Category: Deep Foundations

Posted in Deep Foundations, Geotechnical Engineering

Comments on “Inverse analysis for parameter estimation of sandy soil with axially loaded pile using nonlinear programming”

Posted on by Don Warrington

This is yet another commentary on a paper which cites my work, in this case Inverse analysis for parameter estimation of sandy soil with axially loaded pile using nonlinear programming, which cites Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles. Since 2026 is the tenth anniversary of the publication of that effort, some remarks on why I did that are in order.

Rationale for My Original Study

The current predominant regime in pile dynamics has been around for over half a century now. With tweaks and improvements in computer power and hardware, it has enabled us (well, most of us) to jettison the problematic dynamic formulae for capacity prediction and verification during installation. The whole system, however, relies on the 1D representation of pile/soil interaction to be accurate and the optimization algorithm to find the solution to the inverse problem. Both of these are subject to the kinds of improvements we see in other fields.

Getting to this point was not an easy or straightforward task, both because of the application itself and the code/regulatory environment in which we operate. Much of the struggle to get the current methodology accepted was an uphill battle against the existing “we’ve always done it this way” mentality which settles in, and no doubt this will be the case with a new generation of pile dynamics methodology. But there are some difficult challenges inherent in the physics of this problem, most of which stem from the nature of soils themselves.

I ran into many of these challenges during my study which led to Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles. One colleague from an institution in a neighbouring state felt that my effort was “too ambitious.” He’s probably right, which is why he’s in administration now. But my objective was for this study–and the subsequent papers to fine tune the method–to be a convesation starter, and this paper’s citation of my work is evidence that this is taking place. I sense that efforts to “move the football down the field” in this discipline are taking place, and am gratified to be a part of that effort.

Comments on the Paper Itself

Strictly speaking this paper only has the inverse method as a commonality with my own study. In this case the researchers are dealing with a drilled shaft and are trying to back analyse static capacity. While this sidesteps the rate-dependent problem between dynamic signals and static response, it brings other factors into play, some of which are definite weaknesses in the paper and others where the jury is still out.

Optimisation Technique

Let’s start with one which falls into the latter category: the optimisation technique they chose, which was the Davidon-Fletcher-Powell method. The purpose of optimisation techniques is to find the minima and maxima of “equations” (often they can be expressed in this way, but in this business frequently they can’t) and thus the best solution to the problem. The classic example of this (and one frequently used to test optimisation techniques) is the Rosenbrock Equation, which is

z = (a-x)^2 + b (y-x^2)^2

and is plotted as shown below for a =1 and b = 100.

This has challenged optimisation techniques for a long time. The problem with using something aimed at problems like this is that, in geotechnical engineering, problems look less like this and more like relief maps. The result is having to deal with false minima. For example, if we have a canyon on top of a plateau, a false minimum would be the lowest elevation at the bottom of the canyon rather than the bottom of the cliffs of the plateau, which are generally lower. Multiple false minima are common for problems in this profession, which is one reason why we still use brute force grid optimisation in problems like slope stability. This is why I chose a polytope method for my own study, which is derivative free and “casts a wider net” on the downhill slopes of a problem. It is slow and its results not perfect but I think this is a problem that needs to be addressed if we are to use optimisation techniques for solving geotechinical problems.

A couple of side notes:

  • I did use a quasi-Newton routine related to the DFP method in my study “Analysis of Vibratory Pile Drivers using Longitudinal and Rotational Oscillations with a Purely Plastic Soil Model” because I felt the parameters were “regular” enough to justify its use. The routine I used had an option for the BFGS (Broyden–Fletcher–Goldfarb–Shanno) method. And that leads to…
  • My last course for my PhD degree was in Optimisation. One day our professor–Dr. Kyle Anderson, one of the most brilliant people I’ve come to know–was going on about these techniques, and as you can see Roger Fletcher’s name comes up in many of them. So I leaned over to one of my classmates and said, “Fletcher sure does play both sides of the street.” Dr. Anderson was irritated at seeing whispering, and made me repeat this to the whole class. When I did he thought for a second and said, “He does play both sides of the street.”

The Capacity Issue

In the paper at hand, the optimisation technique starts with initial values and comes to back-analysed values which are then compared to reference values. The problem here is that the reference values are based on single values of toe capacity and soil parameters, the latter of which are related to static methods of analysis. There are two problems which arise in this approach.

The first is the variability of static methods relative to the actual performance of the deep foundation. This is evidenced by the wide scatter in the results these methods return (it’s not quite as bad with drilled shafts as it is with driven piles, but it’s bad enough.)

