MANGALWARI BAZAAR ROAD, SADAR, NAGPUR - 440001. … · 1. Introduction : Formation of soil,...

ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY

MANGALWARI BAZAAR ROAD, SADAR, NAGPUR - 440001.

DEPARTMENT OF CIVIL ENGINEERING

Prof. Rashmi G. Bade, Department of Civil Engineering, Geotechnical Engineering – I 1

Geotechnical Engineering – I

B.E. FOURTH SEMESTER





BECVE402T Geotechnical Engineering – I

Course Outcomes: At the end of the course, the student will have:

Cos Description Bloom’s

Taxonomy

CO1 Find the index and engineering properties of the soil. L1

CO2 Identify the suitability of foundation for a particular type of soil. L3

CO3 Determine properties & demonstrate interaction between water and soil. L5

CO4 Classify and characterize the soils. L4

CO5 Analyze and compute principles of compaction and consolidation

settlements of soil. L4

CO6 Evaluate the stresses in the soil mass. L5

Course Objectives:

S.No. Description

1 To impart knowledge about origin and classification of soils.

2 To impart knowledge about index properties and their determination.

3 To impart knowledge about engineering properties and their determination.

4 To impart knowledge about stress distribution in soil mass.





BECVE 402 T GEOTECHNICAL ENGINEERING-I

Objectives:

1. To impart knowledge about origin and classification of soils.

2. To impart knowledge about index properties and their determination.

3. To impart knowledge about engineering properties and their determination.

4. To impart knowledge about stress distribution in soil mass.

Outcomes:

a. Students would be able to determine the index and engineering properties of the soil.

b. Students would be able to determine the suitability of foundation for a particular type of soil.

c. Students will be able to classify the soils.

d. Students would be able to evaluate the stresses in the soil mass.

Syllabus :

Unit I

1. Introduction : Formation of soil, residual & transported soil, major deposits found in India, soils

generally used in practice such as sand, gravel, organic soil, clay, Betonites, black cotton soil etc.

Introduction to clay mineralogy.

2. Phases of soil: Various soil weight & volume inter-relationship. Density index, methods of

determining in situ density.

Unit II

Index Properties & Their Determination, Water content, specific gravity, sieve analysis, particle size

distribution curve, sedimentation analysis, Differential and free swell value, Consistency of soil,

Atterberge’s limits . Classification of Soil : Particle size classification, Textual classification, Unified

& I.S. classification system, field identification of Expansive soil, Swelling pressure.

Unit III

3. Permeability: Darcy’s law & its validity, Discharge & seepage velocity, factors affecting

permeability, Determination of coefficients of permeability by Laboratory and field methods,

permeability of stratified soil.





4. Seepage: Seepage pressure, quick sand condition, characteristics & uses of flownets, Preliminary

problems of discharge estimation in homogeneous soils, Effective, Neutral and total stresses in soil

mass.

Unit IV

5. Stress Distribution: Stress distribution in soil Mass, Boussinesque equation, point load and

uniformly

distributed load over rectangular & circular areas, Use of Newmarks charts.

Unit V

6. Consolidation: Compression of laterally confined soil, Terzaghis 1-D consolidation theory

(formation of Differential equation), Determination of coefficient of consolidation, Degree of

consolidation. Determination of preconsolidation pressure, Settlement, Rate of settlement.

7. Compaction: Mechanism of compaction, factors affecting compaction, standard & modified

proctor Tests, field compaction equipments, quality control, Advance compaction Techniques,

Nuclear density meter.

Unit VI

8. Shear Strength: Introduction, Mohr Coulombs theory, Drainage condition, Measurement of shear

strength by direct shear test, triaxial test, unconfined compression test, vane shear test, sensitivity.





BECVE 402 P PRACTICAL: GEOTECHNICAL ENGINEERING – I

These shall comprise of ten experiments and terms work to be presented in the form of journal for

assessment of sessional and practical examination.

