Academic Issues – vulcanhammer.net

Seepage and Bottom Heave Calculations for Sheet Pile Braced Cut Trenches

Posted on 9 May 2024 by Don Warrington

Part of Soils in Construction‘s presentation of dewatering is this topic. I cover it in my treatment of flow nets in Soil Mechanics: Groundwater and Permeability II; however, Soils in Construction uses a less computationally intensive approach. In this piece I’ll explain that, give some better graphics than the book had available at the time of publication, and compare them with the flow net/FEA results I discussed in my Soil Mechanics course.

Let us consider the problem of a braced cut, which is commonly used for “cut and cover” construction. Such a construction is shown at the right. One of the challenges of temporary works such as this is to insure that a) there is sufficient pumping capacity to keep the “steel trench” dry, and b) the hydraulic gradient of the water coming up into the trench is sufficiently low to avoid soil boiling and bottom heave due to that soil boiling. (Bottom heave can take place due to other factors as well.) An example of that (showing a flow net) is below to the left.

Because the cut is internally braced, it is usually possible to make the sheeting walls simply penetrate to just below the bottom of the trench. However, in order to mitigate the effects of water flowing from around the cut into the bottom, the sheeting can be extended. The idea is that, the longer the extensions, the longer distance the water has to flow, the increased resistance of the soil to flow, and the lower the hydraulic gradients, which both reduce the flow overall and the possibility that the soil at the bottom of the trench will boil, i.e., enter into a quick condition.

Soils in Construction shows two methods of dealing with this problem:

A “rule of thumb” for sheeting extension; and
Charts to determine the minimum extension of the sheeting. These were developed by Marsland (1953). In the book they were taken from NAVFAC DM 7.01, but since the book’s publication NAVFAC DM 7.1 has redone the graphics, and you can see that below (and click on it to download). It is important to note that there is an error in the lower part of this figure; I checked it against Marsland (1953) and have modified it a bit to restore it to Marsland’s original formulation, the following example will show how it is supposed to be used.

Example Problem

I have used this example for many years and feature it in Soil Mechanics: Groundwater and Permeability II. Consider the braced cut shown below.

The parameters for this problem are as follows:

Braced Sheet Piling Excavation
- Depth of excavation = 38’
- Width of excavation = 32’
- Impervious layer 20’ below the toe of the sheeting
- Length of Sheet Piling = 66’
Water table at the excavation level on the excavation side
Water table 6’ below the top of the sheeting on the soil side
Variables for chart above
- H_w = 38 – 6 = 32′
- D = 66 – 38 = 28′
- H_l= 20′
- H = D + H_l = 28 + 20 = 48′
- W = 16′
- Even though the graphic for the problem doesn’t show it, the problem statement indicates an impervious layer below the excavation; thus, we will use the lower chart for this problem.
Soil Conditions
- Uniform medium sand, k = 0.0003 ft/sec
- Saturated Unit Weight = 115 pcf

We need to, one way or another, insure that the design does not experience soil boiling.

The “rule of thumb” in Soils in Construction states that “the depth of penetration of the cut-off wall below the bottom of the excavation should be a third of the “length” computed. For this wall, the ratio is 28/66 = 42%, which means the rule of thumb is achieved.

Turning to the chart above, we must compute three quantities:

The x-axis ratio of half width of excavation to net hydrostatic head, or W/H_w = 16/32 = 0.5;
the y-axis ratio of penetration required to net hydrostatic head, or D/H_w = 28/32 = 0.875; and
the ratio of the depth between the bottom of the excavation and the impervious layer to the net hydrostatic head, or H/H_w = 48/32 = 1.5.

In this case we only have two values of H/H_w to work with: 1 and 2. For H/H_w = 1, FS ~ 2.5 (this is a very rough extrapolation.) For H/H_w = 2, FS = 1.75. Since H/H_w = 1.5 is in the middle between the two, the FS = (2.5+1.75)/2 = 2.125.

If we want to check our results by neglecting the impervious layer, we use the upper chart, and assuming the soil is closer to being a loose sand, FS ~ 1.4.

So how does this all compare to a flow net/FEA result? Same is given below.

At the right is a flow net generated by the finite element program SEEP-W. At the left is a chart showing the direction of the water flow (arrows) and the hydraulic head (coloured bands.) An in-depth explanation of these can be found at Soil Mechanics: Groundwater and Permeability II. The results are as follows:

Gradient at bottom of excavation = 0.48
Factor of safety = 1.77
Total flow = 1.02 gpm/ft of wall

The critical hydraulic gradient, computed by the methods shown in Computing Pore Water Pressure and Effective Stress in Upward (and Downward) Flow in Soil, is 115/62.4 – 1 = 0.843, which checks with the factor of safety for the actual gradient.

The factor of safety from the chart ignoring the presence of the impervious layer is the closest to the FEA/flow net result. For the chart with the impervious layer, the extrapolation for the lower factor of safety should perhaps be ignored.

A couple of other charts (based on Marsland (1953)) are shown below.

References

Marsland, A.R. 1953. “Model Experiments to Study the Influence of Seepage on the Stability of a Sheeted Excavation in Sand.” Geotechnique, 3(6), 223-241.

The 2:1 Method for Estimating Stresses Under Foundations

Posted on 29 April 2024 by Don Warrington

Readers of my post Analytical Boussinesq Solutions for Strip, Square and Rectangular Loads and those related to it know that the math related to these methods can get complicated, and in any case the idea of a “purely elastic” soil response to load is purely theoretical. So is there a simpler way? The most common simplification used is the 2:1 Method, shown at the right.

The method basically assumes the following:

Uniformly loaded foundation
Only stresses of interest are under the centroid of the foundation, as shown, and only vertical stresses are considered
Stresses decrease as if there is a truncated pyramid below the foundation with a slope of 1H:2V.

As shown, to determine the additional vertical stress $\Delta \sigma_v$ at a distance $z$ below the centre of the foundation, the equation for a rectangular foundation of width B and length L (can be interchanged, but conventionally B is the smaller of the two) for a load Q on the surface is given by the equation

$\Delta \sigma_v = \frac{Q}{(B+z)(L+Z)}$ (1)

If the equation is written in terms of the unit load q, it becomes

$\Delta \sigma_v = \frac{q}{(1+\frac{z}{B})(1+\frac{z}{L})}$ (2)

Obviously for square foundations $B=L$ but the solution is the same.

As an example, let us consider a foundation where $Q=100 kN,\,B=5m,\,L=8m,\,z=3m$ . By substitution into Equation (1), $\sigma_v = 1.14\,kPa$ . If we compute the unit load to be $q = \frac{100}{(5)(8)}=2.5\,kPa$ , substitution into Equation (2) yields the same result.

Although it is possible to apply this method to circular foundations, it is just as easy to use Boussinesq theory under the centre of the foundation. The equation for a circle of radius $r$ and all other variables the same is

$\Delta \sigma_v = q(1 - \frac{z^3}{(z^2+r^2)^\frac{3}{2}})$ (3)

The 2:1 method is the only method taught in Soils in Construction. It is generally used with shallow foundations, but can also be applied to pile groups in clay, as shown at the right. It’s simplicity and reasonable accuracy has brought it acceptance, and further information on it can be found in the Soils and Foundations Reference Manual. The concept has also been applied to pile toes, and you can see this in STADYN Wave Equation Program 10: Effective Hyperbolic Strain-Softened Shear Modulus for Driven Piles in Clay.

Academic Issues, Geotechnical Engineering

Specific Surfaces of Soil Materials

Posted on 24 April 2024 by Don Warrington

One concept that appears at the end of Chapter 1 of Soils in Construction is that of the specific surfaces of soil materials, including data from Lambe and Whitman’s classic text Soil Mechanics. Additional information on this topic can be found in Tsytovich, which is reproduced below. (Tsytovich refers to this as “unit surface area,” but the concept is the same.)

A factor of importance in the evaluation of the properties of solid soil particles is their mineral composition. Thus, some minerals, such as quartz and feldspar, interact only slightly with the surrounding water, whereas other minerals, for instance, montmorillonite, can interact substantially more actively and in a different way. The smaller the particles of a soil, the greater their unit surface area (per cm³ or per gram) and the larger the number of centres of interaction with the surrounding water and in contacts between solid particles proper. For instance, particles of kaolin (a clay mineral) have a unit surface area of 10 m²/g, whereas those of montmorillonite have a very large unit surface area of 800 m²/g, which inevitably affects the properties of natural soils containing particles of montmorillonite. The presence of particles of mica (which are very slippery and have only a negligible shear resistance) has an essential effect on the physical properties of the soils containing such particles; this circumstance must always be taken into account.