The second is that the whole business of the “capacity” of deep foundations–ultimate, allowable or factored–cannot be divorced from the fact that the resistance of piles to load takes place through a distance, or settlement. Capacity doesn’t mean much when it’s decoupled from settlement. For static analysis the Holy Grail needs to be that we can estimate the distribution of pile resistance–both between the shaft and the toe and along the shaft–from static load tests. Using static “capacities” may have made the optimisation method they chose possible to use but it does not really get us to where we need to go. Dynamic testing and methods such as CAPWAP recognise this problem but, as noted earlier, improvements there are possible if not easy to arrive at.

Conclusion

I think this paper is an interesting study as a step towards using optimisation techniques to solve the inverse problem of pile resistance to axial load. But there are many more issues to deal with if we are to come to a workable solution for this problem.

Posted in Deep Foundations, Soil Mechanics

Comments on “Using the Impulse-Response Pile Data for Soil Characterization”

Posted on by Don Warrington

This is another post on a paper (linked to from here) which cites my work, in this case two of them: Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles and Closed Form Solution of the Wave Equation for Piles. The concept is simple but the execution, not so much, and as with anything with geotechnical engineering there are pitfalls on the way to a usable solution.

We start with an existing technology: low-strain integrity testing of piles. A simple example of this is shown above, it’s the Pilewave program from Piletest. (Yes, I’m aware that it’s the Windows 3.1 version, if you’re interesting in running DOS and Windows 3.1 programs to save on the expense of “new” engineering software, you can visit Partying Like It’s 1987: Running WEAP87 and SPILE (and other programs) on DOSBox.)

With that distraction out of the way, note that, as the stress wave goes down and back up the pile, there is attenuation due to the interaction with the soil. In the simple demo of Pilewave, the soil resistance is constant along the shaft. But…if we could determine that the pile didn’t have defects which reflected waves, could we use information from the soil attenuation to determine the type of soil surrounding the pile at any given elevation? The answer in principle is “yes” and this paper, although not unique, it is an interesting step forward.

Pile Integrity Testing is a low-strain technique. That’s in contrast to the high-strain methods we’re used to in pile driving analysis. This one takes a leaf from the seismic refraction method (which will be featured as before in Soils in Construction, Seventh Edition) which is also a low-strain technique, as it is a geophysical method. The idea is that the pile acts as a probe into the soil; the response to exitation can be inversely analysed to determine the types of soils around the pile. As the paper notes, if you divide up the pile into enough “layers” the actual soil layering itself (based on the properties returned to you by the method) will basically emerge from the data.

As is generally the case with inverse methods, the solution is complex; it is described in the paper. There are a few comments that I would like to make as follows:

I hope that this research continues; I think it has potential.

Posted in Civil Engineering, Deep Foundations, Geotechnical Engineering, Pile Driving Equipment

NAVFAC DM 7.2: Deep Foundations

Posted on by Don Warrington

Now we get to another topic of intense interest: deep foundations. No topic in this book has advanced more than this one. When the original was published, driven piles were still the most common deep foundations. As much as we hate to admit it, that’s no longer the case.

But something else has happened along the way: most of the advances in the technology have been promoted and advanced (from a documentation standpoint at least) by the FHWA. Most of the chapter is a summary of those documents, and all of them (except for this one and helical piles, where a commercial book was referenced) are on this site. The summary is a reasonable one (and one which, hopefully, will inspire some textbook revisions) but there are a few points that need to be made.

Bearing Capacity vs. Settlement

Most engineering failure criteria in geotechnical engineering outside of lateral structures are based on what’s been traditionally called a “bearing capacity vs. settlement” paradigm. In current parlance (especially when considering LRFD, which is coming up) that referred to as “strength limit state vs. service limit state.” In NAVFAC DM 7.2: Shallow Foundations we saw both in evidence; which one predominated depended upon the configuration of the foundation and the nature of the soil.

NAVFAC DM 7.2 applies this paradigm to deep foundations as well. However, there is a “minority” school (Bengt Fellenius being its most vocal advocate) who believe that deep foundations basically don’t fail in bearing capacity but in excessive settlement. While structurally that may not be the case, geotechnically it’s hard to argue with this idea if one thinks about it long enough. Although, for example, classical bearing capacity equations have been applied to the pile toe, failure there really isn’t the same as shallow foundations due to the significant overburden. When we add the effects of shaft friction, and we look at the load-settlement curve we get out of a static load test (actual or simulated) we find that somewhere along the curve there is a “failure” point, determination of which depends upon the settlement limitations of the application and how we define “failure” along that curve (which is not univocal in geotechnical engineering.)

