## Inverse Method for Pile Dynamics Using a Polytope Method: IFCEE 2018

This paper–which is part of the STADYN project–was presented at the IFCEE 2018 conference in Orlando, FL, 7 March 2018. The slide presentation for the paper is below.

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The preprint for this paper can be found at ResearchGate.

Posted in Deep Foundations, TAMWAVE

## TAMWAVE: Pile Toe Resistance, and Some More on Pile Shaft Resistance

Update: the original intent for TAMWAVE was to use correlations based on CPT data.  While these correlations have validity, for TAMWAVE this was abandoned, and the reason for that is discussed in this post.

With this post we begin to discuss our “other” project: the TAMWAVE project.  It’s been around a long time but is now being revised.  The concept is to afford students a method of getting acquainted with several aspects of computer-aided driven pile design, including the following:

• Estimating axial capacity of the pile;
• Estimating the axial load-settlement of the pile;
• Estimating the lateral load-settlement of the pile; and
• Determining the drivability of the pile with a given hammer.

The current version of the online software is here.  One thing we’re doing is to designate the entire project as “TAMWAVE,” even though much of the routine isn’t really part of the wave equation program.

When most of the methods we use today were developed back around forty years ago and earlier, there wasn’t a really good way to distribute them away from mainframe computers.  The advent of DOS changed that, but with the shift towards Windows software most of these packages’ successors became proprietary.  Today we have DOSBOX to run these programs but current students, glued as they have been the last decade to their smartphones, find these hard to use. And, although geotechnical engineering isn’t the fastest moving branch of civil engineering, newer methods have been developed to analyse driven piles.

### Overview of Toe Resistance

We’ve discussed in detail some newer methods of estimating the shaft resistance of driven piles, for sands and clays.  Although the original idea was to use them to enhance STADYN, they’re certainly applicable here, albeit with a few modifications.

With toe resistance, one of the advantages of 3D FEA code like STADYN is that it obviates (in theory at least) the need to estimate the toe resistance of the pile, let alone its progressive mobilisation.  That’s illustrated for drilled shafts in Han, Salgado, Prezzi and Lim (2016).  That’s not the case with a 1D routine like TAMWAVE, and so consider we must the toe resistance.  Han, Salgado, Prezzi and Zaheer (2016) (to whom we had recourse earlier) have a convenient listing of the toe methods that “go” with the shaft methods we discussed earlier, along with many others.

Starting with the toe resistance in sand, we have the following:

$q_b = \left( 1-0.0058D_r \right)q_c$

In this case $q_b$ is the unit toe resistance of the pile, $D_r$ is the relative density in percent, and $q_c$ is the uncorrected cone resistance.  For toe resistance there are several schemes for averaging $q_c$ around the toe, dating back to Schmertmann’s research, which is discussed in Fellenius.

For clays, the corresponding formula to Kolk and van der Velde (1996) is this:

$q_b = 0.7 \left( q_t - \sigma_{vo\,toe}\right)$

$q_t$ is the corrected cone resistance at the toe; correction of $q_c$ is also discussed in Fellenius$\sigma_{vo\,toe}$ is the vertical total stress at the toe.

### Soil Property Input and CPT Implementation

The original routine used the method of Dennis and Olson which really requires choosing whether the soil is cohesive or cohesionless and then answering some additional questions which are specific to the method.  The bifurcation of methods between the two soil types for driven piles is common but misleading; soils are seldom entirely one or the other but exhibit characteristics of both.  We plan to address this issue later for STADYN but for now we will stick with it for TAMWAVE.

One of TAMWAVE’s features which is carried over before is that there is only one soil type allowed for the entire length of the pile.  This is largely to preserve the academic nature of the software and discourage commercial use (which is prohibited anyway.)  That simplifies the writing of the code considerably but we must still choose how we should input the soil properties.

For the new version of TAMWAVE we opted to input the soil properties using two parameters.  The first is the two-letter unified code (SM, ML, etc.) for the characteristic soil type for the pile under consideration.  The second is the consistency or density of the soils, which is given using the verbal designations (“loose,” “hard,” etc.) which are customary in geotechnical engineering.  These are translated into actual properties using the “typical” correlations found in the Soils and Foundations Manual and are shown at the top of the page.  This isn’t a very exact method of proceeding but for the purpose of the routine it is adequate.

