Civil Engineering Department
Soil Mechanics803440-3
Introduction
Lecture 3Week 3
2014/2015
UMM AL-QURA UNIVERSITY
Content
• Phase Diagram
• Specific Gravity
• Volume and Weight Relationships
(Porosity, Saturation, Void Ratio, Moisture Content,
Unit Weight)
• Relationships
• Relative Density
Specific Gravity
Gsis defined as the ratio of the unit weight of a given
material to the unit weight of water.
wwws ρ
ρ
g ρ
g ρ
γ
γG
Density ρ
tUnit Weighγ
Specific Gravity
Phase Diagram
Air
Water
Solids
3 Phase System
Phase Diagram
Air
Solids
2 Phase System (Dry)
Phase Diagram
Water
Solids
2 Phase System (Saturated)
Phase Diagram
Phase Diagram
W Total Weight V Total VolumeWw Water Weight Vw Water VolumeWs Solids Weight Vs Solids VolumeWa Air Weight = 0 Va Air Volume
Phase Diagram
W = Ww +Ws
V =Vs +Vw +Va
Vv =Vw +VaV =Vs +Vv
Volume Relationships
Porosity (n)
V
Vn v
Void Ratio (e)
s
v
V
Ve
Degree of Saturation (S)
v
w
V
VS
n1
ne
Prove!!
e1
en
Volume Relationships
Moisture Content (w)
s
w
M
Mw
Unit Weight (γ)
V
Wγ
Dry Unit Weight (γd)
V
Wγ s
d
Prove!!
w1
γγd
Questions?!
Basic Relations
s
w
W
Ww
V
Wγ
V
Vn v
s
v
V
Ve
v
w
V
VS
w
ss γ
γG
γ, e, w, Gs Relationships
Solids Weight in Terms of Specific Gravity Gs
swss
ws
s
w
ss
w
ss
VγGW
γV
W
γ
V/W
γ
γG
swssw VγG w WwW
Water Weight in Terms of Specific Gravity Gs
γ, e, w, Gs Relationships
Soil Unit Weight
vs
swssws
VV
VγwGVγG
Divide by Vs
γ, e, w, Gs Relationships
With the same substitution for Ws we got:
Dry Unit Weight
Void Ratio
Saturation
γ, e, w, Gs Relationships
Group Work
e
γeGγ wssat
1
Prove that for Saturation Condition:
swGe
Questions?!
Soil Unit Weight
vs
swssws
VV
VγwGVγG
Divide by Vs
γ, n, w, Gs Relationships
Substitute for (e) by
n1
ne
Soil Unit Weight
nn
nwγG ws
11
11
γ, n, w, Gs Relationships
nwγG ws 11
Dry Soil Unit Weight (w=0) nγG ws 1
Saturated Soil Unit Weight (Ww= nV) ws γnnG 1
Questions?!
Various Unit-Weight Relationships
Typical Values
Example 3.2
Example 3.4
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