# Void ratio

Void ratio, in materials science, is a dimensionless quantity related to porosity and defined as the ratio:

${\displaystyle e={\frac {V_{V}}{V_{S}}}={\frac {V_{V}}{V_{T}-V_{V}}}={\frac {\phi }{1-\phi }}}$

and

${\displaystyle \phi ={\frac {V_{V}}{V_{T}}}={\frac {V_{V}}{V_{S}+V_{V}}}={\frac {e}{1+e}}}$

where ${\displaystyle e}$ is void ratio, ${\displaystyle \phi }$ is porosity, VV is the volume of void-space (such as fluids), VS is the volume of solids, and VT is the total or bulk volume. This figure is relevant in composites, in mining (particular with regard to the properties of tailings), and in soil science. In geotechnical engineering, it is considered as one of the state variables of soils and represented by the symbol e.[1][2]

Note that in geotechnical engineering, the symbol ${\displaystyle \phi }$ usually represents the angle of shearing resistance, a shear strength (soil) parameter. Because of this, the equation is usually rewritten using ${\displaystyle n}$ for porosity:

${\displaystyle e={\frac {V_{V}}{V_{S}}}={\frac {V_{V}}{V_{T}-V_{V}}}={\frac {n}{1-n}}}$

and

${\displaystyle n={\frac {V_{V}}{V_{T}}}={\frac {V_{V}}{V_{S}+V_{V}}}={\frac {e}{1+e}}}$

where ${\displaystyle e}$ is void ratio, ${\displaystyle n}$ is porosity, VV is the volume of void-space (air and water), VS is the volume of solids, and VT is the total or bulk volume.[3]

## Engineering applications

• Volume change tendency control. If void ratio is high (loose soils) voids in a soil skeleton tend to minimize under loading - adjacent particles contract. The opposite situation, i.e. when void ratio is relatively small (dense soils), indicates that the volume of the soil is vulnerable to increase under loading - particles dilate.
• Fluid conductivity control (ability of water movement through the soil). Loose soils show high conductivity, while dense soils are not so permeable.
• Particles movement. In a loose soil particles can move quite easily, whereas in a dense one finer particles cannot pass through the voids, which leads to clogging.