Foundation Engineering – Plate load test extrapolation on sand A 30 cm × 30 cm test plate on sand settles 10 mm at a given pressure. Estimate the settlement of a 150 cm × 200 cm footing on the same sand under the <em>same</em> pressure.

Introduction / Context:
For cohesionless soils (sands), immediate settlement under a given contact pressure increases approximately in proportion to the foundation width. Hence, settlements from plate load tests can be scaled to predict footing settlements at the same pressure using size factors. This problem tests that proportional reasoning.

Given Data / Assumptions:

• Soil: sand deposit (cohesionless), comparable density and stress history.
• Same net contact pressure for plate and footing.
• Plate size: 0.3 m × 0.3 m; measured settlement s_p = 10 mm.
• Footing size: 1.5 m × 2.0 m; use least dimension B_f = 1.5 m for scaling.

Concept / Approach:

Empirically, for sands the settlement scales roughly with foundation width: s_f ≈ s_p * (B_f / B_p), where B is the least plan dimension. This reflects the larger influence zone and stress bulbs beneath wider foundations at the same pressure.

Step-by-Step Solution:

Verification / Alternative check:

This matches commonly used correlations for granular soils; more refined methods may include depth factors and influence coefficients yet still give values close to the proportional estimate for level ground and moderate embedment.

Why Other Options Are Wrong:

2.0 and 3.02 mm imply smaller settlement for a much larger footing, which contradicts cohesionless soil behavior. 27.8 mm underestimates scaling. 12.5 mm is arbitrary without basis.

Common Pitfalls:

Applying clay (compressibility) correlations to sands, using average dimension instead of least dimension, or changing pressure inadvertently.

Final Answer:

50.0 mm