Civ2201 Soil Mechanics 1-3

CIV2201: SOIL MECHANICS

BY

Dr. Gilbert J. KASANGAKI Department of Civil and Environmental Engineering, Room 254, CEDAT Old building, School of Engineering,

College of Engineering, Design, Art and Technology Makerere University

Mob.: 077 2 536 341 070 6 307 373 Email: [email protected]

[email protected]

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

GEOTECHNICAL ENGINEERING SUB-DEPARTMENT

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Course Content (Full Content Next Page)

Course Content (Full Content Next Page) ................................ i Timelines ..................................................................................... ii Preface ....................................................................................... iii Objectives of Soil Mechanics .................................................... iv Mode of Delivery and Course Assessment ............................... v Assistance and Feedback .......................................................... vi References ................................................................................. vii 1. Introduction ........................................................................ 1

1.1 Definitions.......................................................................................................................... 1 1.2 Importance of Soil Mechanics ........................................................................................... 1 1.3 Particle Size and Shape ...................................................................................................... 2 1.4 Origin and Types of Soil Deposits ..................................................................................... 2 1.5 Nature of Soil Deposits ...................................................................................................... 3 1.6 Clay Minerals ..................................................................................................................... 3

2. Physical Properties and Soil Classification ...................... 6 2.1 Introduction ........................................................................................................................ 6 2.2 Physical Properties of Soil ................................................................................................. 6 2.3 Determination of Physical Properties of Soil..................................................................... 8 2.4 Soil Classification and Description .................................................................................. 10

3. Soil Compaction ............................................................... 21 3.1 Introduction ...................................................................................................................... 21 3.2 Purpose of soil compaction .............................................................................................. 21 3.3 Compaction stresses and their effect................................................................................ 21 3.4 Factors affecting soil compaction .................................................................................... 22 3.5 Laboratory compaction test.............................................................................................. 25 3.6 Full-scale compaction equipment .................................................................................... 28 3.7 Measurement of in-situ density ........................................................................................ 28 3.8 Field control of compaction ............................................................................................. 28 3.9 Worked Examples ............................................................................................................ 31

4. Soil Hydraulics ................................................................. 35 4.1 Introduction ...................................................................................................................... 35 4.2 Water Bearing Layers in Soil ........................................................................................... 35 4.3 Permeability ..................................................................................................................... 36 4.4 Seepage ............................................................................................................................ 42

5. Stresses and Deformation in a Soil Mass ........................ 49

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Timelines

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Preface

Soil Mechanics is a wide-ranging discipline that combines techniques for exploration of soil and groundwater with engineering methods for quantitative description of their behaviour. The skills of the soil scientist (geotechnical engineer) are applied throughout the world in site investigation and exploration, foundations, roads, dams, tunnels, mining, water supply, flood control among others. As such it draws upon several disciplines such as nature of soil deposits, soil phase relations, physical properties of soil, soil compaction, soil hydraulics, stresses and deformations in a soil mass, consolidation and settlement, shear strength and bearing capacity of soils, and to a lesser extent, stability analysis of soils including lateral earth pressures and soil retaining systems.

Accordingly, these subjects are considered, from an engineering point of view, in the first five chapters of this hand out. Soil mechanics is intimately associated with soils slope stability and bearing capacity. Hence chapters six and seven deal with the engineering consideration of these aspects. The other applied aspects of soil mechanics namely soil exploration and ground improvement is dealt with in the remaining chapter.

The handout is prepared to explain the engineering properties and classification of soils, and the operation of its internal processes are described. The commonly occurring types of soil are described, but within limits suitable for engineers. Throughout the handout care has been exercised to focus on the relationship between the different soils and the engineering practices, and so emphasis has been placed on the processes that bear directly upon the structure, engineering quality, and mechanics of soils and on the movement of ground water. An explanation of why it is important to investigate the ground and how the investigations may be conducted has been provided.

This text is written for the undergraduate students of civil engineering in their pursuit of a Bachelor of Science in Civil Engineering Degree so that upon graduation they can involve in soil mechanics itself but also structural engineering, mining, quarrying, water engineering, and building to a greater or lesser extent, that is, all that involves the ground.

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Objectives of Soil Mechanics

The overall long-term objective of Soil Mechanics is to train and develop the skills of undergraduate soil scientists and professionals to meet the needs and requirements of the extractive industries, consultants and contractors, and other branches of civil engineering, to satisfy the national and international demand for specialist soil scientists with basic training in geotechnical engineering, and to prepare them (undergraduate students) for further geotechnical engineering courses.

The immediate objectives are: To provide an understanding of the physical properties of soil and its classification and

description,

To enable students analyse stresses and strains imparted by applied loads,

To enable students to assess soil supporting capability for applied forces,

To introduce students to assessment of soil compressibility in response to loading,

To train students on how to conduct investigations of soils using both the laboratory based and the field based methods.

On completing the course therefore, the students should be able to:

Perform phase calculations on soil/air/water mixtures,

Classify soil using different international classifications systems such as the USCS,

Determine effective stress under hydrostatic situations,

Determine groundwater flow through a homogeneous, isotropic soil and hence assess seepage

Predict consolidation-settlement in cohesive soils

Determine Mohr-Coulomb failure envelope from Direct Shear Box and Triaxial tests

Appreciate the application of different soil exploration and soil improvement techniques.

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Mode of Delivery and Course Assessment

The course shall be conducted through lectures, tutorials and practicals. Students are expected to avail themselves at all time when the course is being delivered.

Soil Mechanics will be assessed through continuous assessment and the final written University examination. The continuous assessment, which will consist of laboratory work and progressive assessment (two assignments and two tests), will contribute 40% of the total 100% marks while the remaining 60% will come from the final written University examination. Laboratory work and progressive assessment will each carry 20%, and assignments and tests, which together constitute progressive assessment, will each carry 10%.

The pass mark for Soil Mechanics is 50%. Any student who gets a mark lower than the pass mark will be required to retake the course when next offered again in order to obtain at least the pass mark of 50%. A student who retakes and fails Soil Mechanics three times shall be discontinued.

A student may retake Soil Mechanics when next offered again to improve his/her pass grade got at the first assessment and this will accordingly be indicated on the students academic transcript. While retaking Soil Mechanics, a student will have to attend all the prescribed lectures, tutorials, practical and field work if any and satisfy all the requirements for the course work component in the course and sit for the final written University examination.

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Assistance and Feedback

The course lecturer, Dr. Gilbert Kasangaki, will be available to answer any questions relating to the academic content of the course. For any difficulties you may have with the administration or running of the course please contact the Head of Department or the School Dean. You can be assured of protection implying that the course lecturer will not be able to directly single out anyone as being the source of information

Dr. Kasangaki will be assessing your work and may provide guidance through the work. He is always willing to help with any problems you may have and provide feedback on your progress where appropriate. The best method of contacting him is by e-mail. He will try and respond to any queries as quickly as possible but be patient; if you do not get a reply please try again in case your message did not get through. You may also contact the Head of Department or School Dean if you have any difficulties or cannot get a response. They will then follow up your query on your behalf. Any questions raised and responses that might be of wider interest will be circulated to all studying the course.

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References

Berry, P. L. and Reid, D. (1988). An Introduction to Soil Mechanics, Terzaghi K., Peck R.B. and Mesri G. (1996). Soil Mechanics in Engineering Practice, 3rd Ed., John Wiley & Sons Inc.

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1. Introduction

1.1 Definitions

Soil Mechanics is a branch of physical science that deals with the study of soil properties and behaviour under the action of physical forces. Soil is any uncemented or weakly cemented accumulation of mineral particles formed by the weathering of rocks, the void space between the particles containing water and or air. Consequently, soil may be described as dry, saturated or partially saturated. It is said to be dry if the voids are full of air and saturated if they are full of water. A partially saturated soil contains both air and water in the voids.

Generally, soil does not possess a linear stress-strain relationship and its behaviour depends on pressure, time and environment. It is sensitive to disturbance and differs from one location to another. The soil mass involved is underground and therefore can only be evaluated from the basis of small samples obtained from isolated locations. Soil is particulate in nature.

1.2 Importance of Soil Mechanics

In practice, a Civil Engineer has many and important encounters with soil. He uses it as a foundation for civil engineering projects such as buildings, roads, dams, and embankments etc. He also uses soil as a construction material e.g. in road construction, building construction, construction of drains, embankment etc. Consequently, it is necessary that the Engineer have sufficient knowledge of the soil conditions of the site where he is to develop a project.