To get to the point where the ultimate load for a deep foundation is determined from predicted settlement, however, is going to take a major shift in how settlement is computed. NAVFAC DM 7.2 recognises the fact that the best way to estimate axial settlement is the t-z method and does not really offer a closed form, back of the envelope method to estimate them (for driven piles at least; drilled shafts get a different treatment.) The most straightforward method I’m aware of–Vesić’s Method of Estimating the Settlement of Driven Piles and Drilled Shafts–was in the previous book but has gone by the wayside. Further complicating things is the fact that many practitioners have used the bearing capacity/strength methods to estimate the ultimate resistances for the t-z method!

The situation we have on this topic is manifestly unsatisfactory but, until computer methods gain wider acceptance–and the wisdom in how to use them correctly–and we obtain more confidence, I suppose we’re stuck with the current paradigm.

Alpha and Beta Methods

This is another one of those “controversial topics” but NAVFAC DM 7.2 pretty much sticks with the current practice of alpha methods for clay soils and beta methods for sands. I’ve spent a great deal of time on this topic on this website in articles such as Shaft Friction for Driven Piles in Clay: Alpha or Beta Methods? To be fair, as is the case with the FHWA’s Soils and Foundations Reference Manual, Fellenius’ beta method for all types of soils is featured. I am more optimistic that this will be resolved in favour of the beta methods than I am with the settlement issue, but things move slowly in this business.

Lateral Loads and Settlements

For the last 30+ years it has been recognised that the p-y methods are the best for longer, laterally loaded piles. (An example of their application can be found in Driven Pile Design: Lateral Loads on Piles.) These, of course, require computer software, which these days is proprietary. An interesting development in the late 1990’s was the CLM 2.0 method, which featured a spreadsheet simplification for obtaining a solution. (I used it for many years in my teaching.) This study, however, shows shortcomings of the CLM method, and the authors of this part of NAVFAC DM 7.2 would have done well to consider this document in their deliberations.

Wave Mechanics

As someone who started out calling this site the “Wave Equation Page for Piling” this topic is of interest. Since this does require a computer solution (except perhaps for the Case Method,) the section on the subject is a good qualitative overview of the topic. In the wake of my Improved Methods for Forward and Inverse Solution of the Wave Equation for Piles I am seeing interest in advancing this technology, and am looking forward to overviews like this in the future.

Posted in Deep Foundations, Geotechnical Engineering

NAVFAC DM 7.2: Overview and Prologue

Posted on by Don Warrington

This is the first of periodic (hopefully not sporadic) articles on the new NAVFAC DM 7.2. In this post I’m going to make some general observations on the book and look at its “Prologue” on shear strength for geotechnical design.

Of the two classic NAVFAC DM 7 volumes, the second–Foundations and Earth Structures–was the “longest in the tooth” largely due to advances in construction technology, and needed upgrading the most. The result of the effort is a long book (721 pages as opposed to 578 in DM 7.1) but one the need for which is greater than 7.1. It also includes some new sections, including one on probabilistic design (LRFD for short) that has been a major change in the way foundations are designed over the last half century.

I’ll get to that later but in the meanwhile here are some general observations:

  • As was the case with DM 7.1, the graphics are greatly improved, and are up to the standards of their civilian counterparts from the FHWA (which have also been an inspiration to the content of this work.) This is good news, not only for the readers of this book but for those publications which use the graphics in their own books. One of the major upgrades to my and Lee Schroeder’s Soils in Construction was using the FHWA’s better graphics; we had no budget at all for illustrations. It’s always needful to be profitable in business, but textbooks have become cash cows (especially with the major publishers and textbooks) with most of the effort going to places like mastering (which has issues of its own) and not on graphics. For books like Soils in Construction, the graphics will be very helpful. One thing that I held back on was replacing every table and graphic in my Soil Mechanics slides with the new DM 7.1 replacements; I found the older ones, although a lot better looking, to show up better on a screen.
  • Pursuant to that, any textbook out there needs to be reviewed in reference to both of these volumes, not only for the graphics but to the content. How soon these changes will appear in textbooks depends upon the publisher; I wouldn’t hold my breath, as many textbooks represent “rearranging deck chairs on the Titanic” rather than moving things forward. In the case of this field, we have an advantage, because…
  • Although DM 7.2 documents many advances in geotechnical engineering, one thing that strikes someone who has followed the history of the profession is struck once again by how conservative this business is. Both volumes get into software solutions but the main audience of both is the geotech who uses formulas (straightforward and otherwise) to achieve their design analysis. This is not to say that this approach is without merit; “black box” technologies are never a good thing from an understanding approach, and can be dangerous when applied indiscriminately. But the nonlinear nature of geotechnical engineering makes some kind of numerical solution (as opposed to a closed form solution) a necessity to deal with the problems geotechnical engineers face. A solution “duo” where closed form solutions (empirical to varying degrees) and numerical ones are used together is the best, and although that’s not the way it’s presented in DM 7.2 it’s a useful guide to put the two together.

