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# Earth Pressure Theories Civil Engineering (CE) Notes | EduRev

## Civil Engineering (CE) : Earth Pressure Theories Civil Engineering (CE) Notes | EduRev

``` Page 1

1

Short Notes for Soil Mechanics & Foundation Engineering
Properties of Soils
Water content
• 100
W
S
W
w
W
=?
W W = Weight of power
W S = Weight of solids

Void ratio
•
v
s
V
e
V
=
V v = Volume of voids
V =  Total volume of soil

Degree of Saturation
• 100
w
v
V
S
V
=?
V w = Volume of water
V v = Volume of voids
0 = S= 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100%

Air Content
• 1
a
c
v
V
as
V
= = -    V a = Volume of air
S r + a c = 1
% Air Void
•
Volume of air
% 100 100
Total volume
a
a
V
n
V
= ? = ?

Unit Weight
• Bulk unit weight
sw
s w a
WW W
V V V V
?
+
==
++

• Dry Unit Weight
s
d
W
V
? =

o Dry unit weight is used as a measure of denseness of soil
• Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total
volume.
sat
sat
W
V
? =
• Submerged unit weight or Buoyant unit weight
Page 2

1

Short Notes for Soil Mechanics & Foundation Engineering
Properties of Soils
Water content
• 100
W
S
W
w
W
=?
W W = Weight of power
W S = Weight of solids

Void ratio
•
v
s
V
e
V
=
V v = Volume of voids
V =  Total volume of soil

Degree of Saturation
• 100
w
v
V
S
V
=?
V w = Volume of water
V v = Volume of voids
0 = S= 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100%

Air Content
• 1
a
c
v
V
as
V
= = -    V a = Volume of air
S r + a c = 1
% Air Void
•
Volume of air
% 100 100
Total volume
a
a
V
n
V
= ? = ?

Unit Weight
• Bulk unit weight
sw
s w a
WW W
V V V V
?
+
==
++

• Dry Unit Weight
s
d
W
V
? =

o Dry unit weight is used as a measure of denseness of soil
• Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total
volume.
sat
sat
W
V
? =
• Submerged unit weight or Buoyant unit weight

2

'
sat w
? ? ? =-

sat
? = unit wt. of saturated soil
? = unit wt. of water
• Unit wt. of solids:
s
s
s
W
V
? =
Specific Gravity
True/Absolute Special Gravity, G
• Specific gravity of soil solids (G) is the ratio of the weight of a given volume of solids to the
weight of an equivalent volume of water at 4 ?.
.
ss
s w w
W
G
V
?
??
==

• Apparent or mass specific gravity (G m):
or  or
.
d sat
m
ww
W
G
V
? ? ?
??
==

where, ? is bulk unit wt. of soil
? = ? sat for saturated soil mass
? = ? d for dry soil mass
G m < G

Relative density (I D)
• To compare degree of denseness of two soils.
1

D
Shear strength
Compressi t
I
bili y
? ?
max
max min
% 100
D
ee
I
ee
-
=?
-

min
min max
11
-
% 100
11
-
dd
D
dd
I
??
??
=?

Relative Compaction
• Indicate: Degree of denseness of cohesive + cohesionless soil

max
D
c
D
R
?
?
=
Relative Density
• Indicate: Degree of denseness of natural cohesionless soil
Some Important Relationships
• Relation between ,
d
??
1
d
w
?
? =
+

(ii)
1
s
V
V
e
=
+
(iii)
1
s
W
W
w
=
+

Page 3

1

Short Notes for Soil Mechanics & Foundation Engineering
Properties of Soils
Water content
• 100
W
S
W
w
W
=?
W W = Weight of power
W S = Weight of solids

Void ratio
•
v
s
V
e
V
=
V v = Volume of voids
V =  Total volume of soil

Degree of Saturation
• 100
w
v
V
S
V
=?
V w = Volume of water
V v = Volume of voids
0 = S= 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100%

Air Content
• 1
a
c
v
V
as
V
= = -    V a = Volume of air
S r + a c = 1
% Air Void
•
Volume of air
% 100 100
Total volume
a
a
V
n
V
= ? = ?

Unit Weight
• Bulk unit weight
sw
s w a
WW W
V V V V
?
+
==
++

• Dry Unit Weight
s
d
W
V
? =

o Dry unit weight is used as a measure of denseness of soil
• Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total
volume.
sat
sat
W
V
? =
• Submerged unit weight or Buoyant unit weight

2

'
sat w
? ? ? =-

sat
? = unit wt. of saturated soil
? = unit wt. of water
• Unit wt. of solids:
s
s
s
W
V
? =
Specific Gravity
True/Absolute Special Gravity, G
• Specific gravity of soil solids (G) is the ratio of the weight of a given volume of solids to the
weight of an equivalent volume of water at 4 ?.
.
ss
s w w
W
G
V
?
??
==

• Apparent or mass specific gravity (G m):
or  or
.
d sat
m
ww
W
G
V
? ? ?
??
==

where, ? is bulk unit wt. of soil
? = ? sat for saturated soil mass
? = ? d for dry soil mass
G m < G

Relative density (I D)
• To compare degree of denseness of two soils.
1

D
Shear strength
Compressi t
I
bili y
? ?
max
max min
% 100
D
ee
I
ee
-
=?
-

min
min max
11
-
% 100
11
-
dd
D
dd
I
??
??
=?

Relative Compaction
• Indicate: Degree of denseness of cohesive + cohesionless soil

max
D
c
D
R
?
?
=
Relative Density
• Indicate: Degree of denseness of natural cohesionless soil
Some Important Relationships
• Relation between ,
d
??
1
d
w
?
? =
+

(ii)
1
s
V
V
e
=
+
(iii)
1
s
W
W
w
=
+

3

• Relation between e and n
1
e
n
e
=
+
or
1
n
e
n
=
-

• Relation between e, w, G and S:
Se = w. G
• Bulk unit weight () ? in terms of G, e, w and
w
? ? , G, e, S r,
w
?
()
1
rw
G eS
e
?
?
+
=
+

(1 )
(1 )
w
Gw
e
?
?
+
=
+
{Srxe = wG}
• Saturated unit weight ( .) sat ? in terms of G, e &
w
?
S r = 1 .
1
sat w
Ge
e
??
+ ??
=
??
+
??

• Dry unit weight ()
d
? in terms of G, e and
w
?
S r = 0
(1 )
11
1
w w a w
d
G G G
wG
e wG
S
? ? ? ?
?
-
= = =
++
+

• Submerged unit weight ( ') ? in terms of G, e and
w
?
sat w
? ? ? = - =
1
'.
1
w
G
e
??
- ??
=
??
+
??

• Relation between degree of saturation (s) w and G
1
(1 )
w
W
S
W
G
?
?
=
+-

• Calibration of Hydrometer

• Effective depth is calculated as
1
1
2
H
e
j
V
H H h
A
??
= + -
??
??
??

where, H 1 = distance (cm) between any hydrometer reading and neck.
h = length of hydrometer bulb
V H = volume of hydrometer bulb
Page 4

1

Short Notes for Soil Mechanics & Foundation Engineering
Properties of Soils
Water content
• 100
W
S
W
w
W
=?
W W = Weight of power
W S = Weight of solids

Void ratio
•
v
s
V
e
V
=
V v = Volume of voids
V =  Total volume of soil

Degree of Saturation
• 100
w
v
V
S
V
=?
V w = Volume of water
V v = Volume of voids
0 = S= 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100%

Air Content
• 1
a
c
v
V
as
V
= = -    V a = Volume of air
S r + a c = 1
% Air Void
•
Volume of air
% 100 100
Total volume
a
a
V
n
V
= ? = ?

Unit Weight
• Bulk unit weight
sw
s w a
WW W
V V V V
?
+
==
++

• Dry Unit Weight
s
d
W
V
? =

o Dry unit weight is used as a measure of denseness of soil
• Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total
volume.
sat
sat
W
V
? =
• Submerged unit weight or Buoyant unit weight

2

'
sat w
? ? ? =-

sat
? = unit wt. of saturated soil
? = unit wt. of water
• Unit wt. of solids:
s
s
s
W
V
? =
Specific Gravity
True/Absolute Special Gravity, G
• Specific gravity of soil solids (G) is the ratio of the weight of a given volume of solids to the
weight of an equivalent volume of water at 4 ?.
.
ss
s w w
W
G
V
?
??
==

• Apparent or mass specific gravity (G m):
or  or
.
d sat
m
ww
W
G
V
? ? ?
??
==

where, ? is bulk unit wt. of soil
? = ? sat for saturated soil mass
? = ? d for dry soil mass
G m < G

Relative density (I D)
• To compare degree of denseness of two soils.
