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Soil Mechanics-I(CENG-2202) Chapter 2 : Simple Soil Properties

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Department of Civil Engineering, Faculty of TechnologyAddis Ababa University

2 .2 GRA IN S IZE DISTRIBUTION

Determination of the size range of particles present in a soil is useful in a wide range of areas

such as soil classification, estimation of hydraulic conductivity, selection of aggregates for

concrete and selection of material for grouting and chemical stabilization. The main

engineering properties of soils arepermeability, compressibility, and shearstrength. The tests

required for determination of engineering properties are generally elaborate and time-

consuming. It may often be necessary to have rough assessment of the engineering properties

without conducting elaborate tests. This is possible if grain size distribution and consistency

limits (to be discussed in the next section) are determined. Various correlations between these

physical properties and other soil properties are then employed.

The method of determination of the size range of particles present in a soil known usually as

mechanical analysis or particle size analysis is achieved by one or a combination of the

following two techniques:a. Sieve analysis used to determine the average grain diameter of coarse-grained soils

having particles larger than 0.075mm, and

b. Hydrometer analysis used to determine the size distribution of fine-grained soils

having particles less than 0.075mm.

SIEVE ANALYSIS

This method involves shaking of a known weight of soil sample through a stack of sieves that

have progressively finer mesh from top to bottom.

The particle diameter in this screening process is the maximum particle dimension to pass

through the square hole of a particular mesh size. Prior to conduction sieve analysis the soilmust first be oven-dried. All lumps are then broken into smaller particles. In the case of

cohesive soils, breaking the lumps into individual particles may not be easy. In this case, the

soil may be mixed with water to make slurry and then washed through the sieve, the process is

thus known as wet sieving.

Some common standard sieves with their standard numbers (US standard) and opening sizes

are listed below.

Sieve no. Opening (mm)

4 4.75

10 2.00

20 0.85

40 0.425

100 0.15

200 0.075

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The sample of soil is placed on the topmost sieve and the nest of sieves, with a pan placed

below the stack, is then placed on a vibrator (sieve shaker) and shaken. The soil retained on

each sieve is determined separately, after oven-drying if it is a wet-sieving process. The results

are plotted on a graph as follows:

i. Determine the mass of soil on each sieve, i.e., M1, M2, , Mnand in the pan, i.e., Mp

ii.

Determine the cumulative mass retained above each sieve. For the 4th sieve from thetop for example, this would be M1+ M2+M3+M4

iii. Calculate the mass of soil passing each sieve. For the 4th

sieve, this is M (M1+

M2+M3+M4)

iv. Calculate the percent of soil passing each sieve (percent finer). Again, for the 4th

sieve,

%Finer4=

+++M

MMMMM )( 4321

After the percent finer of each sieve is calculated in this manner, the results are plotted on a

graph of percentage of particles finer than a given sieve as the ordinate versus the logarithm of

particle sizes. Log scale is used for the abscissa since the ratio of particle sizes from the largestto the smallest in a soil can be greater than 10

4.

HYDROMETER ANALYSIS

Since there is a technical limitation on the size of sieves that could be practically attained, sieve

analysis cannot be used for fine-grained soils because of their extremely small particle size.

The common way of obtaining particle size distribution for such soils is the hydrometer test.

This is based on the principle of sedimentation of soil grains in water. It involves mixing a

small amount of soil into a suspension and observing how the suspension settles in time. The

particles will settle at different velocities, depending on their shape, size, and weight, and the

viscosity of the water.

When a hydrometer is lowered into the suspension it will sink until the buoyancy force is

sufficient to balance its weight. It is thus possible to calibrate the hydrometer such that it reads

the density of the suspension at different times.

The test is conducted in the laboratory by first taking a small quantity of oven dried soil,

usually 50 or 100gm and thoroughly mixing it with distilled water in a glass cylinder called

sedimentation cylinder capable of accommodating 1litre of suspension. Sodium

hexametaphosphate is generally used as a dispersing agent. The volume of dispersed

suspension is then increased to 1000ml by adding distilled water. The glass cylinder is thenrepeatedly shaken and inverted before being placed at a constant temperature. A hydrometer is

placed in the glass cylinder and a clock is simultaneously started. At different times the

hydrometer value is read.

Eventhough not strictly realistic, it is sufficient for practical purposes to assume all the

particles to be spheres and no collision occurs between these spheres. The velocity of the

particles can be expressed by Stokes law. According to Stokes law, the velocity with which a

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grain settles down in a suspension, all other factors being equal is dependent upon shape,

weight, and size of the grains. However in the usual analysis, it is assumed that the soil

particles are spherical and have the same specific gravity (i.e. the average specific gravity of all

grains).

With this assumption, the coarser particles, will settle more quickly than the finer ones. If v

represents the settling or terminal velocity; the procedure could be worked out as follows:Stoke has shown that for a sphere of radius r, the resisting force due to drag resistance offered

by a fluid is given by

R = 6r v

Where = dynamic viscosity in kNsec/m2

r = radius in m

v = velocity in m/sec.

Consider a sphere of unit weight s(kN/m3), and radius r (m) falling in a fluid of unit weight

w, then the two forces acting on it will be:

(i)

Weight of the sphere= (4 r

3/3) s

(ii)Buoyant force of the fluid

= (4 r3/3) w

Therefore the net force with which the sphere fall sis given by

= (4 r3/3) s- (4 r

3/3) w

= (4 r3/3) ( s-w)

The sphere will accelerate for a while, due to this net unbalanced force; but the drag resistance

offered by the fluid, R, increases with velocity, and soon equilibrium of forces is established.

After this the sphere continues its descent with a constant velocity. This constant terminalvelocity (v) will then be represented when the drag force is equated to the net unbalanced force,

i.e.

6r v = (4 r3/3) ( s-w)

Rearranging the terms and the diameter of the sphere as D = 2r we finally obtain,

ws

vD

=

18

But s= sg, and w= wg

=> s-w= g (s- w) = wg (s/w 1) = wg (Gs 1)

Therefore,)1(

18

)(

18

=

=

swsw G

v

Gg

vD

Knowing the height (He) through which the soil particle falls, and the time taken by it, we can

easily determine its velocity (v), i.e. v= He/t and can hence determine its diameter. Substituting

this into the previous equation yields,

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t

H

GG

vD e

swsw )1(

18

)1(

18

=

=

t

HK e=

Where K is a constant=0.00106 at 20C, for which =1.004 x 10-6kNsec/m2 and w =9.79kN/m

3

Hencet

HD e00106.0= where Heis in meters and t is in seconds.

The readings on a hydrometer stem are so marked that they indicate the density of a fluid at the

center of the bulb at any time. These readings are generally graduated on the stem by

subtracting 1 and multiplying the digit by 1000, from the specific gravity. For example, a

specific gravity of 1.03 will be graduated on the stem by (1.03 1) x 1000 = 30.

Accordingly, if the readings or graduations on the hydrometer be represented as Rh, then the

density of the suspension as measured by a hydrometer, will be given by

+=

10001 h

R

To compute the percent finer than the diameter D, the mass per unit of suspension must be

computed first.

Consider 1 unit volume of suspension, at a time t, at the effective depth He. If Ms is the mass

of solids in this 1cc suspension, the mass of water in it will then be

Mw= Vww = (1-Vs)s/Gs= s/Gs Vss/Gs = w Ms/Gs

= 1- Ms/GsThe total mass per unit volume of suspension

M = Mw+ Ms

= Ms+ (1 Ms/Gs) = 1 + Ms Ms/Gs

= 1 + Ms[(Gs 1)/Gs]

Hence the density of suspension

= 1 + Ms[(Gs 1)/Gs] ..since V = 1cc

But the density of the suspension, as measured by the hydrometer, is given as:

+=

10001 h

R = 1 + Ms[(Gs 1)/Gs]

Ms= (R/1000) [Gs/ (Gs 1)]

Percentage finer =suspensioninoriginalccvolumeperunitsolidsofMass

ttimeafterHdepthatvolumeunitpersolidsofMass e

)(

= 100

VM

Ms

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= 1001

11000

V

MG

GR

s

s

In many instances, if the soil has both coarse and fine particle, the results of sieve analysis and

hydrometer analysis are combined on one graph.

Typical grain-size distribution curves are shown in the figure below.

It is evident from this figure that particle-size distribution curve also shows the type of

distribution of various-size particles. Curve (C) represents a type of soil in which most of the

soil solids have the same size. Such soil is termed poorly graded. Curve (A) shows a soil

having two uniformly graded portions and it is called a gap graded soil. Curve (B) represents a

soil in which the particle sizes are distributed over a wide range of and is termed well graded.

A particle size distribution curve is used also to determine the following parameters for the

given soil.

1. Effective size (D10)This is the diameter corresponding to 10% finer in the distribution curve. This size is

particularly important in regulating the flow of water through soils. The higher this

value, the coarser the soil and the better the drainage characteristics.

2. Uniformity coefficient (Cu)

This parameter is defined as

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10

60

D

DCu =

Where D60is the diameter of the soil particles for which 60% of the particles are finer.

A well graded soil has a uniformity coefficient greater than about 4 for gravels and 6

for sands. A soil that has a uniformity coefficient of less than 4 contains particles of

uniform size. The minimum value of Cuis 1 and corresponds to a collection of particles

of the same size.

3. Coefficient of curvature, also called coefficient of gradation or coefficient of

concavity ( Ccor sometimes Cz)

It is defined as

1060

2

30 )(

DD

DCc

=

The coefficient of curvature is between 1 and 3 for well-graded soils. Gap-graded soils

have values outside this range.

2 .3 SOIL CONSISTENCY

When some water is added to a fine grained soil containing clay, the soil shows different

distinct states: solid, semisolid, plastic, and liquid in order of increasing water content.

At larger water content a soil flows as a liquid. As the soil dries, its water content decreases

and at some point, the soil becomes stiff that it can no longer flow as a fluid. This boundary

moisture content is called the liquid limit; and denoted by LL. Immediately after this limit, the

soil can be molded into any shape without rupturing and crumbling. This state is the plastic

state. If drying is continued, the soil will no longer be plastic but becomes semisolid; a statewhere visible cracks appear when molding the soil. The water content at the intersection of

plastic and semisolid states is known as the plastic limitand is denoted by PL.

If the drying process is furthered, the soil will finally be a solid mass and no volume change

can occur beyond this state. The intersection between the semisolid and solid states is called

the shrinkage limit; and denoted by SL.

These various states along with expected stress-strain characteristics are shown in the

following figure.

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The range of water contents over which the soil deforms plastically is known as the plasticity

index, PI. Thus,

PI = LL - PL

Based on the plasticity index, soils may be grouped into different categories as shown in the

following table.

PI Description of soil plasticity

0 Nonplastic

1 - 5 Slightly plastic

5 - 10 Low plasticity

10 20 Medium plasticity

20- 40 High plasticity

>40 Very high plasticity

The liquid and plastic limits are also called the Atterberg limits after the Swedish soil

scientist, A. Atterberg who developed the idea. Typical values are shown below.

Soil type LL (%) PL (%) PI (%)Sand Nonplastic (NP)

Silt 30-40 20-25 10-15

Clay 40-150 25-50 15-100

Atterberg limits could be used as a measure of the soil strength since the state in which a soil is

in has a relation with the strength characteristics. At the liquid state the soil has the lowest

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strength and largest deformation. At the solid state, the soil possesses the largest strength and

lowest deformability.

A measure of strength using the Atterberg limits is known as the liquidity index, LI, and is

defined as;

PI

PLwLI

=

Where wis the in situ moisture content of soil.

Referring to this equation, the state a soil is in can be related to the value of LI as follows.

LI Description of soil strength

LI < 0 Semisolid state High strength but brittle, i.e. sudden

fracture is expected

0 < LI 1 Liquid state Low strength

Because the plasticity of soil is caused by the adsorbed water surrounding clay particles, we

expect that the type of clay minerals and their proportional amounts in a soil will affect the

liquid and plastic limits. On this basis, a quantity called activityis defined as the slope of the

line correlating PI and the clay fractions (finer than 2m) present in the soil.

),(% weightbyfractionsizeclayof

PIA

=

Higher values of activity indicate a higher potential for volume change. Hence,

montmorillonite clays have high values of activity ranging from 1.50 to 7.0.

DETERMINATION OF LIQUID, PLASTIC, AND SHRINKAGE LIMITS

LIQUID LIMIT

The liquid limit is determined from an apparatus that consists of a semispherical brass cup that

is repeatedly dropped onto a hard rubber base from a height of 1cm by a cam-operated

mechanism. The apparatus was developed by A. Casagrande (1932) and the procedure for the

test is called the Casagrande cup method.

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During the test a dry powder of the soil is mixed with distilled water into a paste and placed in

the cup to a thickness of about 12.5mm. The soil surface is smoothed and a groove is cut into

the soil using a standard grooving tool. The crank operation the cam is turned at a rate of 2revolutions per second and the number of blows required to close the groove over a length of

12.5mm is counted and recorded. A specimen of soil within the closed portion is extracted for

determination of the water content. The liquid limit is defined as the water content at which the

groove cut into the soil will close over a distance of 12.5mm following 25 blows. This is

difficult to achieve in a single test. Four or more tests at different water contents are usually

required for terminal blows ranging from 10 to 40. The results are presented in a plot of water

content (ordinate, normal scale) versus terminal blows (abscissa, logarithmic scale). The best

fit straight line to the data points, usually called the flow line, is drawn. We will call this line

the liquid state line to distinguish it from flow lines used in describing the flow of water

through soils. The liquid limit is read from the graph as the water content on the liquid state

line corresponding to 25 blows.

PLASTIC LIMIT

The plastic limit is determined by rolling a small clay sample into threads and finding the water

content at which threads approximately 3mm in diameter will just start to crumble. Two or

more determinations are made and the average water content is reported as the plastic limit.

SHRINKAGE LIMIT

The shrinkage limit is determined as follows. A mass of wet soil, m1, is placed in a porcelain

dish 44.5mm in diameter and 12.5mm high and then oven-dried. The volume of oven dried soil

is determined by using mercury to occupy the vacant spaces caused by shrinkage. The mass of

the mercury is determined and the volume decrease caused by shrinkage can be calculated

from the known density of mercury.

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Referring to the above figure, the shrinkage limit is calculated from

SL = wi(%) w(%)where wi= initial moisture content when the soil is placed in the shrinkage dish

w = change in moisture content (i.e. between the initial moisture content and the

moisture content at the shrinkage limit)

100)(

2

21

2

21

=

m

VV

m

mmSL w

where m1is the mass of the wet soil, m2is the mass of the oven-dried soil, V1is the volume of

wet soil, V2is the volume of the oven-dried soil, and g is the acceleration due to gravity. The

range of water content from the plastic to the shrinkage limits is called the shrinkage index, SI.

SI = PL SLBased on the consistency limits, a useful chart, known as the plasticity chart is prepared that is

highly important in classifying soils for engineering purposes.

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2 .4 ENGINEERING CL A SSIF ICATION OF SOIL

Often, geotechnical engineers encounter the problem of identifying and describing soil.

Various soils with relatively similar engineering properties could be grouped into categories.

This grouping of soils will enable engineers to communicate effectively which would

otherwise be impossible to do so for each specific soil type.

There are different soil classification schemes. Classifications usually depend on the type of

intended use of soil. Different countries have also adapted soil classification schemes to suit

their specific conditions. However the commonest classification schemes are presented here.

1. Particle size classification

In this system soils are classified based on the range of grain sizes. Commonly soil grains with

sizes smaller than 76.2mm and larger than 4.75mm (sometimes 2mm) are taken to be gravel.

