If you are running the unconfined compression test, I'll go ahead and assume that you are dealing with a fine-grained (i.e., cohesive) soil. Therefore, let's discount any contribution from internal friction.
According to the Terzhagi equation, for phi=0 (as appropriate for soils without internal friction), Nc=5.7 so qult=cNc. For undrained analyses, c=Su (cohesion equals the undrained shear strength. Undrained shear strength is equal to one-half the unconfined compressive strength.
So, ultimate bearing pressure would be:
qult=5.7*qu/2 or qu*5.7/2 or 2.85*qu
If you consider a safety factor of 3 q-allowable is then equal to:
q-allow=0.95*unconfined compressive strength. Heck that's about like saying the allowable bearing pressure is equal to the unconfined compressive strength!!
