Author: Don Warrington

Posted in Geotechnical Engineering

NAVFAC DM 7.2: Probability and Reliability in Geotechnical Engineering

Posted on by Don Warrington

The last chapter (the example problems, which we plan to discuss in our last post of the series, are in an appendix) of NAVFAC DM 7.2 is on probability and reliability in engineering. Generally speaking engineers associate this with LRFD, and there have been objections to this being applied to certain geotechnical problems, as Mark Svinkin noted in his Letter Concerning Dynamic Methods. However, these methods are here to stay, and this chapter provides a comprehensive overview of the topic that goes past LRFD, which will be useful to many of the “old heads” unfamiliar with statistical methods. (Statistical methods, like linear algebra, are just about de rigeur in engineering curricula these days, not the case in the past.)

In some ways this is the best written part of the book, probably (pun partially intended) because it was written from the “ground down” (this is a geotech book, after all.) In previous chapters the authors had to wrestle with material which they felt engineers expected and whether to keep certain items or to pitch them. In this case the presentation was free of those conflicts, although the subject matter introduces complexity which can glaze the eyes.

A Basic Declaration

One thing that the chapter sets forth, in common with many presentations on the subject, is that engineers in the past have used “deterministic” methods while now we used “probabilistic” methods. This is simply not true. The factors of safety, as they lumped the uncertainties of loads and resistances into one number, may have been crude in their way of incorporating uncertainty, were in fact a recognition of uncertainty. Attempts to sort out the sources of uncertainty have been ongoing since Isaacs’ famous “factor of ignorance” statement in 1931. Beyond that, geotechs in general have been very aware of the uncertainties of designing structures in and next to the earth, which is why “engineering judgement,” not a well quantified thing in itself, has been critical in the way things get designed and built.

There are three basic problems with statistical methods.

The first is that, while the way the physics are quantified in this profession hasn’t changed (at least not enough, as I’ve noted in this series more than once) the way we deal with uncertainties has made the design process considerably more complicated. That’s why, when teaching Foundation Design and Analysis, I waited until the end to introduce Foundation Design and Analysis: AASHTO LRFD Method. It was hard enough to get the students proficient in the basic physics without adding the complexity of LRFD.

Second, NAVFAC DM 7.2 mentions the fact that some LRFD factors were based on ASD safety factors. This was very much in vogue in Geotechnical LRFD’s early years, as you can see in this document. When this fact was stated during an ASCE national convention in the late 1990’s, Jean-Louis Briaud asked the obvious question: if we’re basing load and resistance factors on ASD, what’s the point of LRFD? That question has been answered in the intervening quarter century to a large extent, but given the variations in geotechnical data (and age; I recently performed a drivability study using boring data from the 1940’s) I don’t think we’re quite there.

Third, the inevitable temptation with the computing power we have at our disposal is to use statistical methods in place of analysing the physics of the problem. This is something that must be stoutly resisted. I am not alone in being concerned about this, as I noted 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.

One thing that statistical methods are much better in doing than ASD is including the effects of “black swan” events such as earthquakes, hurricanes, and ship impacts.

Outline of the Chapter

The chapter has four main sections:

  • An Introduction to the topic.
  • Principles of Statistics and Probability, a nice overview of the basic concepts.
  • Uncertainty in Geotechnical Engineering, outlining the sources, effects of and designing for uncertainty.
  • Applications, including an overview of LRFD. The last doesn’t include a tabulation of load and resistance factors. This is doubtless a wise decision because a) there is more than one system of these, and b) they, like the tax code, have all the stability of Burnham Wood, and are subject to change by their promulgators.

One interesting inclusion of statistical methods are Monte Carlo methods, which are notoriously computationally expensive.

Overall this is an excellent section on a topic which is developing in several ways and will grow in importance in geotechnical analysis and design.

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 Civil Engineering, Geotechnical Engineering, Soil Mechanics

NAVFAC DM 7.2: Shallow Foundations

Posted on by Don Warrington

This week we’ll turn in NAVFAC DM 7.2 to shallow foundations. It’s a well worn path and NAVFAC DM 7.2 does a good job covering it, but there are a points that are worth making. (Settlement for these foundations is covered in NAVFAC DM 7.1.)

