specific gravity void ratio, saturation ,water contents

1. 1
Course No. : CE 341
Course Name: Geotechnical Engineering I
Credit : 3

2. 2
WEIGHT VOLUME RELATIONSHIPS
Mohammad Riduan
Lecturer
Civil Engineering Department
Dhaka International University

3. 3
 Soil deposits comprise the accumulated solid particles plus the
void space between the particles
 The void spaces are partially or completely filled with water or
other liquid.
 Voids space not occupied by fluid are filled with air or other gas.
 Hence soil deposits are referred to as three-phase system,
i.e. Solid + Liquid (water) + Gas (air)
GENERAL

4. 4
 Bulk soil as it exists in nature is a more or less random
accumulation of soil particles, water, and air as shown
above.
 Properties such as strength, compressibility, permeability
are directly related to the ratio and interaction of these
three phases.
 Therefore, an understanding of the terminology and
definitions relating to soil composition is fundamental to the
study of soil mechanics and geotechnical engineering as a
whole.
GENERAL (continued)

5. 5
For purpose of study and analysis it is convenient to represent
the soil mass by a PHASE DIAGRAM, with part of the diagram
representing the solid particles, part representing water or
liquid, and another part air or other gas.
Volumes Weights
PHASE DIAGRAM

6. 6
Phase diagram in terms of mass

7. 7
Possible Cases:

8. 8
The total volume of a given soil sample can be
expressed as:
V Vs Vv Vs VwVa
Where
Va = Volume of air
V = Total volume
Vs = Volume of soil solids
Vv = Volume of voids
Vw = Volume of water
Assuming that the weight of the air is negligible, we
can give the total weight of the sample as
W WsWw
Where Ws = weight of solids
Ww = weight of water
In engineering practice we usually measure the
total volume, V, the mass of water, Mw, and the
mass of dry solid Ms.

9. Porosity and degree of saturation are commonly expressed as a
9 percentage.
Volume Relationships
There are three volumetric ratios that are very useful in
geotechnical engineering , and these can be determined directly
from the phase diagram
1. Void Ratio e 
Vv
Vs
2. Porosity
V
n 
Vv
3. Degree of
Saturation
S 
Vw
Vv

10. Porosity (n) is defined as the ratio of
volume of void to the total volume in a
given volume of soil.
Degree of Saturation (S) is defined as the
ratio of volume of water to the volume of
voids in a given volume of soil.
10
Void Ratio (e) is defined as the ratio of
volume of voids to the volume of solids
in a given volume of soil.

11. 11
Weight or Mass Relationships
The common term used for weight relationships are:
• Moisture content
Moisture content (w) is also referred
to as water content and is defined as
the ratio of weight of water to the
weight of solids in a given volume of
soil:
w 
ww
ws

12. 12
V
 
W
Weight-Volume, Mass-Volume Relationships
I. Unit Weights (N/m3 or kN/m3)
1.Unit weight (total, wet or moist unit weight) ()
is the weight of soil per unit volume.
s
s
s
V
W
 
w
w
V

Ww

3
w
(  9.807kN / m )
2. Solid unit weight
3. Unit weight of water

13. 13
Weight-Volume, Mass-Volume Relationship
(S 100%)
V

Ws Ww
sat

4. Dry unit weight
V
d

Ws

5. Saturated unit weight
6. Submerged unit weight
w
 /
  

14. Note: The density/or unit weight are ratios which connects the
volumetric side of the PHASE DIAGRAM with the mass/or weight
14
side.
Density and Unit Weight
• Mass is a measure of a body's
inertia, or its "quantity of
matter". Mass does not changed
at different places.
• Weight is force, the force of
gravity acting on a body. The
value is different at various
places.
• The unit weight is more
frequently used than the density
is (e.g. in calculating the
overburden pressure).
w
s
w
w
s s
s
Mass
Volume
 
  g 
  g 
G 
g :accelerationduetogravity
  g  9.8m
sec2
Water,  9.8 kN
m3
Unit weight ,  
Weight

Massg
Volume Volume
Density,  

15. 15
The knowledge of specific gravity is required in
calculation of soil properties like void ratio, degree
of saturation and also weight-volume relationship.
Definition: Specific gravity G is defined as the
ratio of the unit weight ( or density ) of soil solids
only to unit weight (or density ) of water.

16. 16
Relationships Between Various Physical Properties
All the weight - volume relationships needed in soil
mechanics can be derived from appropriate
combinations of six fundamental definitions. They
are:
1. Void ratio
2. Porosity
3. Degree of saturation
4. Water content
5. Unit weight
6. Specific gravity

17. 1. Relationship between void ratio and porosity
2. Relationship among Void ratio, Degree of Saturation,
Water content, and Specific Gravity
GsVs
w 
ww 
wVw

wVw

Vw
ws sVs wGsVs
Dividing the denominator and numerator of the R.H.S. by Vv yields:
Se  wGs
This is a very useful relation for solving THREE-PHASE
17
RELATIONSHIPS.

18. 18
3. Relationship among Unit Weight, Void Ratio,
Degree of Saturation and Specific Gravity
Vs Vv

wVw wGsVs
w
1 e
 
W

Ww Ws

wVw sVs
V Vs Vv Vs Vv
 
(SeGs )

Notes:
• Unit weights for dry, fully saturated and submerged cases
can be derived from the upper equation
• Water content can be used instead of degree of saturation.
2
 

sub
• Submerged unit weight can be approximated as

19. 19
Various Unit Weight Relationships

20. 20
Too Much Stress???

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22. 22
Example 1
Part a=??????
Part b= Confused??????
Part c= which formula we can use??
Part d= Let’s try for the last time!!

23. emax
emin
emeasured
dmax d min
d measured
increasing density
m in
m a x
x100
r
e  e
em a x  e
D ( % ) 
Relative Density
The term relative density is commonly used to
indicate the in situ denseness or looseness of
granular soil.

24. Problem: For a given soil sample, emax
= 0.75,
emin=0.46, and Gs =2.68. What is the moist unit weight
of compaction(kN/m3) in field if Dr = 78% and w = 9%?