In particular, one requires the knowledge of soil mechanics to be able to determine whether or not the soils at a given site can support the proposed project and if they cannot determine whether and how they can be improved. This calls for investigation of the soils strength parameters at a site. It is also important in assessing the effect of the proposed project on the surrounding through establishing the possible settlements. The knowledge of soil mechanics is further used to assess whether or not a given soil can be used as a construction material and if not whether it can be improved. If it cannot be improved then a disposal site must be sought for its disposal. Knowledge of soil mechanics is also useful when establishing the effect of soils and civil engineering projects on say buried structures such as tunnels, water supply conduits etc. and when assessing the stability of slopes. Finally, soil mechanics provides a student with the background knowledge for the study of foundations and other applications.

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1.3 Particle Size and Shape

Soil particles are described according to size using terms such as gravel, sand, silt or clay sized. There exists no universally agreed standard for the use of these terms in the definition of particle size. Several agencies have come up with different standards as shown in table below.

Table 1.1: Definitions of particle size Particle Particle size (mm) description BS AASHTO ASTM USCS Gravel 60 2 75 2 > 2 75 4.75 Sand 2 0.06 2 0.05 2 0.075 4.75 0.075 Silt 0.06 0.002 0.05 0.002 0.075 0.005 < 0.075 fines Clay < 0.002 < 0.002 < 0.005

BS - BS 5930: 1981 AASHTO - American Association of State Highways and Transportation Offices ASTM - American Society for Testing and Materials USCS - Unified Soil Classification System

Using for example the BS, soils with particle size in excess of 0.06 mm i.e. sands and gravels are coarse soils whereas soils finer than 0.06 mm i.e. silt and clay are fine soils.

The grains of coarse soils are either angular, sub angular or rounded. Angular grains have sharp edges and relatively flat surfaces e.g. gravels whereas rounded grains have round edges due to abrasion during transportation e.g. sands. Sub angular grains lie somewhat in between angular and rounded grains. The fines however are typically flaky in shape.

1.4 Origin and Types of Soil Deposits

Soil may be broadly classified according to origin as residual or transported soils. Residual soils are those formed by in situ weathering and have remained at their original location. Transported soils, on the other hand, are soils which have been removed from their original location and deposited elsewhere, the principle transportation agents being ice, water and wind.

Transported soils are further classified according to the agent of transportation as either water deposited, glacial or windblown soils. Water deposited soils are those moved and deposited by water e.g. alluvium carried and deposited by rivers, lacustrine soils by lake waters etc. these soils are highly compressible and loose. Glacial deposits are moved and deposited by moving ice

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(glaciers) e.g. moraines. Aeolian soils are moved and deposited by wind e.g. loess soils and dunes that are light in weight.

Other types of soil deposits include fill materials which are moved and placed by man e.g. during excavation, quarrying etc. and organic soils which is rich in organic matter derived from the breakdown of the plant and/or animal tissues by microbes. These soils are referred to as topsoil and are highly compressible and unsuitable for engineering purposes.

1.5 Nature of Soil Deposits

Like soil particles, soil deposits are also described using terms such as gravel, sand, silt or clay but in this case the terms have a different interpretation. A soil deposit of fines with sufficient clay minerals to give the soil distinct stiction and plasticity characteristics no matter the proportion by weight of the particles in the silt and clay sizes is called clay soil. Likewise soil of fines having rather more silt sizes and fewer clay mineral particles is likely to exhibit less pronounced stiction and plasticity characteristics. Soil deposit of this kind is referred to as silt soil.

Stiction is the attraction between fine soil particles as a result of Vander Waals forces between the particles whereas plasticity is the ability of a given soil mass to undergo non recoverable deformation without crumbling.

A soil deposit without clay mineral particles and which exhibit no stiction between individual grains is either sand or gravel depending on the particle size. These soil deposits are associated with a considerable value of gravitational forces compared to clay and silt soils.

In practice soil deposits do not exist in a single size so that depending on the distribution of particle size in the soil deposit, such deposits may be described as sandy clay, gravely silt etc.

Soil deposits, which exhibit stiction and plasticity characteristics owing to the presence of clay mineral particles, are termed as cohesive soils. On the other hand, sands and gravels are often referred to as cohesionless or granular soils. Soil is a permeable material. This is because the voids are interconnected and water can flow through the pore spaces.

1.6 Clay Minerals

Clay minerals are silicates produced by chemical weathering of rocks. They are mostly hydrated aluminium silicates. Clay minerals have a net negative charge with high affinity for water and a

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considerable surface area and surface forces due to electro chemical activity on the surface of particles.

Clay minerals are constructed from two fundamental building units, namely, tetrahedral unit and octahedral unit. A tetrahedral unit consists of four oxygen atoms enclosing one silicon atom whereas an octahedral unit has six hydroxyl groups surrounding one atom of either aluminium or magnesium.

Fig. 1.1: Silicon tetrahedron and Aluminium/Magnesium octahedron

Clay minerals are divided into three main groups depending on the arrangement of the building units in the crystal lattice.

Kaolinite group This group of has a structural block consisting of a sheet of tetrahedral units (symbolised by a trapezoidal) and a sheet of octahedral units (symbolised by a rectangle). The structural blocks are bonded by hydrogen to form a relatively stable lattice structure. This group of clay minerals absorbs little water and has relatively low susceptibility to shrinkage and swelling and variations in water content.

Fig. 1.2: Kaolinite structure

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Illite group This group has a structural block consisting of a sheet of octahedral units sandwiched between two oppositely oriented sheets of tetrahedral units. Aluminium ions (Al 3+) take up some of the silicon ions (Si4+) positions. Potassium ions provide a bond between the structural blocks to form a lattice structure rather less stable than in kaolinite group. Illites exhibit a greater tendency for water absorption than kaolinites, and greater shrinkage and swelling characteristics.

Fig. 1.3: Illite structure

Montmorillonite group The structural block is similar to that of illite group except that in addition to the substitution of aluminium ions (Al 3+) for silicon ions (Si4+) in the tetrahedral units, some of the aluminium ions in the octahedral units are replaced by magnesium ions (Mg2+) and iron ions (Fe 2+). The resulting large net negative charge attracts water molecules and any available cations into the lattice. The interlayer water bond is very weak and unstable compared to the potassium ion bond of the illites. This group exhibit very high water absorption and shrinkage and swelling characteristics.

Fig. 1.4: Montmorillonite structure

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2. Physical Properties and Soil Classification

2.1 Introduction Soil is a multiphase material consisting of solid particles (minerals), liquid (water) and gas (air). A phase is one part of the soil system, which is chemically and physically different from the other parts. Depending on the prevailing conditions soil may be a two - phase or three-phase system. It is always necessary to know the proportions by mass and volume of the various soil phases, which is possible with the use of a soil phase diagram shown below.

Dry soil Saturated soil Partially saturated

Two Phase Three Phase Fig. 2.1: Soil phase diagram

From the phase diagram; Vv = Va + Vw VvVolume of voids, VaVolume of air, VwWater volume VT = Vv + Vs VT Total volume, Vs Volume of solids Similarly,

Mv = Ma + Mw

MT = Mv + Ms But Ma 0

MT = Mw + Ms Mw Mv

2.2 Physical Properties of Soil 2.2.1 Specific Gravity, Gs

Gs waterof volumeequal of Mass

particles soil of Mass=

i.e. Gsss

s

VM

=

Or Gs waterofDensity particles ofDensity

=

i.e. Gsw

s

=

Air

Water

Air

Water

Solids

Solids

Solids

Va

Vs

Vw

Vv VT

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2.2.2 Void Ratio, e Void ratio is the proportion of void spaces in the soil element. It is the ratio of the volume of voids to the volume of solids. It gives a measure of compressibility of the different soil elements.

s

v

VV

e

e

=

=

solids of Volume voidsof Volume

2.2.3 Porosity, n

T

v

VV

n

n

=

=

element soil total theof Volume voidsof Volume

Relationship between void ratio and porosity

From 2, sv eVV = and from the phase diagram, ( )eVVVV ssvT +=+= 1 Therefore, ( ) e

e

eVeV

ns

s

+=

+=

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2.2.4 Water content, w Water content is the ratio of mass of water to mass of solids. It is the proportion of water present

in a soil mass, expressed as a percentage.

i.e s

w

MM

w ==solids of Mass

waterof Mass

2.2.5 Degree of Saturation, Sr Degree of saturation is the ratio of volume of water to the volume of voids. It is the proportion of

void space occupied by water.

i.e. Srv

w

VV

==

voidsof Volume waterof Volume

0 Sr 1

If Sr = 1, then the soil is fully saturated and if Sr = 0, then the soil is dry.

