Posted in Academic Issues, Geotechnical Engineering, Soil Mechanics

SLOPE Stability Software Program

Posted on by Don Warrington

Ever since this site’s predecessor was started in 1997, one of the things it’s “about” is offering useful documents and software at no charge. With software that’s become more difficult as operating systems have changed and some software has become inoperable on newer computer systems. We’ve gotten around that for DOS and Windows 3.1 applications, as shown in Partying Like It’s 1987: Running WEAP87 and SPILE (and other programs) on DOSBox. In this case we’re featuring a Windows-based, 32-bit software program for slope stability called–wait for it–SLOPE. It was developed by the late Arnold Verruijt, whose Soil Mechanics book I used for many years.

Downloading the Software

That’s pretty straightforward: click on the link below and save the file to your computer.

Download SLOPE Stability Software

What you’ll see is slope.zip. Computers and file download sites are getting nervous about raw Windows .exe files, so all you need to do is to extract the one and only slope.exe file from the archive.

Starting SLOPE

Now we come to the first discovery: slope.exe isn’t a program installation file, it is the program! You just double click on it and you will be greeted with the interface shown at the top of the post. The data entry is in the while column under “Input Data.” We will explain the input in an example.

The Example

The example is shown below, it is taken from the Soils and Foundations Reference Manual. The description from there is as follows:

Figure 6-20 shows a 35 ft high slope with a grade of 1.5H:1V. The soil properties within the slope and under it are shown on the figure. Groundwater is immediately under the slope. Calculate the factor of safety for a toe circle by using total stress analysis based on the soil properties shown.

Because slope locates the slip circle of failure, we can ignore the geometry specified in that part of the drawing.

Basic Principle of Operation

SLOPE is based on classical slope stability techniques that goes back to Wolmar Fellenius’ work in the first part of the last century. It assumes that the soil fails along a circular surface, as shown below.

The weight of the soil is driving the soil downward, and this is resisted by the shear resistance along the failure surface (the dashed line.) That resistance is affected by a number of factors, including effective stress along the failure surface, friction of the particles, and cohesion of the soil. The whole mass rotates about the center of rotation, which has to be determined during analysis.

The most common method used–and the one SLOPE uses–is the method of slices. In that method the soil mass is divided into vertical slices, each of which has a mass, some kind of resistance along the failure surface, and (for most of the methods used) how the slices interact with each other.

The theory is described in both Soil Mechanics and the Soils and Foundations Reference Manual. The computations can be laborious, but the really tricky part is determining the location of the center of rotation and the radius R of the failure surface. SLOPE takes care of all of that but it is essential for you to understand how it does that, as its determination of all of these factors is not automatic.

Dealing With Different Expressions of Slope

One common problem with slope stability situations is how the geometry of the slope is defined. There is more than one way of doing it, and the method used in the problem is different than the one used in SLOPE.

The problem states that the slope is 35′ high (the vertical length of the slope) with a grade of 1.5H/1V. This means that, for every foot or meter of height, there are 1.5 feet or meters of horizontal length. In this case the horizontal length is (35)(1.5)/(1) = 52.5′. Alternatively we can compute the angle of slope as arctan(1/1.5) = 33.7 degrees, in which case the length is 35/tan(33.7) = 52.5′

Inputting the Data

SLOPE requires the data to be put in SI units. We will do the conversions as we proceed. The data input is as follows:

  • Length of slope (m) = 52.5′ = 16 m
  • Height of slope (m) = 35′ = 10.7 m
  • Water level left side (m) = 0 (from problem statement, zero is at the toe of the slope)
  • Water level right side (m) = 0 (again from problem statement)
  • Unit weight of water (kN/m3) = 10 (reasonable approximation)
  • Dry unit weight of embankment* (kN/m3) = 120 pcf = 18.9 kN/m3
  • Saturated unit weight of embankment (kN/m3) = 18.9 (in absence of better data, use the same)
  • Cohesion soil in embankment (kN/m2) = 500 pcf = 23.9 kN/m2
  • Friction angle in embankment (degrees) = 20 (from problem statement)
  • Neutral stress coefficient subsoil** = 1.00
  • Dry unit weight subsoil* (kN/m3) = 120 pcf = 18.9 kN/m3
  • Saturated unit weight subsoil (kN/m3) = 18.9 (in absence of better data, use the same)
  • Cohesion soil subsoil (kN/m2) = 1,000 pcf = 47.9 kN/m2
  • Friction angle subsoil (degrees) = 0 (from problem statement)
  • Neutral stress coefficient embankment** = 0.66
  • Lower left corner window*** – x(m)
  • Lower left corner window*** – y(m)
  • Upper right corner window*** – x(m)
  • Upper right corner window*** – y(m)
  • Deepest point of slip circles – y(m) = -25′ = -7.6 m (this is negative as it is below the toe of the slope)

Notes:
* The embankment is above the toe. The subsoil is below it.
** The neutral stress coefficient is more commonly referred to in American practice as the at-rest earth pressure coefficients. For normally consolidated soils, it equals to 1 - \sin(\phi) , and the results are shown in the input list. The entry points for both are out of order, so be careful.
*** This will be explained below.

Choosing the Window Points and the Method of Analyzing the Slices

If we put all of this data into SLOPE, we get the following result:

Before we get some results, we have to make two decisions: what slice analysis method to use and the extent of the window.

Soil Mechanics gives an explanation of Fellenius and Bishop’s methods. SLOPE divides the region in the slip circle into the horizontal slices; the difference between these two methods is that Fellenius’ method does not consider friction between the slices while Bishop’s does. Fellenius’ method does not require an iterative solution and is the most conservative; however, given that the computational effort is done by the program, we will use Bishop’s method, which is in common use.

As far as the “window” is concerned, SLOPE, in common with many slope stability programs, uses a grid optimization method to find the location of the rotational centre. This means that a set of points in a regular grid are each analyzed (along with appropriate slip circles) to get the factor of safety (see sketch above) and after analyzing all of these points picks the one with the lowest factor of safety. It’s easy to see that, using the original grid, not much in the way of useful information can be found as the selection of grid points is too small. For a grid point to be valid, it has to be in the interior of the window, not at the edge, because if it’s at the edge it’s possible that the point will be outside of the window.

The window limits are set using a coordinate system with the origin at the toe of the slope. Generally the slip circle centre will be above and to the left of the upper corner of the slope. Values for y should not be less than the slope height and values for x should be greater than zero and less than the length of the slope.

Getting an acceptable result is an iterative process. Let us assume the following for the window boundaries:

  • Lower left corner window*** – x(m) = 2 m
  • Lower left corner window*** – y(m) – 10.7 m
  • Upper right corner window*** – x(m) – 14 m
  • Upper right corner window*** – y(m) – 15 m

If we apply these and then Bishop’s method for the analysis, we get the following result:

We can see the slip circle centre is in the interior of the grid. If we desire we can shrink the window to get a finer grid and a more precise result.

Sometimes assuming the slip circle going to its lowest point does not result in the lowest factor of safety. To simulate something close to a toe circle, let us set the deepest point at the bottom of the embankment; the result we obtain is as follows:

In this case (with some adjustments to the window) the factor of safety is still higher for our original case.

Reporting the Results

SLOPE is not installed, and as a result does not print out its results. The only way to save the results from the program is to get them off of the screen. This is fairly straightforward: use a grab or screenshot program, which was done with the images in this post. Unfortunately many of my students, for whatever reason, insisted on using their phones to take shots of the literal screen, which generally look awful. This was the technology I used forty years ago when presenting this program; we’ve come a long way since.

Conclusion

SLOPE is a fairly simple program to use. It lacks many of the automation and stratigraphy defining features other slope stability software packages have, and is not suited for use in practice. For academic use, however, it is good, and gets students past one of the most tedious features of geotechnical computation.

