Pavement subgrade evaluation: if the pressure on a CBR specimen at 2.5 mm penetration is 3.5 N/mm^2, what is the California Bearing Ratio (CBR) of the soil?

Introduction / Context:
The California Bearing Ratio (CBR) test evaluates the supporting strength of subgrade soils. The result is expressed as a percentage of a standard load corresponding to a specified penetration (usually 2.5 mm or 5.0 mm).

Given Data / Assumptions:

• Measured pressure at 2.5 mm penetration: 3.5 N/mm^2.
• Standard pressure at 2.5 mm: 70 kg/cm^2 ≈ 6.9 N/mm^2 (accepted convention).
• CBR (%) = (Measured pressure / Standard pressure) * 100.

Concept / Approach:
Convert both values to consistent units (already in N/mm^2). The CBR is a simple ratio relative to the standard curve value for the same penetration depth, multiplied by 100.

Step-by-Step Solution:
CBR = (3.5 / 6.9) * 100.Compute ratio: ≈ 0.5072.Convert to percent: ≈ 50.7%, rounded ≈ 50% for typical reporting.

Verification / Alternative check:
Using the 5.0 mm standard pressure (≈ 10.3 N/mm^2) would give a different percentage; the question explicitly uses 2.5 mm, so 6.9 N/mm^2 is correct.

Why Other Options Are Wrong:

• 10% and 35% underestimate relative to 3.5 vs 6.9.
• 70% overestimates; it would require ≈ 4.83 N/mm^2 at 2.5 mm.

Common Pitfalls:

• Mixing the 2.5 mm and 5.0 mm standard loads.

Final Answer:
50%