CEGB233 Chapter 1

Semester 1, Session 2014/ 2015 CEGB233 (Soil Mechanics)

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Topic 1: Introduction to soil mechanics: Soil description and classification

1.1 The formation of the soil

For engineering purposes soil is best considered as a naturally (mostly) occurring

particulate material of variable composition having properties of compressibility,

permeability and strength.

All soils originate, directly or indirectly, from solid rocks and these are classified

according to their mode of formation as follows:

(i) Igneous rocks, formed by cooling from hot molten material ('magma') within or on

the surface of the earth's crust, e.g. granite, basalt, dolerite, andesite, gabbro, syenite,

porphyry.

(ii) Sedimentary rocks, formed in layers from sediments settling in bodies of water, such

as seas and lakes, e.g. limestone, sandstone, mudstone, shale, conglomerate.

(iii) Metamorphic rocks, formed by alteration of existing rocks due to: (a) extreme heat,

e.g. marble, quartzite, or (b) extreme pressure, e.g. slate, schist.

The processes that convert solid rocks into soils take place at, or near, the earth's surface

and, although they are complex, the following controlling factors are apparent:

(i) Nature and composition of the parent rock.

(ii) Climatic conditions, particularly temperature and humidity.

(iii) Topographic and general terrain conditions, such as degree of shelter or exposure,

density and type of vegetation, etc.

(iv) Length of time related to particular prevailing conditions.

(v) Interference by other agencies, e.g. cataclysmic storms, earthquakes, action of

humans, etc.

(vi) Mode and conditions of transport.

Engineering soil terminology

(i) Rock. Hard rigid coherent deposit forming part of the earth's crust, which may be of

igneous, sedimentary or metamorphic origin.

(ii) Soil. In engineering taken to be any loose or diggable material that is worked in,

worked on or worked with.

(iii) Organic soil. This is a mixture of mineral grains and organic material of mainly

vegetable origin in varying stages of decomposition.

(iv) Peat. True peat is made up entirely of organic matter; it is very spongy, highly

compressible and combustible. Inorganic minerals may also be present and as this

increases the material will grade towards an organic soil. From an engineering point

of view, peats pose many problems because of their high compressibility, void ratio

and moisture content, and in some cases their acidity.

(v) Residual soils. These are the weathered remains of rocks that have undergone no

transportation. They are normally sandy or gravelly, with high concentrations of

oxides resulting from leaching processes, e.g. laterite, bauxite, china clay.

(vi) Alluvial soils (alluvium). These are materials, such as sands and gravels, which have

been deposited from rivers and streams. Alluvial soils are characteristically well

sorted, but they often occur in discontinuous or irregular formations.

(vii) Cohesive soils. Fine soils containing sufficient clay or silt particles to impart

significant plasticity and cohesion.


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(viii) Cohesionless soils. Coarse soils, such as sands and gravels, which consist of rounded

or angular (non-flaky) particles, and which do not exhibit plasticity or cohesion.

1.2 The nature of the grains: Particle size analysis

Soil classification principles

It is necessary to provide a conventional classification of types of soil for the purpose of

describing the various materials encountered in site exploration.

To be sufficiently adequate for this basic purpose, a classification system must satisfy a

number of conditions:

(i) It must incorporate as descriptions definitive terms that are brief and yet meaningful

to the user.

(ii) Its classes and sub-classes must be defined by parameters that are reasonably easy to

measure quantitatively.

(iii) Its classes and sub-classes must group together soils having characteristics that will

imply similar engineering properties.

Most classification systems divide soils into three main groups: coarse, fine and organic.

Table 1.1: Major classes of engineering soils

Particle size analysis and grading

The range of particle sizes encountered in soils is very wide: from around 200 mm down to

the colloidal size of some clays of less than 0.001 mm. Although natural soils are mixtures of

various-sized particles, it is common to find a predominance occurring within a relatively

narrow band of sizes.

When the width of this size band is very narrow the soil will be termed poorly-graded, if it is

wide the soil is said to be well graded. A number of engineering properties, e.g. permeability,

frost susceptibility, compressibility, are related directly or indirectly to particle-size

characteristics.


