Understanding Uniformity Coefficient of Soil

The uniformity coefficient is a measure used in geotechnical engineering to describe the distribution of particle sizes within a soil sample. It helps us understand how uniform or varied the particle sizes are in a soil.

Calculating the Uniformity Coefficient

The uniformity coefficient, commonly denoted by $C_u$, is calculated using a simple formula based on the results of a sieve analysis test. The formula is:

$$C_u = \frac{D_{60}}{D_{10}}$$

Where:

• $D_{60}$ is the particle diameter such that 60% of the soil sample (by weight) is finer than this size.
• $D_{10}$ is the particle diameter such that 10% of the soil sample (by weight) is finer than this size. $D_{10}$ is also known as the effective size.

Interpreting the Uniformity Coefficient ($C_u$)

The value of $C_u$ tells us about the range of particle sizes present in the soil. A larger value of $C_u$ indicates a wider range of particle sizes, meaning the soil is well-graded. A value of $C_u$ close to 1 indicates a narrow range of particle sizes, meaning the soil is uniform or poorly graded.

Why $D_{60}$ is Greater Than or Equal to $D_{10}$

By definition, $D_{60}$ is the size where 60% is finer, and $D_{10}$ is the size where 10% is finer. Since 60% is a larger percentage than 10%, the particle size corresponding to $D_{60}$ must be greater than or equal to the particle size corresponding to $D_{10}$. You need a larger sieve opening to let 60% of the particles pass through compared to the sieve opening that lets only 10% pass through.

Consider the percentages:

• Particles finer than $D_{10}$ account for 10% of the total weight.
• Particles finer than $D_{60}$ account for 60% of the total weight.

If you have a particle size distribution curve, $D_{60}$ will always be at a larger particle size value on the x-axis compared to $D_{10}$, assuming particle size is plotted on the x-axis and percent finer on the y-axis.

Conclusion on the Value of Uniformity Coefficient

Since $D_{60}$ is always greater than or equal to $D_{10}$ ($D_{60} \ge D_{10}$), and $D_{10}$ is a positive value (representing a physical size), the ratio $D_{60} / D_{10}$ must be equal to or greater than 1.

$$C_u = \frac{D_{60}}{D_{10}} \ge 1$$

A perfectly uniform soil, where all particles are the same size, would theoretically have $D_{60}$ very close to $D_{10}$, resulting in a $C_u$ value very close to 1. For any soil with a range of particle sizes, $D_{60}$ will be larger than $D_{10}$, leading to $C_u > 1$.

Therefore, the uniformity coefficient of a soil is always equal to or greater than 1.

Revision Table: Soil Uniformity Coefficient ($C_u$)

Additional Information on Soil Grading

Besides the uniformity coefficient ($C_u$), another coefficient called the coefficient of curvature ($C_c$) is also used to describe the shape of the particle size distribution curve. $C_c$ helps determine if a soil is well-graded or gap-graded.

The formula for the coefficient of curvature is:

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

Where $D_{30}$ is the particle diameter such that 30% of the soil sample (by weight) is finer than this size.

Criteria for well-graded soils typically involve both $C_u$ and $C_c$ values:

• For Gravels (G): $C_u \ge 4$ and $1 \le C_c \le 3$.
• For Sands (S): $C_u \ge 6$ and $1 \le C_c \le 3$.

If these criteria are not met, the soil is considered poorly graded (uniform or gap-graded).