Academic Issues, Geotechnical Engineering

The “Why” and “What” of Soils in Construction

Posted on 22 April 202422 April 2024 by Don Warrington

Anyone familiar with the history of geotechnical engineering is aware that its development can, to some extent, be tracked with the development of its textbooks. Early textbooks tended to be vague and empirical in nature. With new books more theory is found, especially after the works of Terzaghi, Peck, Tschebotarioff and Taylor. By the early 1970’s there was a large selection of textbooks for the undergraduate instructor to choose from in the topics of soil mechanics, foundations or books that featured both.

This selection, which peaked with the end of the “Golden Age” of geotechnical engineering, has thinned considerably, as it has with most textbooks. Soils in Construction made its debut in 1974, right in the middle of the last burst of activity in the field. So why has this textbook endured when so many others have fallen by the wayside?

The answer is simple: it wasn’t aimed at undergraduate civil engineering students but at construction management ones, and in that respect it was far enough ahead of its time to endure but no so far as to die before its time would come.

When I started my career in the 1970’s, people with geotechnical knowledge working for contractors were a rare breed. This is not to say that such people had not taken their place; the likes of Lazarus White comes to mind. But most contractors–especially small and medium size firms, firms which frequently specialised in one or more aspects of geotechnical construction–did not have on staff people with a working knowledge of applied geotechnical theory.

Contractors were not alone in this lack. State DOT’s were likewise short of people with this type of understanding, and they had large sums of public money entrusted to them. The FHWA saw the need to address this issue, and the Soils and Foundations Reference Manual was the result of that effort. Although it can be used in a college setting (I have done this in my Soil Mechanics and Foundation Design and Analysis courses) it takes a lot of work, more work than most academics are used to putting into an undergraduate course.

Soils in Construction is the answer to this dilemma. It is geared towards construction management students whose mathematical level may not be up to that of their engineering counterparts. (But…I always told my students that the only calculus they’d get in my courses is if they didn’t brush their teeth; even for them it is the nature of basic geotechnical engineering.) It enables them to grasp the basics of the application of soil mechanics to practical problems, including temporary works, whose engineering is frequently overlooked but which is often vital for the successful completion of the permanent works to follow.

With this the authors commend this work to our readers, hoping that it will result in more successful geotechnical projects for contractor, owner and engineer alike.

Academic Issues, STADYN

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

Posted on 9 April 202421 April 2024 by Don Warrington

I was intrigued by Purdue University’s Rodrigo Salgado’s “Forks in the road: decisions that have shaped and will shape the teaching and practice of geotechnical engineering.” It comes at a timely point in my own journey in geotechnical education: as I write this response, I am in the process of finishing up and putting a wrap on my last semester of teaching geotechnical courses at the University of Tennessee at Chattanooga. I will explain more about this at the end of the piece but it will probably be the last time I teach these topics “face to face.”

My effort in geotechnical education has never been strictly about the classes I teach at the University. This website has enabled me to disseminate information on the topic for many years, which is implicitly educational. In more recent times I have posted topics of interest, many of which have emerged from my teaching, and I will continue that practice.

With that introduction out of the way, I can proceed to respond to the various topics that Salgado brings up.

Empiricism, science and geotechnical design

As the scion of one of the oldest active families in the business–the Vulcan Iron Works–I feel I am in an interesting position to address this issue. The Warrington-Vulcan hammer was introduced in the late 1880’s into a world where wood piles–the same types of piles driven by the Lake Dwellers in Switzerland–were pretty much the norm. It was also the era when the Engineering News formula (itself an empirical project) came into being. In subsequent years many other types of piling were introduced, but as Salgado notes soil mechanics–with the exception of lateral earth pressures–were pretty much undiscovered territory. Pile dynamics suffered from a similar level of ignorance, one compounded by civil engineers’ historic aversion to things that move. Vulcan was aware of the problems with the dynamic formulae, but it wasn’t until after World War II that these problems were tackled with a more scientific approach, and even then one gets the impression that Smith’s choice of soil model was fortuitous as much as anything else. In the meanwhile Salgado’s statement that “There is a common misconception that all engineering done before the advent of science was conservatively done” was a misconception not shared by those who really understood the problems with the pile dynamics of the first half of the twentieth century.

