Degree of Saturation

SOIL COMPOSITION
WEIGHT – VOLUME The ratio of volume of water to volume of voids.

RELATIONSHIPS s=

Moisture Content

The ratio of weight of water to the weight of solids in a

given volume of soil.

ω=

Unit Weight

The weight of soil per unit volume or sometimes called the

moist unit weight.

Ƴ=

Dry Unit Weight

The weight per unit volume of soil, excluding water.

Vs = volume of soil solids Ƴd =

Vw = volume of water in the voids Moist Unit Weight

Va = volume of air in the voids
Ƴ= =
Vv = volume of voids
[ ]
Ƴ=
Neglecting the weight of air. (Wa = 0)

W = Ww + Ws Ƴd =

(total wt. of soil sample)

Ƴ= (1 + ω)
Let Vs = 1
Ƴ = Ƴd (1 + ω)

Void Ratio
Dry Unit Weight
The ratio of the volume of voids
if the volume of soil solids is one:
to the volume of solids.
e=
e=
e=

e = Vv
Porosity
Ws = Vs Gs Ƴw
The ratio of the volume of voids to the total volume.
Ws = (1) Gs Ƴw
n=
Ws = Gs Ƴw

ω=
e=
ω=
Ƴ
e=
Ww = ω Gs Ƴw
e=
Ƴ= =

e= Ƴ=
Ƴ Ƴ

n= Ƴ ( )
Ƴ=
 Ƴ Ƴ
=

Ƴ Effective unit weight of soil,

Ƴd =
( )
Submerged unit weight,
Ƴ
Ƴd =
Bouyant unit weight:

Ƴ’ = Ƴsat - Ƴw
Degree of Saturation ( )Ƴ
Ƴ’ = - Ƴw
s=
Ƴ Ƴ Ƴ Ƴ
Ƴ’ =
Vw = Ƴ ( )Ƴ
Ƴ’ =
Ƴ
Vw =
Ƴ

Vw = ω Gs
Hydraulic gradient for
Vv = e
Quicksand condition:
s=
icr =

Void ratio of 100% degree of saturation

Air Void Ratio/percentage of air voids
S=1
AVR=Va/V
1=
Air void ratio = n (1 – s)
e = ω Gs s = degree of saturation

n = porosity
Saturated Unit Weight 𝒆 𝝎 𝑮𝒔
Air void ratio = 𝟏 𝒆
of Soil:
ω = water content
Ƴsat = =
Gs = sp.gr.
Ƴ Ƴ
Ƴsat = e = void ratio

Ƴ Ƴ
Ƴsat =

( )Ƴ Air Content
Ƴsat =
Ac = Va / Vv = 1- S

Density of Soil
Zero Air Void Unit Weight
( )
ρ= Ƴ
Ƴzav =
ρw = 1000 kg/m³
Ƴzav = zero air void unit wt.
(density of water)
Gs = specific gravity
Dry Density
Ƴw = unit weight of water
ρd =
ω = moisture content

Moist Unit Weight in terms of

Saturated Density
Degree of Saturation and
( )
ρsat = Void Ratio:
Ƴ=
Ƴ Relative Density or

y = moist unit weight Density Index:

Gs = specific gravity Dr =

e = void ratio Dr = relative density usually in

Yw = unit weight of water Percent or Density index

S = degree of saturation e = in situ void ratio of the soil

Relative Density emax = void ratio of the soil

loosest condition
Dr = Ƴ Ƴ

Ƴ Ƴ
emin = void ratio of the soil in the
Yd = in situ dry unit weight
densest condition
(at a void ratio of e)
Values of emin and emax
Yd(max) = dry unit weight in the densest condition (at void Ƴ
ratio of emax) emin = Ƴ
Ƴ
Ƴ

emax = Ƴ
Ƴ

A soil sample has a porosity of 35% .The soil is 75% saturated

and the specific gravity of solids is 2.68. Determine its void
ratio, dry density, bulk densiity and moisture content.
(Ans : e = 0.54, γd=1.74gm/cc, γ = 2.0 gm/cc,w = l5%) an oven at 105ºC for 24 hours, and its weight reduced by
16.9 gm. Determine the dry density, void ratio, moisture
content and specific gravity of solids.

