Please see FAQ731-376 for great suggestions on how to make the best use of Eng-Tips Fora. See faq158-922 for recommendations regarding the question, "How Do You Evaluate Fill Settlement Beneath Structures?"
"Foundation Engineering for difficult subsoil conditions" 2nd ed 1983 by Leonardo Zeevaert would give you great start. It is very thorough book. You can try to search for it at abebooks.com
Piles and pile groups exhibit nonlinear load-deflection behavior, under both axial and lateral loading. Unless you can closely control either the loads or the movements, there will be no "stiffness matrix" or constant stiffness.
In any event, the stiffness will be a function of the load or deflection, and will be "constant" over only a small range of loads. Don't let elastic solutions fool you - try varying the stiffness by factors of 2 or 3 to evaluate the effects on your structural stresses. And then carefully monitor the structural settlements or movements during construction to check the validity of your assumptions.
I like Zeevaert's book - trying to get a copy. But, for your need, I would strongly suggest that you get a copy of Poulos and Davis' Design of Pile Foundations (1980). They are big into stiffness factors and the like. Also, the book is pretty good in a practical sense as well. Then, there is always Tomlinson's book. Since you are doing a bridge foundation, you must also check out AASHTO's Bridge Specifications.
If your pile group is has no battered piles, you may want to look into a paper by Prof. Mark Randolph, referenced in the Canadian Geotechnical Manual. Again as previously mentioned there is no real stiffness matrix for computer analysis in this area that will reflect actual behaviour.
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