Posted in Uncategorized

Net vs. Gross Ultimate Bearing Pressure

Posted on by Don Warrington

When you’ve taught any course for as long as I taught Soil Mechanics and Foundation Design and Analysis, you’ll sometimes get inquiries from your students about topics that you either didn’t cover or they might have missed. (Many comforted themselves during the course with the thought that “I’ll never go into geotech,” only to have it be their first job.) This topic came from a student from Florida (which is, of course of special interest for a long list of reasons, esp. since I grew up there) who saw on a geotech report about bearing pressure on a shallow foundation (in this case, a pool) citing the net bearing pressure on the foundation.

The topic applies to both bearing capacity and settlement of shallow foundations.  The simplest illustration of this I could find is at the top of the post; it comes from the presentation of Schmertmann’s Method of settlement estimation from the Soils and Foundations Reference Manual, and I discussed it in Foundation Design and Analysis: Shallow Foundations, Settlement.

Using the notation above, the pressure p is the gross bearing pressure on the foundation.  The pressure p0 is the effective stress at the base of the foundation.  The difference between the two is Δp, which is the net bearing pressure on the foundation.

So how is this relevant to foundation design? In the case of Schmertmann’s Method, it is a part of the method. For bearing capacity, the Soils and Foundations Reference Manual has the following to say:

The net ultimate bearing pressure is the difference between the gross ultimate bearing pressure and the pressure that existed due to the ground surcharge at the bearing depth before the footing was constructed, q (= γaDf). The net ultimate bearing pressure can thus be computed by subtracting the ground surcharge (q) from Equation 8-6:

qult net = qult – q (8-14)


qult net = cNcscbc + q (Nq−1) Cwq sqbqdq + 0.5γBfNγCwγsγbγ (8-15)

The structural designer will typically include the self-weight of the concrete footing and the backfill over the footing (approximately equal to γaDf) in the loads that contribute to the applied bearing stress. Therefore, if the geotechnical engineer computes and reports a net ultimate bearing pressure, the effect of the surcharge directly over the footing area is counted twice. Reporting an allowable bearing capacity computed from a net ultimate bearing pressure is conservative and generally not recommended provided that a suitable factor of safety is maintained against bearing capacity failure. If the geotechnical engineer chooses to report an allowable bearing capacity computed from a net ultimate bearing pressure, this fact should be clearly stated in the foundation report.

Bearing capacity theory is explained in Chapter 11 of Soils in Construction.

In general, the ultimate capacity is the more conservative option to use. Combined with the difficulties associated with bearing capacity analysis, I decided not to emphasise net bearing capacity in my teaching. Additionally, for a small pool like the one we had in Palm Beach, bearing capacity failure is remotely possible. For a large (say, Olympic) size pool, we’re dealing with something approaching a mat foundation, and these generally fail in settlement, as noted in Foundation Design and Analysis: Shallow Foundations, Other Topics.

Posted in Geotechnical Engineering, Soil Mechanics

Why Only Rankine?

Posted on by Don Warrington

With release of Soils in Construction, Seventh Edition, we now turn to discuss some of the special topics surrounding this book. One of them is the earth pressure theory we adopted: Rankine earth pressures, level backfill, with provision (when necessary) for cohesive soils. For a textbook this seems awfully restrictive, but there are justifications for this policy.

Rankine earth pressure theory is the most elementary of the earth pressure theories. It is customary, however, in introductory geotechnical courses such as Soil Mechanics and Foundation Design and Analysis, to present all three failure criteria (Rankine, Coulomb and Log-Spiral.) For many years I did so in the first course and went back to expand on that in the second; it was the only topic I formally reviewed from one semester to the next. In spite of that, my students found the topic confusing, never sure which theory applied even when I made it clear (or so I thought.) What I ended up doing was teaching strictly Rankine theory in Soil Mechanics and the others in Foundation Design and Analysis.

