Adi shankara institute of engineering and technology

? =
?
? − ?
? =
?
? + ?

ADI SHANKARA INSTITUTE OF ENGINEERING AND TECHNOLOGY KALADY
Department of Civil Enggineering, ASIET Page 172
ρ
sat
=
𝐌 ( ?𝐚???𝐚??? )
?
d. Submerged Mass Density ( ρ
’
): Submerged mass per unit of total volume.
ρ
’
=
𝑴 ( 𝑺?????𝒈?? )
?
ρ
’
= ρ
sat
- ρ
w
ρ
w
– density of water
e. Mass density of solids ( ρ
s
) : Ratio of mass of solids to the volume of solids
3.5 Volume-Weight Relationship
Volume weight relationships are expressed in unit weight. Weight of soil per unit volume is known as
unit weight.
a. Bulk unit weight ( γ) : Total weight(W) per unit total volume(V).
γ =
?
?
b. Dry unit weight ( γ
d
) : Weight of solids (W
s
) per unit total volume (V).
γ
d
=
Ws
?
c. Saturated Mass Density (γ
sat
) : Bulk unit weight of the soil when it is fully saturated.
γ
sat
=
? ( ?𝐚???𝐚??? )
?
d. Submerged Mass Density ( γ
’
): Submerged weight per unit of total volume.
γ
’
=
? ( 𝑺?????𝒈?? )
?
γ
’
= γ
sat
- γ
w
γ
w
– unit weight of water
e. Unit weight of soil solids ( γ
s
) : Ratio of the weight of solids to the volume of solids.
3.6 Basic Relationships
S.No Relationship in Mass density Relationship in Unit weight
1
? =
?
? + ?
? =
?
? + ?
2
? =
?
? − ?
? =
?
? − ?
3 n
a
=na
c
n
a
=na
c
4
𝛒 =
( 𝐆 + 𝐒? ) 𝛒𝐰
? + ?
𝛄 =
( 𝐆 + 𝐒? ) 𝛄𝐰
? + ?
S.No Relationship in Mass density Relationship in Unit weight
5
ρ
d
=
𝐆𝛒𝐰
? + ?
γ
d
=
𝐆𝛄𝐰
? + ?
6
𝛒?𝐚? =
( 𝐆 + ? ) 𝛒𝐰
? + ?
𝛄?𝐚? =
( 𝐆 + ? ) 𝛄𝐰
? + ?

ADI SHANKARA INSTITUTE OF ENGINEERING AND TECHNOLOGY KALADY
Department of Civil Enggineering, ASIET Page 173
7
𝛒 ’ =
( 𝐆 − ? ) 𝛒𝐰
? + ?
𝛄 ’ =
( 𝐆 − ? ) 𝛄𝐰
? + ?
8
? =
??
𝑺
? =
??
𝑺
9
𝛒? =
𝛒
? + 𝐰
𝛄? =
𝛄
? + 𝐰
10
𝛒? =
? − ?𝐚 𝐆𝛒𝐰
? + 𝐰𝐆
𝛄? =
? − ?𝐚 𝐆𝛄𝐰
? + 𝐰𝐆
4. Properties of soil
Divided into two categories- Engineering and index properties
4.1 Engineering properties
 Permeability – Required for estimation of seepage discharge through earth
 Compressibility- Required for the computation of settlement of structures founded on soil
 Shear strength- Requires to determine the stability of slopes, bearing capacity of soils and
earth pressure
Note: All the above three parameters discussed in detail in upcoming topics .
4.2 Index properties
 Divided into two categories- (1) Properties of individual particles and (2) Properties of soil
mass / aggregate properties
4.2.1 Properties of Individual Particles.
 Determined from a remoulded, disturbed sample.
 Depends on individual grains
 Independent of the manner of soil formation
 Important properties of individual particles of coarse grained soils are particle size
distribution and grain shape
4.2.2 Properties of aggregate properties
 Depends upon mode of soil formation, soil history and soil structure
 Determined from undisturbed samples
 Aggregate property of the coarse grained soils of great practical importance is its relative
density
4.3 Mechanical Analysis/ Particle size analysis ( Refer G.T Lab manual)
It is a method of separation of soils into different fractions based on the particle size. It is shown
graphically on a particle size distribution curve. It is done in two ways
(1) Sieve Analysis – (a) Dry sieve Analysis for coarse grained soils particle size greater than 75
micron – set of sieves used of gravel fraction- 20 mm, 10 mm, 4.75 mm sand fraction 2 mm, 1
mm, 600 μ, 425 μ , 212 μ , 150 μ and 75 μ – (b ) wet sieve analysis is employed if the soil contains
substantial quantity of fine particles.