In all this discussion, don't forget that CBR(in-situ) is often very different from CBR(laboratory) [due to different confinement conditions and the existence of a base at shallow depth in the laboratory mold]. It can also vary considerably due to different laboratory or on-site test...
A CBR of 100% involves an applied stress of 6.9MPa for 2.5mm penetration or 10.3MPa for 5mm penetration.
For a cohesive soil and a circular footing without embedment, Bearing Capacity theory states that applied stress = 1.3 c Nc where c is the undrained cohesion and Nc the cohesion bearing...