Upper and Lower Bound Plasticity

It’s mentioned in both NAVFAC DM 7.1 and NAVFAC DM 7.2 but not really explained: the whole concept of upper and lower bound plasticity. Until recently most American textbooks avoided the subject; I used Verruijt’s coverage of the subject, which had problems of its own but gave a reasonable introduction to the subject. NAVFAC DM 7.2 refers to Terzaghi’s bearing capacity method (which really needs to be retired from use) as an “upper bound” method, but the truth is that all of the bearing capacity methods mentioned–Terzaghi, Brinch-Hansen, Vesić (more about that shortly) and Meyerhof–are all upper bound methods. For a credible lower bound method which is good to illustrate the concept with bearing capacity, take a look at my post Lower and Upper Bound Solutions for Bearing Capacity.

Geotechnical Eccentricity

For both square/rectangular and circular foundations, this gets nice coverage, with illustrations, in NAVFAC DM 7.2. It’s a subject my students wrestled with, especially when juxtaposed with “middle third” types of distributions (and that’s covered too,) and this will be a help.

Vesić’s Method

If there’s one serious lacuna in the presentation on bearing capacity, it’s the lack of coverage of Vesić’s Method. That’s because the FHWA, for better or worse, has adopted it (or a modification of same) as their principal recommended method for bearing capacity.

Groundwater and Layered Stratigraphies for Bearing Capacity

The coverage of both of these topics is extensive and welcome. The groundwater part is basically the same method as the FHWA uses; the layered part is an advance over this or any other method I’ve seen. One question hangs over the festivities: what’s the best way to put them together?

Shallow Foundations on Slopes

This represents a major advance over the old book. My students found Meyerhof’s method hard to use (I did too) and the tabular alternatives given are a welcome break.

Mat Foundations

This is always a difficult topic because, at the end of the day, a computer solution is necessary for a realistic analysis. In the interim NAVFAC DM 7.2 furnishes a method which hopefully will be helpful for preliminary or verification work. One topic that isn’t consistently treated is whether a foundation should be analysed as rigid or flexible in the first place. NAVFAC DM 7.1 was very helpful when I put together When Semi-Infinite Spaces Aren’t, and When Foundations are Neither Rigid Nor Flexible, and a similar approach here would have been helpful.

The rest of the chapter focuses on drainage of shallow foundations and rock and soil anchors. The latter edges into deep foundations, which will be our next topic.

Posted in Civil Engineering, Geotechnical Engineering

NAVFAC DM 7.2: Analysis of Walls and Retaining Structures, Part II: The Rest of the Story

Posted on by Don Warrington

Now that we’ve taken a look at NAVFAC DM 7.2: Analysis of Walls and Retaining Structures, Part I: Will the Real Rankine Theory Please Stand Up?, in this post we’ll look at the rest of the chapter.

Water and Surface Loading Effects

Both of these topics get expanded–and welcome–coverage. Water pressure loads are important and needed the attention, especially for those of who teach–or have taught–these at the undergraduate level. With surface loading, a chart for rectangular loads has been included, similar in concept to the Fadum charts. The traditional Boussinesq (Flamant should be included, per Verruijt) with Terzaghi modifications, but these really need another look (the tests to confirm them date back to Spangler in the 1930’s.) Also extensively treated are compaction loads; although compaction adversely affects the permeability of the backfill, it is unavoidable in many cases.

Earthquake Loads

It’s a clear sign of the conservatism of the industry that, for all of the earthquake research that has taken place since the 1960’s, the method that NAVFAC DM 7.2 chose to feature is the Mononobe-Okabe method, which is a century old. I think the basic problem is that it converts a dynamic problem into a static one, which increases civil engineers’ comfort level with the method. A more thorough treatment of the method is here, but this is yet again another topic where, although NAVFAC DM 7.2 has chosen to reflect current practice, it’s time to more forward.

Rigid Retaining Walls

This is another topic that gets a nice upgrade (with much better graphics,) but I would have included the Corps of Engineers’ (this is an interservice document, after all) method for marine gravity walls.

Although I suspect that it was a political decision to include it, I think it’s time to ditch the Terzaghi “low walls” method of analysis. At the time it was a nice, quick method for engineers armed with slide rules to design walls, but given the computational power–and the relative simplicity of the problem–I think it’s time to move on from this too.

MSE Walls

These have advanced a great deal since the older document; however, the complexity of designing these walls inspired the authors (who had covered many of these issues in NAVFAC DM 7.1) to “punt” to the FHWA’s offerings on the subject. These can be found on our page Mechanically Stabilised Earth (MSE) Walls.