Use of these correlations gives us the following information:

• Unit weight of the soil
• Internal friction angle (cohesionless soils) or undrained shear strength/unconfined compression strength (cohesive soils)
• SPT blow counts, generally corrected to $N_{60}$.

Conspicuously absent from this list are CPT results.  The general trend in pile capacity formulae in recent years is to correlate them to CPT results.  While the advantages of CPT testing are undeniable (and it’s certainly more consistent than SPT testing) the fact is that many of the soil borings that practitioners deal with feature SPT data, as do the typical values that TAMWAVE adopts.  Fortunately we have the correlations developed by Robertson and Campanella which relate the two.  Since the relationship between the two is based upon soil type, and we have that already, it is possible to automate the process and estimate equivalent CPT data from the typical SPT data we already have.  This relationship (and its limitations) is discussed in detail in Fellenius.

### Randolph’s Lateral Earth Pressure Coefficient in Sand using CPT Data

In this post we discussed Randolph’s lateral earth pressure coefficient for sands.  The value for $K_{max}$ can also be determined using CPT data as follows:

$K_{max} = 0.02 \frac{q_c}{\sigma'_{vo}}$

The rest of the formula is the same.

### Conclusion

We have developed a new method of inputting soil data into this routine, along with outlining new methods of estimating the ultimate capacity of piles.  It is now necessary to implement these, which we will outline in a subsequent post.

### References

• Fei Han, Rodrigo Salgado, Monica Prezzi, Jeehee Lim. (2016) “Shaft and base resistance of non-displacement piles in sand.” Computers and Geotechnics, Volume 83, 2017, Pages 184-197, ISSN 0266-352X,  https://doi.org/10.1016/j.compgeo.2016.11.006

## Shaft Friction for Driven Piles in Clay: Alpha or Beta Methods?

In a previous post we discussed beta methods for driven pile shaft friction in sands, which are pretty much accepted, although (as always) the values for $\beta$ can vary from one formulation to the next.  With clays, also as always, things are more complicated.

Since the researches of Tomlinson in the 1950’s, the shaft friction of piles in clays has been thought to be a function of the undrained shear strength of the clay multiplied by an adhesion factor $\alpha$, thus

$f_s = \alpha c_u$

This was seriously challenged by Burland (1973) who noted the following:

Whereas the use of undrained shear strength for calculating the end bearing capacity of a pile appears justified there seems little fundamental justification for relating shaft adhesion to undrained strength for the following reasons:

1. the major shear distortion is confined to a relatively thin zone around the pile shaft (Cooke and Price (1973)).  Drainage either to or from this narrow zone will therefore take place rapidly during loading;

2. the installation of a pile, whether driven or cast-in situ, inevitably must disturb and remould the ground adjacent to the pile shaft;

3. quite apart from the disturbance caused by the pile there is no simple relationship between the undrained strength and drained strength of the ground.

Burland buttressed his case by noting that

$\beta = K tan \phi$

and presenting a graph similar to the following:

where, as seen earlier,

• $K_o = 1 - sin \phi$ is in red.
• $tan \phi$ is in blue.
• $\beta$ is in green.

Since, for the ranges of drained friction angles for clay (20-25 deg.) the value for $\beta$ was relatively constant, value of $\beta$ were relatively invariant with friction angle, and thus could be estimated with relative accuracy.  His empirical correlation was very successful with soft clays, not as much with stiff ones.

The year after Burland made his proposal, McClelland (1974) noted the following:

It is not surprising that there is a growing dissatisfaction with attempts to solve this problem through correlations of $\alpha$ with $c_u$.  This is accompanied by a growing conviction that pile support in clay is frictional in character–that load transfer is dependent upon the effective lateral pressure acting against the side of the pile after it is driven.

However, $\beta$ methods–which would embody McClelland’s preferred idea–have never been universally accepted for pile shaft friction in clays.  A large part of the problem, as noted by Randolph, Carter and Wroth (1979) is that the lateral pressure itself is dependent upon the undrained shear strength of the soils.  It is thus impossible to completely discount the effect of undrained shear strength on the shaft friction, even with the remoulding Burland and others have noted.