A. List of Experiments : Any 10

1. Moisture content and Specific gravity of soil.

2. Grain size Analysis – (Sieve Analysis).

3. Consistency limit, plastic limit and liquid limit of soil.

4. Hydrometer Analysis.

5. Constant Head Permeability test of or Falling Head Permeability test.

6. Consistency limit of soil (shrinkage limit).

7. Field Density by sand replacement method.

8. Field Density by core cutter method.

9. Unconfined compression test.

10. Direct shear Test.

11. Triaxial shear test (Demonstration).

12. Proctors compaction Test and Proctor needle test.

B. One field visit or one case study included in journal.

C. Use of plasticity Chart or Newmarks Chart.

Text book

Sr. No. Title Publication

1 Soil Mechanics & Foundation Engg. by K.R. Arora Std. Publisher

2 Soil Mechanics & Foundation Engg. By B.C.Punmia Laxmi Publication

3 Basic & Applied Soil Mechanics by Gopal Rajan & Rao Newage international Pub.

4 Geotechnical Engg. By P. Raj Dorling Kindersley Pvt. Ltd

5 Geotechnical Earthquake Engg. By Steven L. Kramer Prentice Hall

Reference book

Sr. No. Title Publication

1 Soil Mechanics & Foundation Engg by Modi Std. Publisher

2 Soil Mechanics & Foundation Engg by V.N.S.Murthy CBS Publishe





UNIT – 1 1. Introduction : Formation of soil, residual & transported soil, major deposits found in India, soils generally used in practice such as sand, gravel, organic soil, clay, Betonites, black cotton soil etc. Introduction to clay mineralogy. 2. Phases of soil: Various soil weight & volume inter-relationship. Density index, methods of determining in situ density.





1.1 INTRODUCTION

The word ‘soil’ is derived from latin word ‘solium’, which according to Webster’s dictionary, means the upper layer of the earth that may be dug or plowed; specifically, the loose surface material of the earth in which plant grows.

Terzaghi defined Soil Mechanics as follows

Soil Mechanics is the application of the laws of mechanics and hydraulics to engineering

problems dealing with sediments and other unconsolidated accumulations of solid particles

produced by the mechanical and chemical disintegration of rocks regardless of whether or not they

contain an admixture of organic constituents.

The term Soil Mechanics is now accepted quite generally to designate that discipline of engineering science which deals with the properties and behavior of soil as a structural material.

All structures have to be built on soils. Our main objective in the study of soil mechanics is to lay down certain principles, theories and procedures for the design of a safe and sound structure. The subject of Foundation Engineering deals with the design of various types of substructures under different soil and environmental conditions.

Soil is defined as a natural aggregate of mineral grains, with or without organic constituents that can be separated by gentle mechanical means such as agitation in water. Soils are formed by the process of weathering of the parent rock. The weathering of the rocks might be by mechanical disintegration, and/or chemical decomposition.

1.2 FORMATION OF SOIL

Soils are formed by either (A) Physical disintegration or (B) Chemical Decomposition. (A) Physical disintegration:- Physical disintegration or Mechanical disintegration of rocks occurs

due to following physical processes:- (i) Temperature changes – Different minerals of rock have different coefficients of thermal

expansion. When the stresses induced due to such changes are repeated many times, the particles get detached from the rocks and the soils are formed.

(ii) Wedging action of Ice – Water in the pores and minute cracks of rocks gets frozen in very cold climates. Rocks get broken into pieces when large stresses develop in the cracks due to wedging action of the ice formed.

(iii) Spreading of roots of plants – As the roots of trees and shrubs grow in the cracks and fissures of the rocks, forces act upon the rock. The segment of the rock is forced apart and disintegration of rocks occurs.

(iv) Abrasion – As water, wind and glaciers move over the surface of rock, abrasion and souring takes place. As results in formation of soils.

(B) Chemical Decomposition – When Chemical decomposition or chemical weathering of rocks takes place, original rock minerals are transformed into new minerals by chemical reactions. The





soils formed do not have the properties of parent rock. The following chemical processes generally occur in nature.

(i) Hydration – In hydration, water combines with the rock minerals and results in the formation of a new chemical compound. The chemical reaction causes a change in volume and decomposition of rock into small pieces.

(ii) Carbonation – the carbonic acid reacts with rocks and causes their decomposition. (iii) Oxidation – Oxidation is similar to rusting of steel. (iv) Solution – Some of the rock mineral form a solution with water when they get dissolved in

water. Chemical reaction takes place in the solution and the soils are formed. (v) Hydrolysis – It is chemical process in which water gets dissociated into H+ and OH- ions. The

hydrogen cations replace the metallic ions such as calcium, sodium and potassium in rock minerals and soils are formed with a new chemical decomposition.

