Void Ratio

Void ratio refers to the size of voids to the volume of solids. It is indicated

e=Vv/Vs

It is expressed as a decimal.

Porosity

It is the ratio of volume of voids to the total volume. It is indicated by ‘n’

n=Vv/V

It is usually expressed as a percentage.

1/n=V/Vv= (Vv+vs)/Vv

1/n= 1+ (1/e) = (1+e)/e

n=e/ (1+e) (a)

1/e= (1/n)-1= (1-n)/n

e=n/ (1-n) (b)

In equations (a) and (b), the porosity should be expressed as a ratio and not percentage.

Degree of saturation

The degree of saturation is the quotient of the volume of water to the volume of voids. It is indicated by ‘S’.

S=Vw/Vv

The degree of saturation is normally expressed as a percentage. It is equal to zero when the soil is absolutely dry and 100% when the soil is fully immersed.

Percentage air voids

It is the ratio of volume of air to the total volume.

n_a= Va/V

It is also expressed as a percentage.

Air content

Air content is the ratio of the volume of air to the volume of voids

a_c= Va/Vv

Also,

n_a= n a_c

Water content

The water content (w) is the quotient of the mass of water to the mass of soilids

w= Mw/Ms

It is also known as the moisture content (m). It is articulated as a percentage but used as a decimal in computation.

 

VOLUME-MASS RELATIONSHIPS

1. BULK MASS DENSITY

The bulk mass density (ρ) is known as the total mass (M) per unit volume (V)

ρ=M/V

2. DRY MASS DENSITY

The dry mass density (ρ_d) is known as the mass of solids per unit total volume

ρ_d= Ms/V

3. SATURATED MASS DENSITY

The saturated mass density (ρ_sat) refers to the bulk density of the soil when it is fully immersed.

ρ_sat= Msat/V

 

4. SUBMERGED MASS DENSITY

When the soil is located under the water, it is known as submerged condition. The submerged mass density (ρ’) of the soil is known as the submerged mass per unit total volume.

ρ’= Msub/V

5. MASS DENSITY OF SOLIDS

The mass density of solids (ρ_s) is equivalent to quotient of the mass of solids to volume of solids

ρ_s=Ms/Vs

VOLUME-WEIGHT RELATIONSHIPS

1. BULK UNIT WEIGHT (γ)= W/V
2. DRY UNIT WEIGHT (γ_d)= Ws/V
3. SATURATED UNIT WEIGHT (γ_sat) = Wsat/V
4. SUBMERGED UNIT WEIGHT (γ_subor γ’) = Wsub/V
5. UNIT WEIGHT OF SOIL SOLIDS (γ_s) = Ws/Vs

 

PARTICULAR GRAVITY OF SOLIDS

The particular gravity of soil particles (G) is defined as the ratio of weight of a given volume of solids to mass of an equivalent volume of water at 4° C.

G = ρ_s/ρ_w

The mass density of water ρ_{w at} 4°C is 1gm/ml, 1000 kg/m³ or 1 Mg/m³

 

Basic Relationships

Sl No	Relationship in mass density	Relationship in unit weight
1	n = e/(1+e)	n = e/(1+e)
2	e = n/(1-n)	e = n/(1-n)
3	na = n ac	na = n ac
4	ρ= (G+Se)ρw/(1+e)	γ= (G+Se) γ w/(1+e)
5	ρd = Gρw/(1+e)	γd = G γ w/(1+e)
6	ρsat = (G+e)ρw/(1+e)	γsat = (G+e) γ w/(1+e)
7	ρ’ = (G-1)ρw/(1+e)	γ’ = (G-1) γ w/(1+e)
8	e = wG/s	e = wG/s
9	ρd = ρ/(1+w)	γd = γ/(1+w)
10	ρd = (1-na)G ρw/(1+wG)	γd = (1-na)G γ w/(1+wG)

 

Share it on: