Explanation:
The ratio of the plasticity index (PI) to the flow index (FI) of soil is called the toughness index (TI). It is a measure of the relative strength and toughness of the soil.

Plasticity Index (PI):
The plasticity index (PI) is a measure of the plasticity or the ability of soil to change its shape without cracking or breaking. It is determined by subtracting the liquid limit (LL) from the plastic limit (PL). The PI indicates the range of water content within which the soil behaves as a plastic material.

Flow Index (FI):
The flow index (FI) is a measure of the ability of soil to flow under pressure. It is determined by conducting a flow test on a soil sample using a flow cone. The flow index indicates the ease with which the soil can be compacted and the degree of compaction that can be achieved.

Toughness Index (TI):
The toughness index (TI) is the ratio of the plasticity index (PI) to the flow index (FI) of soil. It is calculated by dividing the PI by the FI.

Interpretation of the Toughness Index:
The toughness index provides information about the strength and toughness of the soil. A higher TI indicates that the soil has a greater ability to withstand deformation and flow under pressure. On the other hand, a lower TI indicates that the soil is more susceptible to cracking or breaking under pressure.

- A high TI suggests that the soil has a higher strength and is more resistant to deformation.
- A low TI suggests that the soil has a lower strength and is more prone to deformation.

Therefore, the toughness index (TI) is a useful parameter in assessing the engineering properties of soil and its suitability for various construction applications. It helps in understanding the behavior of the soil under different loading conditions and in making informed decisions regarding its use in construction projects.