 # What is Void Ratio? : Void Ratio Formula & Relationship with Dry Unit Weight, Porosity, Air Content, Permeability

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The void ratio may be defined as the ratio of the volume of voids to the volume of the solid.

It is generally denoted by e.

Mathematically,

e = Vv / Vs

where,

V= Volume of voids

V= Volume of the solid

### a. Relation Between Void Ratio and Dry Unit Weight

1. The void ratio is calculated for each state of the denseness of the sample.

2. Maximum void ratio takes place at minimum index density.

3. Minimum void ratio takes place at maximum index density.

The relation between void ratio and dry unit weight is given as:

 e = ( G x γwater -γdry ) / γdry

Where,

G = specific gravity

γwater = Unit Weight of Water

γdry = Dry Unit Weight

### b. Relation Between Porosity and Void Ratio

The porosity of soil may be defined as the ratio of the volume of voids to the total volume.

Mathematically,

n = Vv/V

Where,

Vv = Volume of void

V= Total volume

The void ratio is normally utilized in parallel with soil porosity.

Porosity is denoted by n.

The relationship between void ratio and porosity is given as:

 e =  n / (n-1)

or,

 n = e / (e+1)

### c.  Relation Between Air Content and Void Ratio

Air content may be defined as the ratio of the volume of air in the soil mass to the volume of voids in the soil mass.

Air content = (Va /Vv) = Va / (e * Vs)

Va = Volume of air

Vv = Volume of voids

### d.  Relation Between Degree of Saturation, Specific Gravity, Water Content, and Void Ratio

The degree of saturation may be defined as the ratio of the volume of water in the soil mass to the volume of voids in the soil mass.

It is denoted by ‘Sr‘.

The degree of saturation is normally expressed in a percentage.

The degree of saturation is equal to 0 when the soil is completely dry and 100% when the soil is completely saturated.

The relation between the degree of saturation, specific gravity, water content, and the void ratio is given as:

 W x G =  e x Sr

where,

W = water content

G = specific gravity

e= Void ratio

Sr = Degree of saturation

### e. Relationship Between Permeability and Void Ratio

The coefficient of permeability is different from the void ratio as e²/sup >/(1+e).

For a given soil mass, if the void ratio is more then the value of the coefficient of permeability is higher.

Based on different concepts it has been found that the permeability of soil is different from e² or e²/(1+e).

Whatever may be the exact relationship, all soils have Vs log k drawn as a straight line.

K increase with the increment of Void.

( K = Coefficient of Permeability )

### f. Numerical

1. A soil sample having a weight of 0.7 kg and a volume of 3.5 × 10-4 m³. After drying out, the weight was decreased to 0.6 kg. The specific gravity of the particle is given at 2.6.

Determine the following:

a) Moisture content

(b) Dry density

(c) Bulk density

(d) Void ratio

(e) Porosity

(f) Degree of saturation

Solution,

 (a) Moisture contentThe total mass of water (Mw) is 0.7 – 0.6 = 0.1 kgm = Mw / Ms= 0.1/ 0.6= 0.1666or in percentage 16.66% (b) Dry densityρ Dry = Ms / V = 0.6 / 0.00035= 1714 Kg/m³ (c) Bulk densityρ Bulk  = M / V= 0.7/ 0.00035= 2000 kg/m³ To determine the void ratio we must first determine the volume of solids. (a)   ρ s = Ms / Vs = Gs ρ water∴ Vs = Ms /( Gs ρ water)Vs = 0.6 / (2.6 x 1000) Vs =0.000231 m³ (b)   Vv=V-Vs = 0.00035-0.000231 = 0.000119 m³ (c)  Vw = 0.1 / 1000 = 0.0001 m³ (d) Void ratio (e)= Vv / Vs = 0.000119 / 0.000231 = 0.515 (e) Porosity (n)= Vv / V = 0.000119 / 0.00035 = 0.34 (f) Degree of Saturation (Sr) = Vw / Vv = 0.0001/0.000119 = 0.84 = 84 %

### g. References

1. Content Filter & Authenticity Checking Team, Dream Civil International

(Our team checks every content & detail to maintain quality. )

Read Also:  Irrigation with All Methods

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Tell us how we can improve this post? Madhu Krishana Poudel is a distinguished Civil Engineer with extensive experience in site supervision, estimation, and AutoCAD 2D and 3D design. Holding a Bachelor's degree in Civil Engineering from Pokhara University, his work and expertise have earned recognition in reputable sources such as USA Today, Time, Wikipedia, and TheRichest, establishing his credibility and trustworthiness in the construction industry.
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