We use couple of methods for designing posts, typically used as sign standards. I've set them up as MathCAD files.
The first (Embedment of Poles, Sheeting and Anchor Piles, M.A. Drucker, Civil Engineering, Dec 1934)
Max passive pressure at base:
K = Kp * GammaS * W / 1000, where Kp - Coef of Passive Soil Pressure, GammaS - weight of soil(pcf), W - width of embedded post(ft)
Y = ((K - H^2) - 2 * F)^2 / (K - H^3 - 6 * F * L), where H - height of post, F - horiz. force at top of pole, L - total length of post
Max Permissible Soil Pressure at Base; Pmax = K * H
Max Soil pressure at Base; Pbase = Y - Pmax
Point of max soil pressure at top; Ht = (K * H^2 - 2 * F) / Y; Ht = if (Pbase <= 0,0,Pbase)
Max soil pressure at top Ptop = K * (H - Ht); Ptop = if (PBase <= 0,0,Ptop)
The second method if from Civil Engineering Handbook by Urquhart, 1940
Pmax = K * H; where K and H are as above
Pbase = (12 * F * H)/(H^2 * W) + (6 * F)/(H * W); Pbase = if(Pbase <= 0,0,Pbase), where F, H, and W are as above
b = (Pbase * W * H^2) / (3 * (2 * F + Pbase * W * H))
Point of max soil pressure at top; a = H - b, Ht = H - (a / 2)
Max soil pressure at top; (a^2 * Pbase)/(4 * b * H)
For more significant structures, I use a set of Reese and Matlock tables that are excellent, albeit, old...