1. Soil Phase Relationships
‫العلقات الظاهرية للتربة‬
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2. Soil Composition‫مكونات التربة‬
Soil Grains (1‫حبيبات التربة‬
Voids: Water + Air (3 & (2
(‫الفراغات ) عبارة عن ماء وهواء‬
Soil Grain or
particle
Voids
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3. Void Ratio ‫نسبة الفراغات‬
Vv
e=
Vs
Void, Vv
high e = Loose
‫سائب‬
Solid, Vs
low e = Dense
‫كثيف‬
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4. Saturation ‫التشبع بالمياه‬
Vw
Sr = . 100
Vv
Air, Va
Voids, Vv = Vw + Va
Water, Vw fully saturated
Sr = 100 %
‫ا‬
ً‫مشبع تمام‬
Vv = Vw + Va Dry ‫ جاف‬Sr = 0 %
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5. Three Phases of Mineral Soils
Mineral soils are composed of:
 Soil grains ‫حبيبات التربة‬
 Water ‫مياه‬
 Air ‫هواء‬
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6. Weight Volume Relationships
Weight and volume of
soil sample depends on:
 Specific gravity of soil
grains (solids) • Air
 The size and space • Water
between soil grains
(voids and pores)
 Volume of void space • Solids
filled with water
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7. PHASE DIAGRAM
To compute the masses (or weights) and
volumes of the three different phases.
Notation Va air Wa=0
W = weight ‫الوزن‬
V = volume ‫الحجم‬ Vv
s = soil grains Vw water Ww
w = water Vt Wt
a = air
v = voids
Vs soil Ws
t = total
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Idealized Prism
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8. Definitions
Water content (wc) (‫ (محتوى المياه‬is a measure
of the water or Moisture present in the soil.
Ww
wc = X 100% Vv
Va air Wa=0
Ws Vw water Ww
Vt Wt
Expressed as percentage.
Vs soil Ws
Range = 0 – 100+%.
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Phase Diagram
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9. Definitions
Void ratio (e) (‫ (نسبة الفراغات‬is a measure
of the volume of voids.
Va air Wa=0
VV Vv
e= Vw water Ww
VS Vt Wt
Vs soil Ws
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Phase Diagram
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10. Definitions
Porosity (n) (‫ (المسامية‬is also a measure of the
volume of voids, expressed as a percentage.
Va Wa=0
Vv air
n= X 100%
Vv
Vw water Ww
Vt Vt Wt
Vs soil
Theoretical range: Ws
0 – 100%
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Phase Diagram
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11. Definitions
Degree of saturation (Sr) (‫ (درجة التشبع‬is the
percentage of the void volume filled by water.
Va air Wa=0
VW
Sr = X 100% Vv
VV Vw water Ww
Vt Wt
Range: 0 – 100%
Vs soil Ws
Dry
Saturated
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Phase Diagram
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12. Definitions
Bulk density (γ b) (‫ (الكثافة الكلية‬is the density of
the soil in the current state.
Va air Wa=0
Wt Vv
γb = Vw water Ww
Vt Vt Wt
Units: t/m3, g/cm3, kN/m3 Vs soil Ws
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Phase Diagram
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13. Definitions
Saturated density (γ sat) (‫ (الكثافة المشبعة‬is the
density of the soil when the voids are filled
with water.
‫الكثافة المشبعة: هى كثافة التربة عندما تكون الفراغات مملوءة بالماء‬
Submerged density (γsub) (‫ (الكثافة المغمورة‬is the
effective density of the soil when it is submerged.
‫الكثافة المغمورة: هى كثافة التربة الفعالة عندما تكون مغمورة فى الماء‬
γsub= γsat - γw
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14. Definitions
Dry density (γ d) (‫ (الكثافة الجافة‬is the density of the soil
in dry state ‫الكثافة الجافة: هى كثافة التربة فى الحالة الجافة‬
Va Wa=0
Ws air
γd = Vv
Vw water Ww
Vt Vt Wt
Units: t/m3, kg/m3, kN/m3
Vs soil Ws
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Phase Diagram
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15. Phase Relations
Consider a unit volume of the soil solids,
where Vs = 1.
volumes masses
The other volumes can
be obtained from the
air
previous definitions. e
The weights can be Sre water Sreγw
obtained from:
Weight = Density x Volume
Ws γs Vs =1 soil Gsγw
γs = , Gs =
Vs
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γw Soil Phase Relationships
Phase Diagram
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16. Phase Relations
Consider a unit volume of the soil solids,
where Vs = 1.
volumes masses
Vw Vw Vv
= x = Sr e air
Vs Vv Vs e
Ws Sre water Sreγw
= γ s = Gs γ w
Vs
Vs =1 soil
Vv Gsγw
e=
Vs
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Phase Diagram
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17. Phase Relations‫العلقات الظاهرية للتربة‬
From the previous definitions,
Vv e
n= =
Vt 1 + e e
air
Sr e water Sreγw
Ww S r e
wc = =
Ws Gs 1 soil Gsγw
Phase Diagram
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18. Phase Relations
Wt Gs + S r e
γb = = γw
Vt 1+ e
Wt Gs + e e
air
γ sat = = γw
Vt 1+ e Sre water Sreγw
Ws Gs
γd = = γw 1 soil Gsγw
Vt 1 + e
Phase Diagram
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19. Relative Density ‫الكثافة النسبية‬
It is a measure of the soil state of
compactness, and expressed as:
e max - e
Dr =
e max - e min
‫هى الكثافة النسبية وهى حالة الدمك وتستخدم غالبً فى التربة‬
‫ا‬
‫الرملية‬
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20. EXAMPLE 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.
Wc x G s Gs + e
e= γ sat = x γw
Sr 1+ e
0.47 x 2.7 2.7 + 1.27 3.97
e= = 1.27 = x1=
1 1 + 1.27 2.27
e
n=
1+ e
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21. EXAMPLE 1
Solution Using Prism:
Vv 0.47
e= = = 0.47x2.7 = 1.27
Vs 1
2.7
Vv 0.47
n= = = 0.56
Vt 0.47 + 1
2.7 Vv = Vw Ww =
W water
γ sat = = = 0.47 0.47 gm
V
0.47 + 1
= 1.75 gm/cm3 Vs = soil
1 ws= 1.0
0.47 +
2.7 1/2.7
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22. EXAMPLE 2
The weight of a wet specimen of clay is 34.62 gm. The dry
weight = 20.63 gm. Before drying, the specimen was
immersed in mercury and its volume was found to be 24.26
cm3, if Gs = 2.7, calculate the water content Wc, the voids
ratio e, and the degree of saturation Sr.
Solution:
Ww = 34.62 - 20.36 = 14.26 gm
Ww 14.26
Wc = %= x 100 = 70.40%
Ws 20.36
Water content, Wc = 70.40%
where
20.36
Vs = = 7.54 cm3
2.7 x 1.0
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23. Vv = V - Vs
Vv = 24.26 - 7.54 = 16.72 cm3
Vv 16.72
e= = = 2.22
Vs 7.54
Voids ratio, e = 2.22
Vw
Sr = %
Vv
14.26
Sr = 1 x 100 = 85.29 %
16.72
Degree of Saturation, Sr = 85.29%.
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24. QUESTIONS
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