2.2.6 Air Content, Ar Air voids content is the ratio of volume of air to total volume of the soil sample. It is used when dealing with compaction curves in which case it is required that the air content is not greater than the value of porosity.

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ArT

a

VV

==

sample soil of Volumeair of Volume

2.2.7 Bulk Density, b

bT

T

VM

==

element soil theof Volumeelement soil theof Mass

2.2.8 Dry Density, d

dT

s

VM

==

element soil theof volumeTotalsolids of Mass

2.2.9 Saturated Density, sat

satsw

sw

VVMM

+

+=

+

+=

solids of Volume water of Volumesolids of Mass water of Mass

2.2.10 Relative Density, Dr

ratio voidminimum and maximumbetween Differenceratio situ voidin and ratio voidmaximumbetween Difference

=rD

Drminmax

max

ee

ee

=

2.2.11 Unit Weight, Unit weight of soil is the weight of soil element per unit volume of the same soil element.

i.e. V

MgVW

== = g

2.2.12 Submerged Unit Weight,

element soil of volumeTotal

particles soil of weight Effective=

2.3 Determination of Physical Properties of Soil Some of the tests carried out to determine physicals properties of soil are:

2.3.1 Determination of Bulk Density The methods used for the determination of bulk density are the sand replacement method, core

cutter method and water displacement method.

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i) Sand Replacement Method This method is commonly used to determine the in situ density of cohesionless soils. In the

procedure, a hole is made in the ground and all the soil that is removed is collected and its mass

determined, say M1. The mass of a sand-pouring cylinder full of sand of known density, M2 is then

determined; the cylinder is placed over the hole and the valve opened such that the sand drops into

the hole until the hole and the cone are full. The mass of partially full cylinder, M3 is finally

measured so that the mass of sand that has poured can be determined. The cone is calibrated such

that the mass of sand used to fill it is known.

Results

The task is to obtain the volume of the hole excavated.

By definition, bulk density bsample same theof Volume

sample soil of Mass=

b hole theof Volumesoil excavated of Mass

=

But volume of the hole Vsand same theofDensity

hole thefill toused sand of Mass=

b VM1

=

ii) Core Cutter Method This method is most suitable for the determination of the in situ density of cohesive soils. In the

procedure, a core cutter of known weight and internal volume is driven into the ground and

extracted with the soil sample inside. It is then cleaned, trimmed and weighed.

Results

Bulk density cutter of volumeInternal

cutter of Mass soil andcutter of Mass =

2.3.2 Determination of Water Content, w The procedure involves putting a moist sample in a dry clean container of known mass and then

getting the combined mass of the container and the sample. The sample in the container is then

oven dried at a temperature of about 105oC. Too high temperature will cause the organic matter to evaporate. Having cooled the sample is weight in the container.

Results

w container of Mass soildry and container of Mass

soildry and container of Mass soilmoist and container of Mass

=

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2.3.3 Determination of Specific Gravity Gs The procedure involves putting a dry sample of soil into a clean empty container (Pycnometer or Jar) of known mass, M1 and then determining the mass of the container and the sample, M2. Distilled water is then added to the sample to fill the container such that all the air voids are

occupied by water and the mass of the system determined, M3. Finally the container is emptied,

cleaned and then filled with only distilled water and the mass of the container and water

determined, M4.

Results

Gs waterof volumeequal of Mass

solids of Mass=

Gs ( ) ( )231412

MMMMMM

=

2.4 Soil Classification and Description Soil classification is the sorting of soil into groups showing similar characteristics to obtain

consistent and internationally recognised description of soil sample. It is intended to differentiate

between soils, compare different soils, communicate their properties and to a limited extent assess

their suitability for a particular engineering application. Soil classification may either be field

based (carried out in the field) or laboratory based (carried out in the laboratory).

2.4.1 Field Classification The table below shows the different classes of soil and their corresponding properties. Under this

method of classification personal judgement is an important factor.

Table 2.1: Field classification of soil according to their properties Class Properties/Tests

Gravels Can be excavated by spade and constitute bigger size particles.

Sands Can be excavated by spade, have relatively big size particles and gritty

feeling between fingers.

Silts Easy to crumble, can be dusted off by hands when dry.

Clays Particles not visible by naked eye, hard to crumble and stick to the hands

when dry; feel smooth/greasy, exude between fingers when squeezed in

hands.

Organic Have odour, dark colour and can be moulded in the hands and they smear

fingers.

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2.4.2 Laboratory Classification The physical properties and appearance of granular soils are influenced mainly by the distribution

of various particle sizes in the soil deposit and of clay by stiction and plasticity characteristics.

Therefore in the laboratory focus is on the determination of particle size distribution and the

Atterberg limits.

2.4.3 Particle Size Distribution This refers to the distribution by weight of particles within the various size ranges. For coarse-

grained soils sieving is used in the analysis while for fine-grained soils sedimentation is used.

2.4.4 Sieve Analysis In the procedure, a representative soil sample of known mass is passed through a series of standard

sieves having successively finer aperture size and mass retained on each sieve is measured. The

cumulative percentage by mass of the soil sample passing through each sieve is then calculated

and plotted against the corresponding sieve sizes on a semi - log graph.

Results

Sieve size Mass retained Cum. Mass retained Cum. % Passing

No. 1 xx xxx xxxx

No. 2 xx xxx xxxx

2.4.5 Typical Grading Curve

Fig. 2.2: Typical grading curves

Sieves of appropriate sizes for the material being tested are selected from the range of test sieves

commonly used for particle analysis.

2.4.6 Sedimentation Analysis Soils containing silt and clay sized particles are difficult to sieve due to their stiction property and

as a result their particle size distribution is determined by use of sedimentation characteristics of

the particles as they settle out in water.

Cum.% Passing

Particle size

Log scale

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In the procedure, soil is first weighed to determine its mass. It is then put in distilled water to

which a deflocculating agent is added to prevent flocculation. The material is then washed through

a 63m BS sieve (75m ASTM sieve) to remove the coarse particles. The material retained on the sieve is dried and treated as for granular soils.

The suspension formed by the washing process is then put in a cylinder and the sedimentation

process commenced. There are two methods of sedimentation analysis: (a) the pipette method, and (b) the hydrometer method.

2.4.7 The Hydrometer Method The suspension is put in a 1000ml cylinder and vigorously shaken and sedimentation commenced.

The specific gravity of the suspension at depth, h, is then measured at given intervals of time (0.5, 1, 2, 4, 8, 15, 30 minutes, then 1, 2, 4, 8 hours, then 1, 2 days etc) using a hydrometer until the suspension is clear indicating that all the particles have settled. The hydrometer gives a direct

reading for the specific gravity of the suspension.

Results

Diameter of the soil particles is determined from Strokes law, which states that;

V = KD2 V - Velocity of particles

K - Constant of proportionality given by

Kw

ws

18

= and V

t

h=

To determine the percentage by mass of the particles finer than D consider the original suspension

of 1000ml.

Weight of solids = Ws

Volume of solids =ws

s

GW

Volume of water =ws

s

GW

1000

Weight of water = s

s

w GW

1000

Initial density = 1000

1000s

sws G

WW +

13

=

( )w

s

ss

GGW +

10001

Density of suspension at depth, h, after time, t

t ( )

s

stw G

GW1000

1+=

where Wt is weight of solids in suspension at depth,

h, and time, t.

Percentage of particles finer than D

N 100=s

t

WW

t ( )s

ss

w GGNW

000,1001

+= from which

N ( ) ( )wtsss

GWG

=

1000,100

Finally a graph of N against D is plotted with the D (horizontal) scale as a log scale.

2.4.8 Description of Grading Curves A soil is well graded if it contains approximately equal proportions of all particle sizes and is characterised by a relatively smooth curve, covering a wide range of sizes, and is poorly graded if:

(i) The soil contains large and small particles but exhibits a marked absence of particles in an intermediate size range. Soil of this kind is described to as gap graded.

(ii) A high proportion of the particles lie in a narrow size band; the grading is described as uniform and is characterised by a large proportion of the curve being nearly vertical.