This has led to the “hybrid” approach of considering both undrained shear strength and effective stress.  This is embodied in the American Petroleum Institute (2002) specification.  A more advanced version of this is given in Kolk and van der Velde (1996).  They give the $\alpha$ factor as

$\alpha = 0.9\left( \frac {L-z} {d} \right)^{-0.2} \left( \frac {c_u} {\sigma'_{vo}} \right)^{-0.3} \leq 1$

The notation is the same as in this post except that we add $c_u$, which is the undrained shear strength.

In this case the unit shaft friction is given by the equation

$f_s = 0.9\left( \frac {L-z} {d} \right)^{-0.2} \left( \frac {c_u} {\sigma'_{vo}} \right)^{-0.3} c_u$

The first is that we can transform this into a $\beta$ method of the form

$f_s = \beta \sigma'_{vo}$

with the following multiplication

$f_s = 0.9\left( \frac {L-z} {d} \right)^{-0.2} \left( \frac {c_u} {\sigma'_{vo}} \right)^{0.7} \sigma'_{vo}$

(A similar operation appears in Randolph (2005).)

in which case

$\beta = 0.9\left( \frac {L-z} {d} \right)^{-0.2} \left( \frac {c_u} {\sigma'_{vo}} \right)^{0.7}$

The only thing we would have to do is to find a way to incorporate the limiting condition for $\alpha$, which we will discuss shortly.

The second thing is that the term $\left( \frac {L-z} {d} \right)$ appears in both this formulation and that for sands in this post.  The difference is that, while Kolk and van der Velde (1996) use the term in a power relationship, Randolph (2005) uses it in an exponential way.  The basic concept in both is the same: the term is at a maximum at the pile toe and decays toward the mudline.

The two are compared in the figure below.

Here the quantity $\left( \frac {L-z} {d} \right)$ is at the x-axis and the following is at the y-axis:

• Kolk and van der Velde Method for Clays, $\left( \frac {L-z} {d} \right)^{-0.2}$ in red.
• Randolph Method for Sands, $e^{-\mu \left( \frac {L-z} {d} \right)}$ in blue, where $\mu = 0.05$.
• $e^{-\mu \left( \frac {L-z} {d} \right)}$ in green, where $\mu = 0.02$.

The graph illustrates the problem (from a computational standpoint) with the Kolk and van der Velde method: there is a singularity in their coefficient using the power relationship at the pile toe, while the exponential relationship yields a value of unity at this point.  The last correlation in green is approximately the best fit of the exponential relationship with the power relationship of Kolk and van der Velde, using either 1-norm or 2-norm methods.  It is not very good; it would be interesting, however, to see what kind of value for $\mu$ might result if this had been in Kolk and van der Velde’s original statistical correlation equation.

In view of all this, perhaps the best way to enforce the limit is to do so as follows:

$\left( \frac {L-z} {d} \right)\geq1$

From all this, we can say that it is certainly possible to compute shaft friction for driven piles with a $\beta$ method provided we include the effects of the undrained shear strength.

### References

In addition to the original study and previous posts, the following references are noted:

Kolk, A.J., and van der Velde, A. (1996) “A Reliable Method to Determine Friction
Capacity of Piles Driven into Clays.” Proceedings of the 28th Offshore Technology Conference, Houston, TX, 6-9 May.  OTC 7993.

McClelland, B. (1974) “Design of Deep Penetration Piles for Ocean Structures.”  Journal of the Geotechnical Engineering Division, ASCE, Vol. 111, July.

Posted in Deep Foundations

## Deep Foundations for Transportation Facilities: A Historic Perspective

This is a presentation slide show given by Mr. John G. Delphia, Texas Department of Transportation, Bridge Division, Geotechnical Branch Manager.  It’s a nice overview of deep foundations for transportation structures, including both drilled shafts (which TxDOT has excelled at since the days of O’Neill and Reese) and driven piles.

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In addition to our own terms and conditions, please note the terms and conditions of the slide show, which are contained in the last slide and which we agree with.  We should also note that this slide show contains content from our companion site vulcanhammer.info, especially from our pages on differential acting hammers, leaders and onshore hammers.