Void ratio

The void ratio ($e$) of a mixture of solids and fluids (gases and liquids), or of a porous composite material such as concrete, is the ratio of the volume of the voids ($V_{V}$) filled by the fluids to the volume of all the solids ($V_{S}$). It is a dimensionless quantity in materials science and in soil science, and is closely related to the porosity (often noted as $\phi$, or ${\eta }$, depending on the convention), the ratio of the volume of voids ($V_{V}$) to the total (or bulk) volume ($V_{T}$), as follows:

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

in which the total (or bulk) volume ($V_{T}$) of the soil is the sum of the volume of the solids ($V_{S}$) and the volume of voids ($V_{V}$):

$V_{T}=V_{S}+V_{V}$

and

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

where $e$ is the void ratio, $\phi$ is the porosity, V_V is the volume of void-space (gases and liquids), V_S is the volume of solids, and V_T 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 one of the state variables of soils and represented by the symbol $e$.

Note that in geotechnical engineering, the symbol $\phi$ usually represents the angle of shearing resistance, a shear strength (soil) parameter. Because of this, in soil science and geotechnics, these two equations are usually presented using ${\eta }$ for porosity:

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

and

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

where $e$ is the void ratio, ${\eta }$ is the porosity, V_V is the volume of void-space (air and water), V_S is the volume of solids, and V_T is the total (or bulk) volume.

Engineering applications

• Control of the volume change tendency. If the void ratio is high (loose soils), under loading, voids in the soil skeleton tend to decrease (shrinkage) – increasing the contact between adjacent particles and modifying the soil effective stress. The opposite situation, i. e. when the void ratio is relatively small (dense soils), indicates that the volume of the soil is vulnerable to increase (swelling) under unloading – the smectite (montmorillonite, bentonite) partially dry clay particles present in an unsaturated soil can swell due to their hydration after contact with water (when the saturated/unsaturated conditions fluctuate in a soil).
• Control of the fluid hydraulic conductivity (ability of water movement through the soil). Loose soils show an high hydraulic conductivity, while dense soils are less permeable.
• Particles movement. In a loose soil small unbound particles can move quite easily through the larger open voids, whereas in a dense soil finer particles cannot freely pass the smaller pores, which leads to the clogging of the porosity.

See also

• Void (composites)

External links

• Relation between void ratio and porosity