The mass specific gravity of a soil is 1.95, while the specific (Ans : γd = 1.54 gm/cc, e = 0.74, w = 12.7%, Gs = 2.68]
gravity of soil solids is 2.7. If the moisture content of the soil
be 22%, determine the following :

(i) Void ratio (ii) porosity (iii) degree of saturation (iv) dry A saturated clay has a water content of 39.3% and a bulk
density (v) saturated density. specific gravity of 1.84. Determine the void ratio and
specific gravity of particles. (Ans: 2.74, 1.08)
(Ans : (i) 0.69 (ii) 41% (iii) 86% (iv) 1.597 gm/cc (v) 2.00
gm/cc)

The natural moisture content of a soil mass is 11%, while its

void ratio is 0.63. Assuming the void ratio to remain
The saturated and dry densities of a soil are 1.93 gm/cc unchanged, determine the quantity of water to be added
and 1.47 gm/cc respectively. Determine the porosity and to 1m3 of this soil in order to double its moisture content
the specific gravity of the solid grains. Given, specific gravity of solids =2.72. [Ans : 183.3 kg]

(Ans : n = 45.9% ,Gs =2.72)

The moisture content and bulk density of a partially

saturated silt sample were 18% and 19.6 kN/m3 respectively.
A partially saturated soil sample has a natural moisture
The sample was kept in oven at 105º C for 15 minutes,
content of 17% and a bulk density of 2.05 g/cc. If the
resulting in a partial evaporation of the pore water. The
specific gravity of soil solids be 2.66, determine the void
bulk density of the sample reduced to 18.3 kN/m3.
ratio, degree of saturation and dry density of the soil.
Assuming the void ratio to remain unchanged, determine
the final water content of the sample. what would have
What will be the bulk density of the soil if it is :
been its bulk density if the sample was kept in the oven for
(i) Fully 24hours?

(ii) 60% saturated [Ans : 10%, 16.6 kN/m3]

(Ans : Part1; s = 0.52, s = 87 %, γd = 1.7 5 gm/cc Part 2: (i)

2.09 gm/cc (ii) 1.95 gm/cc)
An embankment was constructed with a clayey soil at a
moisture content of 12% . Just after construction, the
degree of saturation of the soil was found to be 55%. The
An undisturbed soil sample has a volume of 50 cc and soil absorbed water during the monsoon and its degree of
weighs 96.5 gm. On oven-drying, the weight reduces to saturation increased to 90%. Determine the water content
83.2 gm. Determine the water content, void ratio, degree of the soil at this stage. What will be the degree of
of saturation of the soil and air porosity. Given, Gs = 2.65. saturation if the moisture content reduces to 5% in the dry
season? Given, Gs =2.68.
(Ans: w =16% e =0.59 ,s =72%,, na = 0.11)
(Ans:19.6% ,22.9%)

A large piece of rock with a volume of 0.65 m 3 has 4%

porosity. The specific gravity of the rock mineral is 2.75. A 90 g sample of dry sands was placed in a pycnometer (a
What is the weight of this rock? Assume the rock is dry. density bottle used for determining the specific gravity of
soil grains), and the pycnometer was filled with water; its
Answer: 16.83 kN mass is 719.3 g. A clean pycnometer was filled with water
and has a mass of 663.2 g. Find the specific gravity of the
sand grains. (Ans: 2.65)

The bulk density and dry density of a soil are 1.95 gm/cc
and 1.58 g/cc respectively. Assuming Gs = 2.68, determine
the porosity, water content and degree of saturation of the
soil.
The in-situ density of a soil mass is to be determined by the
(Ans: n =41% ,w =23%, s =89.2%) core-cutter method. The height and diameter of the core
are 13 cm and 10 cm respectively. The core, when full of
soil, weighs 3155 gm, while the self-weight of the empty
core is 1250 gm. The natural moisture content and the
A cylindrical sample of saturated clay, 7.6 cm high and 38
specific gravity of solids are 12% and 2.66 respectively.
cm in diameter, weighs 149.6 gm. The sample was dried in
Determine the bulk density, dry density and void ratio of
the soil.

[Ans : y= 1.87 gm/cc, yd = 1.67 gm/cc, e = 0.591

In the previous problem, what will be the water content

and bulk density of the soil if, without undergoing any
change in the void ratio, the soil becomes:

(i) Fully saturated

(ii)80% saturated

(Ans : (i) 22% ;2.04gm/cc, (ii) 17.7% , 1.97 g/cc)

A 27.50 lb soil sample has a volume of 0.220 ft3 , a moisture

content of 10.2%, and a specific gravity of solids of 2.65.
Compute the unit weight, dry unit weight, degree of
saturation, void ratio, and porosity.

The moist unit weight of 0.00283 m³ of soil is 54.4 N. If the

moisture content is 12% and the specific gravity of soil solids
is 2.72, determine the following:
A. Moist unit weight
B. Dry unit weight
C. Void ratio
D. Degree of saturation
E. Air content
F. Percentage of air voids