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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