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01/05/23 BYDr.IBRAHIM
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Soil Phase RelationshipsSoil Phase Relationshipsللتربة الظاهرية للتربة العالقات الظاهرية العالقات
01/05/23 Soil Phase Relationships 2
التربة التربة مكونات Soil CompositionSoil Compositionمكونات
Soil Grain or Soil Grain or particleparticle
التربة التربة حبيبات Soil GrainsSoil Grains( ( 11حبيبات
22 & ) & )33 ) )Voids: Water + AirVoids: Water + Air
الفراغات )عبارة عن ماء وهواء(الفراغات )عبارة عن ماء وهواء(
VoidsVoids
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الفراغات الفراغات نسبة Void RatioVoid Ratioنسبة
Solid, VSolid, Vss
Void, VVoid, Vvv
e =e =VVvv
VVss
high e =high e = LooseLooseسائبسائب
low e =low e = DenseDenseكثيفكثيف
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Saturation Saturation بالمياه بالمياه التشبع التشبع
Voids, VVoids, Vv v = V= Vww + V+ Vaa
Air, Va
Water, VWater, Vww
VVvv = V = Vw w + V+ Vaa
SSrr = =
fully saturatedfully saturatedSSrr = 100 % = 100 %
تماما مشبع تماما 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 grains Soil grains التربة التربة حبيبات حبيباتWater Water مياهمياهAir Air هواءهواء
Three Phases of Mineral SoilsThree Phases of Mineral Soils
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Weight and volume of soil Weight and volume of soil sample depends on:sample depends on:Specific gravity of soil grains Specific gravity of soil grains
(solids)(solids)The size and space between The size and space between
soil grains (voids and pores)soil grains (voids and pores)Volume of void space filled Volume of void space filled
with waterwith water
Weight Volume RelationshipsWeight Volume Relationships
• Water
• Solids
• Air
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PHASE DIAGRAMPHASE DIAGRAMTo compute the masses )or weights) and To compute the masses )or weights) and
volumes of the volumes of the threethree different phases. different phases.
soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
Idealized Prism
NotationNotation W = weight W = weight الوزنالوزنV = volume V = volume الحجمالحجمs = soil grainss = soil grainsw = waterw = watera = aira = airv = voidsv = voidst = totalt = total
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DefinitionsWater content )wWater content )wcc)) )) المياه المياه محتوى is a measure is a measure ((محتوى
of the water or Moisture present in the soil.of the water or Moisture present in the soil.
Phase Diagram
s
wc W
Ww
Expressed as percentage.Expressed as percentage.
Range = 0 – 100+%.Range = 0 – 100+%.
X 100%
soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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DefinitionsDefinitionsVoid ratio (e) Void ratio (e) (( الفراغات الفراغات نسبة is a is a ((نسبة
measure of the volume of voids. measure of the volume of voids.
Phase Diagram
S
V
VVe
soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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DefinitionsDefinitionsPorosity (n) Porosity (n) ((المساميةالمسامية)) is also a measure of the is also a measure of the
volume of voids, expressed as a percentage. volume of voids, expressed as a percentage.
Phase Diagram
t
vVVn X 100%
Theoretical range: Theoretical range: 0 – 100%0 – 100%
soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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DefinitionsDefinitionsDegree of saturation (SDegree of saturation (Srr) ) (( التشبع التشبع درجة is the is the ((درجة
percentage of the void volume filled by water.percentage of the void volume filled by water.
Phase Diagram
V
Wr V
VS
Range: 0 – 100%Range: 0 – 100%
X 100%
DryDrySaturatedSaturated
soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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DefinitionsDefinitions
Bulk density (Bulk density (bb) ) (( الكلية الكلية الكثافة is the density is the density ((الكثافةof the soil in the current state.of the soil in the current state.
Phase Diagram
t
tVW
b
Units: t/mUnits: t/m33, g/cm, g/cm33, kN/m, kN/m33 soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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DefinitionsDefinitions
Saturated density (Saturated density (satsat) ) (( المشبعة المشبعة الكثافة is the is the ((الكثافةdensity of the soil when the voids are filled with water. density of the soil when the voids are filled with water.