1.3 RESIDUAL AND TRANSPORTED SOILS

On the basis of origin of their constituents, soils can be divided into two large groups: 1. Residual soils, and 2. Transported soils.

Residual soils are those that remain at the place of their formation as a result of the weathering of parent rocks. The depth of residual soils depends primarily on climatic conditions and the time of exposure. In some areas, this depth might be considerable. In temperate zones residual soils are commonly stiff and stable. An important characteristic of residual soil is that the sizes of grains are indefinite.

Transported soils are soils that are found at locations far removed from their place of

formation. The transporting agencies of such soils are glaciers, wind and water. The soils are named according to the mode of transportation. Alluvial soils are those that have been transported by running water. The soils that have been deposited in quiet lakes, are lacustrine soils. Marine soils are those deposited in sea water. The soils transported and deposited by wind are aeolian soils. Those deposited primarily through the action of gravitational force, as in land slides, are colluvial soils. Glacial soils are those deposited by glaciers. Many of these transported soils are loose and soft to a depth of several hundred feet. Therefore, difficulties with foundations and other types of construction are generally associated with transported soils.

Origin of soils

Soils are formed by weathering of rocks due to mechanical disintegration or chemical decomposition. When rock surface gets exposed to the atmosphere for an appreciable time it disintegrates or decomposes into small particles and thus the soils are formed. Soil may be considered as an incidental material obtained from the geological cycle which goes on continuously in nature. The geological cycle consists of erosion, transportation, deposition and upheaval of soil.





Fig. 1 Geological cycle

1.3 MAJOR SOIL DEPOSITS OF INDIA

The soil deposits of india may be classified in the following five major groups:- (1) Alluvial Deposits – A large part of north India is covered with alluvial deposits. The thickness of

alluvium in the Indo – gangetic and Brahmputra flood plains varies from a few metres. (2) Black Cotton Soils – A large part of central India and a portion of South India is covered with

black cotton soils. These soils are residual deposits. Black cotton soils are clays of high plasticity. They contain clay mineral montmotillonite. The soils have high shrinkage and swelling characteristics. The shearing strength of the soils is extremely low.

(3) Lateritic Soils – Lateritic soils are formed by decomposition of rock, removal of bases and silica, and accumulation of iron oxide and aluminium oxide. Lateritic soils exist in the central, southern and eastern India.

(4) Desert Soils – A large part of Rajasthan and adjoining and adjoining states is covered with sand dunes. In this area, arid conditions exit, with practically little rainfall.

(5) Marine Deposits – Marine deposits are mainly confined along a narrow belt near the coast. In the south – west coast of India, there are thick layers of sand above deep deposits of soft marine clays.

1.4 SOIL SOLIDS GENERALLY USED IN PRACTICE

Soil solids generally used in practice such as:- 1) Sand – it is a coarsed – grained soil, having partical size between 0.075mm to 4.75mm. The soil

is cohesionless and pervious. 2) Gravel – Gravel is a type of coarsed – grained soil. The particle size ranges from 4.75mm to

80mm. It is a cohesionless material. 3) Organic silt – It is a fine grains soil, with particle size between 0.002mm and 0.075mm.It is a

plastic soil and is cohesive. 4) Bentonite – It is a clay formed by the decomposition of volcanic ash with a high content of

montmorillonite. It exhibits the properties of clay to an extreme degree. 5) Hard pan – It is a relatively hard, densely cemented soil layer, like rock which does not soften

when wet. Boulder clays or glacial till is also sometimes named as hardpan.





6) Caliche – It is an admixture of clay, sand, and gravel cemented by calcium carbonate deposited

from ground water. 7) Peat – is a fibrous aggregate of finer fragments of decayed vegetable matter. Peat is very

compressible and one should be cautious when using it for supporting foundations of structures. 8) Loess – It is a fine-grained, air-borne deposit characterized by a very uniform grain size, and

high void ratio. The size of particles ranges between about 0.01 to 0.05 mm. 9) Black cotton soil – It is a residual soil containing a high percentage of the clay mineral

montmorillonite. It has very low bearing capacity and high swelling and shrinkage properties. 10) Clay – It consists of microscopic and sub – microscopic particles derived from the chemical

decomposition of rocks. It contains a large quantity of clay minerals. It exhibits considerable strength when dry. Clay is a fine – grained soil. It is a cohesive soil. The particle size is less than 0.002 mm.

