Shallow Foundation Bearing Capacity (Vesic)
The gross ultimate and allowable bearing pressure of a shallow footing from the soil's own strength: qu = c x Nc + q x Nq + 0.5 x gamma x B x Ngamma with the Vesic bearing-capacity factors from the friction angle, De Beer / Vesic shape factors for square and circular footings, and the customary factor of safety of 3. A 6 ft strip footing 4 ft deep on a phi = 32 medium-dense sand carries 22 ksf ultimate, 7.3 ksf allowable -- the number the footing-area tile has always needed handed to it; a phi = 0 stiff clay pins the Prandtl Nc = 5.14 branch. General shear on a level, concentric footing with deep groundwater; settlement usually governs on sand and is separate. A design aid, not a substitute for a geotechnical engineer's report.
Formula and source
qu = c Nc sc + q Nq sq + 0.5 gamma B Ngamma sgamma; Nq = e^(pi tan phi) x tan^2(45 + phi/2); Nc = (Nq - 1) x cot phi (5.14 at phi = 0); Ngamma = 2 x (Nq + 1) x tan phi; q_all = qu / FS.
The general bearing-capacity equation with the Vesic (1973) factors and De Beer / Vesic shape factors, as compiled in Das, Principles of Foundation Engineering, and FHWA-NHI-16-009 (GEC 6, Shallow Foundations), by name.
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