: تكون عندما التربة كثافة هى المشبعة : الكثافة تكون عندما التربة كثافة هى المشبعة الكثافةبالماء مملوءة بالماء الفراغات مملوءة الفراغات
Submerged density )Submerged density )subsub( ( )) المغمورة المغمورة الكثافة ))الكثافةis the effective density of the soil when is the effective density of the soil when it is submerged. it is submerged.
: عندما الفعالة التربة كثافة هى المغمورة : الكثافة عندما الفعالة التربة كثافة هى المغمورة الكثافةالماء فى مغمورة الماء تكون فى مغمورة sub= sat - wتكون
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DefinitionsDefinitionsDry density (Dry density (dd) ) (( الجافة الجافة الكثافة is the density of the soil in dry is the density of the soil in dry ((الكثافة
state state : الجافة الحالة فى التربة كثافة هى الجافة : الكثافة الجافة الحالة فى التربة كثافة هى الجافة الكثافة
Phase Diagram
t
sVW
d
Units: t/mUnits: t/m33, kg/m, kg/m33, kN/m, kN/m33 soil
air
water
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
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Phase RelationsPhase RelationsConsider a unit volume of the soil solids,Consider a unit volume of the soil solids,where Vs = 1.
soil
air
water
Vs =1 Gsw
SrewSree
Phase Diagram
The other volumes The other volumes can be obtained can be obtained from the previous from the previous definitions.definitions.
Weight = Density x Weight = Density x VolumeVolume
volumes masses
The weights can The weights can be obtained be obtained from:from:
w
ss
s
ss G ,
VW
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Phase RelationsPhase RelationsConsider a unit volume of the soil solids,Consider a unit volume of the soil solids,where Vs = 1.
soil
air
water
Vs =1 Gsw
SrewSree
Phase Diagram
volumes masses
s
vVVe
e S VV x
VV
VV
rs
v
v
w
s
w
wsss
s G VW
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للتربة الظاهرية للتربة العالقات الظاهرية Phase PhaseالعالقاتRelationsRelations
From the previous definitions,From the previous definitions,
soilsoil
airair
waterwater
1 Gsw
SrewSr e
e
Phase Diagram
s
r
s
wc G
eSWWw
e1e
VVn
t
v
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Phase RelationsPhase Relations
soil
air
water
1 Gsw
SrewSre
e
Phase Diagram
wrs
t
tb e1
eSGVW
ws
t
tsat e1
eGVW
ws
t
sd e1
GVW
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النسبية النسبية الكثافة Relative RelativeالكثافةDensityDensityIt is a measure of the soil state of
compactness, and expressed as:
minmax
maxr e - e
e - e = D
الدمك حالة وهى النسبية الكثافة هىالرملية التربة فى غالبا وتستخدم
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EXAMPLE 1EXAMPLE 1A 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 sat.
r
sc
SG x W = e
1.27 = 1
2.7 x 0.47 = e
e + 1e =n
x e + 1e + G = w
ssat
2.273.97 = 1 x
1.27 + 11.27 + 2.7 =
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EXAMPLE 1Solution Using Prism:Solution Using Prism:
soil
water
Vs =
1/2.7ws= 1.0
Ww = 0.47 gm
Vv = Vw = 0.47
1.27=0.47x2.7=
2.71
0.47=VV=e
s
v
0.56=
2.71+0.47
0.47=VV=n
t
v
3
sat
gm/cm 1.75=
2.7147.0
1+0.47
=VW=
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EXAMPLE 2EXAMPLE 2The weight of a wet specimen of clay is 34.62 gm. The The weight of a wet specimen of clay is 34.62 gm. The dry weight = 20.63 gm. Before drying, the specimen was dry weight = 20.63 gm. Before drying, the specimen was immersed in mercury and its volume was found to be immersed 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% 100 x 20.3614.26 %
WW =W
s
wc
3s cm 7.54 =
1.0 x 2.720.36 = V
Solution:Ww = 34.62 - 20.36 = 14.26 gm
Water content, Wc = 70.40%where
01/05/23 Soil Phase Relationships 23
2.22 = 7.54
16.72 = VV = e
s
v
% VV = S
v
wr
% 85.29 = 100 x 16.72
114.26
= Sr
Vv = V - Vs
Vv = 24.26 - 7.54 = 16.72 cm3
Voids ratio, e = 2.22
Degree of Saturation, Sr = 85.29%.
May 1, 2023 Soil Mechanics 24
QUESTIONS