1.5 INTRODUCTION TO CLAY MINEROLOGY

SOIL STRUCTURE

Soil structure is usually defined as the arrangement and state of a aggregate of soil particles in a soil mass. This term includes , in larger sense, consideration of the mineralogical composition, electrical properties, shape and orientation of solid particles ; the nature and properties of soil water and its ionic composition; and the interaction forces between soil particles, soil water, and their adsorption complexes. As far as structure is concerned, soil particles refer not only to the individual mechanical element which are formed by the aggregation of smaller mechanical fraction. Soil structure is an important factor which influences many soil properties, such as permeability, compressibility and shear strength etc. The following types of soil structure are generally recognized: 1) Single grained:- An arrangement composed of individual soil particles.

Fig. 2 Single and Honey comb structure.

2) Honey Comb:-An arrangement of soil particles having a comparatively loose,stable structure resembling honeycomb . The soil mass is composed of loosely arranged bundles of particles , irrespective of the arrangement of the particles within the bundles.





Fig. 3 Flocculated and Dispersed structure.

3) Flocculated:- An arrangement composed of ‘flocs’ of soil particles instead of individual soil particles. The particles are oriented ‘edge- to-edge’ or ‘edge- to face’ with respect to one another.

4) Dispersed:- An arrangement composed of particles having a ‘face-to face’ or parallel orientation. 5) Coarse- grained skeleton:-An arrangement of coarse grains forming skeleton with its interstices

partly filled by a relatively loose aggregation of the finest soil grains.

Fig. 4 Composite Structure (a) Coarse Grained Skeleton, (b) Clay Matrix.

6) Cohesive matrix:- An arrangement in which a particle –to – particle contact of coarse fraction is not possible. The coarse grains remain embedded in a large mass of cohesive fine grains.

1.6 CLAY MINERALS

There are two fundamental building blocks for the clays mineral structures. One is a silica terrahedral unit in which four oxygen or hydroxyls having the configuration of a tetrahedron enclose a silicon atom. The tetrahedral are combined in a sheet structure so the oxygen of the bases of all the tetrahedral are in a common plane, and each oxygen belongs to two tetrahedral. The silica tetrahedral sheet alone may be reviewed as a layer of silicon atom between a layer of oxygen and a layer of hydroxyls .The silicon sheet is represented by the symbol, representing the oxygen basal layer and the hydroxyl apex layer.





Fig. 5 Tetrahedral Unit.

The second building blocks is an octahedral unit in which an aluminium, iron or magnesium atom is enclosed in six hydroxyls having the configuration of an octahedron. The octahedral unit are put together into a sheet structure which may be viewed as two layers of densely packed hydroxyls with cation between the sheet in octahedral co- ordination. This unit is symbolized by and is known as gibbsite. About 15 minerals are ordinarily classified as clay minerals, and these belong to four main groups; kaolin, montmorillonite, illite and palygorskite. Out of these, the first three groups are the most common and will be described here.

Fig. 6 Octahedral Unit and Gibbsite Sheet.

Kaolinite:-

Kaolinite is the most common mineral of the kaoline group. The kaolinite structural unit is made up of gibbsite sheets (with aluminium atom at their centres) joined to silica sheets through the unbalanced oxygen atom at the apexes of the silicas.This structural unit is symbolized by which is about 7 Å(one angstrom, Å=10-7 mm=10-10 m) thick.

The kaolinite mineral or crystal, is stacking of such 7 Å thick sheets symbolized as shown in fig.7.





Fig. 7 Kaolinite Structure.

The structure is like that of a book with each leaf of the book 7Å thick. Successive 7 Å layer are held together with hydrogen bonds. A kaolinite crystal may be made up of often 100 or more such stacking. The kaolinite particles occur in clay as platelets from 1000Å to 20,000Å wide by 100Å to 1000Å thick. Since the hydrogen bond is fairly strong , it is extremely difficult to separate the layer , and as a result kaolinite is relatively stable and water is unable to penetrate between the layers, kaolinite consequently shows relatively little swell on wetting. The platelets carry negative electromagnetic charges on their flat surface which attract thick layer of adsorbed is mixed with water. China clay is almost pure kaolinite.