Rankine is also characterised as the most conservative of the earth pressure theories. In his response to a paper by Terzaghi (reviewed for other reasons in my post An Industry Gets Restless: Terzaghi’s 1929 Paper on Dynamic Formulae and the Response) Lazarus White made the following observation:

In the Nineties, when the writer was an undergraduate student, he was thoroughly imbued with the classical methods of computing earth pressures, bearing values of soil, distribution of pressures, and pile-driving formula commonly taught–Rankine, Baker, Cain and Wellington–and, after his graduation, he set about to apply them…Later, during subway construction, he observed that contractors completely and successfully ignored Rankine and Cain in timbering work, and “got away with it” in so many instances that by no scientific philosophy could their theories be justified.

Of the four methods he mentions, only Rankine is still taught as a “currently” used method, although it too is being displaced by methods such as FEA. So how can the decision to teach only Rankine in Soils in Construction be justified? It is done as follows:

  • It’s good that White’s result was “got away with it” and not a collapsed wall; retaining wall failures tend to be catastrophic. It kept his work out of trouble until better methods could be employed.
  • It was the policy of previous editions of the book, although some attempt has been made to use Rankine in conjunction with Mohr-Coulomb for a theoretically consistent presentation.
  • Soils in Construction is primarily aimed at giving contractors a better understanding of geotechnical issues, not as a design guide. It can be taught in a more geotechnical engineering way but its first task is contractor education.
  • Some introductory geotechnical courses only teach Rankine theory with level backfill, such as Tsytovich, which came as something of a shock to me. Either proficiency in more advanced theories were left to experience or later courses for specialists.
  • As noted and in common with NAVFAC DM 7.2, only level backfill is considered, as discussed in my post NAVFAC DM 7.2: Analysis of Walls and Retaining Structures, Part I: Will the Real Rankine Theory Please Stand Up?. Rankine theory can be extended to sloping backfills but again we did not feel this was necessary for a book such as Soils in Construction.
  • Rankine theory with level backfill is the only theory necessary to take the FE exam; preparation for this was one of the objectives of the “extended” material in the book.

Posted in Academic Issues, Geotechnical Engineering

Soils in Construction, Seventh Edition, Now Released

Posted on by Don Warrington

After almost a year of work, it’s been released, it’s available here. Description is as follows:

Soils in Construction speaks not only to engineers, but to the people who must build with soils in the real world: construction managers, engineering managers, students, and working professionals who need practical judgement as much as theory. Written from the contractor’s point of view, this long-standing classic explains the soil mechanics and foundation principles that shape successful construction projects.

The Seventh Edition has been thoroughly revised with updated graphics, tables, examples, and problems throughout. New and expanded coverage includes weathering and soil origins, soil index properties and classification, effective stress and settlement, contracts and compaction specifications, soils reports and subsurface exploration, embankment construction and control, dewatering, excavation support, shallow and deep foundations, and more. The book also adds appendices that support laboratory instruction and broaden its usefulness as a standalone course text or reference.

We’ll be posting more about this in the coming days. In the meanwhile visit our Soils in Construction page for more information.

Posted in Academic Issues, Civil Engineering

Some Thoughts on Changes in the Engineering Curriculum

Posted on by Don Warrington

This post has been a long time coming. I’ve been teaching engineering for a quarter century now, and when not doing that developing sites like this so that engineers (and others) can learn more about design and construction of geotechnical structures (and all structures, to varying degrees, are geotechnical unless they float on the water, in the air or in space.)

I come from a long time of technically educated people, as visiting my sites vulcanhammer.info and Chet Aero Marine will show. My great-grandfather learned the basics from Smith’s Mechanic at the University of Illinois in the 1870’s and both he and his brother had successful careers as naval architects. So I come to this debate with a long family history in this profession and many years of experience in the design and application of construction equipment, which is why my teaching straddles both Civil and Mechanical engineering. Many of those who have visited this site are familiar with my Soil Mechanics, Soil Mechanics Laboratory and Foundations courses. After teaching these for a long time, it was evident that our students weren’t “getting it” on what I thought were fundamental concepts. Moving to Lee University and teaching Statics and Dynamics only confirmed those suspicions. Added to my experience with Fluid Mechanics Laboratory and later Fluid Mechanics and this post is the sum of my reflections on this experience.

