The correct answer is: C. both compressibility and permeability.
The coefficient of consolidation is a measure of how quickly a soil consolidates under a load. It is affected by both the compressibility of the soil and the permeability of the soil.
Compressibility is a measure of how much a soil will deform under a load. The more compressible a soil is, the more it will deform under a load. This means that the coefficient of consolidation will be higher for a more compressible soil.
Permeability is a measure of how easily water can flow through a soil. The more permeable a soil is, the easier it is for water to flow through the soil. This means that the coefficient of consolidation will be lower for a more permeable soil.
The coefficient of consolidation is an important parameter in geotechnical engineering. It is used to calculate the settlement of foundations and other structures.