Besides visual description, grading may be described numerically in terms of the grading

characteristics, which are the geometric values that give a quantitative analysis of the grading curves for the purpose of describing the soil. The characteristics include:

(a) Coefficient of uniformity, Cu10

60

DD

=

(b) Coefficient of curvature, Cc 6010

230

DDD

=

Where D10, D30 and D60 are characteristics sizes defined as the particle sizes such that 10%, 30% and 60% respectively of the material is finer than that size (Fig. 2.3). Note: According to the Unified Soil Classification System, the greater the value of Cu the less uniform the grading and for a well graded soil, Cu > 4 and 1 < Cc < 3.

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Fig. 2.3: Soil characteristic sizes

2.4.9 Consistency of Fine Grained Soils and Atterberg Limits One of the most important characteristics of fine soils like silt and clay is their stiction and

plasticity characteristics. Depending on the amount of water in the soil, a soil may be liquid, plastic, semi-solid or solid. The water contents at which transitions from one state to another occur

are important and vary from one soil to another. These water contents are referred to as the Atterberg limits or consistency limits.

2.4.10 The Consistency States

Fig. 2.4: Atterberg limits

2.4.11 Liquid Limit Liquid limit of soil is the water content at which the soil passes from the plastic state to the liquid

state. The soil begins to behave like a viscous mud and to flow under its own weight. The symbol of liquid limit is LL.

Determination of liquid limit Liquid limit can be determined using either the Casagrande apparatus or the Cone penetrometer

method. For both methods a dry sample of soil is first sieved through a 425m BS sieve and the material passing is mixed with distilled water on a glass plate to make a uniform paste.

Solid state

SL

Semi solid state

PL

Plastic state

LL

Liquid state

Increasing water content

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For the case of Casagrande apparatus shown in Fig. 2.5, portion of the above paste is placed in the cup which is resting on the hard rubber base and levelled horizontal. The levelled soil is then divided into two halves by a standard grooving tool. The cup is then tapped twice a second and the

number of taps required to bring the two halves together over a length of 13mm is recorded and the moisture content of the soil is found. The procedure is repeated for different water contents

and a semi logarithmic graph is plotted of water content against the number of taps. The water content of the soil corresponding to 25 taps on the graph is taken as the liquid limit of the soil.

Fig. 2.5: Casagrande apparatus

The other method for the determination of liquid limit is the cone penetrometer method whose apparatus is shown in Fig. 2.6. In the procedure, portion of the uniform paste is placed in a metal cup and the surface is struck off level. The cone is then lowered to just touch the surface of soil and dial gauge read. The cone is then released and its penetration into the soil is measured. The

test is repeated at the same water content and again with the same soil at increasing water contents, and a sample of the soil is used each time to determine the moisture content at the time of the test.

A graph of values of cone penetration against water content is plotted and the liquid limit taken as the moisture content corresponding to a cone penetration of 20mm.

Fig. 2.6: Cone penetrometer apparatus

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2.4.12 Plastic Limit Plastic limit is the lowest water content at which the soil remains in plastic state. Any reduction in

this water content changes the soils state to a crumbly semi solid state. The symbol is PL.

Determination of plastic limit Plastic limit of soil is found by rolling a ball of wet soil between the palm of the hand and a glass

plate to produce a thread 3mm thick before the soil just begins to crumble. The water content in this state is taken as the plastic limit of the soil.

2.4.13 Shrinkage Limit This is the water content of the soil at which further loss of the water in the soil will not cause

further reduction in the volume of the soil. It is the water content required to just fill the voids of a soil sample, which has been dried. The symbol is SL.

2.4.14 Consistency Indices There are a number of indices that may be derived from the Atterberg limits, and among them are

the following.

Plasticity index Plasticity index is the measure of the range of water contents over which the soil remains in a

plastic state. Numerically, it is the difference between the liquid limit of the soil and the plastic limit of the same soil.

ie PI = LL PL

Liquidity index This is the measure of the comparison between the in situ water content and its plasticity i.e.

LI = (w PL)/PI

2.4.15 Soil Description Symbols Soil may be described differently by different agencies. According to the BS Classification System soil groups are denoted by group symbols composed of the main and qualifying descriptive letters

having the meanings given Table 2.2 below.

17

Table 2.2: BS Soil Classification System for engineering purposes

18

However, basing on the Atterberg limits soil may be described according to the zone within which the point lies on the plasticity chart shown in Fig. 2.7 below. Fig. 2.8 shows the plot of some soils

from Andibo sub-county in Nebbi district, Uganda.

Fig. 2.7: Plasticity chart

Fig. 2.8: Plasticity chart showing samples from Andibo Dam in Nebbi District

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110

Pla

stic

ity In

dex

%

Liquid Limit %

TP01 TP02 TP03 TP04 TP05 TP06 TP07 TP08 TP09 TP10 TP11 TP12

ML

CL CI CH CV CE

MI MH MV ME

19

In the description, the letter denoting the dominant size fraction is placed first in the symbol group, and if a soil has a significant content of organic matter the suffix O is added as the last letter of the

group symbol. A group symbol may consist of two or more letters e.g. SW : well graded SAND

SCL : clayey SAND (clay of low plasticity) MHSO : organic sandy SILT of high plasticity.

However, basing on the Unified Soil Classification System (Table 2.3) developed in United States, the group symbols consist of a primary and a secondary descriptive letter. Soils exhibiting the characteristics of two groups should be given a boundary classification denoted by dual symbols

connected by a hyphen.

Table 2.3: Unified Soil Classification System (USCS)

20

EXAMPLE OF THE PROBLEMS OF WORKING ON AND USING SOIL AS A MATERIAL

21

3. Soil Compaction

3.1 Introduction Recall that soil is a multiphase material comprising solid grains, air and/or water with its properties and behaviour depending, to a greater extent, on the environment, age and history,

among others. Deposited shallow young soil, for instance, is likely to be looser compared to an old soil at a great depth. Other factors held constant, loose soils are weaker than dense soils; they

have low shear strength, undergo high compressibility and permit considerable passage of water. Therefore, depending on the desired application it might be necessary to increase the degree of soil

particle packing. The process by which soil particles degree of packing is increased is called compaction. It is often achieved through application of a mechanical action and involves expulsion

of fluids particularly air as its space is taken up by the solid grains. Fig. 3.1(a) shows compaction in progress whereas the schematic in Fig. 3.1(b) is an illustration of the effect of compaction on particle packing within the soil system.

(a) Compaction in progress (b) Schematic showing the effect of compaction

Fig. 3.1: Compaction and its effect on particle packing

3.2 Purpose of soil compaction Compaction increases the resistance to deformation, particularly settlement which may result from

superimposed loading of a soil or inundation. It also reduces the permeability of soil thus reducing the possibility of moisture content variations with attendant changes in strength and/or volume. Lastly, compaction increases shear strength of soil thereby improving the stability of the fill

material and particularly of the side slopes of an earth structure.

3.3 Compaction stresses and their effect In general, an increase in the dry density at any given level in a layer of soil will occur if the

stresses exerted by the passage or action of a compactor exceeds the strength of the soil at its

22

existing dry density and moisture content, provided that further expulsion of air form the soil is possible; that is a near zero air void condition has not yet been reached. If at any level the stresses

exceed the strength and near zero void condition has already been reached, a condition of over-stressing exists, excess pore water pressures are generated and plastic deformation of the

soil at constant volume will occur. The general form of the relationship between dry density and depth below the surface of the compacted layer is given in Fig. 3.2.

Fig. 3.2: General form of relationship between dry density and depth in a compacted soil

3.4 Factors affecting soil compaction Compaction, in terms of dry density achieved, depends on moisture content of the material concerned, the compactive effort employed and the nature of the soil. These are pursued further below.

3.4.1 Moisture content For a given soil, the relationship between dry density and moisture content takes the form shown in Fig. 3.3. As the moisture content is increased from some low value, the undrained shearing

resistance of the soil is reduced and the dry density produced by a given compactive effort increases until a maximum dry density is reached at an optimum moisture content when, with well

graded soils, very little air is present in the soil. With uniformly graded soils the air content at maximum dry density and optimum moisture content can be considerable as indicated by the 20%,

30% air void lines (i.e. 80% and 70% degree of saturation lines) shown in Fig. 3.3. At moisture contents above optimum moisture content the shear stresses exerted by the compactor exceed the

23

maximum possible shear strength of the soil and a state of over-stressing exists. Further increases in moisture content can only be achieved by the displacement of solid particles by water and the

dry density reduced, the relationship between dry density and moisture content generally continuing at constant air voids, usually less than 5%.

Fig. 3.3: Typical dry density moisture relationship for a compacted soil

At very low moisture contents, the relationship between dry density and moisture content shows a

reversal in that the dry density increases with decrease in moisture content (Fig. 3.4). This effect is particularly marked when granular soils are compacted using vibratory methods. In some cases the

dry density achieved at near zero moisture content can approach the maximum dry density obtained at saturation moisture content.

Fig. 3.4: Reversal dry density moisture relationship for compacted granular soils

24

3.4.2 Compactive effort For a give soil type, an increase in compactive effort will result in the relationship between dry

density and moisture content being displaced upwards and to the left as shown in Fig. 3.5. An increase in compactive effort is accompanied, therefore, by an increase in maximum dry density

and a decrease in optimum moisture content.

Fig. 3.5: Effect of compactive effort on dry density moisture relationship for a soil

Compactive effort is a function of the energy applied, volume of the compacted soil and the method by which the compaction is carried out. Compaction may be carried out using impact

based methods, vibration based methods, dead-weight rollers or rammers. For a given compaction method the compactive effort is increased by an increase in energy applied and reduced by an

increase in the volume of compacted soil.

In general, the principal method of controlling the energy applied by a given compactive machine is in terms of the number of passes; in other words, the number of times that the machine traverses

a given area of soil. On a laboratory scale, the energy applied may be controlled in terms of the number of blows of a rammer or the rammer dimensions and height of drop, or by duration of

application and speed of a vibrating device. For a given volume of soil at constant moisture content, relationships between dry density and energy applied are as shown in Fig. 3.5.

25

It is therefore important that, whenever values of maximum dry density and optimum moisture content are reported, the compactive effort should also be fully detailed. As a minimum, for

laboratory based compaction, the mass of the rammer, height of drop of the rammer and the number of blows per layer as well as the number of layers involved should be specified. These

affect the applied energy and hence the resultant compaction. In addition, the size of the mould using in the compaction process should be specified as this would affect the compacted volume.

The effective volume of compacted soil in full-scale work is primarily controlled by the depth of

compacted layer. Compaction stresses are highest at the surface of the compacted layer and fall away with increasing depth through the layer. This results in a relationship between dry density

and depth through the layer of the general form shown in Fig. 3.1. The depth of the compacted layer therefore has an effect on the mean dry density of the layer. Assuming all other factor remain

constant, increasing the depth of the layer usually results in a reduction in mean dry density.

3.4.3 Nature of soil Soils of different types have different capacities of absorbing water. For example, a high plasticity

clay have a moisture content in excess of 30% and have a relatively high strength, nonetheless similar strengths may be attained at moisture contents of only 15-20% with a low plasticity clay and at moisture contents less than 10% with sands. The surface area of the coarser particles and the plasticity of finer soils determine the moisture capacity and this, in turn, for a well graded soil,

determines the potential dry density that can be achieved with a given compactive effort. Fig. 3.4 gives the typical relationships between dry density and moisture content for four different types of

soils, namely, gravel, sand, silt and clay.

3.5 Laboratory compaction test Compaction is carried out in the laboratory for the purpose of:

i) Classifying soils, ii) Providing guidance on potential levels of compaction to be achieved in full-scale work, iii) Providing guidance on the most appropriate moisture content at which to compact soil, iv) Providing a standard against which to assess the dry density achieved in-situ.

For whatever purpose, compaction in the laboratory can be carried out using one of the following standard methods: 2.5kg rammer impact, 4.5kg rammer impact, and vibratory compaction methods. These are described below.

26

3.5.1 Compaction test using a 2.5kg rammer This test, with slight vibrations, is specified in the standards BS 1377, ASTM D 698 and AASTHO T 99 as the 2.5kg rammer test. In many European countries, it is referred to as the standard (or basic or normal) Proctor test, in reference to Proctor (1933) who pioneered this type of test in connection with the construction of earth dams.

The requirements of the British Standard version of this test are that soil is compacted in a 1.0 litre mould, internal diameter 105mm, in three approximately equal layers, using a 2.5kg rammer falling through a height of 300mm. The rammer is 50mm in diameter and 27 blows of the rammer are distributed uniformly over each of the layers of soil in the mould. Surplus compacted soil is

struck off flush with the top of the mould and the bulk density of the compacted soil calculated from the mass of soil and volume of the mould. The moisture content of the soil in the mould is

determined and the dry density calculated. A series of tests at various values of moisture content enables a relationship between dry density and moisture content to be plotted, and the maximum

dry density and optimum moisture content for the test method determined.

The size of the mould in British Standard method restricts the maximum particle size that may be used in the test to 20mm. Where significant proportions of soil are excluded from the test,

corrections may be applied to the results or alternatively a larger mould, with the number of blows of the rammer increased in proportion to the increase in volume, and with the use of an increased

maximum particle size, may be employed. The results of a laboratory test where significant proportions of the coarser particles have been excluded, even with the application of a correction,

must be treated with caution. Further information on the correction of test results where coarse particles have been excluded is given in AASTHO T 224 Correction for coarse particles in soil compaction test.

3.5.2 Compaction test using a 4.5kg rammer This test, with slight vibrations, is specified in the standards BS 1377, ASTM D 1557 and AASTHO T 180 as the 4.5kg rammer compaction test, and in many European countries, it is referred to as the Modified Proctor test. The principal is similar to that of the 2.5kg rammer method, but a much larger compactive effort is employed.

The requirements of the British Standard procedure, the soil is compacted in a 1.0 litre mould,

internal diameter 105mm, in five approximately equal layers, using a 4.5kg rammer falling through a height of 450mm. The rammer is 50mm in diameter and 27 blows of the rammer are distributed uniformly over each of the layers of soil in the mould. The bulk density and dry density

27

are determined as for the 2.5kg rammer test and the relationship between dry density and moisture content plotted, from which the maximum dry density and optimum moisture content for the test

method may be determined.

The comments relating to the exclusion of the coarser fraction of the soil, made for the 2.5kg rammer method, also apply in the case of test using the 4.5kg rammer.

3.5.3 Vibratory compaction methods Various forms of laboratory vibratory compaction tests exist. All are designed to produce results with granular materials that are comparable with the dry densities that can be achieved in full-

scale work, where those densities are not attainable using the rammer compaction methods described in the preceding subsections. The soils with which it would be appropriate to use

vibratory compaction methods are free-draining sands and gravels and crushed stones or rock.

The British Standard vibrating hammer compaction test requires a vibrating hammer with a power consumption of between 600 and 750W. Soil is compacted in a cylindrical CBR mould i.e. a mould of 152mm internal diameter, in three approximately equal layers, with 60s of vibration per layer. The tamper attached to the vibrating hammer has a circular foot which almost completely

covers the area of the mould, producing a flat surface to the compacted soil. The total depth of the specimen after compaction should lie between 127 and 133mm for the compaction test to be

acceptable. The bulk density is determined from the mass of the soil, the measured depth of the specimen and the known circular area of the mould. The test is carried out over a range of

moisture content to provide a relationship between dry density and moisture content and hence the maximum dry density and optimum moisture content may be determined.

Because of the size of the mould used in the BS vibrating hammer test, the maximum particle size

that may be incorporated in the sample is 37.5mm. When significant quantities of coarser material are excluded from the test results, if they are to be used as a guide to, or a standard for, full-scale

compaction, should be treated with caution.

The ASTM procedure for determining the maximum index density of cohesionless soils (ASTM D 4253) incorporates a measurement of dry density using a vibrating table. A sample of soil, in either oven-dry or the saturated condition, is vibrated in a mould, with a surcharge of 14kPa, on

the vibrating table for a specified period of time, and the bulk density determined from the measurement of the depth of the compacted soil and the mass of the soil in the mould. The mass

28

of the soil and the size of the mould depend on the maximum size of the soil particle in the sample. The required characteristics of the vibrating table are laid out in the ASTM standard.

3.6 Full-scale compaction equipment Equipment for the compaction of shallow layers in earthworks operations comprise numerous

forms and employ different basic methods of subjecting the soil to compaction stresses. These include smooth-wheel rollers (dead weight), grid rollers, sheepsfoot rollers (dead weight), tamping rollers (dead weight), pneumatic-tyred rollers, vibrating rollers, vibrating plate compactors, power rammers, dropping weight compactors, vibro-tampers, and impact rollers. The students are encouraged to reader about each of the above compaction equipment.

