Module 5 · Lesson 5.1
Shape and depth
Two corrections it is safe to forget, and expensive to.
Why this matters
The bearing capacity equation describes an infinitely long strip footing. Almost nothing you design is one. The corrections are not decoration — for an ordinary square pad they are worth about a fifth of the capacity, and on a tight site that fifth is the difference between a pad and a piled solution.
By the end of this lesson you should be able to
- Say why a square footing is stronger in bearing than a strip
- Apply shape and depth factors and know their direction
- Judge when the extra capacity is worth claiming
A strip footing fails in plane strain: the failure mechanism is the same at every point along its length, and soil can only escape sideways. A square footing fails in three dimensions, and soil must be pushed out around the whole perimeter. That extra confinement is real extra resistance, and shape factors quantify it.
The factors do not all pull the same way. For a square footing at φ′ = 30°, the cohesion and surcharge terms gain — sc ≈ 1.61, sq ≈ 1.58 — while the self-weight term is reduced, sγ = 0.60.
That last one surprises people. The self-weight term depends on the volume of soil inside the mechanism, and a square mechanism encloses proportionally less soil than a strip of the same width.
Depth factors credit something the base equation throws away. The equation treats the soil above founding level as a surcharge — dead weight — and ignores the fact that it also has shear strength. The failure surface has to cut through that soil to reach the surface, and that costs energy.
The factors grow with D/B, so they matter for a basement raft and barely register for a strip footing 600 mm down. At D/B = 0.6, dq ≈ 1.17.
Worked example
What the corrections are worth
Given
- Square pad, B = L = 2.5 m, founded at D = 1.5 m
- Sand, φ′ = 30°, c′ = 0, γ = 19 kN/m³ throughout
- Water table well below the failure zone
- Vesic Nγ
Find
The gain from applying shape and depth factors
Check yourself
Why is the shape factor for the self-weight term, sγ, less than 1 for a square footing when the other two exceed 1?
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint