Toughness index, activity, air content

Toughness index ($I_t$)

The ratio of plasticity index to flow index:

$$I_t = \frac{I_p}{I_f}$$

It measures the shear strength of soil at the plastic limit. Typical values are 0 to 3; low values mean the soil is friable and has low toughness.

Coefficient of curvature ($C_c$)

A shape parameter of the grain size curve:

$$C_c = \frac{D_{30}^2}{D_{10} \times D_{60}}$$

A well-graded gravel or sand has $C_c$ between 1 and 3.

Activity of soil ($A$)

The ratio of the plasticity index to the percent of clay-size particles (< 2 micron):

$$A = \frac{I_p}{\%\ \text{clay fraction}}$$

$A < 0.75$ inactive (kaolinite), 0.75 - 1.25 normal (illite), $> 1.25$ active (montmorillonite). It indicates the swelling potential.

Air content ($a_c$)

The ratio of volume of air to total volume of the soil:

$$a_c = \frac{V_a}{V}$$

Also $a_c = n(1 - S)$, where $n$ is porosity and $S$ is the degree of saturation.