No.

Well, Yes and No. There are some simple closed form solutions such as Engineering News and FHWA modified Gates formula, which under some conditions can give an approximation of total capacity to set, provided some hammer information is known. A much much more accurate solution is a wave equationanalysis, which requires readily available software. The program can give a good estimate of capacity to set for a given driving set up and length. The program can seperate toe capacity from friction, but that is dependent of course on how you model soil conditions.

The gates equation we used in the previous projects is

Qa = 105*(e*Eh)^0.5*log (250/s)/4

where e is the hammer efficiency; Eh is the driving energy in kJ, s is the set in mm/blow.

We used to use 40mm/blow as the maximum rate at capacity. This corresponds to a Qa = 91kN. (I don't know why it is independent to soil condition).

40mm/blow is about 7.6bpf. Comparing to other suggested final sets, I find this driving criteria is too loose.

The formula cited is applicable to the blows per inch while DRIVING,  The refusal or final set may have either freeze or relaxation in the formula which negates any meaningful values.  For a particular combination of pile, hammer and cushion that make up a system in which soil conditions determine the penetration of the pile per blow and the influence of freeze or relaxation must be measured by load testing the pile and then returning to driving the pile after several days and finding the increase or decrease in number of blows per inch.

I would not advocate load testing and restriking for every job. I do suggest a staic anlaysis that used in the Canadian Foundation Manual (an excellent resource, even for those of us on the other side of the border). Significant set up does not occur in all soils, and if it does, it only increses capacity over time., which could be several minutes, a few days or weeks depending on soil conditions. Relaxation, on the other hand is the diminishment of capacity over time, which is not a very common problem and can occur for a varitey of reasons, generally related to the local conditions. Thus in these areas it is important to undertand what causes the relaxation. This can also be caused by changes in effective stresses due to construction or use of the property and should be accounted for in design.
Testing should be appropriate to the scope and risk involved in the work. Load testing, PDA monitering and restrikes may be prudent on some projects. However on many jobs in defined soil conditions with known properties, and relatively light loads, which constitute a large portion of pile work, PDA monitering, wave equation analysis or a good static analysis, are often sufficent for a successful project. Note I do not reccomend the use of dynamic formulas or driving equations for design. For more information on pile driving, go the Pile Driving Contractors Association website www.piledrivers.org

If you are going to use a driving formula for estimating capacity, the Gates formula is preferred over the other dynamic formula because it has better correlation with static load test results. The FHWA in the USA recommends using a dafety factor of 3.5 when using the Modified Gates formula.  More accurate results can be obtained using either Wave Equation Analysis (FS=2.5) or PDA testing (FS=2.25).  So which one you use will depend on how many piles you have to drive and whether the use of a lower factor of safety will result in enough economy to justify the cost of the software or PDA testing.

My work is with the Ohio DOT and we use PDA testing on every structure with driven piles. We use a safety factor of 2.0 because of our extensive history with PDA testing.

This may be the "belt and suspenders" approach, but...

First, even though my family business put the ENR formula in its literature for many years, I'm inclined to agree with Panars that the Gates formula is more accurate.  That being said, my preferred use for this or any other dynamic formula is to make an initial hammer selection to then be refined by the wave equation analysis.

Once you've done that, you should run some kind of static analysis to get an idea of the resistance of the pile.  That information (taking into consideration set up, plugging and other phenomena) can then be entered into a wave equation analysis.  More than the estimated static resistance of the pile should be entered to develop a "bearing graph" or range of blow counts and resistances, which becomes the "equation" you're looking for if you don't use a PDA.

The PDA, when operated and interpreted by knowledgeable personnel, is obviously the next step up, if the economics of the job call for it.  For very large projects a static load and/or Statnamic test can be added.

As far as expense is concerned, if you can use the DOS wave equation program WEAP87, it and the documentation that goes with it can be found at

http://www.vulcanhammer.info/drivability/weap-spile.php

That page also links to my collection of driven pile books for download, including the 1997 FHWA manual on the subject.

http://www.vulcanhammer.net
http://www.vulcanhammer.info