1

D
Shear strength
Compressi t
I
bili y
? ?
max
max min
% 100
D
ee
I
ee
-
=?
-

min
min max
11
-
% 100
11
-
dd
D
dd
I
??
??
=?

Relative Compaction
• Indicate: Degree of denseness of cohesive + cohesionless soil

max
D
c
D
R
?
?
=
Relative Density
• Indicate: Degree of denseness of natural cohesionless soil
Some Important Relationships
• Relation between ,
d
??
1
d
w
?
? =
+

(ii)
1
s
V
V
e
=
+
(iii)
1
s
W
W
w
=
+

3

• Relation between e and n
1
e
n
e
=
+
or
1
n
e
n
=
-

• Relation between e, w, G and S:
Se = w. G
• Bulk unit weight () ? in terms of G, e, w and
w
? ? , G, e, S r,
w
?
()
1
rw
G eS
e
?
?
+
=
+

(1 )
(1 )
w
Gw
e
?
?
+
=
+
{Srxe = wG}
• Saturated unit weight ( .) sat ? in terms of G, e &
w
?
S r = 1 .
1
sat w
Ge
e
??
+ ??
=
??
+
??

• Dry unit weight ()
d
? in terms of G, e and
w
?
S r = 0
(1 )
11
1
w w a w
d
G G G
wG
e wG
S
? ? ? ?
?
-
= = =
++
+

• Submerged unit weight ( ') ? in terms of G, e and
w
?
sat w
? ? ? = - =
1
'.
1
w
G
e
??
- ??
=
??
+
??

• Relation between degree of saturation (s) w and G
1
(1 )
w
W
S
W
G
?
?
=
+-

• Calibration of Hydrometer

• Effective depth is calculated as
1
1
2
H
e
j
V
H H h
A
??
= + -
??
??
??

where, H 1 = distance (cm) between any hydrometer reading and neck.
h = length of hydrometer bulb
V H = volume of hydrometer bulb

4

Plasticity Index (I p):
• It is the range of moisture content over which a soil exhibits plasticity.
I p = W L - W p
W L = water content at LL
W p = water content at PL

I p (%) Soil Description
0
1 to 5
5 to 10
10 to 20
20 to 40
> 40
Non plastic
Slight plastic
Low plastic
Medium plastic
Highly plastic
Very highly plastic

Relative Consistency or Consistency – index (I c):
LN
C
p
WW
I
I
-
=

0

1
C
N L C
NP
For W W I
For W I W
=
=
? ? = ?
?
?=
?

Liquidity Index (I L)
NP
L
P
WW
I
I
-
=
For a soil in plastic state I L varies from 0 to 1.

Consist. Description I C I L
Liquid
Plastic

Semi-
solid

Solid
Liquid
Very soft
soft
medium
stiff
stiff
Very stiff
OR Hard

Hard OR
very hard
<0
0-0.25
0.25-0.5
0.50-0.75
0.75-1.00

>1

>1
>1
0.75-1.00
0.50-0.75
0.25-0.50
0.0-0.25

< 0

< 0

Flow Index (I f)
12
21
log10( / )
f
WW
I
NN
-
=

Toughness Index (I t)
P
T
F
I
I
I
=
• For most of the soils:  0 < I T < 3
Page 5

1

Short Notes for Soil Mechanics & Foundation Engineering
Properties of Soils
Water content
• 100
W
S
W
w
W
=?
W W = Weight of power
W S = Weight of solids

Void ratio
•
v
s
V
e
V
=
V v = Volume of voids
V =  Total volume of soil

Degree of Saturation
• 100
w
v
V
S
V
=?
V w = Volume of water
V v = Volume of voids
0 = S= 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100%

Air Content
• 1
a
c
v
V
as
V
= = -    V a = Volume of air
S r + a c = 1
% Air Void
•
Volume of air
% 100 100
Total volume
a
a
V
n
V
= ? = ?

Unit Weight
• Bulk unit weight
sw
s w a
WW W
V V V V
?
+
==
++

• Dry Unit Weight
s
d
W
V
? =

o Dry unit weight is used as a measure of denseness of soil
• Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total
volume.
sat
sat
W
V
? =
• Submerged unit weight or Buoyant unit weight

2

'
sat w
? ? ? =-

sat
? = unit wt. of saturated soil
? = unit wt. of water
• Unit wt. of solids:
s
s
s
W
V
? =
Specific Gravity
True/Absolute Special Gravity, G
• Specific gravity of soil solids (G) is the ratio of the weight of a given volume of solids to the
weight of an equivalent volume of water at 4 ?.
.
ss
s w w
W
G
V
?
??
==

• Apparent or mass specific gravity (G m):
or  or
.
d sat
m
ww
W
G
V
? ? ?
??
==

