The correct answer is: A. plasticity index to consistency index.
The plasticity index is a measure of the range of water contents over which a soil will remain plastic. The consistency index is a measure of the resistance of a soil to deformation. The toughness index is a measure of the ability of a soil to withstand deformation without breaking.
The plasticity index is calculated as the difference between the liquid limit and the plastic limit. The liquid limit is the water content at which a soil will flow under a standard shear stress. The plastic limit is the water content at which a soil will just crumble when rolled into a thread 1/8 inch in diameter.
The consistency index is calculated as the natural logarithm of the ratio of the liquid limit to the plastic limit.
The toughness index is calculated as the ratio of the plasticity index to the consistency index.
A soil with a high plasticity index will be more plastic than a soil with a low plasticity index. A soil with a high consistency index will be more resistant to deformation than a soil with a low consistency index. A soil with a high toughness index will be more able to withstand deformation without breaking than a soil with a low toughness index.
The toughness index is an important parameter in the design of earthworks and foundations. It is used to assess the risk of soil failure due to deformation.