Montmorillonite:-

This is the most common of all the clay minerals in expansive clay soils. The mineral is made up of sheet like units .The basic structure of each unit is made up of gibbsite sandwiched between two silica sheets, and is symbolised as shown in fig. The thickness of each is about 10Å and the dimension in the other two directions are indefinite. The gibbsite layer may include atoms of aluminium. Iron, magnesium or a combination of these. In addition, the silicon atoms of terahedra may interchange with aluminium atoms.

These structural changes are called amorphous changes and result in a net negative charges on the clay mineral. Cations which are in soil water (i.e Na+, Ca++, K+ etc) are attracted to the negatively charged clay plates and exist in a continuous state of interchange.

The basic 10Å thick units are stacked one above the other like the leaves of a book and

symbolized as shown in fig. there is very weak bonding between the successive sheets and water may enter between the sheets causing the minerals to swell. The spacing between the elemental silica-gibbsite- silica sheets depends upon the amount of available water to occupy the space. For this reason, montmorillonite is said to have an expanding lattice.





Fig. 8 Montmorillonite Structure.

Each thin platelet has a power to attract to each flat surface a layer of adsorbed water approximately 200Å thick, thus separating platelets a distance of 400Å under zero pressure. In the presence of abundance of water, the mineral can , in some cases, split up into about an individual unit layers of 10Å thick. Soil containing montmorillonite minerals exhibit high shrinkage and swelling characteristics, depending upon the nature of exchangeable cations present. Illite:- The structure of illite is similar to that of montmorillonite except that there is always substantial replacement of silicons by aluminium in the tetrahedral layer and potassiums are between the layer serving to balance the charge resulting from the replacement and to tie the sheet units together. The basic unit is symbolically represented as shown in fig.

Fig. 9 Illite Structure.

The cation bond of illite is weaker than the hydrogen bond of kaolinite but is stronger than the water bond of montmorillonite. Due to this , the illite crystal has a greater tendency to split into ultimate platelets consisting of gibbsite layer between two silica layers, than that in kaolinites. However, illite structure does not swell because of movement of water between the sheets, as in the case of montmorillonite .illite clay particle may be 50Å to 500Å thick and 1000Å to 5000Å in lateral dimensions.





1.7 PHASES OF SOIL

1.8.1 SOIL AS A THREE PHASE SYSTEM

A soil mass is a three phase system consisting of solid particles (called soil grains), water and air. The void space between the soil grains is filled partly with water and partly with air. However, if we take a dry soil mass, the voids are filled with air only. In case of a perfectly saturated soil, the voids are filled completely with water. In general, the soil mass has three constituents which do not occupy separate spaces but are blended together forming a complex material. [fig. 2 (a)] the properties of which depend upon the relative percentages of these constituents, their arrangement and a variety of other factors. For calculation purpose, it is always more convient to show these constituents occupying separate spaces, as shown in [fig. 2 (b) (i) and (b) (ii

(i) Weights (ii) Volumes

(a) Element of natural soil. (b) Element separated into three phases.

Fig.10 Soil as a three phase system.

As shown in Fig. 2 (b) (i), the total volume ‘V’ of the soil mass consists of (i) volume of air ‘Va’, (ii) volume of water Vw and (iii) the volume of solids Vs. The volume of voids Vv, is, therefore, equal to volume of air plus the volume of water. Similarly, Fig. 2 (b) (ii) shows the weights. The weight of air is considered to be negligible. Hence the weight of the total voids is equal to the weight of water Ww. The weight of solids is represented by Wd wich is evidently equal to the dry weight of soil sample. The total W of the moist sample is, therefore, equal to (Ww + Wd).





1.9 WATER CONTENT, DENSITY AND UNIT WEIGHTS

1.9.1 VOLUME – MASS RELATIONSHIPS

(a) Water content:- The water content w, also called the moisture content, is defined as the ratio of weight Ww to the weight of soils Wd in a given mass of soil.

The water content is generally expressed as a percentage. (b) Density of soil: - The density of soil is defined as the mass of the soil per unit volume.

(i) Bulk density (ρ):- The bulk density or moist density is the total mass M of the soil per unit of its

total volume. Thus, It is expressed in terms of g/cm3 or kg/m3.

(ii) Dry density (ρd):- The dry density is the mass of solids per unit of total volume (prior to drying) of the soil mass.

(iii) Density of solids (ρs):- The density of soil solids in the mass of soil solids (Md) per unit of

volume of solids (Vs).