For those of you who would like a more specifically geotechnical focus, you might find my 2024 piece 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 interesting.

First, let’s look at the challenges we face:

The Challenges

  1. The growth in the use of numerical methods while the curriculum still emphasizes the use of “hand calculations.” A lot of that is driven by testing; as my CFD professor said after a disastrous midterm (and it was a 500 level course!) testing isn’t perfect but it’s the best thing we have to evaluate whether students are learning the material. Conversely, the problem with simply relying on numerical methods without any recourse at all is that engineers tend to regard results that a computer produces come from Mt. Sinai (the “black box” phenomenon”) and this does not lead to good engineering practice.
  2. We all too frequently lose sight of the fact that our first purpose is to teach people how to think, not just how to make computations or apply formulae. The latter is especially tempting in geotechnical engineering because so many of our formulae are empirical to varying degrees, but we’re not the only people with this problem.
  3. AI, for all of its potential and actual benefits, encourages mental laziness. There, I said it. That’s the root problem with AI, and everything else only leads to that. We don’t need mental laziness in this profession or any other for that matter.
  4. Students’ ability to visualise problems has deteriorated with the growth in computer graphics, from CAD to all kinds of 3D modeling. One thing that vanished before I got into this was students’ ability to draw, but we need to make CAD a solution rather than a problem.
  5. Engineering curricula suffer from being squeezed into a smaller and smaller portion of the course of study engineers are required to take. State school people will recognize the fight with “GenEd” people but it’s not only a problem with state schools.

This last point is not only fueled by the amour-propre of non-STEM faculty; it comes from something that I’ve noticed over the years on Positive Infinity: there is a deep-seated fear that engineers and other scientifically trained people, without the benefit of a liberal arts education, will take over society and enforce a cold, uncultured ethic on everyone else. But that exposes one of the main weaknesses of the American educational system: we warehouse people for over a decade before expecting colleges and universities to impart to them “culture” and “critical thinking skills.” Both of these should be formed long before they step into the halls of “Old Ivy” or “Old Kudzu” (the latter is becoming more important these days.) Our biggest problem is that we cannot agree on a “culture” to teach our young people let alone whether an educational institution of any kind can or should impart such things.

Having said all that, let’s get to the concrete suggestions.

Dial Back or Lose Vector Analysis in Solid Mechanics

One of the advantages of living in the internet era is that we can easily look up books from the past, especially if they’re out of copyright. Engineering education, in a sense, is moving from the oldest knowledge to the newest, the oldest coming first in the early years and as one progresses one learns the newer stuff until, hopefully, the student meets the latest when they get the “terminal degree.” (Geotech warps this process because its transition into true scientific territory is later than other disciplines.)

Now that we have archived textbooks, we can see this process in the books that are readily available. From my great-grandfather’s Smith’s Mechanic to Analytical Mechanics for Engineers to Statics and Dynamics of a Particle, both the content and the pedagogy advance. We also have the Soviet books of a newer vintage; they had a poor economic system but an excellent educational one, and produced texts such as Theoretical Mechanics and Theoretical Mechanics: A Short Course. Other disciplines show the same trend. In all cases engineers trained under these methods went on to produce excellent designs even with the lack of computational power because they were forced to develop serious engineering judgement.

Around World War II we saw in this country a shift to a more precise and analytical approach to teaching solid mechanics. A large part of that was the application of vector analysis, especially for three dimensional problems. When I was taking these courses in the early 1970’s, one could expect to use these in practice. Today that expectation is gone; all problems but the simplest are subject to some kind of numerical method. We would be better off going back to what I call “old coot statics” and dynamics (two-dimensional analysis without vectors) and leave the three-dimensional problems to the numerical methods. Students today, especially with their visualisation problems, need to concentrate on developing their thinking skills and not get bogged down in vector analysis, which in turn is similar enough to linear algebra to develop confusion of both.

An example of the contrast between old coot statics and vector statics can be seen in the example Vector Statics and “Old Coot” Statics: An Example. In the example the two computational methods are set out side by side; the vector analysis is considerably more complicated.

Vector analysis also obscures the fact that a moment is the product of the force and the perpendicular moment arm from the point of application to the line of action of the force. This is illustrated in An Example of 2D Moment Computation. In fact that’s the key problem to vector analysis: the student gets bogged down in setting up the problem rather than understanding its nature.

Problems–especially three-dimensional ones–are best left to numerical methods and emphasis on two-dimensional problems for basic understanding would be a better approach. The last example I’d like to give is An Example of 3D Vector Statics With a Simple Truss. Here we have a problem where (as you can see in the example itself) the vector solution is just too much for the problem; we could either a) use a numerical method or b) split the problem into two two-dimensional problems, one in the x-y plane and the other in the 2-3-4 plane.

The solution in ANSYS (I know this is an old version, we run on a low budget on this site) is below.

I’m aware that vector analysis is well embedded in the teaching of mechanics, but I think it’s time to take a serious look at the problem.

Bring Back Graphical Methods

One hallmark of engineering practice in the past was the use of graphical methods to resolve forces and perform other tasks which would be computationally expensive. The advent of the calculator and later the computer into the profession gave the impression that graphical methods were a thing of the past.

With CAD that’s not the case: we can solve problems with the same precision in CAD we do with either vector analysis or “old coot” statics. An example of this comes from the very first example shown; the graphical solution is given in the article Stiff Leg Derrick Part II: Truss Analysis, and can be seen below. The magnitudes were measured in CAD and the directions were done using the basic derrick layout in CAD.

Another example of a semi-graphical method that gets the short shrift these days is rotation about an instantaneous centre; I give an example of this in Solving a Dynamics Problem using the Instantaneous Centre of Rotation with a Vulcan Design.

Graphical methods will assist visualisation and give students a better feel for the problem, both of which they need in their development as engineers.

Distributed Loads and Concentrated Resultants

This comes out of my geotech teaching but also Fluid Mechanics as well: my students struggled with the transition from distributed loads to concentrated resultants. And the distributions were the usual ones we see in geotech and Fluid Mechanics: linear, either uniform, triangular, or trapezoidal. I’m not sure what the solution is but there are two things we need to consider: a) the aforementioned vector statics and b) the inclusion of algebraically complex loadings with polynomial or other higher order equations. As a practical matter it’s unlikely that a complex loading encountered in practice will obey these equations but will more likely require a stepped type of loading of some kind, which in turn begs a numerical solution.

Keep Basic Fluid Mechanics Basic

Fluid Mechanics has experienced much of the same transition as solid mechanics. From books like Hydraulics and Fluid Mechanics to those we usually teach from now, an emphasis on practical fluid mechanics has been lost. In my own career I have found that many of the problems I had would have been much easier to see if the curriculum I was taught under had stuck with a more basic approach (and books which emphasise that do exist, as you can see from my own course.) What we need is to do the following: a) save much of the more theoretical treatment for an advanced course, paralleling that of mechanics of materials, and b) integrating that type of material into basic Computational Fluid Dynamics, which is a necessity for many fluid mechanics problems.

One other thing worth mentioning is that, in the past, solid and fluid mechanics were more integrated, as you can see in books from Smith’s Mechanic to Mechanics by S.P. Strelkov. We might consider some of this if we decide to seriously rearrange how we teach these subjects.

Putting a Wrap

This is not meant to be an all-inclusive list, and I realise that some of these suggestions will be controversial. Today it’s fashionable in higher education, as it has been down the line for many years, to emphasise the pedagogy methods as opposed to the content. But a simpler, more straightforward approach to subject would lend itself to easier pedagogy; the two aren’t unrelated. The tendency to push practitioners out out teaching–one driven in part by our accreditation process–has left many with an unclear understanding of what is required of engineers once they graduate. There are many issues we face; this piece is only meant to start the conversation, not finish it.