Lecture 2 grain size distribution

INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY

�م وا�� ا�� ا��و�� 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 ClayMIT >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

Gravel Clay 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 complexalumino – 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.

HydroxylAluminum

Silica sheetSilica Tetrahedron

si



Aluminium (or Magnesium) Octahedral UnitThe 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

HydroxylAluminum


The combination of tetrahedral silica units givesa 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 MineralThe 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


7.2Å



Kaolinite MineralThe 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


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


7.2Å



KaoliniteThe 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 particleC

once

ntra

tion

of

ions

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.Dr. Abdulmannan Orabi IUST 46

Mechanical Analysis (Sieve Analysis )

U.S. standard sievesSieve 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

0.001 0.01 0.1 1 10

Particle diameter (mm)

Per

cen

t fi

ner

Per

cen

t (%

) F

iner

by W

eig

ht

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

Per

cen

t (%

) F

iner

by W

eig

ht



�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, sizeand 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

38 =

30 �

0� − 1where,

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

22� −

;<

=(2 − 3)

L1

L2

L

RRc

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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.

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. . 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

0.001 0.01 0.1 1 10


Per

cen

t fi

ner

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.



Per

cen

t fi

ner

Particle size distribution curve #10 #200 #60

10

20

30

40

100

0

0.01 1 10

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

0.001 0.01 0.1 1 10


Per

cen

t fi

ner

Sand Fines Gravel

� 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 % finerSieve

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 = 0.18Cu = 0.45/0.1 = 4.5Cc = 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
