Anchored Sheet Pile Wall Analysis Using Fixed End Method Without Estimation of Point of Contraflexure

The monograph Anchored Sheet Pile Wall Analysis Using Fixed End Method Without Estimation of Point of Contraflexure, which appeared on this site very early in its existence (October 2007) has been very popular.  The online routine described in the report, which you can use, is found here.  The abstract for the paper is found here:

The fixed end method used for the design of anchored sheet pile walls has been used with success since before World War II; however, computational limitations have forced designers to use simplifications such Hermann Blum developed. The original method called for the use of an “elastic line” solution, where the penetration of the sheet piling below the excavation line was estimated using statically indeterminate beam theory. This paper develops the governing equations for the “elastic line” method for a simple case and presents the solution in two ways: parametrically using charts, and for specific cases using an online computer algorithm. Comparison with other solution techniques is presented, and suggestions for broader applications are made. The adjustment of the penetration for the residual toe load is also discussed, and the limitations of current practice in this adjustment are detailed.



Analyzing Sheet Pile Walls with SPW 2006: Part III, Anchored Walls and Some General Comments

In the last post we looked at the SPW 2006 program analyze cantilever walls.  In this post we will look at anchored walls, which are commonly seen with permanent works.  The program, along with the example problem at hand, is hereSome instructions on the basic working of the program is here.

The problem we’ll be analyzing is once again from the BSC Piling Handbook (1984).

BSC Anchored Problem

The soil profile input is similar to the cantilever wall except that it is necessary to put a layer boundary at the anchor point.  Left and right side data, both tabular and graphic, are shown below.


The same comments re Kp, Kn, q and Dw apply here as they do to the cantilever wall.  Note that SPW 2006 allows the entry of differing water table levels on each side of the wall.  Note also in the original BSC diagram that a weep hole is installed in the sheeting.  Proper drainage is essential for the relief of unbalanced hydrostatic forces.

In any case the one input not present with the cantilever wall is the anchorage.  SPW 2006 does not have provision for anchor design.  A brief summary of this is given below, from DM 7; more information on this is found in Sheet Pile Design by Pile Buck.

Anchorage Design


For our purposes we chose to specify a very stiff anchor, which renders the anchorage point essentially a fixed support, as shown at the right.

If one wants to consider the actual anchorage stiffness, it is necessary to determine the length, the cross-sectional area and the material to establish the stiffness, maximum stress and force, and the deflection at which plastic yielding takes place.  If this is too much, a very stiff anchor is necessary; a very flexible anchor will render the calculations nearly useless.  We have not included consideration of the flexibility of the soil bearing against the deadman; this further complicates the anchor input.

The graphical output (using PZ-22 sheeting) is shown below.

It is left as an exercise to show that the sheeting is adequate (or not) for the moment, using the same considerations as for cantilever walls.

The printed output is here.

Because of the soil-structure interaction, it is (in principle) unnecessary to apply Rowe’s moment reduction technique.  That technique was developed to address deficiencies in the classical methods, which did not consider the interaction of the flexible sheeting with the relatively soft soil.  Also, the technique of increasing the sheeting depth until a workable model is achieved is essentially a “free-earth” method.  It is possible to apply the end conditions of the fixed earth (Blum’s or elastic line method) method; however, it can be tedious.  Obviously SPW 2006 is happy to analyze sheeting lengths longer than the minimum required for geotechnical stability, and so if one wants to reduce the maximum moment (and thus the sheeting profile) a solution between the two can be found.

General Comments

As an educational tool, SPW 2006 fits the bill nicely.  It requires very few system resources and no installation.  It has a very comprehensive and detailed input and uses soil-structure interaction methods which are becoming more common with retaining wall software.  (OTOH, many engineers and owners are not “sold” on SSI, and prefer “classical” methods.)

For use in design, SPW 2006 simply lacks many of the convenience features that one expects with commercial software, and these can make using the program a time-consuming and mistake-prone business in a commercial environment.  For those who want to graduate from strictly classical methods to SSI ones, it can be very useful for both training and as a check.  But commercial use of this program is not recommended.

Analyzing Sheet Pile Walls with SPW 2006: Part II, Cantilever Walls

In our last post, we introduced the SPW 2006 sheet piling software, intended for educational purposes.  The software can be downloaded here.  In this installment we’ll look at its application to cantilever walls, i.e., those walls with no additional support other than the soil itself.  These are used in temporary works.  The file for this can be found with the software.

The problem is this one, taken from the BSC Piling Handbook, Fourth Edition (1984).

BSC Cantilever Problem

This is a fairly simple problem except that it has two different soil layers and properties.  We’ll use the active and passive earth pressure coefficient values given in the example, although these can easily be computed from equations given in Verruijt or DM 7.

