Curvature coefficient, abbreviated as \(C_c\), also called coefficient of curvature, or coefficient of gradation, a dimensionless number, describes the shape of the gradation curve between the D10 and D60 points. Specifically, whether the curve is smoothly and progressively graded or whether it has a kink, gap, or uniform flat section.
Curvature Coefficient Formula |
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\( C_c \;=\; \dfrac{ D_{30}^2 }{ D_{60} \cdot D_{10} }\) (Curvature Coefficient) \( D_{30} \;=\; \sqrt{ C_c \cdot D_{60} \cdot D_{10} } \) \( D_{60} \;=\; \dfrac{ D_{30}^2 }{ C_c \cdot D_{10} }\) \( D_{10} \;=\; \dfrac{ D_{30}^2 }{ C_c \cdot D_{60} }\) |
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| Symbol | English | Metric |
| \( C_c \) = Curvature Coefficient | \(dimensionless\) | \(dimensionless\) |
| \( D_{30} \) = the sieve diameter (grain size) which there are 30% of particles go through. | \(in\) | \(mm\) |
| \( D_{60} \) = the sieve diameter (grain size) which there are 60% of particles go through. | \(in\) | \(mm\) |
| \( D_{10} \) = the sieve diameter (grain size) which there are 10% of particles go through. | \(in\) | \(mm\) |
Curvature Coefficient Interpretation
Cc between 1 and 3 - Indicates a smooth, well-graded distribution. Particle sizes are distributed in a continuous, evenly shaped curve with no gaps.
Cc < 1 or Cc > 3 - Indicates a poorly graded distribution. Either uniformly sized particles or a gap graded soil missing intermediate particle sizes.
Classification Thresholds and Source Standard
Engineering Significance
Compaction and Density - Well-graded soils (1 \(\le\) Cc \(\le\) 3, high Cu) pack more efficiently because smaller particles fill voids between larger ones, achieving higher maximum dry densities and better compaction characteristics. Desirable for structural fills, subgrades, and backfill.
Permeability and Filtration - Poorly graded/gap graded soils tend to have more uniform void spaces, often giving higher permeability (useful for drainage layers/filters) but reduced strength/stability compared to well-graded soils.
Shear Strength and Stability - Well graded granular soils generally provide better interlocking and higher shear strength, making them preferable for base courses, embankments, and structural fill.
Filter Design - Gap graded soils (Cc far outside 1–3) can be prone to internal erosion/piping because finer particles may migrate through voids left by missing intermediate sizes.
