phase relationships

1SIVA

Phase Relations

N. Sivakugan

Duration: 6 min 31 s

2SIVA

Copyright©2001

ObjectivesTo compute the masses (or weights) and

volumes of the three different phases.

soil

air

water

Vs

Va

Vw

Ma=0

Ms

MwMt

Vv

Vt

Phase Diagram

NotationM = mass or weightV = volumes = soil grainsw = watera = airv = voidst = total

3SIVA

Copyright©2001

DefinitionsWater content (w) is a measure of the

water present in the soil.

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

Vt

S

W

MMw = X 100%

Expressed as percentage.

Range = 0 – 100+%.

Phase Diagram

4SIVA

Copyright©2001

DefinitionsVoid ratio (e) is a measure of the void

volume.

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

Vt

S

V

VVe =

Phase Diagram

5SIVA

Copyright©2001

DefinitionsPorosity (n) is also a measure of the void

volume, expressed as a percentage.

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

Vt

T

V

VVn = X 100%

Theoretical range: 0 – 100%

Phase Diagram

6SIVA

Copyright©2001

DefinitionsDegree of saturation (S) is the percentage of

the void volume filled by water.

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

Vt

V

W

VVS = X 100%

Range: 0 – 100%

DrySaturated

Phase Diagram

7SIVA

Copyright©2001

A Simple ExampleIn this illustration,

water

air

soil

e = 1

n = 50%

S = 50%

8SIVA

Copyright©2001

DefinitionsBulk density (ρm) is the density of the soil in the

current state.

T

Tm V

M=ρ

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

VtUnits: t/m3, g/ml, kg/m3

Phase Diagram

9SIVA

Copyright©2001

DefinitionsSaturated density (ρsat) is the density of the soil

when the voids are filled with water.

Submerged density (ρ’) is the effective density of the soil when it is submerged.

ρ’ = ρsat - ρw

10SIVA

Copyright©2001

DefinitionsDry density (ρd) is the density of the soil in dry

state.

T

Sd V

M=ρ

soil

air

water

Vs

Va Ma=0

Ms

MwMt

Vw

Vv

VtUnits: t/m3, g/ml, kg/m3

Phase Diagram

11SIVA

Copyright©2001

DefinitionsBulk, saturated, dry and submerged unit weights (γ)

are defined in a similar manner.

Here, use weight (kN) instead of mass (kg).

γ = ρg

kg/m3N/m3 m/s2

Specific gravity of the soil grains (Gs) typically varies between 2.6 and 2.8.

SIVA

Copyright©2001

Phase RelationsConsider a fraction of the soil where Vs = 1.

The other volumes can be obtained from the previous definitions.

soil

air

water

1 Gsρw

SeρwSe

e

Phase Diagramvolumes masses

The masses can be obtained from:

Mass = Density x Volume

13SIVA

Copyright©2001

Phase RelationsFrom the previous definitions,

SS

W

GSe

MMw ==

soil

air

water

1 Gsρw

SeρwSe

e

ee

VVnT

V

+==1

Phase Diagram

14SIVA

Copyright©2001

Phase Relations

WS

T

Tm e

SeGVM ρρ

++

==1

soil

air

water

1 Gsρw

SeρwSe

eW

S

T

Tsat e

eGVM ρρ

++

==1

WS

T

Sd e

GVM ρρ

+==1

Phase Diagram

15SIVA

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.

16SIVA

Copyright©2001 A Suggestion..

If you can remember one thing in phase relations, that should be ..

1 Gsρw

SeρwSee

soil

air

water

17SIVA

Copyright©2001

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