phase relations in soil mechanics

1. Phase Relations
By
Dr. Hanumantharao Chappidi
RGUKT-AP
15/11/17 1
Phase Relations in soil mechanics by Dr. Hanumantharao Chappidi is licensed under a Creative Commons
Attribution-ShareAlike 4.0 International License.

2. Three Phases in Soils
S : Solid Soil particle
W: Liquid Water (electrolytes)
A: Air Air

3. Soil: A 3-Phase Material
Solid
Water
Air
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4. Three Phase Diagram
Solid
Air
Water
Soil Skeleton Idealization:
Three Phase Diagram

6. Soil may be defined as an assemblage of
discrete solid particles of organic or
inorganic composition with air and/or
water occupying the void space amongst
the particles.
Soil can thus have all three phases present in it
- solid, water and air.
If there is no AIR present  SATURATED SOIL
If there is no WATER present  DRY SOIL
Definition of Soil
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7. Three Phase System (interms of
weight)
Volume Weight
Solid
Air
Water
WT
Ws
Ww
Wa~0
Vs
Va
Vw
Vv
VT
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8. soil
air
water
Vs
Va Ma=0
Ms
Mw
Mt
Vw
Vv
Vt
Phase Diagram
Notation
M = mass or weight
V = volume
s = soil grains
w = water
a = air
v = voids
t = total
Three Phase System (interms of mass)
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9. 9
Weight Relationship
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
Phase Diagram
S
W
M
M
w =
Expressed as percentage.
Range = 0 – 100+%.
X 100%
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10. 10
Volume – Volume Relation
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
S
V
V
V
e =
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11. 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
Phase Diagram
T
V
V
V
n = X 100%
Theoretical range: 0 – 100%
Volume – Volume Relation
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12. 12
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
Phase Diagram
V
W
V
V
S =
Range: 0 – 100%
X 100%
Dry
Saturated
Volume – Volume Relation
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13. Volume – Volume Relations
15/11/17 13
PercentageofAirVoids,na =
Va
V
AirContent,ac =
Va
Vv

14. 14
Weight (Mass) – Volume Relation
Bulk density (ρm) is the density of the soil in the
current state.
soil
air
water
Vs
Va Ma=0
Ms
Mw
Mt
Vw
Vv
Vt
Phase Diagram
T
T
m
V
M
=ρ
Units: t/m3
, g/ml, kg/m3
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15. 15
Saturated 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
Weight (Mass) – Volume Relation
15/11/17
UNIT WEIGHT OF SOLIDS = Ws /Vs

16. 16
Dry density (ρd) is the density of the soil in dry
state.
soil
air
water
Vs
Va Ma=0
Ms
Mw
Mt
Vw
Vv
Vt
Phase Diagram
T
S
d
V
M
=ρ
Units: t/m3
, g/ml, kg/m3
Weight (Mass) – Volume Relation
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17. 17
Bulk, saturated, dry and submerged unit weights (γ)
are defined in a similar manner.
γ = ρg
Here, use weight (kN) instead of mass (kg).
kg/m3
N/m3
m/s2
Weight (Mass) – Volume Relation
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18. Soil Unit weight (kN/m3
)
 Bulk (or Total) Unit weight
γ= WT / VT
 Dry unit weight
γd = Ws / VT
 Buoyant (submerged) unit weight
γb = γ- γw
15/11/17 18

19. Soil Density (kg/m3
)
 Bulk (or Total) Density
ρ= MT / VT
 Dry Density
ρd = Ms / VT
 Buoyant (submerged) Density
ρb = ρ- ρw
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20. Specific Gravity
 Unit weight of Water, γw
γw = 9.81 kN/m3 or
γw= 1.0 g/cm3
or γw= 62.4 pcf
(strictly accurate at 4° C)
WaterofVolumeEqualanofWeight
ceSubsaofWeight
GravitySpecific
tan
=
WaterofWeightUnit
ceSubsaofWeightUnit
GravitySpecific
tan
=
Specific gravity of the soil grains (Gs) typically
varies between 2.6 and 2.8.
15/11/17 20

21. Phase Relations
Consider a fraction of the soil where Vs = 1.
soil
air
water
1 Gsρw
Seρw
Se
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:
15/11/17 21

