Posted in Deep Foundations, Geotechnical Engineering

APILE and TZPILE: Their Origins and Antecedents

Posted on by Don Warrington

In the process of doing drivability studies for Pile Hammer Equipment, I’ve noticed that some of them include use of the APILE program. APILE is a program from Ensoft, Inc., which estimates the load-settlement curve of a deep foundation. Although it was originally developed for driven piles, it can also be applied to drilled shafts and other bored piles as well. It’s been around for a while but this brief series of posts will look at two things:

APILE: The Basics

According to its description sheet, APILE’s purpose is as follows:

APILE is used to compute the axial capacity, as a function of depth, of a driven pile in clay, sand, or mixed-soil profiles.

It isn’t the first program to accomplish this; on our companion site we have featured two programs for this purpose:

Both of these programs were useful but suffer from two limitations:

  • The operating systems are obsolete, although with SPILE that can be gotten around with DOSBOX.
  • Both of these are restricted to the FHWA Nordlund/Tomlinson methods. The current version of APILE includes the following:

Several methods are used by APILE for computations of pile capacity: i) American Petroleum Institute (API RP-2A), ii) U.S. Army Corps of Engineers (USACE), iii) U.S. Federal Highway Administration (FHWA), and the iv) revised Lambda method.

The Offshore version features several more. It’s unfortunate that the Fellenius method–which is also an FHWA recommended method, albeit not its favourite–isn’t included, although perhaps it could be in a future version. It’s also unfortunate that the company that Lymon Reese started didn’t include the method developed by Reese’s long-time colleague at the University of Texas, Roy Olson, the Dennis and Olson method.

APILE also has the capability of doing the following:

A short-term, load-settlement curve is generated for the modeled pile using nonlinear soil models and elastic pile material deformation. The APILE program uses two sets of internally generated t-z curves (load-transfer in axial side resistance as function of movement) and Q-w curves (load-transfer in end bearing as function of movement) for developing the load-settlement predictions.

The rudiments of the t-z method (which is the basis of this capability) are discussed here. What this amounts to in simple terms is performing a static load test in the computer, much as the wave equation analysis is used to predict pile behaviour during driving. That leads to the thought that one could use static load tests to determine the distribution of resistance and capacity along the pile shaft and at the pile toe. We’ll get into more detail on that in the subsequent post on APILE but there is a partial solution that is related to APILE, namely TZPILE.

TZPILE

The description sheet for TZPILE gives the following overview:

TZPILE implements the well-known method of soil-structure interaction, commonly called the t-z method, where t-z and Q-w curves are used respectively for load transfers in side resistance and end bearing. The t-z and Q-w curves can be internally-generated for both driven piles and drilled shafts with the input of information on the supporting soil and on the geometry of the pile.

The program can be used as follows:

Curves of short-term settlement as a function of applied loads are essential for some engineering computations; for example, when refined input is needed for the analysis of piles in a group. If a field-load test is performed, the computed curves can be “calibrated” by modifying input information to TZPILE to reach agreement with the experimental curves. The calibrated, site-specific curves can then be used with TZPILE to design the production piles, which may vary from the test piles in geometry and stiffness.

TZPILE is thus intended to perform the reverse task of APILE, i.e., given the results of a static load test, the load-settlement curve is matched and the distribution of resistance along the pile shaft and at the toe is estimated.

So where do these two programs come from? Based on the fact that the two were commercialised when Lymon Reese was still alive and active, it makes sense that, like WEAP and its progeny, the method had its genesis in government developed code. That suspicion was confirmed for me when I saw the text output for a pre-COVID version of APILE, which looked very much like the PX4C3 program which has been featured on this and our companion sites for a long time. So let’s take a look at that effort.

PX4C3

The description for that program is as follows:

PX4C3 is a finite difference program used to compute load settlement characteristics on an axially loaded pile of constant outside diameter. A set of load transfer curves along the pile (i.e., skin friction developed on the side of the pile relative to the absolute axial displacement of the pile section) & four point resistance curve at the pile tip (i.e., relationship between the total axial soil resistance on the base of the pile tip & the pile tip movement) are used in program to obtain non-linear soil-pile relationships. Finite difference equations are used to achieve compatibility between pile displacement & load transfer along the pile & between soil resistance & load transfer along the tip of the pile. A complete description of the program can be found in the document “Background Theory and Documentation of Five University of Texas Soil-Structure Interaction Computer Programs,” Miscellaneous Paper K-75-2, by N. Radhakrishnan and F. Parker.

