In some cases, shallow foundations need to be constructed on top of a slope. Meyerhof developed a theoretical relation for the ultimate bearing capacity for continuous foundations as follows:
Simplifications are made for the case of purely granular soils (c=0) and purely
cohesive soils (f=0).
The factor Ncq for purely cohesive soils is a function of the ratio of Df/B and the stability number Ns where Ns=gH/c.
The factor Ngq for purely granular soils is a function of the ratio of Df/B and f.
Values of Ncq and Ngq as functions of Ns f, and Df/B can be derived from graphs found in "Principles of Foundation Engineering", B. M. Das, Ch. 3.