The general bearing capacity equation
qu = c′NcFcsFcdFci + qNqFqsFqdFqi + ½γB′NγFγsFγdFγi. The bearing capacity factors Nq and Nc come from Prandtl and Reissner. Nγ has several published forms: Vesic is the most common in textbooks, Meyerhof and Hansen are slightly lower. Shape factors follow De Beer, depth factors Hansen, and inclination factors Meyerhof. A factor of safety of 3 on qu is usual for gross allowable pressure.
Groundwater
Water above the founding level reduces the overburden q (submerged unit weight below the water table), and the Nγ term uses γ′ = γsat − γw. When the water table is between the base and a depth B below it, γ in the Nγ term is interpolated between γ′ and γ. Deeper water has no effect.
Eccentric and inclined loads
For an eccentric load the footing is replaced by an effective footing B′ = B − 2e (Meyerhof), loaded centrally. The capacity and the applied pressure both use the effective area A′ = B′L′. Keep e ≤ B/6 so that the whole base stays in contact. Inclined loads reduce all three terms through the inclination factors.
Worked example
A 2 × 3 m footing at 1.5 m depth, c′ = 10 kPa, φ′ = 30°, γ = 18 kN/m³, water table at 2.5 m, P = 1500 kN with eB = 0.1 m. Nq = 18.40, Nc = 30.14, Nγ = 22.40. B′ = 1.8 m, B′/L′ = 0.6, q = 27 kPa, and γ in the Nγ term = 14.53 kN/m³ (water 1.0 m below the base). The three terms are 506 + 814 + 223 = 1542 kPa, so qall = 514 kPa. The applied pressure is 1500/5.4 = 278 kPa – OK.
FAQ
Should I use the gross or net allowable pressure?
Compare the gross applied pressure (column load + footing + backfill over the base area) with the gross allowable, or the net applied pressure with the net allowable. Don't mix them.
What about clay under undrained loading?
Enter φ = 0 and c = cu. Then Nc = 5.14, Nq = 1, Nγ = 0, and qu = 5.14cu·Fcs·Fcd + q.