What is the formula for the coefficient of uniformity (Cu)?

• A. Cu = D10 / D60
• B. Cu = D60 / D30
• C. Cu = D60 / D10
• D. Cu = D30 / D10

Answer: (C)

The coefficient of uniformity (Cu) is a critical measure in soil mechanics that helps determine the gradation or distribution of particle sizes in a soil sample. It quantifies the range of particle sizes and indicates how uniform or graded the soil is. The proper formula for calculating Cu is based on the effective particle sizes, specifically using D10 and D60.

D10 and D60 refer to the grain sizes at which 10% and 60% of the soil sample's total mass, respectively, is composed of particles smaller than these diameters. The ratio of D60 to D10 is significant because it highlights the spread of particle sizes—essentially showing how well- or poorly-graded the soil is. A higher coefficient of uniformity indicates a broader range of particle sizes, which is typically associated with better drainage properties and less susceptibility to consolidation.

Using this understanding, the correct choice is the formula Cu = D60 / D10, which accurately represents the definition of how uniform a soil sample is based on its particle size distribution. The other options fail to correctly represent the relationship that defines Cu and do not align with the accepted standard in soil mechanics.