Understanding Sand Classification by IS Code

Soil classification is an essential part of geotechnical engineering. According to Indian Standards (IS), coarse-grained soils like sand and gravel are classified based on their particle size distribution characteristics, specifically using the coefficient of uniformity ($C_u$) and the coefficient of curvature ($C_c$). These coefficients are derived from the grain size distribution curve.

What are $C_u$ and $C_c$?

• Coefficient of Uniformity ($C_u$): This indicates the range of particle sizes present in a soil. It is calculated as the ratio of $D_{60}$ to $D_{10}$, where $D_{60}$ is the particle size for which 60% of the soil is finer, and $D_{10}$ is the particle size for which 10% of the soil is finer. A higher $C_u$ value indicates a wider range of particle sizes. Mathematically, it is expressed as:

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

• Coefficient of Curvature ($C_c$): This reflects the shape of the grain size distribution curve between the $D_{10}$ and $D_{60}$ sizes. It is calculated using $D_{10}$, $D_{30}$, and $D_{60}$, where $D_{30}$ is the particle size for which 30% of the soil is finer. A $C_c$ value between 1 and 3 indicates a smoothly graded curve. Mathematically, it is expressed as:

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

IS Criteria for Classifying Sand (S)

For sands, the classification into 'well-graded' (SW) or 'poorly-graded' (SP) often depends on $C_u$ and $C_c$, assuming the percentage of fines (silt and clay, passing the 75-micron sieve) is less than 5%.

• Well-graded Sand (SW): A sand is classified as well-graded if it meets the following two conditions simultaneously:
  • The coefficient of uniformity ($C_u$) is greater than or equal to 6 ($C_u \ge 6$).
  • The coefficient of curvature ($C_c$) is between 1 and 3, inclusive ($1 \le C_c \le 3$).
• Poorly-graded Sand (SP): A sand that does not meet the criteria for SW is classified as poorly-graded. This happens if $C_u < 6$ OR $C_c < 1$ OR $C_c > 3$.

Other classifications like Silty Sand (SM) or Clayey Sand (SC) depend on the percentage and plasticity of fines.

Applying the Given Values

In this problem, we are given the following values for a sand sample:

• Coefficient of uniformity ($C_u$) = 7.5
• Coefficient of curvature ($C_c$) = 2.5

Let's check the conditions for Well-graded Sand (SW):

• Is \(C_u \ge 6\)? Given \(C_u = 7.5\). Since \(7.5 \ge 6\), the first condition is met.
• Is \(1 \le C_c \le 3\)? Given \(C_c = 2.5\). Since \(1 \le 2.5 \le 3\), the second condition is also met.

Since both the conditions for well-graded sand (SW) are satisfied, the sand is classified as SW according to IS.

Comparing this with the options provided:

• GP (Poorly-graded Gravel) - Incorrect (It's sand, not gravel)
• SP (Poorly-graded Sand) - Incorrect (Conditions for SW are met)
• SW (Well-graded Sand) - Correct (Conditions \(C_u \ge 6\) and \(1 \le C_c \le 3\) are met)
• GW (Well-graded Gravel) - Incorrect (It's sand, not gravel)

Conclusion

Based on the given coefficient of uniformity (\(C_u = 7.5\)) and coefficient of curvature (\(C_c = 2.5\)), and applying the IS classification criteria for sands assuming low fines content, the sand is classified as Well-graded Sand (SW).