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Figure 1.1 shows the British Standard range of particle sizes. The particle-size analysis of a

soil is carried out by determining the weight percentages falling within bands of size

represented by these divisions and sub-divisions. In the case of a coarse soil, from which

fine-grained particles have been removed or were absent, the usual process is a sieve analysis.

A representative sample of the soil is split systematically down to a convenient sub-sample

size* and then oven-dried. This sample is then passed through a nest of standard test sieves

arranged in descending order of mesh size. Following agitation of first the whole nest and

then individual sieves, the weight of soil retained on each sieve is determined and the

cumulative percentage of the sub-sample weight passing each sieve calculated.

Figure 1.1: British standard range of particle sizes

From these figures the particle-size distribution for the soil is plotted as a semilogarithmic

curve (Figure 1.2) known as a grading curve.

Figure 1.2: Grading curve

Where the soil sample contains fine-grained particles, a wet sieving procedure is first carried

out to remove these and to determine the combined clay/silt fraction percentage. A suitably

sized sub-sample is first oven-dried and then sieved to separate the coarsest particles (>20

mm). The sub-sample is then immersed in water containing a dispersing agent (sodium

hexametaphosphate: a 2 g/litre solution) and allowed to stand before being washed through a

63 μm mesh sieve. The retained fraction is again oven-dried and passed through a nest of

sieves. After weighing the fractions retained on each sieve and calculating the cumulative


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percentages passing each sieve, the grading curve is drawn. The combined clay/silt fraction is

determined from the weight difference and expressed as a percentage of the total sub-sample

weight. The coarsest fraction (>20 mm) can also be sieved and the results used to complete

the grading curve.

The grading curve is a graphical representation of the particle-size distribution and is

therefore useful in itself as a means of describing the soil. For this reason it is always a good

idea to include copies of grading curves in laboratory and other similar reports. It should also

be remembered that the primary object is to provide a descriptive term for the type of soil.

This is easily done using the type of chart shown in Figure 1.3 by estimating the range of

sizes included in the most representative fraction of the soil. For example, curve A may be

taken to represent a poorly graded medium SAND: poorly graded because the curve is steep,

indicating a narrow range of sizes, and medium SAND, since the largest proportion of the

soil (approximately 65 per cent) lies in medium-sand sub-range. Curve B represents a well-

graded material containing a wide range of particle sizes; from fine sand to medium gravel;

this soil is properly described as a well-graded GRAVEL SAND, since about half the soil is

gravel and the other half sand. Curve C also represents a well-graded material which is

predominantly sand, but with a significant silt fraction (about 20 per cent); this soil should be

described as a very silty SAND, the noun indicating the predominant fraction. Curve D

indicates a sandy SILT, e.g. an estuarine or deltaic silt; curve E indicates a typical silty

CLAY, e.g. London Clay or Oxford Clay.

Figure 1.3: Typical particle size distribution curves

A further quantitative analysis of grading curves may be carried out using certain geometric

values known as grading characteristics. First of all, three points are located on the grading

curve to give the following characteristic sizes (Fig. 2.4):

d10 = Maximum size of the smallest 10 per cent of the sample




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Fig. 2.4: Grading characteristics

From these characteristic sizes, the following grading characteristics are defined:

Effective size = d10 mm

Uniformity coefficient, 10

60

d

dCu

Coefficient of gradation,

1060

2

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dd

dCg

Both Cu and Cg will be unity for a single-sized soil, while Cu < 3 indicates uniform grading

and Cu > 3 a well-graded soil.

Most well-graded soil will have grading curves that are mainly flat or slightly concave,

giving values of Cg between 0.5 and 2.0. One useful application is an approximation of the

coefficient of permeability, which was suggested by Hazen.

Coefficient of permeability (k) = Ck (d10)2 m s

-1

Where Ck = a coefficient varying between 0.01 and 0.015.


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Worked Example 1.1: The results of a dry-sieving test are given below: plot the particle size

distribution curve and give a classification for the soil.


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Worked example 1.2: A full wet/ dry sieve analysis was carried out with the following

results:


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1.3 The structure (Fabric) of soil

For convenience, it is useful to divide soil into two major groups: coarse and fine.