3.7 Measurement of in-situ density The measurement of density of compacted soil is a frequent, often essential, requirement during

placement of fill. Allowance has to be made, usually by carrying out a number of determinations over an area of compacted soil, for the real variability in the state of compaction arising from

vibrations in soil type, moisture content and compactive effort applied.

It is important that the measurements of in situ density are carried out in such a way that the quality of compaction is determined as accurately as possible; thus it is important that the

complete depth of layer being compacted is included in the sample or that the least compacted part of the layer is sampled. The dry density normally decreases towards the bottom of the layer, where

the compaction stresses are lowest, and the density in the lower regions of the compacted layer may be critical to the satisfactory performance of the compacted fill. Normal procedures attempt

to measure the average density through the complete depth of the compacted layer. However, where particularly deep layers are being compacted (say in excess of 300mm thickness) it may be advisable to determine the variation of density throughout the layer (by carrying out the measurement of density at various levels) or to concentrate on the density of the lower 100-150mm of the layer. Some of the methods used in the evaluation of field density were discussed in chapter two where the reader is referred for details.

3.8 Field control of compaction Field control of compaction is the act of monitoring the factors that affect the level of compaction

with the view of keeping them within the range that give the desired compaction. It therefore means that for a successful field control of compaction, there should be some specifications to be

achieved. Two general groups of specifications can be used; namely, end results specifications and

29

method specifications. In the former, a quantifiable property of the compacted soil is specified; whilst in the latter the procedure to be used in the compaction process is detailed.

3.8.1 End-result specifications Using relative compaction, the problems of variability with the specification of compaction in terms of dry density can be overcome. The dry density achieved in the compaction process can be

expressed as a percentage of the maximum dry density obtained by a specified compactive effort in the laboratory. The actual percentage specified can vary depending on the application of the

earthwork construction and the type of the soil, but usually, for 2.5kg rammer test, it is in the range 90-100%. Where soil varies from place to place in a compacted layer, it is often necessary to establish the maximum dry density at each location of measurement of the in-situ dry density.

Using relative density, DR, the relative density form of specification ASTM D 4253 and ASTM D 4254 is often applied to cohesionless soils, where the effect of moisture content is less than with other soils, and compares the void ratio of the in-situ material with the maximum and minimum void ratios determined in the laboratory. Maximum void ratio (emax) is normally determined by pouring dry soil into a mould, and the minimum void ratio (emin) can be determined by a form of vibratory compaction, usually with full saturated soil.

%100minmax

max

=

ee

eeDR

Where e is the void ratio of the in situ; or, in terms of dry density,

( )( ) %100minmax

minmax

=

ddd

dddRD

Where maxd is the maximum dry density; mind is the minimum dry density and d is the in situ

dry density.

Using air voids, the measurement of the air remaining in the compacted soil is a logical expression of the state of compaction considering that the reduction of air voids is implicit in the compaction

process. Air voids, Va, content is determined from the expression,

%100100

11100

+=

w

GV

sw

da

Where w is the density of water; sG is the specific gravity and w is the water content.

30

For practical purposes, Gs may be assumed to be constant unless there are large variations in soil type. As indicated by the expression, therefore, an increase in moisture content at constant dry

density leads to a reduction in air voids and it is necessary to ensure that a low air content is not achieve at the expense of using poor quality soil of excessively high moisture content. Commonly

specified values for well graded soils are a maximum of 10% air voids for bulk earthworks and 5% air voids for high quality applications, to be achieved at moisture contents within specified limits or below a specified upper limit.

Using shear strength, the compaction process can be specified in terms of the resulting shear strength of the soil, assuming that the soil is amenable to the measurement of in situ shear strength

(for example, shear vane, penetrometer needle) or to the extraction of undisturbed samples for subsequent unconfined compression tests or triaxial tests. This method assesses both the

effectiveness of the compaction process and the quality of the soil used (shear strength is dependent on both dry density and moisture content of the soil) and care should be taken in assigning reasons for any results that fail to comply with the specification.

Using proof rolling, the degree of deformation on the surface of the compacted soil resulting from the passage of a roller of specified dimensions and loading can be used as an indication of the

standard of compaction achieved. As with shear strength specifications, this method assesses both the effectiveness of the compaction process and the quality of the soil and, as such, deformations

produced under the roller need careful interpretation. One advantage of the proof rolling specification method is that it highlights areas of doubtful quality to which further more rigorous

tests can be applied.

3.8.2 Method specifications In a method specification for compaction the precise procedure to be used is laid down. Thus the

type of compactor, mass, speed of travel, and any other factors influencing performance such as frequency of vibration, together with the thickness of individual layers to be compacted and the

number of passes of the machine, are all specified.

This particular specification provides as wide a choice of compaction plant as possible. Soils are

divided into several classes and procedures for use of the compaction plant are given for each class. The number of passes and thickness of layer are designed to provide a compactive effort

capable of achieving an adequate state of compaction with the more difficult soil conditions likely to be encountered.

31

3.8.3 Control moisture content The influence of moisture content on the compaction process and the state of compaction achieved

with a given compactive effort has been discussed in subsection 3.4.1. The minimum state of compaction required in a method specification must take account of the natural moisture content

of the soil to be used or of any change in moisture content that the engineer may require to bring the soil to a condition compatible with his design. For example:

a) In arid areas where water is scarce it may be necessary to achieve the best compaction possible at moisture contents well dry of the optimum for most normal types of compaction

plant.

b) The clay core of a dam may require the soil to be wetted to bring it to sufficiently low shear strength so that its compaction will provide a virtually impermeable material of low air voids content.

c) In countries where dry and wet seasons alternate it is considered beneficial for the long-term performance of embankments to compact clay soils at moisture contents equal to

or wetter than the optimum moisture content of the 2.5kg rammer compaction test.

Under certain circumstances, therefore, such as (b) and (c) above, it may be necessary to add water to the soil, importing the water by browser and mixing it into the soil by disc harrow, rotary

cultivator or mechanical stabiliser. The control of the condition of the earthwork material before and during its compaction is, therefore, an integral part of the compaction operation.

With the relative compaction form of specification, however, the separate control of moisture

content is necessary. In some instances the moisture content is measured and compared with other soil properties such as the plastic limit or the optimum moisture content in a laboratory

compaction test. Measurement of shear strength have also been used particularly the moisture condition test, a form of strength test in which the compactive effort needed to compact a sample

of soil fully is determined.

3.9 Worked Examples Problem 1 The undisturbed soil at a given borrow pit was found to have a water content of 18%, void ratio of

0.55 and specific gravity of 2.75. The soil is to be used as a rolled fill having a finished volume of 60,000m3. The soil will be excavated by means of a shovel and dumped onto trucks having a capacity of 4.5m3 each when loaded to capacity. When loaded to capacity, each truck contains 5,000kg. During construction, the trucks dump their load on the fill, the material is spread and

32

broken up after which a sprinkler adds water until the moisture content is 20%. The soil and water are thoroughly mixed and compacted until the dry density is 1.85tonnes/m3 (1.0ton = 1000kg).

i) Assuming each load is a capacity load, how many truckloads are required to construct the fill?

ii) What volume in m3 of the excavated material will remain in the borrow pit? iii) How many litres of water will have to be added per truckload? Assume that moisture lost

by evaporation during excavation, hauling and handling is negligible. iv) What will be the saturated moisture content if the volume of soil increased from its original

volume by 20%.

Note that all formulae used should be derived from first principles.