22. 22
Phase Relations
From the previous definitions,
soil
air
water
1 Gsρw
Seρw
Se
e
Phase Diagram
SS
W
G
Se
M
M
w ==
e
e
V
V
n
T
V
+
==
1
15/11/17
na = n ac
ac = 1 - S

23. 23
Phase Relations
soil
air
water
1 Gsρw
Seρw
Se
e
Phase Diagram
W
S
T
T
m
e
SeG
V
M
ρρ
+
+
==
1
W
S
T
T
sat
e
eG
V
M
ρρ
+
+
==
1
W
S
T
S
d
e
G
V
M
ρρ
+
==
1
15/11/17

24. 24
Phase Relations
soil
air
water
1 Gsϒw
Seϒw
Se
e
Phase Diagram
γ =
WT
VT
=
GS + Se
1+e
γW
γd =
WS
VT
=
GS
1+ e
γW
γsub = γsat −γw =
GS − 1
1+ e
γW
γd =
γ
1+ w

25. 25
Phase Relations
soil
air
water
1 Gsϒw
Seϒw
Se
e
Phase Diagram
γ =
WT
VT
=
GS (1+ w)
1+ e
γW
γd = GsγW (1− n)
γd =
γ
1+ w
γ = Gsγw (1+ w)(1− n)

26. 26
 Do NOT 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.
Important Note
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27. 27
A Suggestion.. If you can remember one thing in
phase relations, that should be ..
1
Gsρw
SeρwSe
e
soil
air
water
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28. 28
Quiz
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.
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29. Weight Relationships
 Weight Components:
– Weight of Solids = Ws
– Weight of Water = Ww
– Weight of Air ~ 0
 Define Water Content
Water Content, w(%) =
?
?
×100%
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30. Volumetric Relationships
 Volume Components:
– Volume of Solids = Vs
– Volume of Water = Vw
– Volume of Air = Va
– Volume of Voids = Va + Vw = Vv
 Define Void Ratio and Porosity
Void Ratio, e =
?
?
Porosity, n(%) =
?
?
×100%
15/11/17 30

31. Volumetric Relationships
 Volume Components:
– Volume of Solids = Vs
– Volume of Water = Vw
– Volume of Air = Va
– Volume of Voids = Va + Vw = Vv
 Define Degree of Saturation
Degree of Saturation, S(%) =
?
?
×100%
15/11/17 31

32. 32
water
air
soil
In this illustration,
If e = 1 and n=50% then S = ?
S = ___ %
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33. Quiz
15/11/17 33
PercentageofAirVoids,na =
?
?
AirContent,ac =
?
?

34. Questions
1. What is the degree of saturation for saturated soil
and why?
2. What is the degree of saturation for dry soil and
why?
3. What is the range of degree of saturation?
4. How do you get the void ratio from laboratory
tests, provide the equation.
5. Flow through soil can be measured using
porosity / void ratio?

35. 1. What is the relation between specific gravity of soil
solids void ratio and dry unit weight?
2. What is the value of ‘e’ for fully saturated soil in terms
of water content and specific gravity ?
3. Calculate the value of Degree of saturation of clayey
soil if the value of water content is 0.126 and the value
of void ratio is 0.66 and G is 2.71.
4. Find out the void ratio, if the dry unit weight of a clay
deposit is 17.1kN/m3
and G is 2.71.
5. What are the reasons for the wide range variations of the
magnitude of void ratio in naturally occurring sands?
Practice session

36. Practice session
6. A soil sample of 3.81cm diameter and 7.62cm height is collected
from the field and observed the wet weight of 1.668N and oven dry
weight of 1.4N from the laboratory. Also observed the specific
gravity as 2.7 in the laboratory. Evaluate the water content, bulk unit
weight, dry unit weight, void ratio and degree of saturation.
7. A natural soil deposit has a bulk unit weight of 20 kN/m3
and water
content of 5%. Estimate the amount of water (in litres) required to be
added to 1 m3
of soil to raise the water content to 20%. Assume the
void ratio to remain constant. Take specific gravity of soil solids as
2.7.

37. Online Practice Links
15/11/17 37
http://www.edumine.com/xtoolkit/xmlicon/soil_mechanics_1.htm
http://groundwatersoftware.com/calculator
_12_phase_relationships.htm
https://www.wisc-online.com/learn/career-
clusters/stem/eng2502/weight-volume-relationships-
introduction-to-a