Understanding Soil Grading and Coefficients

Soil grading refers to the distribution of particle sizes in a soil sample. It's a crucial characteristic that affects the soil's engineering properties like shear strength, permeability, and compressibility. Soils can be broadly classified as well-graded, poorly-graded, or gap-graded.

To quantify the particle size distribution obtained from a sieve analysis, two important coefficients are used: the Coefficient of Uniformity ($C_u$) and the Coefficient of Curvature ($C_c$).

Defining Coefficient of Uniformity and Coefficient of Curvature

These coefficients are calculated using specific particle sizes determined from the particle size distribution curve:

• $D_{10}$: The particle size for which 10% of the soil sample is finer by weight. This is also known as the effective size.
• $D_{30}$: The particle size for which 30% of the soil sample is finer by weight.
• $D_{60}$: The particle size for which 60% of the soil sample is finer by weight.

The formulas for the coefficients are:

• Coefficient of Uniformity ($C_u$):

\(C_u = \frac{D_{60}}{D_{10}}\)

• Coefficient of Curvature ($C_c$):

\(C_c = \frac{D_{30}^2}{D_{10} \times D_{60}}\)

Criteria for Well-Graded Soils

Well-graded soil contains a good distribution of particle sizes, from coarse to fine, resulting in a dense and stable structure. According to the Unified Soil Classification System (USCS), the criteria for well-graded gravel (GW) and well-graded sand (SW) are defined based on their $C_u$ and $C_c$ values.

As seen from the table, for both well-graded gravel and well-graded sand, the Coefficient of Curvature ($C_c$) must fall within the range of 1.0 to 3.0. The question asks for the coefficient of curvature for a "well graded soil," which generally refers to gravel or sand in the context of these grading coefficients.

Therefore, for a soil to be classified as well graded (specifically gravel or sand), its coefficient of uniformity must meet a minimum value ($>4$ for gravel, $>6$ for sand), AND its coefficient of curvature must be between 1.0 and 3.0, inclusive.

Conclusion on Coefficient of Curvature Range

Based on the standard soil classification criteria, the coefficient of curvature for a well-graded soil (gravel or sand) must be from 1.0 to 3.0.

Revision Table: Key Soil Grading Concepts

Additional Information on Soil Grading

Besides well-graded soils, other types of grading exist:

• Poorly-graded soil: Soil that consists mainly of particles of approximately the same size (uniform soil) or has a very narrow range of particle sizes. This typically results in low $C_u$ values and often $C_c$ values outside the 1-3 range.
• Gap-graded soil: Soil that contains particles of both coarse and fine sizes, but lacks particles in an intermediate size range. The particle size distribution curve will show a relatively flat section, and $C_c$ values might be outside the 1-3 range even if $C_u$ is high.

Well-graded soils are generally preferred for engineering purposes like road bases, foundations, and embankments because they can be compacted to achieve high densities and strength due to the interlocking of different-sized particles and the filling of voids by finer particles.