I have a method that was apparently published by someone named Boghrat in 1990. It accounts for the slope by neglecting some of the embedment. I would google Boghrat and try to get a hold of the reference. If you find that the reference is unavailabe, write back and I'll post the solution. Alternately, the AASHTO Guide Specification for the Structural Design of Sound Barriers has a method that involves the passive pressure coefficient.
Miecz, I couldn't find the method by Boghrat, but googling him led me to a paper published by P. McDonald - "Laterally Loaded Pile Capacity Re-visited" (Australia New Zealand Conference on Geomechanics). I haven't bought it yet, but it says it has a method of determining capacity adjacent to a slope. Looks worth the $33 cost. If you can post the method by Boghrat, I would appreciate it, but I already owe you big time because I was at a dead end until you replied. Thank you very much.
I searched for Boghrat and apparently there is someone in Mexico and/or Iran that has studied behavior of drilled shafts. I wasn't able to find anything with a date and title that looked promising. The method (see attached link) was submitted to me by a contractor with the reference. It looks reasonable to me. Please let me know what you find.
