Bearing Capacity of soil

The load or pressure developed under the foundation without introducing any damaging movement in the foundation and in the supporting soil is known as the bearing capacity of the soil, or in other words, the load which the soil under the foundation can bear without getting failed is known as the bearing capacity of the soil.
Ultimate Bearing capacity:
As the name suggests, it is the minimum load which can cause the shear failure of the supporting soil.
Net ultimate bearing capacity(qnf)
If we subtract the weight of the soil replaced by the footing, from the qf, we get net ultimate bearing capacity. It is the minimum net pressure causing shear failure,
numerically, qnf = qf- YD
here, Y= unit weight of soil
             D= Depth of foundation.

Safe Bearing Capacity(qs):
Simply, maximum pressure which the soil can carry without risk of shear failure is called safe bearing capacity.                   or    qs= qnf/F + YD.
where, F =Factor of Safety with which net ultimate bearing strength is to be divided.
Allowable Bearing Capacity:
It is the pressure which is considered safe both with respect to shear failure and settlement of the footing.

Rankine's Minimum depth of foundation:
You can use the formula given to find out the minimum depth of the footin.
According to theories given by Rankine,
 Depth, D = q/Y [( 1-  sin@' )/ (1+sin@')]^2
where, q= intensity of loading (N/mm2)
@' = effective angle of shearing
Y= density of the soil solids.

(Ref:GATE 2013, GK Publishers)