Which of the following statement(s) is/are true regarding coefficient of curvature Cc? (i) Cc is a crucial soil mechanics parameter used to determine if a soil is well-graded (ii) A higher Cc (>3) infers that the soil is well-graded
- AOnly (i)Correct
- BOnly (ii)
- CBoth (i) and (ii)
- DNeither (i) nor (ii)
Solution
Concept
Particle size gradation criteria and coefficient of curvature
Formula
Cc = (D30)2 / (D60 × D10)
Step-by-step solution
1. Statement (i) is correct: Coefficient of curvature Cc = (D30)2 / (D60 × D10) evaluates the smooth gradation of particle sizes on a grain size distribution curve. 2. Statement (ii) is incorrect: A well-graded soil must have Cc strictly between 1 and 3 (1 ≤ Cc ≤ 3). 3. If Cc > 3 or Cc < 1, the soil is categorized as gap-graded or poorly graded. 4. Hence, only statement (i) is true. Answer: A
Explanation
The coefficient of curvature Cc = (D30)2 / (D60 × D10) is an essential index parameter used alongside the uniformity coefficient (Cu) to evaluate particle size distribution. For a soil to be classified as well-graded, Cc must fall strictly within the range of 1 to 3; a value greater than 3 indicates gap-graded or poorly graded soil.
Why the other options are wrong
B) Incorrect because statement (ii) violates standard soil classification criteria (IS 1498 / USCS). C) Incorrect because statement (ii) is false. D) Incorrect because statement (i) correctly identifies Cc as a key gradation metric.
Shortcut
Well-graded soil: 1 ≤ Cc ≤ 3. If Cc > 3, it is not well-graded.
Common mistake
Assuming higher Cc values indicate better gradation without recognizing the 1 to 3 acceptance boundary.
Correct answer: A) Only (i)