Solution to problem 1

Given: For soil borrow pit: 75.2 ,55.0 %,18 === sii Gew

Finished volume: 3000,60 mV f =

Truck capacity: kgm 000,5 , 5.4 3

Compaction moisture: %20=fw

Target dry density: 33,

/1085.1 mkgfd =

i) Truck loads required per truck carried Mass

pit from material fill of mass Total=

But total mass, ( ) sssws MwwMMMMM +=+=+= 1

Also, f

sfd V

M=

,

Therefore, ffds VM ,=

kg83 1011.1600001085.1 ==

Remember, swi wMMw == and %18

Therefore, Truck loads required is given by,

( ) loads truck 196,265000

1011.118.15000

1 8=

=

+=

kgkgMw s

33

Note that one can also use the mass of solids since it remains constant i.e.,

Mass of solids per truck, truckkgw

MMi

trucks /288.423718.015000

1,=

+=

+=

Mass of solids in a fill, kgVM ffds83

,1011.1000,601085.1 ===

Truck loads loads truck196,26288.42371011.1 8

=

=

ii) Volume of excavation that remains in the borrow pit vs VV +=

For a single truck, volume of solids, svws

truckstrucks eVVG

MV == and ,

,

Therefore, total volume per truck, ( ) ( ) ( )ewGM

eVViws

trucktruckstruck ++

=+= 11

1,

( ) per truck 388.255.0118.11075.2

5000 33 mVtruck =+

=

Total volume for 26,196 trucks 3564,62196,26388.2 m==

iii) Litres of water to be added per truck load, ( ) per truck water of mass Initial - Final =truckL

But initial mass of water in the soil per truck, kgMwM trucksitruckinitialw 712.76218.1500018.0

,,,===

And final mass of water in the soil per truck, kgMwM trucksftruckfinalw 458.84718.150002.0

,,,===

Therefore mass of water to be added per truck, litres 75.84712.762458.847,,

==truckaddedwM

iv) Saturated moisture content if soil swell by 20% is calculated as follows:

Volume of soil per truck after swelling, 3,,,,

388.22.1 mVVVVV truckwtruckstruckvtrucksswell =+=+=

Recall that volume of solids per truck, 33, 1075.218.15000

mV trucks

=

Volume of water after swelling per truck, 33, 32477.11075.218.15000388.22.1 mV truckw =

=

34

Recall that mass of water given water density multiplied by the volume of water.

Therefore saturated moisture content per truck, %3.3118.1/50001032477.1 3

=

=sw

35

4. Soil Hydraulics

4.1 Introduction Soil is said to be a permeable material since it contains continuous voids through which water can

flow. Water in soil exists either in solid state, liquid state or gaseous state. The state of concern is

the liquid state. The source of water is mainly rainfall and water below the ground surface is

known as sub surface water and is divided into different zones:

(a) A saturated zone where the top surface of water is at atmospheric pressure and is known as the water table or phreatic surface. Below the water table soil is saturated and can flow freely

due to the hydraulic gradient. This phreatic water is subject to gravitational forces and has an internal pore pressure greater than atmospheric pressure.

(b) Aeration (Vadose) zone, which lies between the water table and the ground surface. Immediately above the water table is the capillary fringe, which holds capillary water by

surface tension forces (internal pore pressure is less than atmospheric pressure). The soil in this zone remains saturated due to capillary action and above it is the partially saturated sub

zone of transient percolating water, moving downwards to join the phreatic water below the water table.

When water flows through a permeable soil, it exerts a frictional drag force on the particles. The

effect of this force per unit volume is known as seepage pressure.

4.2 Water Bearing Layers in Soil There are basically three types of water bearing layers in soil: (a) Pervious layers; have favourable water transmitting properties. (b) Semi pervious layers; have unfavourable water transmitting properties. (c) Impervious layers; are associated with negligible transmission of water.

A combination of the above water bearing layers in the soil is known as an aquifer. There are three types of aquifers: confined aquifers, semi-confined aquifers and unconfined aquifers.

4.2.1 Confined aquifers Confined aquifers occur when a saturated pervious layer is sandwiched between two impervious

layers.

Fig. 4.1: The schematic illustrating the confined aquifer

Saturated pervious layer

Impervious layer

Impervious layer

36

4.2.2 Semi-confined aquifers Semi-confined aquifers occur when a saturated pervious layer is bedded between an impervious

layer and a semi impervious layer.

Fig.4.2: The schematic illustrating a semi-confined aquifer

4.2.3 Unconfined aquifers Unconfined aquifers occur when a saturated pervious layer is bedded between an impervious layer

and a pervious layer.

Fig.4.3: The schematic illustrating the unconfined aquifer

4.3 Permeability Permeability is the measure of the ease with which water flows through rocks and soil. It is important when dealing with seepage under dams, land drainage or ground water lowering. The flow of water through soil is governed (accounted for) by Darcys law and Bernoulis law. These are explained below.

4.3.1 Darcys Law States that the flow of water, V, through a saturated soil is proportional to the hydraulic gradient assuming laminar flow i.e.,

V or V = K

Where K is the coefficient of permeability, which depends on:

(a) The size of the particles. (b) The porosity of the soil. (c) The particle size distribution. (d) The shape and orientation of soil particles. (e) The degree of saturation. (f) The viscosity of soil water, which varies with temperature.



Impervious layer

Pervious layer

Impervious layer

Semi impervious layer

37

The hydraulic gradient, , is the ratio of the hydraulic head across soil to the length of flow path

through soil and velocity of flow, V, is the ratio of discharge through the soil to the cross sectional area, A, of the soil i.e.,

V = Q/A or Q = K A

4.3.2 Determination of Permeability Coefficient, K (a) Laboratory Methods of Determination

(i) Coarse Soils The permeability of coarse-grained soils is determined in the laboratory using constant head Permeameter apparatus. The specimen is put in the Perspex cylinder of cross sectional area, A. A coarse filter is incorporated above and below the sample to prevent it from being washed away.

A steady vertical flow of water under a constant total head is maintained through the soil and the quantity of water flowing per unit time, q, is measured. Manometer tapping from the side of the cylinder enables the hydraulic gradient, =h/L, to be measured. Results

From Darcys law;

VAqKi ==

Aq

LhK =

AhqLK =

Fig. 4.4: The constant head Permeameter apparatus

A series of tests should be run each at a different rate of flow and an average value of K determined. Note that prior to running the test a vacuum is applied to ensure that the degree of saturation under flow will be close to 100%.

L

h

Perspex Cylinder

38

(ii) Fine-grained soils

Fig. 4.5: Falling head Permeameter apparatus

For fine-grained soils the falling head Permeameter is used. A coarse filter is placed at each end of the specimen and a standpipe of cross sectional area, a, is connected to the top end of the cylinder. Water drains through a reservoir of constant level. The standpipe is filled with water and the measurement is made of time, t1 for which the water level (relative to water level in the reservoir) to fall from h0 to h1.

At any intermediate time, t, the water level in the standpipe is given by h and its rate of change is

given by .dtdh

Computations

Applying Darcys law; VAqKi ==

dtdh

aKAiq ==

dtdh

aLhKA =

Rearranging and integrating both sides;

=1

0

1

0

t

t

h

h

dtL

AKhdh

a

( )010

1 ttL

AKhh

aIn =

( ) 10

1001

log3.2hh

ttAaLK

=

A series of tests should be run using different values of h0 and h1 and/or standpipes of different

diameters.

h0 h1 L

Reservoir

Standpipe of area, a

39

(b) In situ Methods of Determination These are justified due to the difficult in simulation of field conditions in the laboratory. The commonest in situ method is the well pumping test, which is suitable for homogeneous coarse-

grained soil strata. The method, however, is dependent on the confinement of the strata.

(i) Determination of Permeability in Unconfined Aquifers

Fig. 4.6: Well Pumping Test (Unconfined Aquifer)

A test well is bored to the bottom of the stratum under observation and at least two observation

wells are dug in the neighbourhood of the test well. Pumping from the test well is then done until

steady state conditions are established. Draw down of the water table takes place as a result of

pumping and when the steady states are established the water levels in the observation wells will

correspond to the new water table.

Let the boreholes be located at distances r1 and r2 from the well and the water table levels in them

h1 and h2 respectively. The slope of the water table gives the hydraulic gradient at any distance r.

= drdh

This is known as the Dupuit assumption and it is reasonably accurate accept at points close to the well. Assuming radial flow and applying Darcys law:

drdh

rrhKAKiq pi2==

=2

1

2

1

21h

h

r

r

hdhKdrr

q pi

( )21221

2 hhKr

rqIn =

pi

dh dr

r

h Direction of flow

h2 h1

r1

r2 q

Impervious material

40

( )21221

2

hhr

rqIn

K

=pi

The above equation is applied to each pair of boreholes and an average value of K determined.

(ii) Determination of Permeability in Confined Aquifers

Fig. 4.7: Permeability in confined aquifers

The procedure is similar to that described under the determination of permeability coefficient in

unconfined aquifers. In this case the height, H, will remain constant and assuming radial flow the

surface area of flow is given by:

rrHA pi2=

Darcys law gives;

AKiq =

drdhHrKq pi2=

=2

1

2

1

21h

h

r

r

dhHKdrr

q pi

( )121

2 2 hhHKr

rqIn =

pi

( )121

2

2 hhHr

rqIn

K

=pi

Read about the Piezometer and Tube methods.

