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.


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.


  • 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,

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