(i) Coarse soils will be classified as those having particle sizes >0.06 mm, such as SANDS

and GRAVELS. Their grains will be rounded or angular and usually consist of

fragments of rock or quartz or jasper, with iron oxide, calcite, mica often present. The

relatively equidimensional shape is a function of the crystalline structure of the

minerals, and the degree surrounding depends upon the amount of wear that has taken

place.

(ii) Fine soils are finer than 0.06 mm and are typically flaky in shape, such as SILTS and

CLAYS. Very fine oxides and sulphides, and sometimes organic matter, may also be

present. Of major importance in an engineering context is the flakiness of the clay

minerals, which gives rise to very large surface areas.


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1.4 The current state of the soil: Phase relationship, Relative density of granular soil,

Limits of consistency of clay (Liquid, Plastic and Shrinkage Limits, Liquidity and

Plasticity Indexes)

Classification of fine soils

In the case of fine soils, it is the shape rather than size of particles that has the greater

influence on engineering properties. The combination of very flaky particles and

circumstances which may bring about changes in water content results in a material (soil)

having properties which are inherently variable. For example, the shear strength of cohesive

soils will vary markedly with changes in water content. Also, soils with flaky particles

behave as plastic material: an increase in applied stress usually brings about an irrecoverable

deformation, while the volume remains constant or is reduced and without any signs of

cracking or disruption.

Figure 1.4: Consistency relationship

Since the plasticity of fine soils has an important effect on such engineering properties as

shear strength and compressibility, plastic consistency is used as a basis for their

classification. The consistency of a soil is its physical state characteristic at a given water

content. Four consistency states may be defined for cohesive soils: solid, semi-plastic solid,

plastic and liquid. The change in volume of a saturated cohesive soil is approximately

proportional to a change in water content; the general relationship is shown in Figure 1.4. The

transition from one state to the next in fact is gradual; however, it is convenient to define

arbitrary limits corresponding to a change over moisture content:

wL = the liquid limit: the water content at which becomes plastic.

wP = the plastic limit: the water content at which the soil ceases to be liquid and the soil

ceases to be plastic and becomes a semi-plastic solid.

wS = the shrinkage limit: the water content at which drying-shrinkage at constant stress

ceases.


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The two most important of these are the liquid and plastic limits, which represent respectively

the upper and lower bounds of plastic states; the range of plastic states is given by their

difference, and is termed the plasticity index (IP).

IP = wL - wP

The relationship between the plasticity index and the liquid limit is used in the British Soil

Classification System to establish the sub-groups of fine soil; Figure 1.5 shows the plasticity

chart used for this purpose. The A-line provides an arbitrary division between silts and clays,

and vertical divisions (of percentage liquid limit) define five degrees of plasticity:

Low plasticity: wL < 35%

Intermediate plasticity: wL = 35% - 50%

High plasticity: wL = 50% - 70%

Very high plasticity: wL = 70% - 90%

Extremely high plasticity: wL > 90%

A given soil may be located in its correct sub-group zone by plotting a point, having

coordinates given by the soil's plasticity index and liquid limit. An explanation of the sub-

group symbols is given in Table 1.2.

Figure 1.5: Plasticity chart for the classification of fine soils


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Table 1.2: Sub-group symbols in the British Soil Classification System

The relationship between the soil's natural water content and its consistency limits, i.e. its

natural or in situ consistency, is given by the liquidity index (IL):

P

PL

I

wwI

where w = natural or in situ water content.

Clearly, from Figure 1.5, the significant values of LI are:

IL < 0: soil is in semi-plastic solid or solid state.

0 < IL < l: soil is in plastic state.

IL > l: soil is in liquid state.

The consistency limits represent the plasticity characteristics of the soil as a whole. Plasticity,

however, is mainly determined by the amount and nature of the clay minerals present. The

different clay minerals possess different degrees of flakiness. Also, even 'clays' may only

comprise 40-50 per cent clay minerals. The degree of plasticity of the clay fraction itself is

termed the activity of the soil:

Activity = IP/ % clay particles (<2 μm)

Some typical values of activity for some common clay minerals and soils are given in Table

1.3.


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Table 1.3: Activity of clays

Determination of consistency limits

The three consistency limits (wL, wP and wS) are determined by arbitrary test routines in the

laboratory.

