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, for idealized porous media with a rigid and undeformable skeleton structure (i.e., without variation of total volume ( $V_{T}$ ) 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 ( $V_{T}$ ) of an ideal porous material is the sum of the volume of the solids ( $V_{S}$ ) and the volume of voids ( $V_{V}$ ):

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

(in a rock, or in a soil, this also assumes that the solid grains and the pore fluid are clearly separated, so swelling clay minerals such as smectite, montmorillonite, or bentonite containing bound water in their interlayer space are not considered here.)

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 $e$ .^[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, in soil science and geotechnics, these two equations are usually presented using ${\eta }$ for porosity:^[3]^[4]

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.^[5]

Applications in soil sciences and geomechanics

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 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 a high hydraulic conductivity, while dense soils are less permeable.
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 smaller pores, which leads to the clogging of the porosity.

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
^ Pearson, F. J. (1999). "What is the porosity of a mudrock? In: Aplin, A.C., Fleet, A.J. & Macquaker, J.H.S. (Ed.). Muds and mudstones: Physical and fluid flow properties". Geological Society, London, Special Publications. 158 (1): 9–21. doi:10.1144/GSL.SP.1999.158.01.02. ISSN 0305-8719.
^ Pearson, F. J.; Fernández, A. M.; Gaboriau, H.; Waber, H. N.; Bath, A. (2003). "Annex 10: Porosity and Water Content of Mont Terri Claystones. In: Mont Terri Project – Geochemistry of Water in the Opalinus Clay Formation at the Mont Terri Rock Laboratory". Retrieved 2024-06-09.
^ Craig, R. F. Craig's Soil Mechanics. London: Spon, 2004, p.18. ISBN 0-203-49410-5.

External links

[1] Lambe, T. William & Robert V. Whitman. Soil Mechanics. Wiley, 1991; p. 29. ISBN 978-0-471-51192-2

[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

[Pearson1999-3] Pearson, F. J. (1999). "What is the porosity of a mudrock? In: Aplin, A.C., Fleet, A.J. & Macquaker, J.H.S. (Ed.). Muds and mudstones: Physical and fluid flow properties". Geological Society, London, Special Publications. 158 (1): 9–21. doi:10.1144/GSL.SP.1999.158.01.02. ISSN 0305-8719.

[Pearson2003-4] Pearson, F. J.; Fernández, A. M.; Gaboriau, H.; Waber, H. N.; Bath, A. (2003). "Annex 10: Porosity and Water Content of Mont Terri Claystones. In: Mont Terri Project – Geochemistry of Water in the Opalinus Clay Formation at the Mont Terri Rock Laboratory". Retrieved 2024-06-09.

[5] Craig, R. F. Craig's Soil Mechanics. London: Spon, 2004, p.18. ISBN 0-203-49410-5.

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Fahrer / Team für die Suche eingeben:

Fahrer / Team für die Suche eingeben:

Langbahn Team – Weltmeisterschaft

Void ratio

Applications in soil sciences and geomechanics

See also

References

Further reading

External links