Lecture 2 grain size distribution

INTERNATIONAL UNIVERSITY
FOR SCIENCE & TECHNOLOGY
‫وا‬ ‫م‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬
CIVIL ENGINEERING AND
ENVIRONMENTAL DEPARTMENT
303322 - Soil Mechanics
Origin of soil & Grain Size
Dr. Abdulmannan Orabi
Lecture
2

Das, B., M. (2014), “ Principles of geotechnical
Engineering ” Eighth Edition, CENGAGE
Learning, ISBN-13: 978-0-495-41130-7.
Knappett, J. A. and Craig R. F. (2012), “ Craig’s Soil
Mechanics” Eighth Edition, Spon Press, ISBN: 978-
0-415-56125-9.
References
Dr. Abdulmannan Orabi IUST 2

Origin of Soil and Grain Size
The knowledge of sizes of solid particles comprising
a certain soil type and their relative proportion is
useful because it is used in;
Soil classification
Soil filter design
Predictions the behavior of a soil with respect
to shear strength, settlement and permeability

The classification of soils for engineering purposes
requires the distribution of grain sizes in a given
soil mass.
Soil can be range from boulders or cobbles of several
centimeters in diameter down to ultrafine-grained
colloidal materials.
Grain Size Distribution

Soils generally are called gravel, sand, silt, or clay,
depending on the predominant size of particles
within the soil.
Soil – Particle Size
The standard grain size analysis test determines the
relative proportions of different grain size as they
are distributed among certain size range.

To describe soils by their particle size, several
organizations have developed particle-size
classifications.
Particle-Size Classifications
Name of
organization
Grain size (mm)
Gravel Sand Silt Clay
MIT >2 2 to 0.06 0.06 to 0.002 < 0.002
USDA >2 2 to 0.05 0.05 to 0.002 < 0.002
AASHTO 76.2 to 2 2 to 0.075 0.075 to 0.002 < 0.002
USCS 76.2 to 4.75 4.75 t0 0.075 < 0.075
6Dr. Abdulmannan Orabi IUST

Gravels are pieces of rocks with occasional particles of
quartz, feldspar, and other minerals.
Sand particles are made of mostly quartz and feldspar.
Silts are the microscopic soil fractions that consist of
very fine quartz grains and some flake-shaped
particles that are fragments of micaceous minerals.
Clays are mostly flake-shaped microscopic and
submicroscopic particles of mica, clay minerals, and other
minerals.

Soils can be divided into cohesive and non-cohesive
soils. Cohesive soil contains clay minerals and posses
plasticity. Non-cohesive means the soil has no shear
strength if no confinement .Sand is non-cohesive and
non-plastic.
Furthermore, gravel and sand can be roughly classified
as coarse textured soils, wile silt and clay can be classified
as fine textures soils.

GravelsSand

Coarse –grained soilsFine –grained soils
GravelClay
Medium
Gravel
Coarse
Sand
Silt

• Angular particles are those that have been freshly broken up and
are characterized by jagged projections, sharp ridges, and flat
surfaces.
• Subangular particles are those that have been weathered to the
extent that the sharper points and ridges have been worn off.
Angular Subangular
Shape of bulky particles

• Subrounded particles are those that have been weathered to a
further degree than subangular particles.
• Rounded particles are those on which all projections have been
removed, with few irregularities in shape remaining.
• Well rounded particles are rounded particles in which the few
remaining irregularities have been removed.
RoundedSubrounded Well Rounded
Shape of bulky particles

A soil particle may be a mineral or a rock fragment.
A mineral is a chemical compound formed in nature
during a geological process, whereas a rock fragment
has a combination of one or more minerals. Based on
the nature of atoms, minerals are classified as
silicates, aluminates, oxides, carbonates and
phosphates.
Structure of Clay Minerals
Out of these, silicate minerals are the most important
as they influence the properties of clay soils.

