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Academic Issues, Geotechnical Engineering, Soil Mechanics

SLOPE Stability Software Program

Posted on 22 August 2026 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.

Geotechnical Engineering, Soil Mechanics

Why Only Rankine?

Posted on 17 August 2026 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.

Academic Issues, Geotechnical Engineering

Soils in Construction, Seventh Edition, Now Released

Posted on 2 July 20262 July 2026 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.

Deep Foundations, Geotechnical Engineering

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

Posted on 16 January 2026 by Don Warrington

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

Rationale for My Original Study

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

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

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

Comments on the Paper Itself

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

Optimisation Technique

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

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

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

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

A couple of side notes:

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

The Capacity Issue

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

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

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

Conclusion

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

Geotechnical Engineering, Academic Issues, Civil Engineering

RIP J. David Rogers

Posted on 27 September 202527 September 2025 by Don Warrington

Another giant in our profession has passed into the heavenlies:

Dr. J. David Rogers passed away on August 23, 2025, surrounded by his family and prepared to meet his Savior and Lord Jesus Christ.

A popular retired Missouri University of Science and Technology (MS&T) professor, David will be remembered for his love of teaching, his wide range of interests and knowledge, as well as his endearing sense of humor.

He was surely one of the greats of geotechinical engineering, and I have featured articles of his on this site, including Engineering Geology in the Civil Engineering Curriculum and Determination Of Earth Pressure Distributions For Large-Scale Retention Structures.

I got to meet him once in 2005 when the History Channel featured the Vulcan #2 hammer at a distributor’s yard in New Jersey. I am also indebted to him for much of the material in my own post Getting to the Bottom of Terzaghi and Peck’s Lateral Earth Pressures for Braced Cuts. In the photo at the top, that’s him at the right being interviewed by the channel. (He spent most of this time talking about Gow and the Chicago caissons, but Vulcan was expanding into marine and other applications.) He was doing what he was a master at: communicating, he was one of our industry’s best in that respect.

He had his own website and you can visit it here.

Memory eternal.