Bearing Capacity Factor Nc

$N_c$ is not an independent result but a consequence: Prandtl's plasticity solution ties the cohesion term to the surcharge term through $N_c = (N_q - 1)\cot\varphi$. With $N_q$ = 18.40 at φ = 30°, $N_c$ = 17.40 ÷ tan 30° = 30.14: again the tabulated value. At φ = 35°, $N_q$ = 33.30 gives $N_c$ = 46.12.

The interesting case is φ = 0, where cot φ blows up and the formula is useless, but the limit is finite and famous: $N_c$ → π + 2 = 5.14. That is the undrained bearing capacity of saturated clay, $q_u = 5.14\,c_u$ for a strip footing and about $6.2\,c_u$ for a square or circular one, and it is the single most-used number in shallow foundation design on clay. The trap is applying the φ = 0 analysis with a drained strength, or vice versa: undrained (total stress, $c_u$, φ = 0) governs immediately after construction, drained (effective stress, c′, φ′) governs decades later, and a clay foundation must be checked for both. Skempton's 1951 paper set out that two-case discipline and it has not been improved on.