Sheet Piles and Other Flexible Retaining Structures

As the co-author/editor of Sheet Pile Design by Pile Buck, I need to point out that many advances have been made in the reference materials on sheet pile design since US Steel’s Steel Sheet Piling Design Manual. The principal author of US Steel’s manual was Harry Lindahl, who went on to author the Pile Buck Steel Sheet Pile Design Manual (an immediate successor to US Steel’s manual) and began work on Sheet Pile Design by Pile Buck, a work which was interrupted by his untimely death and which I had the privilege to finish.

With that out of the way, we can proceed as follows:

  • The treatment of anchored walls includes the introduction of what the Corps refers to as a shear mobilisation factor (SMF,) but which NAVFAC DM 7.2 refers to as a safety factor. The two are, strictly speaking, not the same. The SMF is featured in A Simplified Method to Design Cantilever Gravity Walls. The factor of safety in sheet piling design is generally a straight reduction of the passive earth pressure coefficient, which would include both frictional and cohesive portions of the soil strength (the Corps’ method includes that but it isn’t included in NAVFAC DM 7.2.)
  • Rowe’s Moment Reduction method gets overhauled graphics, but it should be pointed out that it is necessitated by the reality of soil-structure interaction (SSI,) which is better handled by a software solution. A simple implementation of this can be found in Analyzing Sheet Pile Walls with SPW 2006 (although I don’t recommend it for commercial use, it’s good to see how such software works and for academic use.) The problem with software like this–and this is common with many numerical methods–is that the results of the software given the same data are not exactly the same with different software packages and numerical methods. Software like SPW911 (more about that in a moment) are replications of “closed form” methods which should give the same results following the same procedures, but do not take some of the complexities of actual application into account. That leads to the procedure itself, with issues such as…
  • I am not sure why NAVFAC DM 7.2 is averse to the use of the “simplified method” for cantilever walls, the conventional method is retained as normative. This has been in SPW911 for many years and used elsewhere with success, but there are American practitioners which have stuck with the conventional method.
  • The chart solutions given in NAVFAC DM 7.2 are a carryover from the old book; except for academic use, I don’t think they’re very useful. OTOH I don’t see regular design of sheet pile walls without software with some hand checks; as the anchored bulkhead design scenarios show, the calculations can become very complex very quickly. That’s true whether you use “hand solution automations” such as SPW911 or more sophisticated software.
  • The braced cuts coverage gives more modern research into the whole issue of lateral pressure distribution but does not address some of the structural issues which I discuss in my post Getting to the Bottom of Terzaghi and Peck’s Lateral Earth Pressures for Braced Cuts.
  • Cellular cofferdams get a broad overview, but the complexity of the topics prohibits much more than that. We deal with this in Sheet Pile Design by Pile Buck.

Overall the treatment of these walls is an improvement over what we had before. Some of the issues are the function of the editorial decisions of the authors, but many are issues in the sheet pile community that themselves have not been resolved, as was the case with the lateral earth pressures.

Posted in Civil Engineering, Geotechnical Engineering, Soil Mechanics

NAVFAC DM 7.2: Analysis of Walls and Retaining Structures, Part I: Will the Real Rankine Theory Please Stand Up?

Posted on by Don Warrington

Now we get into a topic which has certainly been of interest to me, the co-author/editor of Sheet Pile Design by Pile Buck. I’m going to begin by tackling the subject of lateral earth pressure theories. NAVFAC DM 7.2‘s treatment of this subject is illuminating but raises many questions about how these relate to each other and to the design of retaining walls.

Acknowledging the Source of Jaky’s Equation

I’ll start with another topic, namely that of Jaky’s Equation, which is the “standard” for at-rest earth pressure theories. The first thing that comes up is the definition of the coefficient of earth pressure, given as

K_o = \frac{\sigma'_h}{\sigma'_z} (4-1)

The hard truth here is that this is the definition of any lateral earth pressure coefficient; the difference is which theory is applied. It’s not just for at-rest earth pressures.

Turning to Jaky’s Equation, the equation for at-rest lateral earth pressure coefficients is given as

K_o = (1-\sin\phi')OCR^{\sin\phi'} (4-2)

Obviously for normally consolidated soils (OCR = 1) this reduces to

K_o = 1-\sin\phi'

but this is Jaky’s Equation, which is the basis for Equation (4-2). I think that credit needs to be given to its originator as has been the case with textbooks and reference books for many years.

Will the Real Rankine Theory Please Stand Up?

