There are emprical correlations published by Terzaghi (1955) for the lateral loading of piles. However, I have failed to find a good reference for empirical correlations for the coefficient of horizontal subgrade modulus of a 8 inch minus well graded rock fill. In my case the rock fill is used as a cellular fill (75 foot dimater cell) for a Bresting Dolphin in a maring structure. The coefficient of horizontal subgrade modulus is required by the structural designer for reinforcement design of the cell.
Can you provide me with direction to any new research or publications on this subject.
Since you choose to go down this analytical approach I suggest you should try to manupulate the p-y curves (pult=kh*y) given in the Msc thesis of Clark Shane from the North Carolina State University 2001 "Development of p-y curves for a well graded gravel". The document is readily available in the web. Since this values were obtained for piles you need to introduce wall effects.