(i) Determination of liquid limit

The apparatus (Figure 1.6) consists basically of a stainless steel cone 35 mm long with an

apex angle of 30' and having a mass (including the shaft) of 80 g. The cone is mounted on a

stand which will allow it to be dropped and then held in position while its vertical movement

is measured.

The soil is first dried sufficiently for it to be broken up by a mortar and pestle, with care

being taken not to break individual particles. The soil is then sieved and only the material

passing a 425 pm mesh sieve taken for testing. This is then thoroughly mixed with distilled

water into a smooth thick paste, and stored in an air-tight container for 24 hr to allow full

penetration of the water.

At the time of testing, the soil is remixed for 10 min and a portion of it placed in the brass

cup. Care must be taken not to entrap air bubbles, and then the surface is struck off level with

the top of the cup. After placing the cup on the base of the stand (Figure 1.7),the cone is

lowered so that it just touches and marks the surface of the soil paste; the dial gauge is then

set and the reading noted. The cone is released to penetrate the soil paste for exactly 5 s and

relocked in its new position; a second dial gauge reading is now taken. The difference

between the first and second dial readings gives the amount of cone penetration (mm).

The penetration procedure is repeated several times on the same paste mix and an average

penetration obtained, after which a small portion of the soil is taken and its water content

determined. The whole of the penetration procedure is then repeated with paste mixes having

different water contents, five or six times in all.


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Figure 1.6: Cone penetrometer for liquid limit test

A graph is drawn of cone penetration/water content (Figure 1.7) and the liquid limit of the

soil taken as the water content corresponding to a penetration of 20 mm.

Figure 1.7: Graph of cone penetration/water content


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(ii) Determination of the plastic limit

It is usual to prepare sufficient natural or air-dried soil as a paste with water for both the

liquid and plastic limit tests. Approximately 20 g of the soil paste is moulded in the hand until

it dries sufficiently for slight cracks to appear. The sample is then divided into two

approximately equal (10 g) portions and each of these divided into four sub-samples. one of

the sub-samples is taken and rolled into a ball and then it is rolled on a glass sheet to form a

thread of soil. The rolling, using the palm and fingers with light pressure, is continued until

the diameter of the thread reaches 3 mm. In this event, the soil is re-formed into a ball; the

action of handling the soil has the effect of drying it; it is then re-rolled on the glass sheet (i.e.

at a lower water content). This procedure of rolling and re-rolling is continued until the thread

starts to crumble just as the diameter of 3 mm is reached; at this point the thread fragments

are placed in an airtight container. The same process is carried out on the other three sub-

samples, and the crumbled threads of all four gathered together and their combined water

content found. The same procedure is followed with the other 10 g portion. The average of

the two water contents is reported as the plastic limit. In spite of the seeming arbitrary nature

of this test procedure, an experienced technician can obtain plastic limit results with very

good reproducibility.

(iii) Linear shrinkage test

For soils with very small clay content the liquid and plastic limit tests may not produce

reliable results. An approximation of the plasticity index may be obtained in such cases by

measuring the linear shrinkage and using the following expression:

IP = 2.13 × LS

The soil is prepared as for the liquid limit test and a 150 g specimen taken for the linear

shrinkage test; this is then thoroughly remixed with distilled water to form a smooth

homogeneous paste at approximately the liquid limit of the soil (although the exact water

content is not critical). The soil/water paste is placed into a brass mould (Figure 1.8), taking

care not to entrap air, and the surface struck-off level. The soil is air-dried at 60-65°C until it

has shrunk clear of the mould and then placed in an oven at 105-110°C to complete the

drying. After cooling, the length of the sample is measured and the linear shrinkage obtained

as follows:

Figure 1.8: Linear shrinkage mould


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Worked Example 1.3: In a liquid limit test on a fine-grained soil, using a cone

penetrometer, the following results were recorded.

In a plastic limit test on the same soil the plastic limit was found to be 25 pre cent. Determine

the liquid limit and plasticity index of the soil and classify it according to the British Soil

Classification System.

The plot of cone penetration/ water content is shown in Figure 1.9, from which the liquid

limit is found to be 57 per cent.