The Original Sins of Mohr-Coulomb and the Associated Flow Rule

I have to confess that my thinking on these topics has been formed by two processes: 1) my years of teaching a discipline where the topics do not have as immediate an integration one to another as other branches of civil engineering, and 2) my dissertation, which wasn’t complete until 2016. The latter involved writing geotechnical finite element code from the ground up, which gives me something of a greater appreciation for the issues which Salgado brings up than many who teach this course on an undergraduate level.

Let’s start with Mohr-Coulomb itself: I used it in my FEA code with the following justification:

Based on this and the elasto-plastic discussion, the Mohr-Coulomb failure model was chosen. As Abbo et.al. (2011) point out: “The Mohr–Coulomb yield criterion provides a relatively simple model for simulating the plastic behavior of soil. Other more sophisticated constitutive models for predicting the behavior of soil have been developed over the past three decades, however the complexity of these models, as well as the additional testing required to determine the various soil parameters involved, minimizes their utility for practicing geotechnical engineers. The Mohr–Coulomb yield function is also of importance to finite element researchers and practitioners as it forms the basis of many analytical solutions. These analytical solutions serve as crucial benchmarks for validating numerical algorithms and software.” This observation is supported by McCarron (2013).

In spite of its limitations, Mohr-Coulomb still has its place in geotechnical engineering. Salgado focuses on two serious problems with Mohr-Coulomb: the sharp division between cohesionless and cohesive soils and the use of the associated flow rule, an issue which doesn’t emerge in many “closed form” solutions but is certainly an important one in finite element code.

To illustrate my own journey with the first problem, having come from a deep foundations background, I was taught the cohesionless/cohesive dichotomy which is built into the whole “alpha/beta” method business. That was challenged by John Burland a long time ago. The key to ditching alpha methods–and by doing this use beta methods–is to note that the cohesion of a soil is a function of its effective stress (and other variables.) It is for this reason why I have not taught alpha methods for driven piles for some time but prefer Fellenius’ Method, recognising that the student may find themselves forced to use another method once “in the wild.” (One of these days we’ll fix that dichotomy embedded in O”Neill and Reese’s method for drilled shafts.) Fellenius’ Method has its own problems (it requires the student to use some judgement, which they haven’t quite developed) but I think in the end beta methods will win out.

But there is a more compelling factor at work: the most important single factor in the behaviour of a soil is its grain size distribution. With this soils don’t neatly divide themselves into two categories; it’s a continuum from coarse-grained to fine-grained soils. Even the classification system doesn’t quite do this justice; it’s hard to argue that a soil with 51% fines is that much different (all other things being equal) to one with 49% fines, even though they will have different classifications and the former will be considered “cohesive” and the latter “cohesionless.”

Looking at things this way, “purely” cohesive or cohesionless soils–each at the extreme of grain size distribution–are rare exceptions rather than the rule. This means that, from a Mohr-Coulomb standpoint, virtually all soils have a non-zero $c$ and $\phi$ , something that Salgado notes engineers figured out a long time ago (erroneously, in his opinion.) But that’s just the beginning of the problem, we must now deal with the other quantity that Salgado brings up: dilatancy. And that in turn leads us to the business of the associated flow rule.

Once again my position on that topic is in my dissertation:

Except for purely cohesive soils, a purely associated flow rule is to be avoided for soil materials in the model. Such a rule is acceptable for many engineering materials but does not realistically model the dilation of soils, especially cohesionless ones. The downside to this is that the elasto-plastic constitutive matrix is non-symmetric, which, strictly speaking, will result in a non-symmetric stiffness matrix, increasing the cost of the problem solution.

With an associated flow rule $\phi = \psi$ and the dilatancy is “locked” into the value of the friction angle. With a non-associated rule $\phi \neq \psi$ and we must determine the value of $\psi$ . The literature on meaningful values of $\psi$ isn’t as copious as one would like but the situation is improving. Including the dilatancy solves many of the problems that Salgado raises with the Mohr-Coulomb failure criterion, especially the sole reliance on the Mohr-Coulomb failure function. (An implementation of such a rule is here.) His application of a non-associated flow rule to the bearing capacity problem is intriguing, and would be more intriguing except for the fact that generally settlement is a more important failure mode to consider than bearing capacity. (Application of this to Coulomb and log-spiral failure of retaining walls is another matter altogether.)

