Void ratio

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

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

and

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

where $e$ is void ratio, $\phi$ is porosity, V_V is the volume of void-space (such as fluids), 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 as one of the state variables of soils and represented by the symbol e.^[1]^[2]

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

e = \frac{V_V}{V_S} = \frac{V_V}{V_T - V_V} = \frac{n}{1 - n}

and

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

where $e$ is void ratio, $n$ is 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.^[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.

References

↑ Lambe, T. William & Robert V. Whitman. Soil Mechanics. Wiley, 1991; p. 29. ISBN 978-0-471-51192-2
↑ Santamarina, J. Carlos, Katherine A. Klein, & Moheb A. Fam. Soils and Waves: Particulate Materials Behavior, Characterization and Process Monitoring. Wiley, 2001; pp. 35-36 & 51-53. ISBN 978-0-471-49058-6
↑ Craig, R. F. Craig's Soil Mechanics. London: Spon, 2004, p.18. ISBN 0-203-49410-5.

Geotechnical engineering

on-site	Cone penetration test Standard penetration test Monitoring well piezometer Borehole Crosshole sonic logging Nuclear densometer test Static load testing

laboratory	Atterberg limits California bearing ratio Direct shear test Hydrometer Proctor compaction test R-value Sieve analysis Triaxial shear test Hydraulic conductivity tests Water content tests

Soil

Clay Silt Sand Gravel Peat Loam Loess

properties	Soil classification Hydraulic conductivity Water content Void ratio Bulk density Thixotropy Reynolds' dilatancy Angle of repose Cohesion Porosity Permeability Specific storage

mechanics	Effective stress Pore water pressure Shear strength Overburden pressure Consolidation Compaction Shear wave Lateral earth pressure

Stability

Plaxis
GEO5
SEEP2D
STABL
SVFlux
SVSlope
UTEXAS

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Void ratio

Engineering applications

See also

References