Those grains with sizes between 4.75mm (sometimes 2mm) and 0.075mm are considered to be

sand. All grains with sizes ranging between 0.075mm and 0.002mm are termed to be siltswhile clays are those with size less than 0.002mm.

Such a system is useful to classify soils of the same grain size. It also serves as an input for

other more elaborate classification systems. However since soil is usually an aggregate of a

range of sizes, this system has a very limited use.

2. Textural classification

This system is also based solely on grain size. It is but modified to accommodate a mixture of

grain sizes. We can thus have a combination naming such as silty clay, sandy clay, etc. This

system still doesnt account for the plasticity of soils and also gravels are not included in it.

Two figures showing the use of this classification are presented below. To use these diagrams,

one should first determine the percentage of clay, silt, and sand in the sample. Having these

values and drawing the arrows in the manner shown on the diagrams, the intersection of the

three arrows is then noted. Depending on where this point falls, the soil is then given the name

of the region in the diagram as shown with dotted lines.

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3. AASHTO Classification system

Usually used for highway construction, this system takes into account both grain sizes and

plasticity characteristics of a soil. According to this system, soil is classified into seven major

groups: A-1 through A-7. Soils classified under groups A-1, A-2, and A-3 are granular

materials of which 35% or less of the particles pass through the No. 200 sieve. Soils of whichmore than 35% pass through the No. 200 sieve are classified under groups A-4, A-5, A-6, and

A-7. These soils are mostly silt and clay-type materials. The classification system is further

based on the following criteria:

1. Grain size

a. Gravel: fraction passing the 75mm sieve and retained on the No.10 (2mm) sieve

b.

Sand: fraction passing the No.10 sieve and retained on the No. 200 sieve

c. Silt and clay: fraction passing the No.200 sieve

2. Plasticity: the term silty is applied when the fine fractions of the soil have a plasticity

index of 10 or less. The term clayey is applied when the fine fractions have a plasticity

index of 11 or more.

3.

If cobbles and boulders (size larger than 75mm) are encountered, they are excluded

from the portion of the soil sample from which classification is made. However, the

percentage of such material is recorded.

To classify a soil according to AASHTO classification system as presented on the next page,

one must apply the test data from the left to right. By process of elimination, the first group

from the left into which the soil parameters fit is the correct classification.

The figure below shows where the range of LL and PI plots fall on the plasticity chart for those

groups containing fines; i.e. groups A-2, A-4, A-5, A-6, and A-7.

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4. Unified Soil Classification system (USC)

Originally proposed by Casagrande in 1942 during the Second World War, this system was

then revised by in 1952. At present this system is widely used by engineers. Inorder to use this

classification system, the following points must be kept in mind:

1.

The classification is based on material passing the 75mm sieve.2. Coarse fraction = percent retained above No. 200 sieve = 100 - F200= R200

3. Fine fraction = percent passing No. 200 sieve = F200

4. Gravel fraction = percent retained above No. 4 sieve = R4

It follows thus that the percentage of sand = R200 R4.

In this system, there are two major soil categories:

a.

Coarse-grained soils: these are gravelly and sandy in nature with less than 50% passing

through the No. 200 sieve. The group symbols start with prefixes of either Gor S. G

stands for gravel or gravelly soil, and S for sand or sandy soil.

b. Fine grained soils: with 50% or more passing through the No. 200 sieve. The group

symbols start with prefixes of M, which stands for inorganic silt, Cfor inorganic clay,

and O for organic silts and clays. The symbol Pt is used for peat, muck, and other

highly organic soils.

Other symbols (secondary) used in this system are:

Wfor well graded

Pfor poorly graded

Lfor low plasticity (LL

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Inorder to assign group names to each group in the USC system, an elaborate system was

created by ASTM. The flowcharts of group naming are presented in the follwing pages.

4

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Flow chart for assigning group names for gravelly and sandy soil as per ASTM

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Flow chart for assigning group names for inorganic silty and clayey soils as per ASTM

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Flow chart for assigning group names for organic silty and clayey soils as per ASTM

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