The load on a square footing 2 m × 2 m resting on a deep deposit of clay is 600 kN. If the unconfined compressive strength of clay is 100 kN/m², the failure occurs at 20% of strain for Terzaghi’s influence factor It = 0·95, and Poisson’s ratio of soil ν = 0·5, the average immediate settlement will be nearly
- A34 cm
- B43 cmCorrect
- C52 cm
- D61 cm
Solution
Concept
Immediate (elastic) settlement of a footing
Formula
ρi = q B (1 − ν²) It / E
Step-by-step solution
1. q = 600 / (2 × 2) = 150 kN/m². 2. E = qu / strain at failure = 100 / 0.20 = 500 kN/m². 3. ρi = 150 × 2 × (1 − 0.25) × 0.95 / 500 = 0.4275 m ≈ 43 cm.
Explanation
The immediate settlement is computed from the theory of elasticity using the contact pressure, the width of the footing, Poisson's ratio, the influence factor and the modulus of the clay (here the secant modulus from the unconfined compression test).
Why the other options are wrong
34, 52 and 61 cm do not follow from the formula.
Shortcut
ρ = qB(1 − ν²)I/E, E = qu/ε.
Common mistake
Using E = qu/2ε.
Correct answer: B) 43 cm