It’s official: Soils in Construction, the textbook I have been a co-author on for more than twenty years, is now set to have a Seventh Edition sometime in the next twelve months.
The main objective of this edition is to bring things up to date, and that especially includes the graphics. This book has been around for over fifty years and, although the photos we have used have been very good for instructional purposes, advances in graphic design make it important that these be kept up to date where this is possible.
If you or the organisation you work for have photos or diagrams of geotechnical construction work that you think might be useful for the book, go to the contact page and send a message. Full credit (but no monetary compensation) will be given for submissions that are actually used.
I recently received in inquiry from an organisation which has proposed a shallow foundation of an embankment. They used (wisely IMHO) an FEA analysis to estimate the settlement. The owner’s response was that, since their result was a little greater than Hough’s Method, and Hough’s method reputedly overestimates the settlements by a factor of 2, that the FEA analysis overestimated the settlements. They referred this person to my posts Getting to the Legacy of B.K. Hough and his Settlement Method and Closing the Loop (or at least trying to) on Hough’s Settlement Method, which is evidently about the only ongoing discussion of the topic around these days.
Both of these posts have two objectives: a) they attempt to trace the development of the method, both by Hough and those who came after, and b) to begin the journey to a resolution of the accuracy of the method. The problem with both of these is that the problem is simple to state but, because of the nature of the evidence, difficult to resolve. I’ll start with a brief review of these two objectives and then set forth a worked example (something that is admittedly lacking in my first two posts) to see how things work out. I’ll end with some thoughts on how to more accurately determine the values of C’, which is the core issue with this method.
The Method and Its Development: A Review
“The SPT is a dynamic test, while soil bearing capacity is a matter of statics, interpreting one in terms of the other is analogous to determining the bearing capacity of piles from pile driving formulas. Consequently, it is felt that attempts to present correlations between blow counts and bearing capacities of soils would be an oversimplification of a much too complex subject.” From Fletcher (1965)
“Hough’s Method” is not univocal; he presented it in two forms in Hough (1959) and Hough (1969). The governing equation is the same for both:
(1)
This equation is identical to Equation (3) of my post The Sorry State of Compression Coefficients except for the form of the variables. In some places equations like this are used for fine-grained soils; this is explained in Verruijt.
The basic problem is determining C’ and there are two difficulties with this:
Hough changed the SPT N vs. C’ curves in the intervening decade between the two forms.
We’re not informed what type of SPT hammer Hough used, or if/how he corrected them as we do now (there’s no evidence that he did.)
Let’s start with the first problem: the curves reproduced from the 1959 version (from the FHWA’s Soils and Foundations Manual) are here:
Figure 1 Bearing capacity index (C’) values used in Modified Hough method for computing immediate settlements of embankments (from FHWA (2006))
We’ll deal with the business of N160 shortly. There is no evidence that Hough meant to restrict his method to embankments.
The chart from the 1969 version is reproduced below (my reproduction):
Figure 2 Hough’s Method Relationship between N Values and C’ Values (redrawn from Hough (1969))
One of the more thoughtless things the FHWA has done in publishing this method is never presenting any equations for these curves, which are easily obtained using linear regression. I have done this and you can see them in Getting to the Legacy of B.K. Hough and his Settlement Method.
Obviously these sets of curves are not identical; the soil classifications he uses aren’t either, and there are five (5) curves in the 1959 version while there are seven (7) in the 1969 one.
Turning to the second problem, in neither of Hough’s original monographs is any kind of correction–mechanical or overburden–are mentioned. The FHWA has consistently added overburden correction. As far as mechanical correction is concerned, in Design and Construction of Driven Pile Foundations, 2016 Edition the FHWA has assumed (not unreasonably) that Hough obtained data from a donut hammer and their correction (which also includes overburden correction) looks like this:
Figure 3 Values of the Compression Index C’ for granular soil (from FHWA (2016))
In the same vein I shifted the x-axis of Figure 2 for N60 values as shown below.
Figure 4 Relationship of N60 Values to C’ for Hough (1969) Method Assuming Original Donut Hammer
With that out of the way, the best way to illustrate the use of Hough’s Method is using a worked example, in this case a retaining wall foundation from A Simplified Method to Design Cantilever Gravity Walls. The diagram at the top of the page shows the foundation; the settlement calculations for a variety of methods (using the U.S. Army Corps of Engineers’ CSANDSET program) are given there. Let’s begin by reproducing those results below.
This program includes a fairly broad selection of methods, from elastic/theoretical ones to purely empirical ones. These methods are described in the program manual. While some of them may not be really applicable to this type of foundation, they show the wide variations of these methods, which suggests that there is not a consensus on computing these values.
Hough’s Method is not included. The detailed solution to the problem is contained in this spreadsheet. We assumed that the soil was well-graded fine to medium sand. There are four variations to the results, which are shown below:
As has been documented widely, the results of Hough’s Method are generally above most of the methods used in CSANDSET, although in the case of Schmertmann’s Method (which has been widely disseminated) the difference is not so great. The largest of the Hough’s Method variations is the Closing the Loop (or at least trying to) on Hough’s Settlement Method proposal, so I ran this with the N1(60) values, which resulted in settlements between the two FHWA methods.
One thing I would caution about using an “academic” problem as an illustration is that the parameters–many of which are taken from “typical” values–may not be representative of what actually occurs in the field, and may yield less than satisfactory results, especially for methods with a strong empirical basis. I ran into this problem with Driven Pile Design: Three Methods of Analysis. On the other hand field results are specific to their location and may not be representative of soils that the geotechnical engineer can expect to encounter.
New Values of C’
I’m not sure how much progress has been really made in this discussion. First I summarised my last two posts on Hough’s Method and how it comes up with the value of the compression constant C’, which is an alternative method of using consolidation settlement techniques to estimate one-dimensional settlement. Then I applied this to an example. Both of these have some value but they don’t get to the heart of the issue: we need more reliable (or at least values of which we understand the source) of the compression constant C’.
One hallmark of many of the fixes for this method is the invocation of overburden correction, which (as we saw above) reduces the resulting settlement. Doing this reminds me of something my Computational Fluid Dynamics I professor put in his notes many years ago:
Also, a few words need to be said about how one should interpret results ensuing from a computational simulation. There are a couple of anecdotal-based observations that are often used to describe how to approach a calculated result: (1) Computed results are guilty until proven innocent, and (2) There’s nothing more dangerous than answers that look about right. These observations are related but have slightly different interpretations. The first says that newly computed results should always be viewed with aggressive skepticism. In other words, a CFD practitioner should never accept a computed result as “truth” or representative of Mother Nature until exhaustive means have been taken to ensure that the result is a “reasonable” approximation to reality. The second observation simply means that if a calculation gives results that are orders of magnitude different from those intuitively expected, then the results can usually be quickly judged as erroneous and there is work to do to find out why. The difficult part comes when a calculation gives results that are “close” to what was expected. Such an outcome often lulls the researcher and/or practitioner into thinking that “all is well” and there is no reason to continue scrutinizing the results. However, it is very possible that a “good” answer was obtained for the wrong reason.
Compression constant typical values aren’t exactly plentiful. This table, from Verruijt, is one I have put in my course materials for many years (for log10 formulations):
Type of Soil
C’
Sand
20-200
Silt
10-50
Clay
4-40
Peat
1-10
Another tabulation comes from this source, converted to log10 values:
Soil
Minimum C’
Maximum C’
Loess silt
6.5
19.6
Clay
13.0
52.2
Silts
26.1
65.2
Medium dense and dense sands
65.2
87.0
Sand with gravel
108.7
None
Hough (1969) himself suggests another way forward. Referring to his table of compression coefficient parameters reproduced in Getting to the Legacy of B.K. Hough and his Settlement Method, we start by noting that he computes the values of Cc using the following equation:
(2)
Since the compression coefficient and constant are related in this way
(3)
we can combine these equations and compute the compression constant thus
(4)
Doing this for Hough’s values of a and b (and one should be aware of the caveats he puts on values of b) for a range of void ratios yields the following tabular result:
Hough’s Coefficients
Initial Void Ratio e0 (first row) Values of C’ (rows that follow)
Soil Type
a
b
1.1
1
0.9
0.8
0.7
Clean Gravel
0.05
0.5
70.0
80.0
95.0
120.0
170.0
Coarse Sand
0.06
0.5
58.3
66.7
79.2
100.0
141.7
Medium Sand
0.07
0.5
50.0
57.1
67.9
85.7
121.4
Fine Sand
0.08
0.5
43.8
50.0
59.4
75.0
106.3
Inorganic Silt
0.1
0.5
35.0
40.0
47.5
60.0
85.0
Silty sand and gravel
0.09
0.2
25.9
27.8
30.2
33.3
37.8
Clean, coarse to fine sand
0.12
0.35
23.3
25.6
28.8
33.3
40.5
Coarse to fine silty sand
0.15
0.25
16.5
17.8
19.5
21.8
25.2
Sandy silt (inorganic)
0.18
0.25
13.7
14.8
16.2
18.2
21.0
Silt, some clay; silty clay; clay
0.29
0.27
8.7
9.4
10.4
11.7
13.6
Organic silt, little clay
0.35
0.5
10.0
11.4
13.6
17.1
24.3
Graphically this is what it looks like:
Although I would be reluctant to reconstruct the method based on this, it shows one important thing: there’s more than one way to get to these constants. If we want to have a method for consolidation settlement type solutions for cohesionless soils, we need to pursue all of the following:
SPT correlations, based on current practice for correcting and applying the results.
CPT correlations. Although not appropriate in all stratigraphies (what method is?) CPT is very useful and more consistent than the SPT in those stratigraphies where it can be applied successfully.
Basic soil properties such as void ratio, relative density and unit weight. This suggests lab tests on undisturbed samples; the problem here is that getting undisturbed samples of cohesionless materials into a consolidation testing machine is easier said than done.
It’s also possible to use tests such as the pressuremeter and dilatometer, but these would only be meaningful in places where they are commonly used.
Doing all of these things would advance our understanding of the settlement of shallow foundations and give us more meaningful comparison with finite element methods.
Unlinked References
Fletcher, G.F.A. (1965) “Standard Penetration Test: Its Uses and Abuses.” Journal of the Soil Mechanics and Foundations Division : Proceedings of the American Society of Civil Engineers. Vol. 94 No. 4, pp. 67-75. It is interesting to note that Fletcher cites Hough’s First Edition of Basic Soils Engineering, while Hough (1969) cites Fletcher (1965).
Hough, B.K. (1959). “Compressibilty as the Basis for Soil Bearing Value,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 85, Part 2.
Hough, B.K. (1969). Basic Soils Engineering. Second Edition. New York: Ronald Press Company.
Although the inclusion of these is “obvious,” some background is in order.
When the original DM 7.01 and 7.02 were introduced, examples were scattered throughout the books, and were of variable quality, generally not very detailed. Combined with the terse (and sometimes cryptic) guidance, the lack of detailed examples made them difficult to use in an academic setting for something other than a supplement, and including more examples would have made the concepts clearer.
DM 7.01 and 7.02 came at the end of a fruitful period of knowledge expansion in geotechnical engineering, but even towards the end of the 1980’s things were happening (many documented in NAVFAC DM 7.2) that really begged for an update. With the pedagogical deficiencies noted earlier, a comprehensive teaching document was needed to educate engineers and other practitioners in the science of geotechnical engineering, and that came forth in the Soils and Foundations Reference Manual. Although many of the facts (and figures, albeit redrawn) came from DM 7.01 and 7.02, the book was structured for an educational setting, complete with worked examples (which you can see now in NAVFAC DM 7.2.) Although it was intended primarily for short courses, it could be used for undergraduate students, and (with supplements) I used it in both my Soil Mechanics and Foundation Design and Analysis courses.
It is my hope that the FHWA will revise the nearly twenty year old Soils and Foundations Reference Manual, which is complementary to these new DM 7 documents.
An Announcement About DM 7.1
This site was quick to publish NAVFAC DM 7.1 when it came out in 2022, and it has been a success. There were a few typos and places where revision was needed, and about the time NAVFAC DM 7.2 came out Change 1 to NAVFAC DM 7.1 was also released. That Change was incorporated into the print document and can now be ordered. Whether you never bought NAVFAC DM 7.1 before or just want a corrected copy, it’s available both from the publisher and now in distribution, so you can order it in places such as amazon.com.
Some Parting Observations
The whole DM 7 project, including both NAVFAC DM 7.1 and NAVFAC DM 7.2, was a monumental task. While I voiced my objections about many things, most of these were about the state of geotechnical practice and how it can be improved. As books which document the state of the practice, NAVFAC DM 7.1 and NAVFAC DM 7.2 will become necessary references.
With many thanks to the authors and all of those who worked on these books, just one thing: don’t wait so long to update it…
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.
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
(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
(4-2)
Obviously for normally consolidated soils (OCR = 1) this reduces to
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 and simply presents the chart for 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.
(1)
(2)
(3)
(4)
(4-1)
(4-2)
and simply presents the chart for 
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.