Prologue: Shear Strength for Geotechnical Design

The first section of the book isn’t a chapter strictly speaking but is better described as an excursus on the topic of shear strength. My guess (I haven’t as of now discussed the details of this book with its editor) is that it was added due to feedback from DM 7.1; it really belongs in that document.

One of those “conservative” things about both documents is their sticking with Mohr-Coulomb as the “go-to” failure theory in soil mechanics. I discuss this in more depth in My Response to Rodrigo Salgado’s “Forks in the road: decisions that have shaped and will shape the teaching and practice of geotechnical engineering” and an announcement but the bottom line is that, even with all of the alternative failure models that have been developed (such as Cam Clay) none is as widely applicable across the spectrum of soil types as Mohr-Coulomb, and this doesn’t look to change for the foreseeable future.

The prologue chiefly deals with two topics: non-linear failure envelopes and the applicability of different testing methods to different soil conditions. Non-linear failure envelopes have been understood to exist for a long time and get some coverage in the old DM 7 but in this case some additional quantification of these is presented, especially as they relate to “y-intercept” issues of cohesion in various soils when a purely linear failure envelope is used. Application of different testing methods to different soil conditions (including the composition and the drainage state) is helpful; many texts get bogged down on this topic and it’s sometimes hard to figure out how to use the information. In this document the presentation is more concise.

Although it’s probably beyond the authors’ scope on this prologue, there are two topics which could use some further discussion in both of these volumes.

The first is the simple question: what is failure? For most engineered materials the first form of failure considered is yield failure, which is the transition from elastic/path independent behaviour to plastic/path dependent behaviour. With soils how successful this is depends in part upon how elastic the soil is before failure and how sharp the transition is across the failure envelope. There are other ways of dealing with the non-linearity of soils. A hyperbolic model, for example, posits that there really is no failure point; the slope of the line progressively flattens with increasing shear stress. Some soils are amenable to a specific type of modelling and some aren’t. Defining failure also depends upon the application as well.

The second is the issue of dilatancy, which isn’t discussed much in either volume. As detailed in my response to Salgado, this doesn’t get the coverage–or quantification–it deserves in most geotechnical literature, and is one of those things that geotechnical engineers need to be made more aware of. DM 7 was and is a “state of the practice” document, and hopefully by the time our government gets around to revising it again it will take its rightful place in this applied science.

Posted in Deep Foundations, Geotechnical Engineering

It’s Official: NAVFAC DM 7.2 is Now in Print

Posted on by Don Warrington

I’ve described this site as the “printed home of NAVFAC DM 7,” and that’s certainly been the case (along with the download home) for a long time. Now that we finally have NAVFAC DM 7.2 as replacement for the venerable NAVFAC DM 7.02, it’s time to announce that this is in print and available.

A brief table of contents of this book is as follows:

  • Prologue: Shear Strength for Geotechnical Design
  • Geotechnical Design in Problem Soils and Specialty Construction Methods
  • Excavations
  • Earthwork, Hydraulic and Underwater Fills
  • Analysis of Walls and Retaining Structures
  • Shallow Foundations
  • Deep Foundations
  • Probability and Reliability in Geotechniical Engineering

Thank you for your patience with this. In the coming weeks I’ll be doing a review of the various sections of the book. It’s an interesting and helpful revision to the work and I’m looking forward to digging into it.

The previous volume stated the following:

DM 7.1 has been on the bookshelf of many civil engineers, it has been used in many graduate and undergraduate soil mechanics classed attended by generations of geotechnical engineering students, and charts and correlations from the document have been cited in numerous textbooks and research papers.

The main reason it ended up on bookshelves is because we’ve spent the last fifteen years or so putting it out and you’ve been buying it. The “new” DM 7.1 has followed the trend; we hope you find DM 7.2 in print satisfactory as well.