In soils, the permeant or pore fluid is mostly water whose variation in property is generally very less. Permeability of all soils is strongly influenced by the density of packing of the soil particles, which can be represented by void ratio (e) or porosity (n).
In sands, permeability can be empirically related to the square of some representative grain size from its grain-size distribution. For filter sands, Allen Hazen in 1911 found that k » 100 (D10)2 cm/s where D10= effective grain size in cm.
Different relationships have been attempted relating void ratio and permeability, such as k µ e3/(1+e), and k µ e2. They have been obtained from the Kozeny-Carman equation for laminar flow in saturated soils.
where ko and kT are factors depending on the shape and tortuosity of the pores respectively, SS is the surface area of the solid particles per unit volume of solid material, and gw and h are unit weight and viscosity of the pore water. The equation can be reduced to a simpler form as
For Silts and Clays
For silts and clays, the Kozeny-Carman equation does not work well, and log k versus e plot has been found to indicate a linear relationship.
For clays, it is typically found that
where Ckis the permeability change index and ek is a reference void ratio.