Grain-size index — in standard sieve/gradation terminology, the effective size of a soil (the size corresponding to 10% finer by weight) is denoted by:

Introduction / Context:
Effective size is a key descriptor from the particle-size distribution curve used to estimate permeability, filter criteria, and stability against piping in granular soils. It is extracted at a fixed cumulative percentage finer, making it a reproducible single-number index across tests.

Given Data / Assumptions:

• Gradation curve is plotted on semi-log paper (size on log scale, percent finer on linear scale).
• Percent finer values at D10, D30, D60 are available or readable.
• Sample is representative and oven-dried for sieve analysis.

Concept / Approach:

The effective size is defined as the particle diameter at 10% passing (by weight). By convention this is denoted D10. It is used directly in empirical equations like Hazen’s formula for hydraulic conductivity and in filter design rules where D15 or D10 of filter and base soils are compared.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check by reading D60 and D30 to compute Cu and Cc; the curve should be smooth without abrupt steps for natural soils.

Why Other Options Are Wrong:

D20, D30, D60, D50 are valid percentile sizes but do not define the effective size per convention.

Common Pitfalls:

Reading off linear scale for size; mislabeling axes; using wet sieve mass without proper drying and correction.

Final Answer:

D10