The approximate ultimate bearing capacity under a long footing at the surface of a soil is given by Prandtl’s equation as

q_u=(c/tan f) +1/2g_drybOK_p[K_pe^{ptan f}-1]

where
q_u = ultimate bearing capacity of soil, lb/ft² (kg / m²)
c = cohesion, lb/ft² (kg / m²)
f = angle of internal friction, degree
g_dry = unit weight of dry soil, lb/ft³ (kg / m³)
b = width of footing, ft (m)
d = depth of footing below surface, ft (m)
K_p = coefficient of passive pressure
= [ tan ( 45 + f / 2 ) ]²
e = 2.718

For footings below the surface, the ultimate bearing capacity of the soil may be modified by the factor 1 + Cd / b. The coefficient C is about 2 for cohesionless soils and about 0.3 for cohesive soils. The increase in bearing capacity with depth for cohesive soils is often neglected.