Stress Distribution by Load Dispersion – Average Stress Beneath a Footing A 2 m × 1 m footing applies a uniform contact pressure of 150 kN/m² to the soil surface. Assuming a load dispersion of 2 vertical to 1 horizontal in soil, what is the average vertical stress at a depth of 1.0 m beneath the footing?

Introduction / Context:
Approximate stress distribution beneath footings is sometimes estimated using a load-dispersion (bulb) method. A common assumption is a linear spread with a specified vertical:horizontal slope. This gives a quick estimate of average stress at depth for preliminary checks when rigorous elasticity solutions are not required.

Given Data / Assumptions:

• Footing size: 2 m × 1 m.
• Contact pressure at base: 150 kN/m² (uniform).
• Dispersion slope: 2 vertical : 1 horizontal (i.e., 0.5 m horizontal spread per metre depth on each side).
• Depth of interest: z = 1 m below the base.

Concept / Approach:

With 2V:1H dispersion, the plan dimensions of the “stress bulb” increase by z × 0.5 on each side. The total load remains constant with depth; the average stress equals total load divided by the enlarged area at depth.

Step-by-Step Solution:

Verification / Alternative check:

A more rigorous check with Boussinesq theory would produce a non-uniform stress field, but the average over an enlarged bulb area remains close to this estimation for preliminary design.

Why Other Options Are Wrong:

• 75, 80, 100 kN/m²: Do not follow from the assumed dispersion geometry and constant total load.

Common Pitfalls:

Using 1H:2V instead of 1V:2H; forgetting to spread on both sides; mistakenly changing the total applied load with depth.

Final Answer:

50 kN/m²