"Formulas for Stress and Strain" shows a load case for square or circular load areas on a semi-infinite body. However, they don't show a load distribution, just the maximum stress in the semi-infinite body. Anyway, the reference for those is Timoshenko & Goodier's "Theory of Elasticity". Don't be surprised if getting stresses down in the body requires evaluating series expressions.
"Structural Engineering Handbook" mentions a 30 degree distribution, then refers to Newmark's influence chart, based on Boussinesq's equation (which is presumably what is in Timoshenko's work above).