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The relation between void ratio (e) and porosity (n) is
n=e1+eтАЛ
n=1+eeтАЛ
e=1+nnтАЛ
e=n1тИТnтАЛ
n=1+eeтАЛ
Void ratio (e) is defined as the ratio of the volume of voids (VvтАЛ) to the volume of solids (VsтАЛ), while porosity (n) is the ratio of the volume of voids (VvтАЛ) to the total volume (V). The relationship n=1+eeтАЛ is derived from these volumetric definitions by observing that the total volume V=VsтАЛ+VvтАЛ.
Void ratio (e) is defined as the ratio of the volume of voids (VvтАЛ) to the volume of solids (VsтАЛ), while porosity (n) is the ratio of the volume of voids (VvтАЛ) to the total volume (V). The relationship n=1+eeтАЛ is derived from these volumetric definitions by observing that the total volume V=VsтАЛ+VvтАЛ.
n=1+eeтАЛ тАФ Porosity in terms of void ratio
e=1тИТnnтАЛ тАФ Void ratio in terms of porosity
The soil mass is considered a three-phase system comprising solids, water, and air. By setting VsтАЛ=1, we get VvтАЛ=e, which makes the total volume V=1+e. Substituting these into the definition of porosity n=VVvтАЛтАЛ, we obtain n=1+eeтАЛ. Similarly, algebraic rearrangement allows us to express e in terms of n as e=1тИТnnтАЛ.
Void ratio (e) can range from 0 to infinity, whereas porosity (n) is always less than 1 (0 < n < 1).
For soil, e is a more commonly used parameter in calculations involving consolidation, while n is used in permeability studies.
Both e and n are unitless measures of the relative density of the soil packing.
Simplifies conversion between different soil state descriptors.
Essential for calculating unit weight and degree of saturation.
Mathematical expressions can be easily confused if signs are misplaced.
Porosity does not have a linear relationship with void ratio, making simple estimation difficult.
Geotechnical design for soil settlement analysis.
Determination of seepage velocity in saturated soils.
Option A is mathematically incorrect (n>1 is impossible for soil).
Option C represents e in terms of n incorrectly; the correct form is e=n/(1тИТn).
Option D is an algebraic inversion error.
B is correct тАФ The relationship between porosity (n) and void ratio (e) is defined by the formula n=1+eeтАЛ.
Always remember the simple mnemonic: 'n' (porosity) is always smaller than 'e' (void ratio) for the same soil sample, which helps in checking the direction of the fraction (1+e in the denominator ensures n<1).