The Arya/O'Neill/Pincus book solves the problem by assuming the foundation is totally rigid (relative to the softness of the soil). It then reduces the dynamic behaviour of the foundation to five uncoupled degrees of freedom (X,Y,Z,XX,YY). These are then trivial to solve as five separate SDOF problems.
Mfgalvez, if you are looking for pre-written software for the first part of this (the reduction of the problem to five uncoupled degrees of freedom, allowing for such things as depth of embedment), I am not aware of any. But, if I recall correctly, the book gives some references so you can check back to the original research for the formulae used. If it is the second part that you want a pre-written program for, almost any structural analysis program with a dynamic capability will do it for you (unless it falls over because the problem is over-trivial for it).
Two comments on the method. Firstly, Arya/O'Neill/Pincus do not spell out how you need to combine the motions of the five DOFs to come up with your estimate for the actual motion at any given point. This is very easy, but it still needs to be done. Secondly, the method assumes no coupling, ie the five DOFs are completely independent of each other. If you want to be thorough, you need to investigate possible coupling between X & YY, and between Y & XX. A method for this can be found between the two books:
» "Foundations for Machines: Analysis and Design", by S.Prakash and V.Puri, John Wiley & Sons, 1988, in its chapter 6; and
» "Foundation Analysis and Design", by J.E.Bowles, McGraw-Hill, 1977, in its section 20-8.
Disclaimer. I have a deep affection for the Arya/O'Neill/Pincus book because the very first spreadsheet I ever wrote was one implementing this method.
