Does anyone have ever heard about a driving formula that separately takes into account the end bearing resistance and the skin friction ? In other words, is there a driving formula where the ratio between end bearing and skin friction is explixitly used ?
There are hundreds of dynamic formulae around. The common thing for all of them is that they are fundamentally wrong and based on faulty assumptions, and, therefore, worthless. Of course, many in the field, such as piling foremen and job superintendents, are able to come up with a right answer using a dynamic formula. This is not because they use a good formula, but because they are intelligent and able to rationalize their experience. The formulae is incidental to their accomplishment even if they believe in it themselves.
Unless you are interested in the history of piling practice, why bother with the formulae? Get hold of a copy of a wave equation program. Even the out-of-date, but free, FHWA WEAP of the 1980's would do a better job for you than any formula. Better still, do yourself a favor and purchase a copy of GRL WEAP (www.pile.com). You may not come up with the right results---you will need some understanding of the pile driving process first, but at least you will be wrong in a scientifically correct way, which will make you able to learn and progress from the mistakes and frequent mis-chosen input as you go along. That is, if you are able to compare your analysis results to dynamic measurements.
Dynamic formulae must have been created with more lives than a dozen cats. We write Year 20001 and highway departments such as the Ministry of Transportation in Ontario and Caltrans in California, just to mention a few, include dynamic formulae in their contract specifications---Hiley and Gates, respectively. The Ontario office even supplies Hiley formulae in nomograms. It would be laughable were it not for the waste of tax payers money and the demonstrated lack of engineering sense shown in maintaining these obsolete analysis tools.
The theory behind the dynamic formulae makes it impossible to differentiate between shaft and toe resistance in the pile because it assumes the pile to be a rigid mass. This assumption of course is the first of many problems with the dynamic formulae.
Bengt mentioned the "free wave equation programs"; same is available at