Figure 1.9


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Worked Example 1.4: After a series of laboratory tests, the following data were established

for a fine soil:

Worked Example 1.5: The results of a linear shrinkage test were:


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Exercises

1.1-1.3 The following data were recorded during particle size analysis tests in the laboratory.

Plot the grading curve in each case and determine the grading characteristics. Using this

information classify the soil according to the British Soil Classification System.


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1.4 From the grading characteristics given below sketch the grading curves for the three

soi1s.

1.5 The following results were recorded during a cone penetrometer test on a cohesive soil:

1.6 Following laboratory tests on four soils, the data given below were determined. For each

soil, give the class according to the British Soil Classification System and calculate the

activity and liquidity index.


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The soil model and basic properties

The basic physical properties of a soil are those required to define its physical state. For the

purposes of engineering analysis and design, it is necessary to quantify the three constituent

phases (solid, liquid and gas) and to be able to express relationships between them in

numerical terms. For example, a soil's water content is simply the ratio of the mass of water

to the mass of solid. Densities, i.e. the relationships between mass and volume, are also

important measures of a soil's physical state. In a typical soil, the solid, liquid (water) and gas

(air) are naturally intermixed, so that relative proportions are difficult to visualise. It is

therefore convenient to consider a soil model in which the three phases, while still present in

their correct proportions, are separated into distinct amounts.

Several possible phase models can be proposed (Figure 1.9), each taking its name from that

quantity providing a reference amount of unity. For example, the unit solid volume model is

based on I volume unit, e.g. 1 m3, of solid material; the unit solid mass model on 1 mass unit,

e.g. 1 kg; the unit total volume model on 1 volume unit of all three phases combined together.

For most purposes in soil mechanics, the unit solid volume i.e model is the most convenient,

since the solid constituents of soil (with the exception of peaty material) may be considered

to be incompressible. The model is therefore constructed, as it were, about 1 unit (l m3) of

solid material, which may be expected to remain constant. All other quantities are now

referenced to this amount. A given soil is therefore depicted as a fixed volume of solid

material, together with varying amounts of water and air. The amount of volume in the soil

not occupied by solids is termed the voids volume, the ratio of voids volume to solid volume

being e. In a perfectly dry soil there is no water and the void space is entirely air; in a

saturated soil the void space is full of water.

In Figure 1.10, the soil model is shown in detail with the various mass and volume

dimensions indicated. From this basic model several important quantities may now be

defined.

Figure 1.9: Three-phase soil models (a) Unit solid volume (b) Unit solid mass (c) Unit total

volume


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Figure 1.10: Unit solid volume soil model


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Worked Example 1.5 For a soil having a void ratio of 0.750 and percentage saturation of

85 per cent, determine the porosity and air-voids ratio.


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Worked Example 1.6 An oven tin containing a sample of moist soil was weighed and had a

mass of 37.82 g; the empty tin had a mass of 16.15 g. After drying, the tin and soil were

weighed again and had a mass of 34.68 g. Determine the void ratio of the soil if the air-voids

content is (a) zero (b) 5 per cent (Gs= 2.70).


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Soil densities


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Unit weight


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Worked Example 1.7 In a sample of moist clay soil, the void ratio is 0.788 and the degree of

saturation is 0.93. Assuming Gs = 2.70, determine the dry density, the bulk density and the

water content.

Worked Example 1.8 The bulk density of a sand in a drained condition above the water

table was found to be 2.06 Mg/m3 and its water content was 18 per cent. Assume Gs= 2.70

and calculate: (a) the drained unit weight, and (b) the saturated unit weight and water

content of the same sand below the water table.


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Worked Example 1.9 After a laboratory compression test, a cylindrical specimen of

saturated clay was found to have a mass of 157.28 g and a thickness of 17.4 mm. After then

drying to constant weight, its mass was 128.22 g. If the grain specific gravity is 2.68,

calculate: (a) the end-of-test water content and void ratio, and (b) the void ratio and water

content at the start of the test when the thickness was 18.8 mm, and assuming that the

diameter remains constant and the sample remains saturated.