Based on this, the left side soil profile after input looks like this:


And the right side:


We note the following:

  • The difference between the two is the first layer on the left side, as we would expect.
  • We have a uniform surcharge q which is carried from the top downwards.  It’s possible to vary that surcharge with depth; however, the program has no method of automatically computing variations in surcharge loading due to surface loads such as line and strip loads.
  • The water table level is shown in all layers.
  • The passive earth pressure coefficients have been reduced by a factor of 1.5.  There is more than one way to include a factor of safety for earth pressure; these methods are discussed in Sheet Pile Design by Pile Buck.
  • The Kn (“neutral” or “at-rest” earth pressure coefficient) has been computed using Jaky’s Equation, discussed here.
  • The stroke is probably the “stickiest wicket” in terms of soil properties.  There are several ways of computing this, depending upon the amount of information on the soil you have at hand.  Probably the simplest way to do this is to use a chart such as appears in DM 7, which is reproduced below.

DM7 Figure 1

Selecting the proper case from the table at the bottom, the stroke can be computed as follows:

D_w = H\left( \frac{Y}{H}^* \right)

It is possible to be very precise with this calculation.  For example, one could estimate the penetration below the dredge line D to use as a value of H , but this becomes very tedious during the iteration process.  It’s also possible (and probably better) to use the different values of passive ratios on the left side vs. active ones on the right, since these pressures predominate on their respective sides.  Neither of these was used in the example, although the latter option is probably the more realistic one.

In any case the soil profile looks like this:


The correspondence of the sections with the original problem is easily seen.

Now we select a sheeting length and a profile.  We’ll select a length of 10 m (you will need to iterate from a short length, perhaps 6m and go upwards until you get a result that does not produce an error.)  We’ll also start by assuming Profile #1 (Hoesch 95.)  Running this yields the following beam diagrams:


The maximum moment is around 235 kN-m/m.  But is this section suitable for this level of  moment?  The simplest way is to compute the maximum moment the sheeting section is capable of, and this can be done using the equation

M_{max} = \frac{\sigma_{max}\left[EI \right]}{Eh}

Here \sigma_{max} is the maximum allowable bending stress, E is the modulus of elasticity, and h is the distance from the neutral axis to the extreme fiber of the sheet (see previous post for a discussion of this.)  The sheeting database is reproduced below:


Assuming that the sheeting is made of ASTM A572 Fr. 50 with an allowable stress of 220 MPa, for Hoesch 95 the maximum moment is as follows:

M_{max} = \frac{(220)(1000)(14863.6)}{(210)(1000000)(.19)} = 82 \frac{kN-m}{m}

Obviously this is too light of a section for the moment level.  This indicates that the EI of an acceptable section should be \frac{235}{82} = 2.9 times the current one, or about AZ13-700.  As an exercise this should be checked.  This ratio method is indicative and not absolute; since the program uses soil-structure interaction, the stiffness of the sheets affects the moment distribution, as is the case in actual application.

The solution printout is here.

In the next post, we will consider the case of an anchored wall.

Analyzing Sheet Pile Walls with SPW 2006: Part I, Introduction

Vulcor-VHD2-CaliforniaThe design of sheet pile walls–and specifically analyzing them from the standpoint of sliding, overturning, and excessive bending stresses–is one of the more challenging aspects of geotechnical design.  That’s because sheet piling are totally dependent upon balancing the lateral earth pressures on both sides of the wall while at the same time insuring their structural integrity.

Simple solutions for the problem are given in texts such as Verruijt and can be analyzed using charts such as one sees in DM 7.02. But real world problems are seldom this simple.  The methodology used to analyze sheet pile walls using “classical” techniques is described in detail in Sheet Pile Design by Pile Buck, and software for that purpose–very useful to simplify the complex calculations from multi-layer soil profiles–is available in packages such as SPW 911.  The expense of this software is easily justified for the practitioner who needs to design these walls in a timely and accurate fashion.

But how does one learn the basics of sheet piling software?  And how can educators teach their students the basics of its use?  The purpose of this article is to introduce the SPW 2006 software, from providing a download link to giving the basics of its use to showing some examples for both cantilever and anchored walls.