Clay minerals are very tiny crystalline substances
evolved primarily from chemical weathering of
certain rock forming minerals, they are complex
alumino – silicates plus other metallic ions.
Clay minerals

Different arrangements of atoms in the silicate
minerals give rise to different silicate structures.
Clay minerals are composed of two basic units:
(1) silica tetrahedron and
(2) alumina octahedron.
These units are held together by ionic bonds.
Clay minerals

Silica Unit consists of a silicon ion surrounded by four
oxygen ions arranged in the form of a tetrahedron. A
combination of tetrahedrons forms a silica sheet. The basic
units combine in such a manner as to form a sheet.
Hydroxyl
Aluminum
Silica sheetSilica Tetrahedron
si

Aluminium (or Magnesium) Octahedral Unit
The octahedral unit has an aluminium ion or a
magnesium ion endorsed by six hydroxyl radicals or
oxygen arranged in the form of an octahedron. In some
cases, other cations (e.g. Fe) are present in place of Al
and Mg.
Alumina sheetAlumina Octahedron
Hydroxyl
Aluminum

The combination of tetrahedral silica units gives
a silica sheet (Figure b).
Three oxygen atoms at the base of each tetrahedron are
shared by neighboring tetrahedra.

The octahedral units consist of six hydroxyls
surrounding an aluminum atom (Figure c), and the
combination of the octahedral aluminum hydroxyl units
gives an octahedral sheet.
This also is called a gibbsite sheet (Figure d.)

From an engineering point of view, three
clay minerals of interest are
- Kaolinite,
- Illite, and
- Montmorillonite
Types of Clay Minerals

Kaolinite consists of repeating layers of elemental silica-
gibbsite sheets in a 1:1 lattice.
The atoms in a crystal are arranged in a definite orderly
manner to form a three dimensional net-work, called a
“lattice.”
Kaolinite
Silica sheet
Gibbsite sheet
Silica sheet
Gibbsite sheet
H bond
7.2Å

Kaolinite Mineral
The basic kaolinite unit is a two-layer unit that is formed
by stacking a gibbsite sheet on a silica sheet. These basic
units are then stacked one on top of the other to form a
lattice of the mineral.
Kaolinite
Silica sheet
Gibbsite sheet
Silica sheet
Gibbsite sheet
H bond
7.2Å

Kaolinite Mineral
The layers are held together by hydrogen bonding .
The strong bonding does not permit water to enter the
lattice. Thus, kaolinite minerals are stable and do not
expand under saturation. Kaolinite is the most
abundant constituent of residual clay deposits.
Kaolinite
Silica sheet
Gibbsite sheet
Silica sheet
Gibbsite sheet
H bond
7.2Å

• Each layer is about 7.2 ( 0.72 Nm)thick.Å
• A kaolinite particle may consist of over 100 stacks.
•Si4Al4O10(OH)8 Platy shape
•There is no interlayer swelling
Kaolinite
Silica sheet
Gibbsite sheet
Silica sheet
Gibbsite sheet
H bond
7.2Å

Kaolinite
The surface area of the kaolinite particles per unit mass is
about 15 m^2/g.
The surface area per unit mass is defined as specific surface
Joined by strong
hydrogen bond….no
easy separation

Illite consists of a gibbsite sheet bonded to two
silica sheets—one at the top and another at the
bottom. It is sometimes called clay mica.
The illite layers are bonded by potassium ions.
Potassium
10 Å
Silica sheet
Gibbsite sheet
Silica sheet
Silica sheet
Gibbsite sheet
Silica sheet
Illite
26

The negative charge to balance the potassium
ions comes from the substitution of aluminum
for some silicon in the tetrahedral sheets.
Potassium
10 Å
Silica sheet
Gibbsite sheet
Silica sheet
Silica sheet
Gibbsite sheet
Silica sheet
Illite

The bond with the non-exchangeable K+ ions are
weaker than the hydrogen bond in the Kaolite but
is stronger than the water bond of
montmorillonite.
The illite crystal does not swell so much in the
presence of water as does in montmorillonite
particles.
Illite

Montmorillonite has a structure similar to that of
illite—that is, one gibbsite sheet sandwiched between
two silica sheets.
Montmorillonite
10 Å
Silica sheet
Gibbsite sheet
Silica sheet
Silica sheet
Gibbsite sheet
Silica sheet
nH2O and exchangeable

In montmorillonite there is isomorphous substitution of
magnesium and iron for aluminum in the octahedral sheets.
Montmorillonite
10 Å
Silica sheet
Gibbsite sheet
Silica sheet
Silica sheet
Gibbsite sheet
Silica sheet
The specific surface is about 800 m^2/g.

