Bearing Capacity Factor Nq
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Nq answers a precise question: how many times the surcharge beside a footing can the footing itself carry, on friction alone? Ludwig Prandtl solved the plastic wedge problem for metals in 1920 and Hans Reissner extended it to a surcharged surface in 1924, giving this closed form. At φ = 30° it evaluates to e^(π tan 30°) × tan²(60°) = 6.134 × 3.000 = 18.40, and at 35° to 33.30 — the numbers printed in Das's Table 3.3 and in every foundation code appendix.
The trap is which Nq. Terzaghi's own 1943 factor uses a different failure surface and gives 22.46 at 30°, over 20% higher; Meyerhof, Hansen and Vesic all adopted the Prandtl–Reissner value above, which is what modern practice and this page use. Mixing a Terzaghi Nq with a Vesic Nγ produces a bearing capacity that belongs to no theory at all. The second trap is the exponential: Nq roughly doubles for every 5° of friction angle, so a φ estimated 3° too high from an SPT correlation inflates capacity by 40%. That sensitivity is why site investigation is cheaper than optimism.
- = Surcharge bearing capacity factor
- = Angle of internal friction
- Surcharge bearing capacity factor — Bearing Capacity Factor Nc, Terzaghi Ultimate Bearing Capacity (Strip Footing)
- Angle of internal friction — Rankine Active Earth Pressure Coefficient, Rankine Passive Earth Pressure Coefficient