The Basics

First the download: it’s here

SPW 2006 was developed by Arnold Verruijt and some description of the software is given in the download.  It has several important features that need to be mentioned up front:

  1. It doesn’t require installation; it’s a standalone executable that can be run, say, from a flash drive.  That makes it simpler to run on systems other than your own (like a university’s.)  It’s a Windows 32-bit executable; it runs fine in just about any Windows environment from 2000 onward (and maybe before) and will also run nicely in Linux under Wine.
  2. Unlike some of Verruijt’s software, it has a data file, which is an ASCII file that can be edited if you know what you’re doing.  (If you don’t, don’t.)  When you start the program, it’s very important to load a previously developed file (such as Demo.spw) before you start, for reasons given below.  You’ll need to be diligent in saving it often, because the program isn’t consistent in telling you if you’ve altered the file before the program closes.
  3. The program is capable of printed output; however, I strongly urge you to have on your computer the capability of putting the printed output into an Adobe Acrobat file.  Doing this will make it easier for you to save the output for use later.  You can also do screen shots of some of the output, as will be evident shortly.
  4. The program input and output is strictly in SI units.

When you run the software and open the demo file, you are greeted with something like this:


You’ll notice the toolbar on the upper right; the first three are obviously (from left to right) open file, new file, and save file.  Next to that is the print command.  The “check mark” is for the output options:


I strongly suggest that all of these be checked.  After that we have the soil layer properties, which come up like this:


You will note the “Loading Step” Option.  This is a departure from some earlier sheet pile programs in that the first loading step shows the soil layering on both sides to be the same.  Subsequent loading steps show the soil layering after “excavation” from the “original state.”  Thus for this, Loading Step 1 show this for the left side:


And for the right side:


Note that the right side looks pretty much like the original.  The left side’s first two layers have zero Wd (dry unit weight) which is the way you tell the program the layers are “excavated” for a given side.  The “?” mark is the button for online help, which explains the variables, for each of the input tables.

Screenshot_20180423_154359One variable that needs some explanation is the Dw, or “stroke” of the soil.  SPW 2006 incorporates soil-structure interaction (SSI,) which means that the force of the soil varies as the wall moves away (or towards it) rather than the “all or nothing” approach common with classical methods.  We’ll discuss this in more detail with the cantilever wall example.

The next button is for the anchors, we’ll explain those when we get to the anchored wall example.  Unlike some classical software packages, SPW 2006 designs for a non-rigid anchor.  This, it’s necessary to note the maximum allowable anchor force and the displacement necessary to achieve that force.  We’ll explain this in more detail with the anchored example.

Screenshot_20180423_155208After this is the axial force exerted on top of the wall.  Using sheet pile walls for bearing is common in Europe but hasn’t quite caught on in the US.  Provisions for forces at both bottom and top of the sheet pile and a moment at the top of the pile are available.

Screenshot_20180423_155516The last input dialogue box is the sheet pile catalogue.  It contains a selection of steel sheet piling (although the program can certainly accommodate other materials.)  The input of sheet pile section properties is probably the strangest aspect of the program for the following reasons:

  1. The database is limited to twenty (20) sections.
  2. The database is at the end of every data file.  That’s why you need to start with a data file already developed; if you don’t, you won’t get the database.
  3. Verruijt’s original database had a collection of U-sheeting from Larssen and Hoesch.  In our download in the demo, cantilever and anchored examples we give the database you see, which includes some Z-shapes.
  4. To pick one of these, you don’t pick one directly from the table, but the last entry in the General Data is the Profile number; the number you pick is the profile from the table.
  5. The database doesn’t feature the moment of inertia directly but an EI quantity which is the product of the modulus of elasticity and the moment of inertia.  This becomes significant in estimating the maximum moment and stresses.
  6. The “h” variable is confusing the way Verruijt defines it: “height of cross-section, in m.”  For U-sheeting and the European practice of using two U-sections as one bending beam, that amounts to making the “h” the same as c in \frac{Mc}{I} .  American designers have always been reluctant to allow this.  On the other hand, Z-sections have never had this dispute.  For this database, the “h” is the distance from the outer face of the sheeting to the neutral axis, or the “c in \frac{Mc}{I} , assuming American practice for Z-sheets and European practice for U-sheets.

The two examples will show how this data is used.

The program gives a simple profile that, for the “Loading Step 1” looks like this:


It is important to inspect this before running the program, using the “calculator” button.  It’s easy to make a mistake, especially if you have more than one loading step (i.e., are modeling a progressive excavation, which is a common problem in sheet piling design.)

Unlike more sophisticated programs, it’s necessary to manually increment the pile penetration beyond the dredge line to determine the necessary length of the pile.  You can do this in meter increments, 500 mm increments, or whatever step you would like, but you need to start with a very short penetration beyond the dredge line and increase it until you don’t get a floating point error in the calculations.   This is done by changing the depth of the last layer in the soil profile input and re-running the calculations.

Once you’ve done this and arrived at a pile penetration, you can output the beam results for the sheet piling.  This comes out in two ways: first, tabular:


And graphical:


We will discuss how to analyze this data with the cantilever wall example.  The printed output has much more detail than this.