Terzaghi Bearing Capacity
Ultimate and allowable bearing capacity of shallow foundations on c-φ soils. Strip, square, and circular footings, with shape factors. Per Terzaghi (1943) with Vesić bearing-capacity factor formulas.
Defaults: 5-ft square footing, 3-ft embedment, c = 500 psf, φ = 30°, γ = 120 pcf, FS = 3 — typical sandy clay residential foundation.
When Terzaghi applies
The Terzaghi bearing-capacity equation is for general shear failure of a shallow foundation with Df/B ≤ 1. For deeper foundations, use Meyerhof or Hansen with depth factors. For local-shear or punching failure (loose sand, soft clay), reduce φ to φ' = arctan(0.67 tan φ) and reduce c to 0.67c. The full Hansen and Vesić methods include depth, shape, inclination, ground, and base factors — this calculator implements only shape factors (the most common manual case).
Shape factors used here
- Strip: sc = sq = sγ = 1.0
- Square: sc = 1.3, sq = 1.0, sγ = 0.8 (Terzaghi)
- Circular: sc = 1.3, sq = 1.0, sγ = 0.6 (Terzaghi)
Modern Hansen/Vesić shape factors depend on B/L and φ:
sc = 1 + (Nq/Nc)(B/L); sq = 1 + (B/L) tan φ; sγ = 1 − 0.4(B/L). For square or circular, B/L = 1. Use these for tighter estimates.
φ = 0 (clay) special case
For undrained analysis of saturated clay (φ = 0): Nc = 5.14, Nq = 1.0, Nγ = 0. The equation simplifies to qult = 5.14 cu sc + γ Df. For square footing on clay: qult ≈ 6.2 cu + γ Df. This is the classic short-term (undrained) bearing capacity check.
Factor of safety
Standard FS = 3 for both static dead load and live load. Some agencies require FS = 2.5 for total stress with high reliability soil data, or FS = 4 for poorly-defined parameters. For seismic-only loads, FS as low as 2 may be allowed (lateral seismic event is short-duration).
Settlement, not bearing capacity, often controls
For most working stress designs, allowable bearing pressure is limited by tolerable settlement (typically 1 in / 25 mm total) rather than ultimate capacity. A clean sand might have qult > 20 ksf but be limited by settlement to 4 ksf. Always check both. For foundations on stiff clay, qult/FS often governs.
Reference: Terzaghi, K. (1943). Theoretical Soil Mechanics. Wiley. Vesić, A.S. (1973). "Analysis of Ultimate Loads of Shallow Foundations." JSMFD ASCE, 99(SM1). Bowles, J.E. (1996). Foundation Analysis and Design, 5th ed., McGraw-Hill.