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

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

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

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

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

6. Definitions
Degree of saturation (S) is the percentage of the void volume filled by water.
soil
air
water Vs Va
Ma=0 Ms Mw Mt Vw Vv Vt
X 100%
Range: 0 – 100%
Dry
Saturated
Phase Diagram

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

8. Definitions
Bulk density (m) is the density of the soil in the current state.
soil
air
water Vs Va
Ma=0 Ms Mw Mt Vw Vv Vt
Units: t/m3, g/ml, kg/m3
Phase Diagram

9. Definitions
Saturated density (sat) is the density of the soil when the voids are filled with water.
Submerged density (’) is the effective density of the soil when it is submerged.
’ = sat - w

10. Definitions Dry density (d) is the density of the soil in dry state.
air
water Vs Va
Ma=0 Ms Mw Mt Vw Vv Vt
Units: t/m3, g/ml, kg/m3
Phase Diagram

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

12. Phase Relations Consider a fraction of the soil where Vs = 1.
The other volumes can be obtained from the previous definitions.
air e Se
water
Sew
The masses can be obtained from: 1
soil
Gsw
Mass = Density x Volume
volumes
masses
Phase Diagram

13. Phase Relations From the previous definitions, soil air water 1 Gsw
Sew Se e
Phase Diagram

14. Phase Relations
soil
air
water 1
Gsw
Sew Se e
Phase Diagram

15. Try not to memorise the equations
Try not to memorise the equations. Understand the definitions, and develop the relations from the phase diagram with VS = 1;
Assume GS ( ) 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.

16. If you can remember one thing in phase relations, that should be ..
A Suggestion.. 1
Gsw
Sew Se e
soil
air
water
If you can remember one thing in phase relations, that should be ..

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