At the top of the code is the following:

C WRITTEN BY H. COLE & L. REESE, U. OF TEXAS
C COMPUTES LOAD SETTLEMENT CHARACTERISTICS OF AN AXIALLY LOADED PILE
C
C 'LOAD VS SETTLEMENT FOR AXIALLY LOADED PILE'L.REESE,SYMP ON BEAR-
C ING CAPACITY OF PILES ,CNTRL BLDG RES INST,ROORKEE,INDIA,1964.
C 'UNIV OF TEXAS SOIL-STRUCTURE INTERACTION PROGRAMS'RADHAKRISHNAN &
C PARKER,WES,MISC.PAPER TO BE RELEASED 12-73.
C CONTACT N RADHAKRISHNAN OR F. PARKER, WES, VICKSBURG, MISS.
C************************************************************
C -PROGRAM USES THE GIVEN LOAD TRANSFER VS PILE MOVEMENT
C-----CURVES AND COMPUTES THE LOAD SETTLEMENT CHARACTERISTICS OF AN
C-----AXIALLY LOADED PILE
C-----LOAD TRANSFER VS PILE MOVEMENT CURVE IS DESIGNATED AS P-Z CURVE
C---PX4C3 INTERPOLATES POINT BEARING VALUES CORRESPONDING TO A GIVEN
C-----TIP MOVEMENT FROM A PREVIOUSLY INPUT POINT BEARING VS TIP MOVEMENT
C-----CURVE

The only thing that needs correction is that Reese’s co-author of the code, “H. Cole,” is in fact Harry Coyle of Texas A&M University. Evidently Radhakrishnan and Parker’s paper took longer to get “out the door” than they thought it would; the report is initially dated May 1975 (a year and a half after the date given in the code) and this was marked out on the report to July 1979, although the report described not one but five programs, one of which is the ancestor of the COM624 lateral load code which was developed both by the Corps and the FHWA and is the basis for LPILE.

APILE1

No history of this program “family” would be complete without the inclusion of APILE1. This program was used for the 1988 master’s thesis of Ronald Ungaro at Texas A&M entitled “Development of Design Parameters for H-Piles in Sand Using Static Analysis.” Ungaro, working under Harry Coyle’s direction, referenced this program as “Coyle, H.M., Marine Foundation Engineering, Unpublished class notes, Texas A&M University, Spring, 1987.” It’s reasonable to assume that Coyle had access to the code he had helped to write and that, to borrow a phrase from the open source community, APILE1 is a “fork” of PX4C3. Whether the APILE1 that is the first version that appears in Ensoft’s chronicling of the software’s history is the same as this one is not clear, although Ensoft’s note that APILE1 was “interactive” could apply by the standards of the time to PX4C3 as well.

So Why Did It Take So Long?

It’s a fair question to ask: why a piece of software whose basis was first established in the early 1970’s took so long to its first commercialisation? There are several good reasons why this is so:

  • The road to the first version of PX4C3 wasn’t a short one. It is a challenging problem, especially for the computers and numerical methods of the time. Geotechnical problems are nonlinear in a sense that are a step above those for many other disciplines (such as CFD) and for that reason these problems have always lagged behind the state of the art in civil engineering for other disciplines.
  • A necessary prerequisite for a program to be used would be for “typical” t-z curves for various soil types to be developed. The accuracy of the program to predict load-settlement relationships at the pile head depends on the accuracy of the t-z curves at each point along the pile shaft and their counterparts at the pile toe. Determining these was ongoing during the time PX4C3 was being developed, so implementing this was sort of like “building the plane while flying it.” An overview of that topic is given in Mosher and Dawkins’ 2000 work Theoretical Manual for Pile Foundations. (The graphic at the top comes from there.) Much of the work that established Reese as a geotechnical great was his research on the lateral counterparts to t-z curves, the p-y curves, and this effort (in conjunction with the University of Houston’s Mike O’Neill) ran parallel in duration to the t-z curves.
  • As noted in his memorial tribute, Lymon Reese founded Ensoft the year after he retired from the University of Texas, which would be 1985. Commercialisation before that would probably run into the university’s conflict of interest policies.

At this point how we got to this point is established. But are we using this technology to the fullest? In the next post we will consider this question.

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.