Question

The coefficient of uniformity in soil gradation is the ratio of

• A. \(D_{60}\) to \(D_{10}\).
• B. \(D_{10}\) to \(D_{60}\).
• C. \(D_{50}\) to \(D_{10}\).
• D. \(D_{10}\) to \(D_{50}\).

Hint:

Always remember: \(D_{60}\) is always greater than or equal to \(D_{10}\), so the coefficient of uniformity \(C_u \ge 1\).
Therefore, the ratio must place the larger value (\(D_{60}\)) in the numerator.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The coefficient of uniformity (\(C_u\)) is a key dimensionless parameter used in soil mechanics to evaluate the range of particle sizes in a soil sample.

Step 2: Key Formula or Approach:
The coefficient of uniformity is defined as:
\[ C_u = \frac{D_{60}}{D_{10}} \] where:
\(D_{60}\) = particle size such that 60 % of the soil particles by weight are finer than this size.
\(D_{10}\) = particle size such that 10 % of the soil particles by weight are finer than this size (effective size).

Step 3: Detailed Explanation:
Gradation curve parameters help classify soils as well-graded or poorly-graded.
The coefficient of uniformity represents the ratio of the diameter \(D_{60}\) to the effective size \(D_{10}\).
A high \(C_u\) value indicates a well-graded soil containing a wide range of particle sizes, whereas a low \(C_u\) (near 1) indicates a uniform, poorly-graded soil.

Step 4: Final Answer:
The correct option is 1, which corresponds to \(D_{60}\) to \(D_{10}\).