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Gates Dynamic Formula

Gates Dynamic Formula

I am looking for the Gates Dynamic Formula.  A google search only found references to it, and none of my books have it.  If someone could provide this I would greatly appreciate it.

RE: Gates Dynamic Formula

Reference: Design and Construction of Driven Pile Foundations, Workshop Manual - Volume II, Section 16.3, Page 16-6, NHI Course Nos. 13221 and 13222, Publication No. FHWA HI 97-014, Revised November 1998

Gates Formula
Ru = [7 x (Er)^0.5 x log(10Nb)] - 550

Ru = Ultimate pile capacity (kN)

Er = Manufacturer's rated hammer energy (Joules) at the field observed ram stroke

log(10Nb) = logarithm to base 10 of the quantity 10 multiplied by Nb

Nb = number of hammer blows per 25mm at final penetration

The manual recommends using a safety factor of FS = 3.5 when using the Gates formula.

Bowles' Foundation Analysis and Design, 1968, gives the Gates formula as:

P = (1/7) x (kE)^0.5 x (1-log(s))

P = safe load capacity, tons (FS = 3)

E = gross hammer energy, ft-lbs

k = 0.75 for drop hammers or 0.85 for all other hammers

s = set per blow for last 6 inches of penetration or for at least 20 blows (refusal)

RE: Gates Dynamic Formula

I don't have the URLs at hand - but open the Ohio and/or Washington DOT Geotechnical Design Manuals and you will find it there (can't remember which one off hand).  Gates' formula has been modified several times by various researchers - the most famous is the one by Olson and Flaate (1967 or so - ASCE GeoJournal with a companion paper several years later) where he modified a number of formulas based on quite a number of pile load tests (but this, again, has been modified in the DOT manuals I alluded to earlier). See for a thorough review of many different studies of Dynamic Pile Capacity (pag 66 to 68 explains Olson and Flaate's work) See also:   but I cannot actually access the article - perhaps you can. You can see the original Gates formula in Bowles - Ed 5 Table 17-1.  Also in .    
  The above should get you started. (I googled " Flaate Dynamic Formula Piles "

RE: Gates Dynamic Formula

Gates Formula is also listed in the AASHTO Bridge Design manual in 10.5 or 10.7.

So there is this drunk stumbling aound this lamp post at a city street corner one night. A cop walks up to him and says "What are ya do'in Chalie?" " I lost my wallet" he replies. So the cop helps him look for it. After a few minutes, the cop says "Where do you think you lost it?" To which the drunk replies "Outside of Jimmies Bar, about halfway down the block." "Then why are you looking here?" asks the cop. "Because the light is better here."

This is kind of how I feel about dynamic formulas. They are fast easy to use do not require a lot of input data and have an equal chance of being right or wrong. In this day and age, I would strongly advocate for wave equation, supported by a resonable static anaysis. It is much more accurate, and really does not take a long time to prepare.

RE: Gates Dynamic Formula

FHWA's Design and Construction of Driven Pile Foundations can be found at

They have worked examples to go with it.

And I entirely agree with DRC1's assessment of dynamic formulae.  The wave equation programs can be found in the same place.

RE: Gates Dynamic Formula

Thanks for the information.  The reason I wanted this was to double check on someone else's work for which I was going to be doing some piling observations (he refered to the Gates Dynamic Formula).  Just looking at the numbers something seemed "odd".  Lacking experience, I wanted to check it out for myself.  As it turns out my college text did have the formula.  I was surprised by the variations available for this formula.

The numbers worked out as they given, so all should be good.

DRC1, I like your observation of dynamic formulas.  Again, thanks for the help and input.   

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