1. 28/05/15 BY
Dr.IBRAHIM
1
Soil Phase RelationshipsSoil Phase Relationships
‫للتربة‬ ‫الظاهرية‬ ‫العلقات‬‫للتربة‬ ‫الظاهرية‬ ‫العلقات‬

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‫التربة‬ ‫مكونات‬‫التربة‬ ‫مكونات‬Soil CompositionSoil Composition
Soil Grain orSoil Grain or
particleparticle
‫التربة‬ ‫حبيبات‬‫التربة‬ ‫حبيبات‬11((Soil GrainsSoil Grains
22( &( &33((Voids: Water + AirVoids: Water + Air
( )‫وهواء‬ ‫ماء‬ ‫عن‬ ‫عبارة‬ ‫الفراغات‬( )‫وهواء‬ ‫ماء‬ ‫عن‬ ‫عبارة‬ ‫الفراغات‬
VoidsVoids

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‫الفراغات‬ ‫نسبة‬‫الفراغات‬ ‫نسبة‬Void RatioVoid Ratio
Solid, VSolid, Vss
Void, VVoid, Vvv
e =e =
VVvv
VVss
high e =high e = LooseLoose
‫سائب‬‫سائب‬
low e =low e = DenseDense
‫كثيف‬‫كثيف‬

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SaturationSaturation ‫بالمياه‬ ‫التشبع‬‫بالمياه‬ ‫التشبع‬
Voids, VVoids, Vvv = V= Vww + V+ Vaa
Air, Va
Water, VWater, Vww
VVvv = V= Vww + V+ Vaa
SSrr ==
fully saturatedfully saturated
SSrr = 100 %= 100 %
‫ا‬ً‫تمام‬ ‫مشبع‬‫ا‬ً‫تمام‬ ‫مشبع‬
VVww
VVvv
. 100. 100
DryDry ‫جاف‬‫جاف‬ SSrr = 0 %= 0 %

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Mineral soils are composed of:Mineral soils are composed of:
Soil grainsSoil grains ‫التربة‬ ‫حبيبات‬‫التربة‬ ‫حبيبات‬
WaterWater ‫مياه‬‫مياه‬
AirAir ‫هواء‬‫هواء‬
Three Phases of Mineral SoilsThree Phases of Mineral Soils

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Weight and volume ofWeight and volume of
soil sample depends on:soil sample depends on:
Specific gravity of soilSpecific gravity of soil
grains (solids)grains (solids)
The size and spaceThe size and space
between soil grainsbetween soil grains
(voids and pores)(voids and pores)
Volume of void spaceVolume of void space
filled with waterfilled with water
Weight Volume RelationshipsWeight Volume Relationships
• Water
• Solids
• Air

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PHASE DIAGRAMPHASE DIAGRAM
To compute the masses (or weights) andTo compute the masses (or weights) and
volumes of thevolumes of the threethree different phases.different phases.
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt
Idealized Prism
NotationNotation
W = weightW = weight ‫الوزن‬‫الوزن‬
V = volumeV = volume ‫الحجم‬‫الحجم‬
s = soil grainss = soil grains
w = waterw = water
a = aira = air
v = voidsv = voids
t = totalt = total

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Definitions
Water content (wWater content (wcc)) ((‫المياه‬ ‫محتوى‬‫المياه‬ ‫محتوى‬)) is a measureis a measure
of the water or Moisture present in the soil.of the water or Moisture present in the soil.
Phase Diagram
s
w
c
W
W
w =
Expressed as percentage.Expressed as percentage.
Range = 0 – 100+%.Range = 0 – 100+%.
X 100%
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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DefinitionsDefinitions
Void ratio (e)Void ratio (e) ((‫الفراغات‬ ‫نسبة‬‫الفراغات‬ ‫نسبة‬)) is a measureis a measure
of the volume of voids.of the volume of voids.
Phase Diagram
S
V
V
V
e =
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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DefinitionsDefinitions
Porosity (n)Porosity (n) ((‫المسامية‬‫المسامية‬)) is also a measure of theis also a measure of the
volume of voids, expressed as a percentage.volume of voids, expressed as a percentage.
Phase Diagram
t
v
V
V
n = X 100%
Theoretical range:Theoretical range:
0 – 100%0 – 100%
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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DefinitionsDefinitions
Degree of saturation (SDegree of saturation (Srr)) ((‫التشبع‬ ‫درجة‬‫التشبع‬ ‫درجة‬)) is theis the
percentage of the void volume filled by water.percentage of the void volume filled by water.
Phase Diagram
V
W
r
V
V
S =
Range: 0 – 100%Range: 0 – 100%
X 100%
DryDry
SaturatedSaturated
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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DefinitionsDefinitions
Bulk density (Bulk density (γγbb)) ((‫الكلية‬ ‫الكثافة‬‫الكلية‬ ‫الكثافة‬)) is the density ofis the density of
the soil in the current state.the soil in the current state.
Phase Diagram
t
t
V
W
b
=γ
Units: t/mUnits: t/m33
, g/cm, g/cm33
, kN/m, kN/m33 soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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DefinitionsDefinitions
Saturated density (Saturated density (γγsatsat)) ((‫المشبعة‬ ‫الكثافة‬‫المشبعة‬ ‫الكثافة‬)) is theis the
density of the soil when the voids are filleddensity of the soil when the voids are filled
with water.with water.
‫بالماء‬ ‫مملوءة‬ ‫الفراغات‬ ‫تكون‬ ‫عندما‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫المشبعة‬ ‫الكثافة‬‫بالماء‬ ‫مملوءة‬ ‫الفراغات‬ ‫تكون‬ ‫عندما‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫المشبعة‬ ‫الكثافة‬
Submerged density (Submerged density ( γγsubsub )) ((‫المغمورة‬ ‫الكثافة‬‫المغمورة‬ ‫الكثافة‬)) is theis the
effective density of the soil when it iseffective density of the soil when it is
submerged.submerged.
‫الماء‬ ‫فى‬ ‫مغمورة‬ ‫تكون‬ ‫عندما‬ ‫الفعالة‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫المغمورة‬ ‫الكثافة‬‫الماء‬ ‫فى‬ ‫مغمورة‬ ‫تكون‬ ‫عندما‬ ‫الفعالة‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫المغمورة‬ ‫الكثافة‬
γsub= γsat - γw