Potassium ions are not present as in illite, and a large
amount of water is attracted into the space between the
layers. There exists interlayer swelling, which is very
important to engineering practice (expansive clay).
Montmorillonite
10 Å
Silica sheet
Gibbsite sheet
Silica sheet
Silica sheet
Gibbsite sheet
Silica sheet

When water is added to clay, these cations and a few
anions float around the clay particles.
This configuration is referred to as a diffuse double layer
The cation concentration decreases with the distance from
the surface of the particle
Clay Minerals
Larger negative charges are derived from larger specific
surfaces.
The clay particles carry a net negative charge on their
surfaces.

The force of attraction between water and clay
decreases with distance from the surface of the
particles. All the water held to clay particles by
force of attraction is known as double-layer
water.
The innermost layer of double-layer water,
which is held very strongly by clay, is known as
adsorbed water
This water is more viscous than free water is .
Clay Minerals

Water molecules are polar. Hydrogen atoms are not
axisymmetric around an oxygen atom; instead, they occur
at a bonded angle of 105° . As a result, a water molecule
has a positive charge at one side and a negative charge at
the other side. It is known as a dipole.
Dipolar water is attracted both by the negatively charged
surface of the clay particles and by the cations in the
double layer. The cations, in turn, are attracted to the soil
particles.
Clay Minerals

There is usually a negative electric charge
on the crystal surfaces and electro –
chemical forces on these surfaces are
therefore predominant in determining their
engineering properties.
Clay Minerals

Clay Minerals
Diffuse double layer
Distance from the clay particle
Concentrationofions
Anions
Cations
Surface of
clay particle

For all particle purpose , when the clay content
is about 50% or more. The sand and silt
particles float in clay matrix and the clay
minerals primarily dictate the engineering
properties of the soil.
Clay Minerals

Types of Soil Structures
• Single grained structure.
• Honeycomb structure.
• Flocculated structure and dispersed structure – in the case of
clay deposits.
• Course-grained skeleton structure and matrix structure – in
the case of composite soils.
Soil Structures

1) Single grained structure
Found in the case of coarse-grained soil deposits. When
such soils settle out of suspension in water, the particles settle
independently of each other.
Major force causing their deposition is gravitational and the
surface forces are too small to produce any effect. There will
be particle-to-particle contact in the deposit.
The void ratio attained depends on the relative size of
grains.
Soil Structures

2) Honeycomb structure
Associated with silt deposits.
When silt particles settle out of suspension, in additional to
gravitational forces, the surface forces also play a significant
role. When particles approach the lower region of
suspension they will be attracted by particles already
deposited as well as the neighbouring particles leading to
formation of arches.
The combination of a number of arches leads to the honey
comb structure.
Soil Structures

3) (a) Flocculated structure
There will be edge-to-edge and edge-to-face contact
between particles.
Soil Structures

3) (b) Flocculated structure
The particles will have face to face contact as shown below:
Soil Structures

4) (a) Course-grained skeleton
The course-grained skeleton structure can be
found in the case of composite soils in which the
course-grained fraction is greater in proportion
compared to fine-grained fraction. The course-
grained particles form the skeleton with particle
to particle contact and the voids between these
particles will be occupied by the fine-grained
particles.
Soil Structures

4) (b) Cohesive matrix structure
The cohesive matrix structure can be found in
composite soils in which the fine-grained fraction is
more in proportion compared to course grained
fraction. In this case the course-grained particles
will be embedded in fine-grained fraction and will
be prevented from having particle-to-particle
contact. This type of structure is relatively more
compressible compared to the more stable course
grained structure.
Soil Structures

Two types of grain size analyses are typically performed
1) Mechanical analysis also know as sieve analysis.
Sieving is generally used for coarse-grained soils. (for
particle sizes larger than 0.075 mm in diameter)
2) Hydrometer analysis ( sedimentation )
Sedimentation procedure is used for analyzing fine-
grained soils.( for particle sizes smaller than 0.075 mm
in diameter).

Mechanical Analysis (Sieve Analysis)
Using sieve analysis one can determine the grain
size distribution of soils and classify the soil into
sands and gravels. Sieves are made of woven
wires with square openings which decrease in
size as the sieve number increases; this allows the
grains to be sorted by size. Table in the slide No
6 gives a list of the U.S. standard sieve numbers
with their corresponding size of openings; most
commonly used sieves are highlighted in red.

