elevation” specification vs. a blow count specification.  For the former, an independent pile capacity determination is an absolute must.  For the latter, one might be able to use the pile capacities if and only if he or she can successfully “back them out” from the allowable capacities, because the design factors/factors of safety will vary from one job and owner to the next.  Some job specs make that easy, most don’t.

Even if this can be accomplished, there is the second problem: the ultimate capacity of interest to the designer and the one of interest to the pile driver are two different things.  Consider this: the designer wants to know the pile with the lowest capacity/greatest settlement for a given load.  The pile driver wants to know the pile with the highest capacity.  If you use the design values, you may find yourself unable to drive many of the piles on a job or only with great difficulty.  I’m seeing a disturbing trend towards using the ultimate capacity for design and running into drivability problems.

As far as responsibility is concerned, that of course depends upon the structure of the contract documents.  I’ve discussed the contractor’s role; I would like to think that any driven pile design would include some consideration of the drivability of the piles.

Some of the FHWA publications I offer both in print and online (including the Driven Pile Manual) have sample specifications which you may find helpful.

Hope this long diatribe is of assistance.

After this, there’s another way of looking at this problem from an LRFD (load and resistance factor design) standpoint that might further illuminate the problem.  The standard LRFD equation looks like this:

\sum _{i=1}^{n}{\it \gamma}_{{i}}Q_{{i}} \leq \phi\,R_{{n}}

This is fine for design.   With drivability, however, the situation is different; what you want to do is to induce failure and move the pile relative to the soil with each blow.  So perhaps for drivability the equation should be written as follows:

\sum _{i=1}^{n}{\it \gamma}_{{i}}Q_{{i}} \geq \phi\,R_{{n}}

It’s worthy of note that, for AASHTO LRFD (Bridge Design Specifications, 5th Edition)  \phi can run from 0.9 to 1.15, which would in turn force the load applied by the pile hammer upward more than it would if typical design factors are used.  Given the complexity of the loading induced by a hammer during driving, the LRFD equation is generally not employed directly for drivability studies, and the fact that \phi hovers around unity makes the procedure in LRFD very similar to previous practice.

The problem I posed re the hardest pile to drive vs. the lowest capacity pile on the job is still valid, especially with non-transportation type of projects where many piles are driven to support a structure.  When establishing a “standard” pile for capacity, it is still the propensity of the designer to select the lowest expected pile capacity of all the pile/soil profile combinations as opposed to the highest expect pile resistance of all the pile/soil profile combinations necessary for drivability studies.

Put another way, the designer will tend to push the centre of the probability curve lower while the pile driver will tend to push the centre of the probability curve higher.  This is a design process issue not entirely addressed by LRFD, although LRFD can be used to help explain the process.