# About that “Warrington Method” For Vibratory Pile Drivability

Every now and then something comes up that you really didn’t expect. That took place with a paper published this year cited “W.J. Lu, B. Li, J.F. Hou, X.W. Xu, H.F. Zou, L.M. Zhang, “Drivability of large diameter steel cylinders during hammer-group vibratory installation for the hong kong–zhuhai–macao bridge,” Engineering (2022), doi: https://doi.org/10.1016/j.eng.2021.07.028.” (You can download the preprint here.) The project itself is of interest and the pile driving certainly is; they vibrated 22m diameter pipe piles with a group of vibratory hammers. In addition to the sheer magnitude of the piles, any time piles are vibrated the questions of both drivability and capacity come up.

The whole business of vibratory drivability and the axial capacity of the piles that result is one of those questions that should have been resolved sooner but has not. We have been working on this problem since the days of Savinov and Luskin in the late 1950’s/early 1960’s (more about that in a moment) but we are still not where we should be. The whole business of vibrated piles, the changes vibrations make in various types of soils, and the residual effects from that vibration on the axial capacity are complex, is in some ways more complex than impact hammers. Progress has been made but not as quickly as one would like.

The rate of progress is, in part, evidenced by the fact that Lu et.al. (2022) reached back to my 1990 paper “Methods for Analysis of the Drivability of Piles by Vibration,” which I presented at the Transportation Research Board Annual Meeting. (I was told beforehand that this meeting is held on the coldest week of the year in Washington, DC, something I can attest to.) From this paper, Lu et.al. (2022) featured the “Warrington Method” for drivability analysis thus:

As much as I am flattered by their characterisation, I cannot take credit for this. The method was developed by the Tünkers concern, whose main claims to fame have been a) the use of a damper similar to the auxiliary dampers common on the market today and b) the use of self-synchronising eccentrics similar to those used in impact-vibration hammers. At the time I characterised it as a “parametric method,” which meant that “(c)ertain characteristics are tested against some kind of standard to determine drivability.” The governing equation for this method is as follows:

$F_{dyn} \ge \sigma A_s$ (1)

where

• Fdyn = dynamic force, kN
• σ = unit shaft soil resistance, kPa (given in the table above)
• As = shaft area of soil, m2

Tünkers modified it for sheet piles; however, these days most sheet piling specifications include the “coating area” of the sheet which can be used to determine As. In any case the method only was applicable if the peak-to-peak amplitude was greater than or equal to 4.76 mm. One thing that is worth observing is that the toe resistance is ignored; the effects of toe resistance are discussed for a very early model in the monograph Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance. Obviously the method is intended for what we normally call “non-displacement” or more accurately “low-displacement” piles.

Getting back to Lu et.al. (2022,) I’d like to make two observations on their application of the method.

The first is that the application of the Tünkers Method to GRLWEAP is an extension/extrapolation of the method. It was never intended to be used in this way. That said, the results are, subject to the next comment, reasonable.

The second is that the Tünkers Method is a drivability method, not a capacity method. With capacity considerations, a “lower bound” solution is what is being sought, while for a drivability method an “upper bound” solution is the goal. In drivability studies the objective is to specify a vibratory pile driver that is large enough to get the piles into the ground in a reasonable period of time. Drivability methods–impact and vibratory–tend to be conservative, and this was certainly borne out in Lu et.al. (2022) for this method.

But can we still use the Tünkers Method as a parametric method for hammer sizing on projects that are not so large as a bridge between Hong Kong and Macau? The answer is “yes” if we take a different approach to some of the parameters. That brings us back to the original parametric method, the Savinov and Luskin Method, which I discuss in my 1990 paper based on Methods for Approximate Calculation of the Parameters of Vibratory Drivers and Impact-Vibration Hammers. This method underwent variations in the Soviet literature, and I look at the method from an earlier standpoint in Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance.

The Tünkers Method addresses one omission of the original Savinov and Luskin method, namely a convenient method to estimate the shaft resistance during vibration. Later versions add their own methods of estimating this resistance, but the Tünkers Method relates this to the familiar ranges found in boring logs. This makes it more suitable, for example, to use with layered soils. Once this vibrated resistance is computed it can be compared with the dynamic force to size the hammer.

However, the amplitude requirement of the Tünkers Method probably needs an upgrade. This can and has been done with peak amplitudes and accelerations, but intuitively the best one is probably the peak velocity, as discussed in Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance. This method also addresses another important parameter of vibratory driving, namely the static downward force of the system, which includes both the vibrating portion (exciter box, clamp and pile) and the static portion (suspension, bias weights.) This still leaves uncertain the sinking speed of the pile during vibration, but for sizing purposes and smaller projects it should be adequate.

All of this, however, should not obscure the achievement of Lu et.al. (2022,) which has advanced our understanding of installing piles by vibration.