Mechanical Analysis (Sieve Analysis )
U.S. standard sieves
Sieve No. Opening (mm) Sieve No. Opening
(mm)
- 25 0.71
3/8” - 30 0.60
4 4.75 35 0.500
5 4.00 40 0.425
6 3.35 45 0.355
7 2.80 50 0.300
8 2.36 60 0.250
10 2.00 70 0.212
12 1.70 80 0.180
14 1.40 100 0.150
16 1.18 120 0.125
18 1.00 140 0.106
20 0.85 200 0.075

The method of sieve analysis described here is
applicable for soils that are mostly granular with
some or no fines. Sieve analysis only classifies soils
into sizes and does not provide information as to
shape or type of particles.
The U.S. No. 200 sieve (0.075mm) is the smallest
sieve size typically used in practice
Small size of sample is 500g

For coarse-grained soil, a sieve analysis is
performed in which a sample of dry soil is
shaken mechanically openings since the total
mass of sample is known, the percentage
retained or passing each size sieve can be
determined by weighing the a mount of soil
retained on each sieve after shaking.

In the sieve analysis, a series of sieves having
different sized openings are stacked with the
large sizes over the smaller( a pan is placed
below the stack).
Pan

For measuring the distribution of particle
sizes in a soil sample, it is necessary to conduct
different particle-size tests.
Wet sieving is carried out for separating fine
grains from coarse grains by washing the soil
specimen on a 75 micron sieve mesh.
Dry sieve analysis is carried out on particles
coarser than 75 micron.

Samples (with fines removed) are dried and
shaken through a set of sieves of descending
size. The weight retained in each sieve is
measured. The cumulative percentage quantities
finer than the sieve sizes (passing each given sieve
size) are then determined.
To conduct a sieve analysis, one must first oven-
dry the soil and then break all lumps into small
particles.

The resulting data is presented as a distribution
curve with grain size along x-axis (log scale)
and percentage passing along y-axis (arithmetic
scale).
100
20
40
60
80
0
0.0010.010.1110
Particle diameter (mm)
Percentfiner

Percent(%)FinerbyWeight 0.6 0.0754.75 2.0 0.425 0.150. 25
Particle Diameter (mm)
(mm)
Particle-size Distribution Curve

Particle-size Distribution Curve
1010.01
0.850.075 4.752.00.4250.15 0. 25
#200 #100 #60 #40 #20 #10 #4
Particle Diameter (mm)
0.1
Percent(%)FinerbyWeight

For materials finer than 150 µm, dry sieving
can be significantly less accurate.
This is because the mechanical energy
required to make particles pass through an
opening and the surface attraction effects
between the particles themselves and between
particles and the screen increase as the
particle sizes decreases.
Limitations of Sieve Analysis

Wet sieving analysis can be utilized where
the material analysed is not affected by the
liquid – except to disperse it.
Suspending the particles in a suitable
liquid transports fine material through the
sieve much more efficiently than shaking
the dry material.

Sieve analysis assumes that all particles
will be round – and will pass through the
square openings
Particle size reported assumes that the
particles are spherical,
Elongated particle might pass through the
screen end-on, but would be prevented from
doing so if it presented itself side-on.
59
Dr. Abdulmannan Orabi IUST

Hydrometer analysis is a widely used method of
obtaining an estimate of the distribution of soil
particle sizes from the No. 200 (0.075 mm) sieve to
around 0.01 mm. The data are presented on a semi-
log plot of percent finer vs. particle diameters and
may be combined with the data from a sieve analysis
of the material retained (+) on the No.200 sieve.
Sedimentation Analysis (Hydrometer)
Hydrometer analysis is based on the principle of
sedimentation of soil grains in water.

In this method, the soil is placed as a
suspension in a jar filled with distilled
water to which a deflocculating agent
is added. Sodium hexametaphosphate
generally is used as the dispersing
agent. Soil particles are allowed to
settle from a suspension. The
decreasing density of the suspension is
measured at various time intervals.

The procedure is based on the principle that in
a suspension, the terminal velocity of a
spherical particle is governed by the diameter
of the particle and the properties of the
suspension. The concentration of particles
remaining in the suspension at a particular
level can be determined by using a hydrometer.

Hydrometer analysis is based on the principle of
sedimentation of soil grains in water. When a soil
specimen is dispersed in water, the particles settle at
different velocity, depending on their shape, size
and weight and the viscosity of the water.
The lower limit of the particle size determined by
this procedure is about 0.001mm
The sample size is 50g passing #10
Sometimes 100-g samples also can be used.