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Worked Example 1.10 A specimen of clay was tested in the laboratory and the following

data were collected:

Determination of specific gravity of soil particles

For fine soils, a density bottle of about 50 ml capacity is used. For coarse soils, a 500 ml or

1000 ml container is used, which may be either an ordinary gas jar (Figure 1.11(a)) or a

special glass jar, fitted with a conical screw top, which is called a pycnometer (Figure

1.11(b)).


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Figure 1.11: (a) Gas jar (b) Pycnometer

An appropriate quantity of dried soil (depending on the particle size) is placed in the jar and

weighed. The jar is then filled with de-aired water and agitated to remove any air bubbles.

After carefully topping-up with water, the jar is weighed again. Finally, the jar is emptied and

cleaned, and then filled with de-aired water and weighed again.

An alternative procedure is to weigh the jar empty and then full of water. A pre-weighed

quantity of soil is then poured into the jar and stirred. After carefully topping-up with water,

the jar is weighed again. The quantities are now as follows:


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Worked Example 1.11 A pycnometer used in a specific gravity test was found to have a

mass of 524 g when empty and 1557 g when full of clean water. An air-dried sample of

cohesionless soil having a mass of 512 g was placed in the jar and stirred to expel any

entrapped air. The pycnometer was then carefully filled with clean water, when it had a total

mass of 1878 g. Determine the specific gravity of the soil.

Exercises

1.7 In a laboratory test a mass of moist soil was compacted into a mould having a volume of

964 cm3. Upon weighing, the mass of soil was found to be 1956 g. The water content was

found to be 13 per cent and the grain specific gravity was 2.70.

Calculate: (a) the bulk and dry density, (b) the void ratio and porosity, (c) the degree of

saturation, and (d) the air-voids content of the soil.

1.8 Using the model soil sample, show that:

1.9 In a sample of moist soil the porosity is 42 per cent, the specific gravity of the particles

2.69 and the degree of saturation 84 per cent. Determine: (a) void ratio, (b) bulk and dry

densities, (c) water content, and (d) saturation bulk density (assuming no swelling takes

place).

1.10 A core-cutter cylinder of internal diameter 100 mm and length 125 mm was used to

obtain a sample of damp sand from a trial hole. After trimming the ends, the total mass of


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the cylinder and soil was 3508 g; the mass of the empty cylinder was 1525 g. After oven-

drying, the soil on its own weighed 1633 g. If the specific gravity was also found to be

2.71, determine the bulk and dry densities, the water content, the void ratio and the air-

voids content of the sample.

1.11 A dry quartz sand has a density of 1.61 Mg/m3 and a grain specific gravity of 2.68.

Calculate its bulk density and water content when saturated at the same volume.

1.12 A saturated cylindrical specimen of clay soil has a diameter of 75.0 mm and a

thickness of 18.75 mm and weighs 155.1 g. lf the water content is found to be 34.4 per

cent, determine the bulk density and void ratio of the specimen. lf the original thickness

of the specimen was 19.84 mm, what was the initial void ratio?

1.13 A sandy soil has a saturated density of 2.08 Mg/m3. When it is allowed to drain the

density is reduced to 1.84 Mg/m3 and the volume remains constant. If the grain specific

gravity is 2.70, determine the quantity of water in litres/m2 that will drain from a layer of

the sand 2.2 m thick.

1.14 A cohesive soil specimen has a void ratio of 0.812 and a water content of 22.0 per

cent. The grain specific gravity is 2.70. Determine: (a) its bulk density and degree of

saturation, and (b) the new bulk density and void ratio if the specimen is compressed

undrained until it is just saturated.

1.15 A sandy soil has a porosity of 38 per cent and the grain specific gravity is 2.69.

Determine: (a) the void ratio, (b) the dry unit weight, (c) the saturated unit weight, and (d)

the bulk unit weight at a water content of 17 per cent.

1.16 A laboratory specimen is to be prepared by ramming soil (Gs = 2.68) into a cylindrical

mould of diameter 104 mm. The finished specimen is to have a water content of 16 per

cent and an air-voids content of 5 per cent. Determine: (a) its void ratio and dry unit

weight, and (b) the quantities of dry soil and water required to be mixed together in order

to form a specimen 125 mm long.

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CEGB233 Chapter 1

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