Bearing Capacity and Foundations
Walk a marker up the load-settlement curve to failure, then back to the safe load — where settlement, not strength, usually decides the answer.
Skip to the animationLoading a footing traces a load-settlement curve from elastic compression through local yielding to general shear failure — and design divides the ultimate capacity by about 3, though the settlement limit usually governs first.
The load-settlement curve
- 1At low load the ground compresses roughly in proportion, and unloading recovers most of it.
- 2Shear zones form beneath the footing edges, and the curve bends away from the elastic line.
- 3The zones join into a continuous slip surface reaching the ground surface.
- 4The footing punches down and the soil beside it heaves up — general shear failure.
In dense soil this is sudden general shear; in loose soil it is a gradual local or punching failure with no clear peak, which makes ultimate capacity a matter of definition rather than observation.
Terzaghi's three terms
| Term | Source | Dominates in |
|---|---|---|
| c·N_c | Soil cohesion | Saturated clay |
| q·N_q | Surcharge from soil beside the footing | Sand, where N_q rises exponentially with φ′ |
| ½γB·N_γ | Soil's own weight beneath the footing | Wide footings on granular soil |
The bearing capacity factors depend only on the friction angle. In clay the cohesion term carries almost everything; in sand it vanishes and depth becomes dominant — which is why burying a footing deeper helps enormously in sand and barely at all in clay.
Width cuts both ways
Width appears in the ½γBN_γ term, so a wider footing has greater capacity per unit area in sand. But width also increases the depth of soil stressed, so a wide raft on clay settles far more than a narrow footing at the same pressure. Capacity and settlement pull in opposite directions.
Factors of safety
Ultimate capacity is divided by about 3 — larger than in structural design, because soil properties are variable, the ground is never fully investigated, and the consequences are severe.
In practice the settlement limit, commonly 25 mm total and 20 mm differential, often governs first — so the foundation is sized by movement rather than by strength.
Piles
A pile carries load by shaft friction along its length and end bearing at its toe. The two mobilise at very different displacements: friction in a few millimetres, end bearing only after settlement of about 10% of the pile diameter.
So at working load a pile is usually carrying almost entirely on friction — which is why a friction pile works in deep soft clay with no hard stratum beneath it at all.
The numbers you will be asked for
- Terzaghi, strip footing
q_u = c·N_c + q·N_q + ½γB·N_γ
- Undrained clay
q_u = 5.14 c_u + q
- Net safe bearing capacity
q_ns = (q_u − q) / F, with F ≈ 3
- Pile capacity
Q_u = Q_shaft + Q_base = ΣA_s f_s + A_b q_b
- Typical settlement limit
25 mm total, 20 mm differential
Watch it work
Check yourself
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