Foundation Bearing Capacity Lab

Shallow Footing

SAFE

Footing width B 1.5 m

Soil friction angle φ 28°

Soil cohesion c 5 kPa

Applied load P 400 kN/m

Ultimate q_u

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Allowable q_a (FS=3)

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Applied pressure

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Factor of safety

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How it works

A shallow strip footing transfers its load to the soil beneath it. The soil fails not by crushing but by shearing along a wedge that pushes outward and upward — Terzaghi's general shear-failure mechanism. The ultimate bearing capacity superposes three independent contributions: the soil's own cohesion, the surcharge (weight of soil beside the footing) and the self-weight of the failing wedge itself.

q_u = c·N_c + q·N_q + 0.5·γ·B·N_γ
N_q = e^(π·tanφ)·tan²(45°+φ/2)
N_c = (N_q−1)·cotφ   (→5.14 as φ→0)
N_γ = (N_q−1)·tan(1.4φ)
q = γ·D   (γ=18 kN/m³, D=1.2 m fixed)

Footing width B — a wider footing spreads load over more soil, raising q_u through the N_γ term, but also raises the total applied load for a given pressure.
Friction angle φ — denser, more granular soils interlock more and resist shear far more strongly; N_q and N_γ both grow exponentially with φ.
Cohesion c — clay-like stickiness that adds strength independent of confining pressure, dominant when φ is low.
Applied load P — the column load carried per metre of footing length; pressure = P / B. When it exceeds q_u the wedge shears and the footing punches into the ground.

Engineers rarely design to q_u itself — a factor of safety (here 3) sets the allowable pressure q_a = q_u/3, keeping working loads well inside the elastic range and limiting settlement, not just preventing collapse.

Footing Safe soil Failure wedge

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