Index ranges: typical ratio e_max / e_min for silty sand For a silty sand, what is a typical order of magnitude for the ratio of maximum void ratio to minimum void ratio (e_max / e_min) used in relative density work?

Introduction / Context:
Relative density and the range between e_max and e_min are important for granular soils to quantify looseness or denseness. Silty sands, due to fines content, usually have a more limited spread in void ratio than very clean, uniformly graded sands or gravels.

Given Data / Assumptions:

• Silty sand with moderate fines (passing 0.075 mm).
• Typical laboratory determinations of e_max and e_min per standard methods.
• Order-of-magnitude estimation rather than a single universal value.

Concept / Approach:

Empirical ranges show many sands have e_max roughly 0.8–1.1 and e_min roughly 0.4–0.6, giving e_max/e_min commonly around 1.5–2.5. Fines tend to constrain rearrangement, limiting the spread compared with very clean uniform sands or gap-graded materials.

Step-by-Step Solution:

Verification / Alternative check:

Textbook tables for typical index ranges support ratios close to 2 for many silty sands.

Why Other Options Are Wrong:

Values 3–5 suggest a much wider void ratio range than is typical for silty sands and are more characteristic of unusual gradations or testing anomalies.

Common Pitfalls:

Assuming a single value applies to every deposit; ignoring fines plasticity, which can further narrow the range.

Final Answer:

2.0