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Thevoid ratio (${\displaystyle e}$) of amixture of solids and fluids (gases and liquids), or of aporouscomposite material such asconcrete, is the ratio of the volume of thevoids (${\displaystyle V_V}$) filled by the fluids to the volume of all the solids (${\displaystyle V_S}$). It is adimensionless quantity inmaterials science and insoil science, and is closely related to theporosity (often noted as${\displaystyle \varphi }$,${\displaystyle \eta }$ (sometimes simply written asn), orε, depending on the convention), the ratio of the volume ofvoids (${\displaystyle V_V}$) to the total (or bulk) volume (${\displaystyle V_T}$), as follows:

${\displaystyle e=\frac{V_V}{V_S}=\frac{V_V}{V_T-V_V}=\frac{\varphi }{1-\varphi }}$

in which, for idealizedporous media with a rigid and undeformable skeleton structure (i.e., without variation of total volume (${\displaystyle V_T}$) when the water content of the sample changes (no expansion or swelling with the wetting of the sample); nor contraction or shrinking effect after drying of the sample), the total (or bulk) volume (${\displaystyle V_T}$) of an ideal porous material is the sum of the volume of the solids (${\displaystyle V_S}$) and the volume of voids (${\displaystyle V_V}$):

${\displaystyle V_T=V_S+V_V}$

(in arock, or in asoil, this also assumes that the solid grains and the pore fluid are clearly separated, so swellingclay minerals such assmectite,montmorillonite, orbentonite containing bound water in their interlayer space are not considered here.)

and

${\displaystyle \varphi =\frac{V_V}{V_T}=\frac{V_V}{V_S+V_V}=\frac{e}{1+e}}$

where${\displaystyle e}$ is the void ratio,${\displaystyle \varphi }$ is theporosity,V_V is the volume of void-space (gases and liquids),V_S is the volume of solids, andV_T is the total (or bulk) volume. This figure is relevant incomposites, inmining (particular with regard to the properties oftailings), and insoil science. Ingeotechnical engineering, it is considered one of the state variables of soils and represented by the symbol${\displaystyle e}$.^[1][2]

Note that ingeotechnical engineering, the symbol${\displaystyle \varphi }$ usually represents the angle of shearing resistance, ashear strength (soil) parameter. Because of this, in soil science and geotechnics, these two equations are usually presented using${\displaystyle \eta }$ for porosity:^[3][4]

${\displaystyle e=\frac{V_V}{V_S}=\frac{V_V}{V_T-V_V}=\frac{\eta }{1-\eta }}$

and

${\displaystyle \eta =\frac{V_V}{V_T}=\frac{V_V}{V_S+V_V}=\frac{e}{1+e}}$

where${\displaystyle e}$ is the void ratio,${\displaystyle \eta }$ is the porosity,V_V is the volume of void-space (air and water),V_S is the volume of solids, andV_T is the total (or bulk) volume.^[5]

• Control of the volume change tendency. Suppose 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 soileffective 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 – thesmectite (montmorillonite,bentonite) partially dryclayparticles present in an unsaturated soil can swell due to theirhydration after contact with water (when the saturated/unsaturated conditions fluctuate in a soil).
• Control of the fluidhydraulic conductivity (ability of water movement through the soil). Loose soils show a high hydraulic conductivity, while dense soils are lesspermeable.
• Particle movement. Small, unbound particles can move relatively quickly through the larger open voids in loose soil. In contrast, in dense soil, finer particles cannot freely pass the smallerpores, which leads to the clogging of theporosity.

• Pore space in soil
• Void (composites)

• Bates, R.L.; Jackson, J.A. (1987-10-15).Glossary of Geology, Third Edition – American Geological Institute, Alexandria. Amazon.com: Books 9780913312896. American Geological Institute.ISBN 0913312894.

• Materials science
• Soil mechanics
• Earth sciences
• Soil science
• Mining terminology
• Physical quantities

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