This method is based on Stoke’s law:
=
−
18
= !, #/%
= % % ! & '( )
= * +% ! & % * ,() %, -/ #.
= * +% ! & '( ), -/ #.
= * (# ) & % ,() %, #
where:
(2 − 1)

=
18
−
=
18
0 − 1
×
2
3
From Stoke’s law, the diameter can be given as
or
If the units of η are g.sec/cm^2 , L is in cm ,
t is in min, and D is in mm, then
(##)
10
=
18 (-. % / #
0 − 1 (-/ #.
×
2
3(min) × 60

The grain diameter can be calculated from a
knowledge of the distance and time of fall.
=
30
0 − 1
×
2
3
For computational purpose, equation can be
simplified even further to
= 8
2
3
8 =
30
0 − 1
where,
T = time (min) recorded from the beginning of the sedimentation.
(2 − 2)

where
= the length of the hydrometer stem
= the length of the hydrometer bulb
= volume of the hydrometer bulb
A = cross-sectional area of the sedimentation
cylinder
L2
VB
L1
L = Distance between water surface and center
of gravity of hydrometer bulb
2 = 29 +
1
2
2 −
;<
=
(2 − 3)

L1
L2
L
RRc
..........
..........
.....
..........
....
....
.....
..........
..........
. .
. . .
. . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. .
. . .
. . .
. .
. . .
. . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . . L
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
. . . . .
. . . . . .
. . . . .
L1
L2
Center of
gravity of
hydrometer
bulb
Definition of L in Hydrometer

The values of K as function of specific gravity and
temperature are given in table (ASTM2004):

In the laboratory, the hydrometer
test is conducted in a sedimentation
cylinder usually with 50 g of
oven-dried sample. The soil is
mixed with water and a dispersing
agent, stirred vigorously, and
allowed to settle to the bottom of a
measuring cylinder.

The length of the hydrometer projecting above the
suspension is a function of the density , so it is
possible to calibrate the hydrometer to read the
density of the suspension at different time. The
calibration of the hydrometer is affected by
temperature and the specific gravity of the
suspended solids.

Reading the density of the suspension at
different time.
....
....
..........
..........
...
. . .
. . .
. . .
. . .. . .
. . .
. . .
. . .
...
....
.......
.......
......
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
....
....
..........
............
. . .
. . .
. . .
. . .. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .. . .
. . .
. . .
. . .
....
....
..........
........... . .
. . .
. . .
. . .. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
..
L
L
L
Start T1 T2 T3

By knowing the amount of soil in suspension, L,
and t, we can calculate the percentage of soil by
weight finer than a given diameter.
The hydrometer should float freely and not touch
the wall of the sedimentation cylinder.

For Type 152H hydrometers, the effective depth
can be given as
L = 16.3 – 0.164 R
where R is the reading on the
hydrometer in grams of solids
per liter of suspension. The
effective depth is the distance
that the soil has settled that can
then be used to calculate velocity.
(2 − 4)

The equation for the percentage of the soil
remaining in suspension is
?@ =
( AB
C
100%
AB = AEBFGEH − I ) )) + + JK
( =
1.650
2.65 0 − 1
a = correction factor required when the specific gravity of
the soil grains is not equal to 2.65 and given by the
following equation
where:
(2 − 5)
(2 − 6)

C = *)! #(%% & M & + % N% *
+ M M!*) # ) (+( !% %
JK = )) + &( )& )
#, )( N)
Finally, the percent passing for the fines
taken for the hydrometer analysis (N’)
and for the total soil sample (N) were
computed by:
? =
?@ O PP
100
F200 = % finer of #200 sieve as a percent
(2 − 7)

For soils with both fine and coarse grained
materials a combined analysis is made using
both the sieve and hydrometer procedures.

Sieve analysis Hydrometer analysis
#10 #200#60
20
40
60
80
100
0
0.0010.010.1110
Percentfiner
Particle size distribution curve
Sieve analysis and hydrometer analysis

Curve I represent a soil in which most of the soil grains are
the same size. This is called poorly graded soil.
I
II
III
Data obtained from Sieve Analysis

Curve II represents a soil in which the particle
size distributed over a wide range termed well
graded.
Curve III represents a soil might have a
combination of two or more uniformly graded
fraction. This type of soil is termed gap graded.

