The document discusses soil phase relationships and defines key terms. It describes how soil is composed of grains, water, and air which occupy volumes. The volume of voids is critical and affects other properties. Terms defined include void ratio, porosity, saturation, bulk density, saturated density, dry density, and relative density. Examples are provided to demonstrate calculating various phase properties from given data.

1. Soil Phase Relationships
‫العلقات الظاهرية للتربة‬
05/04/12 Soil Phase Relationships 1

2. Soil Composition‫مكونات التربة‬
Soil Grains (1‫حبيبات التربة‬
Voids: Water + Air (3 & (2
(‫الفراغات ) عبارة عن ماء وهواء‬
Soil Grain or
particle
Voids
05/04/12 Soil Phase Relationships 2

3. Void Ratio ‫نسبة الفراغات‬
Vv
e=
Vs
Void, Vv
high e = Loose
‫سائب‬
Solid, Vs
low e = Dense
‫كثيف‬
05/04/12 Soil Phase Relationships 3

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 %
05/04/12 Soil Phase Relationships 4

5. Three Phases of Mineral Soils
Mineral soils are composed of:
 Soil grains ‫حبيبات التربة‬
 Water ‫مياه‬
 Air ‫هواء‬
05/04/12 Soil Phase Relationships 5

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
05/04/12 Soil Phase Relationships 6

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
05/04/12 Soil Phase Relationships
Idealized Prism
7

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+%.
05/04/12 Soil Phase Relationships
Phase Diagram
8

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
05/04/12 Soil Phase Relationships
Phase Diagram
9

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%
05/04/12 Soil Phase Relationships
Phase Diagram
10

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
05/04/12 Soil Phase Relationships
Phase Diagram
11

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
05/04/12 Soil Phase Relationships
Phase Diagram
12

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
05/04/12 Soil Phase Relationships 13

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
05/04/12 Soil Phase Relationships
Phase Diagram
14

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
05/04/12
γw Soil Phase Relationships
Phase Diagram
15

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
05/04/12 Soil Phase Relationships
Phase Diagram
16

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
05/04/12 Soil Phase Relationships 17

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
05/04/12 Soil Phase Relationships 18

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
05/04/12 Soil Phase Relationships 19

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
05/04/12 Soil Phase Relationships 20

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
05/04/12 Soil Phase Relationships 21

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
05/04/12 Soil Phase Relationships 22

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%.
05/04/12 Soil Phase Relationships 23

24. QUESTIONS
April 5, 2012 Soil Mechanics 24