Bearing capacity is the soil’s side of the foundation bargain, and the classical estimate is the general Terzaghi-form equation qu = c·Nc + q·Nq + 0.5·γ·B·Nγ — one term each for cohesion, overburden beside the footing (q = γ·Df), and the soil’s self-weight under the footing width B. The three bearing-capacity factors all ride on the friction angle: Nq = e^(π·tanφ)·tan²(45 + φ/2), Nc = (Nq − 1)/tanφ, and Meyerhof’s Nγ = (Nq − 1)·tan(1.4φ); for an undrained clay at φ = 0 they collapse to Nc = 5.14, Nq = 1, Nγ = 0. Square and circular footings pick up the classical Terzaghi shape factors (1.3 on the cohesion term; 0.4 or 0.3 on the self-weight term).
A 2 m strip footing at Df = 1.5 m in soil with c = 20 kPa, φ = 30°, γ = 18 kN/m³ runs the whole chain: Nc = 30.14, Nq = 18.40, Nγ = 15.67 give term-by-term 602.8 + 496.8 + 282.0 = 1,381.6 kPa ultimate, and dividing by FS = 3 leaves a gross allowable of 460.6 kPa. Gross allowable includes the existing overburden; net allowable subtracts the surcharge first, (qu − q)/FS — the additional pressure available above the soil the excavation removed.
Where no geotechnical report exists, US prescriptive design falls back on IBC Table 1806.2: five broad material classes keyed to USCS symbols, each with a presumptive vertical bearing value — 2,000 psf for a silty sand (SM), 1,500 psf for a lean clay (CL) — deliberately conservative floors that a site investigation almost always improves on, and unavailable altogether for mud, organic soils, peat, and unprepared fill. The theory carries its own fine print too: concentric vertical load, level ground, no water table in the influence zone — submerged soils take a buoyant unit weight, and eccentric or inclined loading needs separate corrections.