Terzaghi Ultimate Bearing Capacity (Strip Footing)

Terzaghi's 1943 Theoretical Soil Mechanics broke the collapse load of a strip footing into three independent contributions and simply added them: cohesion holding the failure surface together, surcharge beside the footing resisting the heave, and the self-weight of the soil inside the failure wedge, which is the only term that knows how wide the footing is. Take c = 25 kPa with $N_c$ = 20, a surcharge q = 30 kPa with $N_q$ = 10, and γ = 18 kN/m³ under a B = 2 m footing with $N_\gamma$ = 8: $q_u$ = 500 + 300 + 144 = 944 kPa.

The traps are numerous and expensive. First, the N-factors are theory-specific: Terzaghi's, Meyerhof's, Hansen's and Vesic's tables differ by 20% or more, and you must take all three from one author. Second, this is the strip form; square, rectangular and circular footings need shape factors, and inclined or eccentric loads need more still. Third, $q_u$ is a gross ultimate pressure at collapse, typically three times what the footing will actually be allowed to carry, and on most real jobs settlement, not bearing failure, is what governs the footing size anyway. Fourth, if the water table rises into the failure zone, γ becomes γ′ and the third term nearly halves.