The coefficient of curvature for well graded soil lies between:
Try it first: pick an option, then read the explanation.
Detailed Explanation
The coefficient of curvature (Cc) is one of two key numeric grading parameters (alongside Cu, see Q23-24) used to numerically confirm whether a coarse-grained soil qualifies as well graded.
Why "1 to 3" Is Correct
For a soil to be classified as well graded (the W in GW or SW), its coefficient of curvature must lie between 1 and 3 (inclusive). This single Cc range applies identically to both well-graded gravel (GW) and well-graded sand (SW) — only the Cu threshold differs between the two (see Q7).
Why the Other Options Are Wrong
- 1 to 2: too narrow a range — this doesn't match the full 1-to-3 window the actual well-graded criterion allows.
- 1 to 5: too wide a range — this would incorrectly classify some poorly graded soils (Cc outside 1-3 but within 1-5) as well graded.
- 5 to 7: far outside the actual criterion entirely — the true well-graded Cc range starts at 1, not 5.
Key Point
1 ≤ Cc ≤ 3 is the single, universal well-graded curvature criterion for BOTH gravel and sand — unlike the Cu threshold, which differs by soil type (see Q7, Q23).
Key Concepts for Students
- This exact 1-to-3 range is used directly in Q7's SW classification example and referenced again in Q30's "none of the above" question.
- Cc measures the shape/smoothness of the grading curve, complementing Cu, which measures its overall width — both are needed together to fully characterize grading (see Q1's Going Deeper table).
- See Q25 for the exact formula used to calculate Cc: (D30)²/(D60 × D10).
- A Cc value outside 1-3, even with a Cu value that meets its threshold, is still enough on its own to disqualify a soil from being "well graded" — both conditions must hold simultaneously.
Going Deeper: Why Cc Needs Its Own Separate Criterion (Beyond Cu)
Cu alone (the ratio D60/D10) tells you how wide a soil's particle-size range is, but it says nothing about the curve's shape in between those two points — a soil could have a wide overall range (high Cu) while still having a gap or an unusual kink in the middle of its distribution.
The grain-size distribution curve plots % finer by weight (Y-axis) against particle size on a log scale (X-axis). D10, D30, and D60 are the particle sizes at which 10%, 30%, and 60% of the sample (by weight) is finer.
Cc, using the D30 midpoint value alongside D60 and D10, checks specifically whether the curve is smoothly and evenly distributed across that range, not just wide. A soil with a genuinely smooth, evenly-spread grading curve will have Cc land naturally between 1 and 3; a soil with an unusual shape (even one with a technically high Cu) can fail this criterion. This is why both Cu AND Cc must be checked together — passing only one of the two criteria is not sufficient to call a coarse-grained soil well graded (see Q7's full GW/SW criteria table).