What formula is used to obtain the value of PI?

The formula to obtain the value of PI, or Plasticity Index, is calculated using the difference between the Liquid Limit and the Plastic Limit of a soil sample. The Plasticity Index is a crucial parameter in geotechnical engineering as it provides insight into the plasticity characteristics of soil, which influences its behavior under various conditions.

The Liquid Limit represents the water content at which the soil changes from a plastic state to a liquid state. In contrast, the Plastic Limit is the water content at which the soil changes from a semi-solid state to a plastic state. By subtracting the Plastic Limit from the Liquid Limit, you determine the range of moisture content over which the soil behaves plastically. A higher Plasticity Index indicates more plastic behavior, which can affect the soil’s engineering properties, such as strength, compressibility, and overall stability.

The other options do not represent valid calculations for the Plasticity Index and would not yield useful or relevant geotechnical data. For example, the sum of Liquid Limit and Plastic Limit does not reflect the soil’s plastic behavior, and neither do the combinations involving the Shrinkage Limit or Moisture Content with Maximum Dry Density. These parameters serve different purposes in soil characterization and analysis.