Particle size distribution curve can be used to
determine the following parameters for a given soil
Effective size D10
This parameter is the diameter in the particle size
distribution curve corresponding to 10 % finer. The
effective size is a good measure to estimate the
hydraulic conductivity and drainage through soil.
The higher the D10 value, the coarser the soil and
the better the drainage characteristic.

Percentfiner
Particle size distribution curve
#10 #200#60
10
20
30
40
100
0
0.01110
50
60
70
80
90
D30 D10D60

Uniformity coefficient (Cu); This parameter is
defined as
where
= diameter corresponding to 60 % finer.
Coefficient of gradation (CC ); This parameter
is defined as
JG =
XP
9P
JB =
.P
9P∗ XP
XP
.P = diameter corresponding to 30 % finer.
The grading characteristics are then determined
as follows:
(2 − 8)
(2 − 9)

The percentage of gravel, sand, silt and clay size particles
present in soil can be obtained from the particle distribution
curve.
Sieve analysis Hydrometer analysis
#10 #200#60
20
40
60
80
100
0
0.0010.010.1110
Percentfiner
Sand FinesGravel

A sieve analysis is used to determine the grain
size distribution of coarse-grained soils.
For fine-grained soils, a hydrometer analysis
is used to find the particle size distribution.
Particle size distribution is represented on a
semilogarithmic plot of % finer versus
particle size
Summary

The particle size distribution plot is used to
determine the different soil textures ( percentage of
gravel, sand, silt, and clay ) in soil.
The effective size is the diameter in the particle size
distribution curve corresponding to 10 % finer.
Two coefficients – the uniformity coefficient and
the coefficient of curvature are used to characterize
the particle size distribution.
Summary

A sample of a dry coarse-grained material of mass
500 grams was shaken through a nest of sieves
and the following results were obtained:
Sieve No. Opening , mm Mass retained, g
4 4.75 0
10 2.00 14.8
20 0.85 98
40 0.425 90.1
100 0.15 181.9
200 0.075 108.8
pan 6.1
Worked Example

Solution
Worked Example
Tabulate data to obtain % finer
Sieve
No.
Mass
retained , g
% Retained
On each sieve
∑( %Retained) % Finer
4 0 0 0 100-0 =100
10 14.8 3.0 3.0 100-3=97
20 98.0 19.6 22.6 100-22.6=77.4
40 90.1 18 40.6 100-40.6=59.4
100 181.9 36.4 77.0 100-77=23
200 108.8 21.8 98.8 100-98.8=1.2
pan 6.1 1.2 100
Total mass M = 499.7 g

Worked Example
Solution
Effective size= 0.1mm

Calculate Cu and Cc
D60= 0.45 D30 = 0.18
Cu = 0.45/0.1 = 4.5
Cc = 0.72
Extract percentage of gravel, sand, silt,
and clay.
Gravel = 0 %
Sand = 98.8 %
Silt and Clay = 1.2 %
Worked Example
Solution

Relative Density
Relative density ( Dr ) is sometimes used to describe
the state condition in cohesionless soil.
Relative density ( Dr ) is an index that quantifies the
degree of packing between the loosest and densest
possible state of coarse-grained soils as determined
by experiments:
^ =
_E` − P
_E` − _ab
(2 − 10)

Relative Density
where:
is the maximum void ratio
( loosest condition),
is the minimum void ratio ( densest
condition ), and is the current void ratio.
^ =
_E` − P
_E` − _ab
_E`
_ab
c

Relative Density
The relative density can also be written as:
^ =
de − de(_ab)
de fgh − de(_ab)
×
de fgh
de
de fgh =
d ∗ 0
1 + _ab
de fij =
d ∗ 0
1 + _E`
de =
d ∗ 0
1 + c
(2 − 11)

Relative Density
A description of sand based on relative density is
given in the following table:
Dr ( % ) Approximate Angle of
internal friction , Ф
Description
0 – 15 25 – 30 Very loose
15 – 35 27 – 32 Loose
35 – 65 30 – 35 Medium dense or firm
65 – 85 35 – 40 Dense
85 – 100 38 – 43 Very dense

Lecture 2 grain size distribution

Lecture 2 grain size distribution

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (18)

Similar to Lecture 2 grain size distribution

Similar to Lecture 2 grain size distribution (20)

Recently uploaded

Recently uploaded (20)

Lecture 2 grain size distribution