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DefinitionsDefinitions
Dry density (Dry density (γγdd)) ((‫الجافة‬ ‫الكثافة‬‫الجافة‬ ‫الكثافة‬)) is the density of the soilis the density of the soil
in dry statein dry state ‫الجافة‬ ‫الحالة‬ ‫فى‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫الجافة‬ ‫الكثافة‬‫الجافة‬ ‫الحالة‬ ‫فى‬ ‫التربة‬ ‫كثافة‬ ‫هى‬ :‫الجافة‬ ‫الكثافة‬
Phase Diagram
t
s
V
W
d
=γ
Units: t/mUnits: t/m33
, kg/m, kg/m33
, kN/m, kN/m33
soil
air
water
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt

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Phase RelationsPhase Relations
Consider a unit volume of the soil solids,Consider a unit volume of the soil solids,
where Vs = 1.
soil
air
water
Vs =1
Gsγw
SreγwSre
e
Phase Diagram
The other volumes canThe other volumes can
be obtained from thebe obtained from the
previous definitions.previous definitions.
Weight = Density x VolumeWeight = Density x Volume
volumes masses
The weights canThe weights can
be obtained from:be obtained from:
w
s
s
s
s
s G,
V
W
γ
γ
γ ==

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Phase RelationsPhase Relations
Consider a unit volume of the soil solids,Consider a unit volume of the soil solids,
where Vs = 1.
soil
air
water
Vs =1
Gsγw
SreγwSre
e
Phase Diagram
volumes masses
s
v
V
V
e =
eS
V
V
x
V
V
V
V
r
s
v
v
w
s
w
==
wss
s
s
G
V
W
γγ ==

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‫للتربة‬ ‫الظاهرية‬ ‫العلاقات‬‫للتربة‬ ‫الظاهرية‬ ‫العلاقات‬Phase RelationsPhase Relations
From the previous definitions,From the previous definitions,
soilsoil
airair
waterwater
1 Gsγw
Sreγw
Sr e
e
Phase Diagram
s
r
s
w
c
G
eS
W
W
w ==
e1
e
V
V
n
t
v
+
==

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Phase RelationsPhase Relations
soil
air
water
1 Gsγw
Sreγw
Sre
e
Phase Diagram
w
rs
t
t
b
e1
eSG
V
W
γγ
+
+
==
w
s
t
t
sat
e1
eG
V
W
γγ
+
+
==
w
s
t
s
d
e1
G
V
W
γγ
+
==

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‫النسبية‬ ‫الكثافة‬‫النسبية‬ ‫الكثافة‬Relative DensityRelative Density
It is a measure of the soil state of
compactness, and expressed as:
minmax
max
r
e-e
e-e
=D
‫فى‬ ‫ا‬ً ‫غالب‬ ‫وتستخدم‬ ‫الدمك‬ ‫حالة‬ ‫وهى‬ ‫النسبية‬ ‫الكثافة‬ ‫هى‬
‫الرملية‬ ‫التربة‬

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EXAMPLE 1EXAMPLE 1
A sample of saturated clay has a water content Wc =
47.0% and specific gravity Gs = 2.7. Calculate the voids
ratio e, the porosity n, and the saturated unit weight γsat.
r
sc
S
GxW
=e
1.27=
1
2.7x0.47
=e
e+1
e
=n
x
e+1
e+G
= w
s
sat γγ
2.27
3.97
=1x
1.27+1
1.27+2.7
=

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EXAMPLE 1
Solution Using Prism:Solution Using Prism:
soil
water
Vs =
1/2.7
ws= 1.0
Ww =
0.47 gm
Vv = Vw
= 0.47
1.27=0.47x2.7=
2.7
1
0.47
=
V
V
=e
s
v
0.56=
2.7
1
+0.47
0.47
=
V
V
=n
t
v
3
sat
gm/cm1.75=
2.7
1
47.0
1+0.47
=
V
W
=
+
γ

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EXAMPLE 2EXAMPLE 2
The weight of a wet specimen of clay is 34.62 gm. TheThe weight of a wet specimen of clay is 34.62 gm. The
dry weight = 20.63 gm. Before drying, the specimen wasdry weight = 20.63 gm. Before drying, the specimen was
immersed in mercury and its volume was found to beimmersed in mercury and its volume was found to be
24.26 cm24.26 cm33
, if G, if Gss = 2.7, calculate the water content Wc,= 2.7, calculate the water content Wc,
the voids ratio e, and the degree of saturation Sthe voids ratio e, and the degree of saturation Srr..
70.40%100x
20.36
14.26
%
W
W
=W
s
w
c ==
3
s cm7.54=
1.0x2.7
20.36
=V
Solution:
Ww = 34.62 - 20.36 = 14.26 gm
Water content, Wc = 70.40%
where

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2.22=
7.54
16.72
=
V
V
=e
s
v
%
V
V
=S
v
w
r
%85.29=100x
16.72
1
14.26
=Sr
Vv = V - Vs
Vv = 24.26 - 7.54 = 16.72 cm3
Voids ratio, e = 2.22
Degree of Saturation, Sr = 85.29%.

24. May 28, 2015 Soil Mechanics
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QUESTIONS