At this point we run into the serious problem: how to implement the solutions properly in the class setting. The problem we have in geotechnical engineering is that, in order to consider the effects of elasticity (assuming that exists, which is problematic,) plasticity and dilatancy in “one shot,” you really need finite element code, which can move from elastic to plastic deformation continuously. Most of the “hand” solutions we’ve used up to now have assumed either an elastic state or a plastic one, and the latter with an associated flow rule, as Salgado observes. I think that, moving forward, we need to consider numerical methods as the best way to solve problems in this profession. But it is dangerous to rely on these solely; they tend to become “black boxes” in the hands of many practitioners, whose results are taken as “final” even when they are erroneous. (Those of us involved in pile dynamics are all too aware of this problem.) The hand solutions in these cases need to be ancillary to make sure we are not doing something really stupid with the numerical ones, and I think our education needs to reflect that.

Shear Strain Localisation

The way I have dealt with this issue is to use the lower and upper bound concept, one which I have borrowed from Verruijt. By showing that there is a beginning of failure in the “surface” (a term Salgado objects to) and an end we can bracket the beginning and the end of plastic failure, which shows a truth students need to get used to in soil mechanics: our designs inherently have a degree of failure; the question that remains is how much is acceptable. Some of Verruijt’s examples of lower and upper bound are lame but that can be fixed. It’s also interesting that Salgado picked as a primary example a driven pile. In spite of being the driven pile person I am, I would not, but perhaps that’s because we get to slope stability, lateral earth pressures and bearing capacity before deep foundations. But a more comprehensive solution to the problem would be to pitch the “bearing capacity in piles” concept altogether and base design on load-settlement, which forces us to consider the progressive failure of the shaft surface from the head down and finally the failure of the toe itself.

Since he brought up the subject of driven piles and the “groundbreaking” studies of Randolph and Wroth: in that study they included varying the modulus of elasticity as one got away from the shaft surface. It is possible to use a hyperbolic stress-strain model of the soil to vary this with the strain continuously, as I demonstrate here.

Particulate Modelling and Artificial Intelligence

One thing I’m thankful that my dissertation committee (or one member) talked me out of was particulate modelling. I think that the non-homogeneity of soils and particle shapes will make this a challenging pursuit; continuum modelling should suffice for the foreseeable future.

Salgado is spot on about using any kind of artificial intelligence and machine learning without inclusion of physical modelling: it will not work. Reducing our analysis to a statistical pursuit with no regard for the basic physics of the problem–ours or anyone else’s–will lead to disaster. I have commented on this in other fora and hope our community will resist the temptation of yet another type of “magical thinking” that permeates our society.

Our World In Stress

I usually reserve things like this to another site but since he brought it up:

Our fertility rate globally is dropping. The biggest problem we have with this is that our democracies are not prepared on dealing with funding the consequences of that change. So we will not have so many people who are consuming.
I find it difficult to understand why, since the central problem is the emission of carbon dioxide, nuclear power is not included in the solutions. The anti-nuclear movement had its genesis in the 1960’s and 1970’s, a time when the mood among many was decidedly anti-technological. It’s time for a change.
It is ironic that the methods used by the oft-demonised oil industry are now key to offshore wind.

The second point, in a sense, leads me to why I am departing my 20+ years of teaching geotechnical engineering in a university setting. This fall, Lord willing, I will begin teaching at Lee University, my church’s institution of higher learning. They are beginning an engineering program which has not developed to the point of being discipline-specific. I think, however, that Lee needs an engineering program, its students need the option of one, and that the liberal arts centred educational system, one we inherited from the British and have had since before the Republic began, has failed us, not only in producing a leadership class totally incapable of informed decision on technological issues, but also bereft of what Antoine Arnauld and Pierre Nicole called Logic, or the Art of Thinking. Much of this is an outcome of the same era as the anti-nuclear movement; we have replaced a pursuit of understanding with a pursuit of raw power, and the end result will be that we will end up with neither.

In summary, I think that Salgado’s idea is basically a good one. In addition to what I have observed above, I think that his program will be easier to implement in a well-funded and deep-research institute such as Purdue than in places (and there are many) where geotechnical engineering is an afterthought.