This document defines key terms and relationships used in soil phase relations, including: water content, void ratio, porosity, degree of saturation, bulk density, saturated density, dry density, and specific gravity. It presents a simple example and shows how to derive equations for these parameters using a soil's masses, volumes, and void ratio based on a total soil volume of 1. The document emphasizes understanding definitions over memorization and derives relationships from a phase diagram representation.

1. Phase Relations
N. Sivakugan
Duration: 6 min 31 s
SIVA 1

2. Copyright©2001 Objectives
To compute the masses (or weights) and
volumes of the three different phases.
Va Ma=0
air
water
soil
Vs
SIVA 2
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
Notation
M = mass or weight
V = volume
s = soil grains
w = water
a = air
v = voids
t = total

3. Copyright©2001 Definitions
Water content (w) is a measure of the
water present in the soil.
Va Ma=0
air
water
soil
Vs
W
M
X 100%
SIVA 3
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
S
w = M
Expressed as percentage.
Range = 0 – 100+%.

4. Copyright©2001 Definitions
Void ratio (e) is a measure of the void
volume.
Va Ma=0
air
water
soil
Vs
V
V
SIVA 4
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
S
e = V

5. Copyright©2001 Definitions
Porosity (n) is also a measure of the void
volume, expressed as a percentage.
Va Ma=0
air
water
soil
Vs
n = V X 100%
V
V
SIVA 5
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
T
Theoretical range: 0 – 100%

6. Copyright©2001 Definitions
Degree of saturation (S) is the percentage of
the void volume filled by water.
Va Ma=0
air
water
soil
Vs
S = V
W
V
X 100%
SIVA 6
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
V
Range: 0 – 100%
Dr
y Saturate
d

7. Copyright©2001 A Simple Example
SIVA 7
air
water
soil
In this illustration,
e = 1
n = 50%
S = 50%

8. Copyright©2001 Definitions
Bulk density (rm) is the density of the soil in the
current state.
Va Ma=0
air
water
soil
Vs
T
r = M
m V
SIVA 8
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
T
Units: t/m3, g/ml, kg/m3

9. Copyright©2001 Definitions
Saturated density (rsat) is the density of the soil
when the voids are filled with water.
Submerged density (r’) is the effective density
of the soil when it is submerged.
r’ = rsat - rw
SIVA 9

10. Copyright©2001 Definitions
Dry density (rd) is the density of the soil in dry
state.
Va Ma=0
air
water
soil
Vs
S
r = M
d V
SIVA 10
Mw
Ms
Mt
Vw
Vv
Vt
Phase Diagram
T
Units: t/m3, g/ml, kg/m3

11. Copyright©2001 Definitions
Bulk, saturated, dry and submerged unit weights (g)
are defined in a similar manner.
Here, use weight (kN) instead of mass (kg).
g = rg
N/m3 kg/m3 m/s2
Specific gravity of the soil grains (Gs) typically
varies between 2.6 and 2.8.
SIVA 11

12. Copyright©2001 Phase Relations
Consider a fraction of the soil where Vs = 1.
SIVA
air
Se
water
Serw soil
1 Gsrw
e
Phase Diagram
The other volumes can
be obtained from the
previous definitions.
Mass = Density x Volume
volumes masses
The masses can be
obtained from:

13. Copyright©2001 Phase Relations
From the previous definitions,
Serw Se
soil
w = M W
=
Se
G
n V
V
SIVA 13
air
water
1 Gsrw
e
Phase Diagram
S S
M
e
e
V
T
+
= =
1

14. Copyright©2001 Phase Relations
Serw Se
soil
r = M T
= +
r
m e
r = M T
= +
r
sat e
r M S
r
d e
SIVA 14
air
water
1 Gsrw
e
Phase Diagram
W
S
T
G Se
V
+
1
W
S
T
G e
V
+
1
W
S
T
G
V
+
= =
1

15. Copyright©2001
Try not to memorise the equations.
Understand the definitions, and develop the
relations from the phase diagram with VS = 1;
Assume GS (2.6-2.8) when not given;
Do not mix densities and unit weights;
Soil grains are incompressible. Their mass
and volume remain the same at any void ratio.
SIVA 15

16. Copyright©2001 A Suggestion..
If you can remember one thing in
phase relations, that should be ..
air
water
SerSe w
1 Gsrw
e
soil
SIVA 16

17. Copyright©2001 Testing Times…
State whether the following are true or false?
(a) Dry density is greater than submerged density
(b) In unsaturated soils, water content is always less
than 100%.
(c) Larger the void ratio, larger the porosity.
SIVA 17
True
False
True