Wave Equation Analysis 1

Yes...or you could use older standards such as the ENR formula, Janbu, or similar pile driving criteria.

The wave equation predicts the ultimate capacity of a pile for a given hammer and cushion system in an assumed soil profile AT THE END OF INITAL DRIVE. As with any analytical tool it is not perfect and should be verified with a test pile program. It does make a more reliable perdiction than Engineering News Formula. It also allows you to acess fuel settings and energy rating for driving with a diesel hammer. If the piles are light say 40 tons or less and the consequenses of settlement are not great, Then you may be able to design piles based on Wave equation. However, for most applications, a test pile program should be used that incoperates at least PDA and prefferably CAPWAP and static load testing.
The wave equation will not tell you actual energy transfer.
The wave equation will not predict relaxation or set up
Monotube and taper piles require residual stress analysis.

Statistically, (Wave Equation analysis of piles) WEAP performs better than the ENR formula at estimating the capacity of a driven pile.

Statistically, the ratio of predicted static capacity to actual capacity (as determined by a static load test and using the Davisson offset criteria) is about the same. However, the WEAP approach has a smaller standard deviation and COV.

The FHWA modified Gates formula has statistically much better results than either WEAP or the ENR formula in terms of ratio of predicted capacity, std deviation and COV.

See NCHRP Report 507 and FHWA NHI-05-052 for more information. Discussion of dynamic methods for estimating pile capacity is in FHWA NHI-05-042/-043. The first two publications should be available for download from the internet. The last two publications are available on CD from DFI (
There are much better formulas than the ENR formula. The ENR formula should not be used. Period.

As DRC1 says, verify/calibrate with at least one actual test pile before you finalize the design if the number of piles and consequences of excessive pile movement warrant.

J