Stress Distribution in Soil MCQ with answer and solution

Concept

Boussinesq theory gives vertical stress at any point in soil due to a point load. From it we draw stress isobars, vertical pressure on a horizontal plane, and vertical pressure on a vertical line.

Formula

σ_z = (3Q / 2πz²) × [1 / (1 + (r/z)²)]^5/2

Step-by-step solution

1. Boussinesq gives vertical stress σ_z at depth z and radial distance r. 2. Fix z and vary r: we get vertical pressure on a horizontal plane. 3. Fix r and vary z: we get vertical pressure on a vertical line. 4. Join points of equal σ_z: we get a stress isobar (pressure bulb). 5. Option B matches. Answer is (B).

Explanation

Boussinesq theory gives vertical stress below a point load. If we keep depth fixed and change radial distance, we get the vertical pressure distribution on a horizontal plane. This is one of the three standard diagrams.

Why the other options are wrong

A: The correct term is stress isobar, not strain isobar. C: Standard diagrams use horizontal planes and vertical lines, not inclined planes. D: An oblique plane diagram is not a standard Boussinesq diagram.

Shortcut

Remember the three Boussinesq diagrams: stress isobar, horizontal plane, vertical line.

Common mistake

Choosing 'strain isobar' because it sounds like 'stress isobar'.