Soil Bearing Capacity and Spread Footing Design
A spread footing is the simplest and most economical shallow foundation type: a pad of reinforced concrete that distributes a concentrated column or wall load over a large enough soil area to keep contact pressures within the soil’s bearing capacity. The structural engineer sizes the footing for flexural and shear demands in the concrete; the geotechnical engineer establishes the allowable bearing pressure from soil investigations. Understanding both sides of the interface — the soil failure modes and the concrete demand — is essential for economical and reliable footing design.
Ultimate Bearing Capacity Theory
Terzaghi’s general bearing capacity equation (1943) describes the ultimate resistance of a soil beneath a footing of width B at depth Df below the surface:
qult = cNc + γDfNq + 0.5γBNγ
where c is the soil cohesion, γ is the soil unit weight, and Nc, Nq, Nγ are dimensionless bearing capacity factors that are functions of the internal friction angle φ. For a purely cohesive soil (saturated clay in undrained loading, φ = 0), Nc = 5.14, Nq = 1, Nγ = 0, so qult = 5.14su + γDf. For a cohesionless sand (c = 0), the bearing capacity depends entirely on the friction angle through Nq and Nγ, and grows significantly with footing depth Df and width B.
Meyerhof’s extension of Terzaghi adds shape factors (sc, sq, sγ) for non-strip footings, depth factors (dc, dq, dγ) for the beneficial effect of soil overburden above the footing base, and inclination factors for footings subject to eccentric or inclined loads. The full general bearing capacity equation used in AASHTO LRFD and FHWA practice is:
qult = cNcscdcic + γDfNqsqdqiq + 0.5γBNγsγdγiγ
The allowable bearing capacity qallow = qult / FS, where FS is typically 3.0 using ASD methods, or the factored resistance φqult under LRFD with φ = 0.50 for general shear failure.
Settlement Governs in Practice
For most spread footings on cohesionless soils, allowable bearing pressure is controlled by settlement rather than shear failure. A safety factor of 3.0 against shear failure typically corresponds to settlements of 25 mm (1 inch) or less for typical footing sizes — which is often within the tolerable range. But on loose sands or soft clays, bearing capacity is adequate at the geotechnical factor of safety while settlements are excessive.
| Soil type | Typical allowable bearing pressure | Settlement control or strength control? |
|---|---|---|
| Dense gravel | 6,000–12,000 psf | Strength (large safety factor) |
| Dense sand | 3,000–6,000 psf | Settlement (25 mm limit) |
| Stiff clay | 1,500–3,000 psf | Long-term consolidation settlement |
| Medium clay | 750–1,500 psf | Consolidation settlement critical |
| Soft clay / loose fill | Not recommended without treatment | Both inadequate |
Consolidation settlement in clay proceeds over months or years as excess pore pressure dissipates. The primary consolidation settlement Sc = [CcH/(1+e0)] log(σ′v0 + Δσ′)/σ′v0, where Cc is the compression index, H is the compressible layer thickness, and e0 is the initial void ratio. Differential settlement between adjacent footings is typically the more damaging condition: a uniform settlement of 25 mm across a frame causes no distress, while a differential settlement of 12 mm between adjacent columns creates significant frame moments and facade cracking.
Footing Proportioning: Concrete Design
Once the required plan area A = P / qallow is established from geotechnical data, the structural engineer sizes the footing concrete for two limit states:
- One-way (beam) shear: At a critical section located d from the column face, the upward soil pressure on the overhanging portion must be resisted by the concrete without shear reinforcement (stirrups are not typically used in footings). ACI 318 limits the one-way shear demand to φVc = φ(0.75λ√f′c)bd, which directly governs the required footing depth d for a given plan dimension.
- Two-way (punching) shear: At a critical perimeter d/2 from the column face, the footing must resist the net upward force acting on the area outside the perimeter. This check mirrors the punching shear check in flat slabs, except the pressure is upward soil pressure rather than downward applied load. The critical perimeter check almost always requires a deeper footing than the one-way check.
- Flexure: The footing bends as a cantilever from the column face. The critical section for flexure is at the column face, and the required bottom reinforcement in each direction is designed for the factored moment Mu = qu(L − c)2/8 per unit width, where c is the column dimension and L is the footing plan dimension.
The iterative nature of footing design — selecting a plan size from geotechnical capacity, then checking structural depth and reinforcement, then verifying punching shear requires a deeper footing which changes the self-weight which changes the net pressure — is best handled by a simple spreadsheet rather than manual iteration. For preliminary sizing, a rule of thumb that effective depth d ≈ (L − c) / 2 satisfies punching shear for most common column sizes and bearing pressures serves as a useful first-pass estimate before detailed checking.