4.3.3 Permeability in Anisotropic Soils For anisotropic soils the coefficient of permeability in the horizontal direction, Kx is different from

the coefficient of permeability in the vertical direction, Kz and this is so because of stratification of

h2 h1

r1

r2 q

H

Impervious material

Impervious material

New water table level

41

soil layers. The effective coefficient of permeability, K for two-dimensional flow of water in soil

is given by:

zx KKK =

Horizontal and Vertical Coefficient of Permeability

A soil element of isotropic layers of thickness h1, h2, , hn having coefficients of permeability K1,

K2, , Kn respectively with horizontal boundaries as shown above is considered. Total area is

equal to the area of a single layer with thickness n

ih1

in which the coefficients of permeability in

the directions parallel and normal to stratification are given as Kx and Kz respectively.

For one-dimensional flow in the horizontal direction the equipotentials are vertical and hence the

hydraulic gradient in the layers is constant and equal to x.

Considering an element of soil into the paper with thickness of one unit. xx AKiq =

( ) xxnx iKhhhq +++= ...21 =

n

xii

n

xxi iKhiKh11

=

n

i

n

ii

x

h

KhK

1

1

For one-dimensional flow in the vertical direction the condition for continuity requires that the rate

of flow through each layer is constant and that the equivalent rate, Vz through a single layer is

constant.

iiz iKV =

nniKiKiK == 2211

zzz iKV =

h1

h2

hn

K1

K2

Kn

Z

X

42

Head loss over the total depth n

ih1

is equal to the sum of the individual head losses through the

layers.

1

1

__

_

hH

fllowoflengthlossheadi ==

11 ihH =

Overall head loss

n

n

zzzzzznn

n

iz hKiKh

KiKh

KiKihihihhi +++=+++== ...... 2

21

12211

1

=n

i

iz

n

i Kh

Kh11

=

n

i

i

n

i

z

Kh

hK

1

1

Note: always Kx > Kz implying that seepage occurs more rapidly in the direction parallel to

stratification than in the direction normal.

Table 4.1: Typical Values of K Soil type K(mm/sec) Gravels >10-2

Sands 10-2 10-5

Silts 10-5 10-8

Clays < 10-8

4.4 Seepage Seepage is the flow of water in the soil. Water flows from the point of high water level to that of

lower water level due to difference in pore water pressure. As seepage occurs pore water pressures

adjust from their initial values to their final values, during which time seepage is a function of time. Finally when pore water pressures are in equilibrium flow becomes independent of time and

steady state flow conditions prevail.

43

4.4.1 Seepage in Two Dimensions (Two Dimensional Flow)

Consider the general case of seepage in two dimensions in a soil, which is homogeneous and

isotropic. Assuming that water is incompressible i.e. the mass of water entering the soil element is

equal to that leaving the element. Darcys law gives:

x

hKKiV xx

== and z

hKKiV zz

==

Negation indicates that velocity increases in the opposite sense of hydraulic gradient.

Assuming a fully saturated element of dimensions dx, dy and dz the volume of water entering per

unit time, Ve

dydxVdzdyVV zxe .... +=

The components of discharge velocity of water entering the element are Vx and Vz and the rates of

change of discharge velocity in the x and z directions are x

Vx

and

z

Vz

respectively. Volume

of water leaving per unit time is:

dydxzz

VVdzdyxx

VVV zzxxL ..

++

+=

Assuming steady flow conditions, Le VV =

0=

+

dxdydzz

Vdxdydzx

V zx

0=

+

z

Vx

V zx

This is the steady flow equation in two dimensions in the soil and its solution can be obtained by

use of any of the following methods:

1. Complex variables method.

2. Finite difference method.

3. Finite element method.

4. Electrical analogy method.

5. Hydraulic models method. 6. Try and error (graphical) method.

Vz

Vx

x x+dx

z

z+dz

dx dy

dz

44

4.4.2 The Graphical Method This involves construction of flow nets over an area where seepage occurs. The paths taken by

moving water particles as the water flow through a permeable material may be represented

pictorially by a series of flow lines. Flow lines are nearly parallel curved lines since water tends to take the shortest path from point to point but only change direction in smooth curves.

The point of equal head of water on each flow line can be joined to give a series of curves known as equipotential lines. The equipotential lines cross the flow lines at right angles. The pattern of approximate squares formed by these two sets of lines is known as a flow net.

4.4.3 Flow Net Construction A cross section of the site and structure is drawn to scale and the boundary conditions i.e.

impermeable strata, points of singularity, points of shield etc examined. Flow lines are then drawn

to start and finish at right angle to the inlet and outlet surfaces whereas equipotential lines start and

finish at right angle to the impervious layer. The equipotential lines should be drawn

approximately perpendicular to the flow lines such that the length and width of each area enclosed

by intersecting and adjacent pairs of lines are equal.

Note: When constructing a flow net it is always advisable not to draw too many lines; four or five flow

channels are adequate.

4.4.4 Flow Net Application (a) Estimation of Seepage

Consider a unit thickness of a portion of flow as measured into the paper. If the flow pattern is

drawn correctly then the drop in the piezometric head will be constant between successive

equipotential lines.

structure

Inlet surface Outlet surface

Impervious layer

Equipotential line

Flow line

h Datum

45

hdN

h= where; Nd - total number of head drops from inlets to outlets.

h - drop in head between any two adjacent equipotential lines. h - difference in total head between first and last equipotentials.

Hydraulic gradient, 11 LN

hLhi

d

=

=

Seepage velocity, 1LN

KhKiVd

==

Seepage, 1

2

LNKhLAreaVelocityq

d

== but 21 LL

dNKhq =

Total seepage, fd

NNKhQ = where fN is the number of flow channels across any section. The

units commonly used are m3/day.

(b) Pressure Distribution on the Base of a Structure In analysing the stability of a structure (for instance a dam) it is important to obtain the uplift pressure (thrust), which is the function of pore water distribution, on the bottom of the structure. This pressure can be obtained from the flow net. By definition, pressure head due to pore water at

any point is the height to which water would rise in a standpipe if its lower tip was placed at that

point.

In the analysis, several points are selected at the bottom of the structure and the total pressure at

each point obtained using the following formula:

Pressure head hNn

d

d=

The elevation head for each point is determined relative to the datum level and the pressure head is

calculated using Bernoullis equation. The results are tabulated as shown below.

L1

L2

a

b

c

d

flow

46

Point Total Head Elevation Head Pressure Head Pore Water Pressure

n (m) (m) (m) (kN/m2) ** *** *** ** ******

A graph of pressure head is made with respect to the points along the base of the structure. The up

thrust is calculated from the area of the pressure distribution multiplied by the unit weight of water

or directly from the plot.

4.4.5 Effects of Seepage on Soil Stability (a) Equilibrium Conditions

Under equilibrium conditions there will be no flow of water through the soil.

At section x-x,

Total vertical pressure, ZH satw +=

Pore water pressure, ( )ZHU w += Effective pressure, ( )ZU wsat ==1

(b) Downward Flow Through Soil One Dimensional flow

At x-x,

Total vertical pressure, ZH satw += and Pore water pressure, ( )hZHU w += Effective pressure, ( ) hZU wwsat +==1 The effective pressure is increased by wh which is the seepage pressure exerted by the flowing water.

x x

H

Z Flexible tube

Permeable soil

x x

H

Z Flexible tube

Permeable soil

h Over flow

Add to maintain level

47

(c) Upward Flow Through Soil

At section x-x,

Total vertical pressure, ZH satw +=

Pore water pressure, ( )hZHU w ++= Effective pressure, ( ) hZU wwsat ==1 The effective pressure is decreased by wh which is the seepage pressure.

4.4.6 Piping This occurs when the upward seepage pressure becomes equal to the submerged weight of the soil

above a certain point. Water forces an overlying soil mass to move upwards and the surface

appears to boil. It occurs when the effective stress is equal to zero.

For upward flow; ( ) hZU wwsat ==1 At critical conditions, ( ) 01 === hZU wwsat c

w

wsat iZh

=

=

1=w

satci

Factor of Safety Against Piping

1.. >=iiSOF c

Where i is the average exit hydraulic gradient.

Note:

The quick condition rarely occurs in cohesive soils due to the force of attraction

between the particles. It occurs more in fine sands.

The quick condition occurs less in coarse sands and gravels as these are big in

size and so have larger pores.

x x

Z Flexible tube

Permeable soil

H

h

Civ2201 Soil Mechanics 1-3

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Transcript of Civ2201 Soil Mechanics 1-3