Now we get to the interesting part: the nature of Rankine Theory. The fact that, for vertical walls with level backfill and no wall-soil friction, the lateral earth pressure equations for both Rankine and Coulomb theory are the same. This has led to a good deal of confusion on the subject, such as “Rankine theory is just Coulomb theory with no wall friction,” but this is not the case. Rankine Theory is based on the application of Mohr’s Circle, while Coulomb Theory has its origins in static equilibrium of soil wedges. NAVFAC DM 7.2 does a good job making this distinction but in the process a few observations are in order.

First, while NAVFAC DM 7.2 goes into detail on the level backfill/vertical wall case, it does not include the “extensions” developed for sloping backfill. It states that “…there are published techniques that can accommodate inclined backfills.” I discuss one of these in my post Rankine and Coulomb Earth Pressure Coefficients. Excluding these restricts the use of Rankine theory in the same way we see in, say, Tsytovich, except that provision for cohesion is included.

Pursuant to that inclusion, NAVFAC DM 7.2 redraws this diagram from DM 7.02 in this way:

If they’re serious about making a clear distinction between Rankine and Coulomb theories, they need to eliminate the failure surfaces in the diagrams. I’m as aware as anyone of the role failure surfaces play in things such as anchor design, but it doesn’t change the basic nature of the theories. (I’m aware that there are rupture surfaces in Rankine theory, but they are different than wedge failure. Inclusion of a diagram such as is shown below (from this source) would have clarified the distinction.)

Finally, I don’t understand why they included the material on wall/soil interface friction angles in the section on Rankine theory, since Rankine theory doesn’t take into account wall/soil friction (it doesn’t consider soil/soil friction along a failure surface either.)

And as for Coulomb…

The presentation on Coulomb theory is similar to that in the old book with redrawn graphics and some tighter limits on acceptable limits of parameters such as wall friction and backfill angle. As was the case with the old book, NAVFAC DM 7.2 includes charts for vertical walls with sloping backfill and no wall friction for both the earth pressure coefficients and failure plane angle. And, like the old book, it doesn’t really explain why these charts are important. Should we ignore wall friction in many cases (the old book implied that we could for active pressures)? And how do the results of Coulomb theory under these conditions compare with the “Rankine extensions” with which the new book dispenses but are found in practice? (The answer to the last question can be found in the post Rankine and Coulomb Earth Pressure Coefficients.) I think that, with topics like this where there is significant variance in the way the theory is applied, DM 7 in general tends to “punt” on issues like these.

Coulomb earth pressure inevitably lead to the issue of trial wedge methods for complex geometries and stratigraphies. Personally I think that, with the advent of FEA, trial wedge methods are obsolete. NAVFAC DM 7.2 notes that “…finite element and finite difference soil structure interaction software can be used to solve these types of problems, but considerable skill is required to obtain meaningful results.” The same observation could be made about trial wedge methods. As someone who spent two decades in geotechinical education (and more if you include my work on this site) I don’t see the generation of engineers coming up developing the skill set for trial wedge methods.

Log-Spiral Methods

Log-spiral theory (especially in the passive case) has two significant advantages over Coulomb theory: it more accurately models the failure surface (FEA eliminates the need to do that, it figures it out for itself) and that in turn results in a smaller soil wedge and lower (less unconservative) earth pressure coefficients. Using these require a chart solution, and NAVFAC DM 7.2 makes a significant advance in that it abolishes the correction table for different values of \frac{\delta}{\phi} and simply presents the chart for \frac{\delta}{\phi} = \frac{2}{3} as a typical value. The new book expresses doubts about the accuracy of these correction factors, but there’s one thing for sure: it’s much less confusing and subject to error in use, and will make classroom teaching of this method much easier. My only concern about these is applying them to walls where soil/wall friction is minimal, as is the case with fibreglass and vinyl sheet piling.

The FHWA’s Solution

In its discussion of the log-spiral method, NAVFAC DM 7.2 states that (…passive pressure should be computed using the log spiral method and not the Coulomb method.” This is obviously due to the advantages of log-spiral methods discussed above. It’s worth noting (and the book should have done so) that the FHWA’s usual solution to this problem is to use Coulomb active/log-spiral passive combinations in practice, as they explain in the Soils and Foundations Reference Manual. This would have buttressed support for their case and given the engineer more definitive guidance in what can be a confusing topic.

Lateral earth pressure is the oldest analytic topic in geotechnical engineering; Coulomb published his paper in the same year the American colonies declared their independence from Great Britain. It is an indication of the nature of the field that we still do not have a firm consensus on how these are to be precisely computed and applied.