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 Nc = 20, a surcharge q = 30 kPa with Nq = 10, and γ = 18 kN/m³ under a B = 2 m footing with Nγ = 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.