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

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Department of Civil Engineering, Faculty of Technology

Addis Ababa University

2.2 GRAIN SIZE 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 are permeability, compressibility, and shear strength. 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 soil must 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, …, Mn and in the pan, i.e., Mp ii. Determine the cumulative mass retained above each sieve. For the 4th sieve from the

top for example, this would be M1+ M2+M3+M4 iii. Calculate the mass of soil passing each sieve. For the 4th sieve, this is ΣM – (M1+

M2+M3+M4) iv. Calculate the percent of soil passing each sieve (percent finer). Again, for the 4th sieve,

%Finer4 = ∑

∑ +++−

MMMMMM )( 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 largest to the smallest in a soil can be greater than 104. 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 then repeatedly 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 Stoke’s law. According to Stoke’s 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 = 6π η r v Where η = dynamic viscosity in kN·sec/m2 r = radius in m v = velocity in m/sec. Consider a sphere of unit weight γs (kN/m3), and radius r (m) falling in a fluid of unit weight γw, then the two forces acting on it will be:

(i) Weight of the sphere = (4 π r3/3) · γs

(ii) Buoyant force of the fluid = (4 π r3/3) · γw

Therefore the net force with which the sphere fall sis given by = (4 π r3/3) · γs - (4 π r3/3) · γw

= (4 π r3/3) ( γs - γw) 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 terminal velocity (v) will then be represented when the drag force is equated to the net unbalanced force, i.e. 6π η r v = (4 π r3/3) ( γs - γw) Rearranging the terms and the diameter of the sphere as D = 2r we finally obtain,

ws

vDγγη−

=18

But γs = ρs g, and γw = ρw g => γs - γw = g (ρs - ρw) = ρw g (ρs/ ρw – 1) = ρw g (Gs – 1)

Therefore, )1(

18)(

18−

=−

=swsw Gv

GgvD

γη

ρη

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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tH

GGvD e

swsw )1(18

)1(18

−=

−=

γη

γη

t

HK e=

Where K is a constant=0.00106 at 20ºC, for which η=1.004 x 10-6kNsec/m2 and γw = 9.79kN/m3

Hence t

HD e00106.0= where He is 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 hR

ρ

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 = Vwρw = (1-Vs)ρs/Gs = ρs/Gs – Vsρs/Gs = ρw – Ms/Gs = 1- Ms/Gs The 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 ρ = 1 + Ms [(Gs – 1)/Gs] ………………………..since V = 1cc But the density of the suspension, as measured by the hydrometer, is given as:

⎥⎦⎤

⎢⎣⎡ +=

10001 hR

ρ = 1 + Ms [(Gs – 1)/Gs]

Ms = (R/1000) [Gs/ (Gs – 1)]

Percentage finer = suspensioninoriginalccvolumeperunitsolidsofMass

ttimeafterHdepthatvolumeunitpersolidsofMass e

)(

= 100×V

MM s


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= 100111000

×⎥⎦

⎤⎢⎣

⎡− V

MGGR

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

DD

Cu =

Where D60 is 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 Cu is 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 ( Cc or sometimes Cz) It is defined as

1060

230 )(

DDD

Cc ×=

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 state where visible cracks appear when molding the soil. The water content at the intersection of plastic and semisolid states is known as the plastic limit and 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;

PIPLwLI −

=

Where w is 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 Plastic state – Intermediate strength

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 activity is defined as the slope of the line correlating PI and the clay fractions (finer than 2µm) present in the soil.

),(% weightbyfractionsizeclayofPIA

−=

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 2 revolutions 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 ×⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=

mVV

mmm

SL wρ

where m1 is the mass of the wet soil, m2 is the mass of the oven-dried soil, V1 is the volume of wet soil, V2 is 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 – SL Based 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 CLASSIF 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 silts while 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 doesn’t 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 which more 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 G or 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, C for 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: W for well graded P for poorly graded L for low plasticity (LL<50) H for high plasticity (LL≥50) The following table and the associated plasticity chart give the details of the soil classification system to determine the group symbols.


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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.

74


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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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