where, ? is bulk unit wt. of soil
? = ? sat for saturated soil mass
? = ? d for dry soil mass
G m < G

Relative density (I D)
• To compare degree of denseness of two soils.
1

D
Shear strength
Compressi t
I
bili y
? ?
max
max min
% 100
D
ee
I
ee
-
=?
-

min
min max
11
-
% 100
11
-
dd
D
dd
I
??
??
=?

Relative Compaction
• Indicate: Degree of denseness of cohesive + cohesionless soil

max
D
c
D
R
?
?
=
Relative Density
• Indicate: Degree of denseness of natural cohesionless soil
Some Important Relationships
• Relation between ,
d
??
1
d
w
?
? =
+

(ii)
1
s
V
V
e
=
+
(iii)
1
s
W
W
w
=
+

3

• Relation between e and n
1
e
n
e
=
+
or
1
n
e
n
=
-

• Relation between e, w, G and S:
Se = w. G
• Bulk unit weight () ? in terms of G, e, w and
w
? ? , G, e, S r,
w
?
()
1
rw
G eS
e
?
?
+
=
+

(1 )
(1 )
w
Gw
e
?
?
+
=
+
{Srxe = wG}
• Saturated unit weight ( .) sat ? in terms of G, e &
w
?
S r = 1 .
1
sat w
Ge
e
??
+ ??
=
??
+
??

• Dry unit weight ()
d
? in terms of G, e and
w
?
S r = 0
(1 )
11
1
w w a w
d
G G G
wG
e wG
S
? ? ? ?
?
-
= = =
++
+

• Submerged unit weight ( ') ? in terms of G, e and
w
?
sat w
? ? ? = - =
1
'.
1
w
G
e
??
- ??
=
??
+
??

• Relation between degree of saturation (s) w and G
1
(1 )
w
W
S
W
G
?
?
=
+-

• Calibration of Hydrometer

• Effective depth is calculated as
1
1
2
H
e
j
V
H H h
A
??
= + -
??
??
??

where, H 1 = distance (cm) between any hydrometer reading and neck.
h = length of hydrometer bulb
V H = volume of hydrometer bulb

4

Plasticity Index (I p):
• It is the range of moisture content over which a soil exhibits plasticity.
I p = W L - W p
W L = water content at LL
W p = water content at PL

I p (%) Soil Description
0
1 to 5
5 to 10
10 to 20
20 to 40
> 40
Non plastic
Slight plastic
Low plastic
Medium plastic
Highly plastic
Very highly plastic

Relative Consistency or Consistency – index (I c):
LN
C
p
WW
I
I
-
=

0

1
C
N L C
NP
For W W I
For W I W
=
=
? ? = ?
?
?=
?

Liquidity Index (I L)
NP
L
P
WW
I
I
-
=
For a soil in plastic state I L varies from 0 to 1.

Consist. Description I C I L
Liquid
Plastic

Semi-
solid

Solid
Liquid
Very soft
soft
medium
stiff
stiff
Very stiff
OR Hard

Hard OR
very hard
<0
0-0.25
0.25-0.5
0.50-0.75
0.75-1.00

>1

>1
>1
0.75-1.00
0.50-0.75
0.25-0.50
0.0-0.25

< 0

< 0

Flow Index (I f)
12
21
log10( / )
f
WW
I
NN
-
=

Toughness Index (I t)
P
T
F
I
I
I
=
• For most of the soils:  0 < I T < 3

5

• When I T < 1, the soil is friable (easily crushed) at the plastic limit.

• Shrinkage Ratio (SR)
12
12
100
d
VV
V
SR
ww
-
?
=
-

V 1 = Volume of soil mass at water content w 1%.
V 2 = volume of soil mass at water content w 2%.
V d = volume of dry soil mass
?
1
1
100
()
d
d
s
VV
V
SR
WW
?? -
?
??
??
=
-

If w 1 & w 2 are expressed as ratio,
1 2 1 2
12
12
( ) / ( ) /
,
dw
s
V V V V V
SR But w w
W W W
? --
= - =
-

?
1
.
sd
d w w
W
SR
V
?
??
==

Properties Relations
hip
Governing
Parameters
Plasticity      ? Plasticity Index
Better
Foundation
Material upon
Remoulding
?  Consistency
Index
Compressibility      ? Liquid Limit
Rate of loss in
shear strength
with increase in
water content
? Flow Index
Strength of
Plastic Limit
? Toughness
Index

Compaction of Soil

Optimum moisture content
max
()
1
d imum
optimum
w
?
? =
+

max
()
d imum
? = Maximum dry density
? = Density of soil
optimum
w = Optimum moisture content

```
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## Foundation Engineering

18 videos|20 docs|7 tests

,

,

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,

;