for sloping ground, I'd use a chart solution. I think the NAVAC DM 7.1 or 7.2 has such chart solutions for active or passive earth pressure. To obtain the at-rest earth pressure, that's a bit of a different question. There is no chart solution, so we have to use, "Common sense!" In pure Rankine conditions, the coefficient of at-rest earth pressure is usually 1.5 times the coefficient of active earth pressure (i.e., (tan^2(45-phi/2))/(1-sin phi)=1.5.
So, take the active earth pressure from the chart solution for sloping ground and multiply it by 1.5.
Now, how does that help? You see, under lateral loading, you will mobilize much more strength that suggested by at-rest earth pressure. Firstly, it's a pile, so plane-strain conditons do not apply. To account for arching effects, we use a term called C-sub-p, which is approximated by phi/10. To consider lateral capacity, we'd also consider passive pressure, which is also derived from chart solution for sloping ground.
Next topic should then be, "What are the deflections?" For that you'd need to develop your p-y curve, based on some sense of subgrade modulus.
f-d
ípapß gordo ainÆt no madre flaca!