(iv) Saturated density (ρsat) :- When the soil mass is saturated, its bulk density is called saturated density. Thus, saturated density is the ratio of the total soil mass of saturated sample to its total volume.

(v) Submerged density (ρ’) :- The submerged density is the submerged mass of soil solids

(Md) sub per unit of total volume V of the soil mass.

The submerged density or buoyant density is also expressed as

Where ρw is the density of water which may be taken as 1 g/cm3 for calculation purposes.





(c) Unit weight of soil mass:- The unit weight of a soil mass is defined as its weight per unit volume.

(i) Bulk unit weight (𝛶) :- The bulk weight or moist unit weight is the total weight W of a soil mass per unit of its total volume V.

Thus,

(ii) Dry unit weight (𝛶d) :- The dry unit weight is the weight of solids per unit of its total volume (prior to drying) of the soil mass.

(iii) Unit weight of solids (𝛶s) :- The unit weight of soil solids is the weight of soil solids Wd per unit volume of solids (Vs).

(iv) Saturated unit weight: - When the soil mass is saturated, its bulk unit weight 𝛶 is called the saturated unit weight 𝛶 is called the saturated unit weight 𝛶sat . Thus, saturated unit weight is the ratio o the total weight of a saturated soil sample to its total volume.

(v) Submerged unit weight: - The submerged unit weight 𝛶’ is the submerged weight of soil solids (Wd) sub per unit of total volume V of the soil mass.

It is also expressed as

(d) Inter – conversion between density and unit weight:- In order to convert the density (expressed in terms of g/cm3) into unit weight (kN/m3) multiply the former by 9.81. This is so because

1 g/cm3 =

Hence, 𝛶 (kN/m3) = 9.81 x ρ (g/cm3)

1.9.2 SPECIFIC GRAVITY

Specific gravity G is defined as the ratio of the weight of a given volume of soil solids at a given temperature to the weight of an equal volume of distilled water at that temperature, both weights being taken in air. In other words, it is the ratio of the unit weight of soil solids to that of water. The Indian Standard specifies 270C as the standard temperature for reporting the specific gravity.





2.0 VOLUMETRIC RELATIONSHIPS

2.1 VOIDS RATIO, POROSITY AND DEGREE OF SATURATION

(1) Voids ratio – Voids ratio e of a given soil sample is the ratio of the volume of voids to the volume of soil solids in the given soil mass.

Thus,

(2) Porosity – The porosity n of a given soil sample is the ratio of the volume of voids to the total volume of the given soil mass.

Thus, The voids e is generally expressed as a fraction, while the porosity n is expressed as a percentage and is, therefore, also referred to as percentage voids.

(a) SOIL ELEMENT IN (b) SOIL ELEMENT IN

TERMS OF e TERMS OF n

Fig.11 Voids ratio and porosity.

Fig. 3 (a) shows the soil element interms of voids ratio e, the volume of solids, by definition would be equal to 1, and the total volume equal to (1 + e). Similarly, if the volume of the voids is taken equal to n hence the volume of solids would be equal to (1 – n). From fig. 3 (a), we have by definition of porosity, --------------(i) Similarly, from Fig.3 (b), we get by definition of voids ratio, ----------------(ii)





Equations (i) and (ii) give two relations between n and e. Combining, we get,

Or (3) Degree of Saturation (S) – The degree of saturation (S) is the ratio of the volume of water to the volume

of voids. Thus The degree of saturation is usually expressed as a percentage. For fully saturated sample Vw = Vv and hence S = 1. For a perfectly dry sample, Vw = zero, and hence S = 0.

(4) Percentage air voids – It is the ratio of volume of air to the total volume. Thus --------------(iii)

(5) Air content – The air content ac is defined as the ratio of volume of air voids to the volume of air voids.

Thus --------------(iv) Therefore form eqns (iii) and (iv), we get,

2.2 DENSITY INDEX

The term density index ID or relative density or degree of density is used to express the relative compactness of a natural soil deposit. The density index is defined as the ratio of the difference between the voids ratio of the soil in its loosest state emax and its natural voids ratio e to the difference between the voids ratios in the loosest and densest states:

Where





emax= voids ratio of sand in its loosest state

emin = void ratio m its densest state e = natural voids ratio of the deposit. This term is used for cohesionless soil only. When the natural state of the cohesionless soil is in its loosest form, e = emax and hence ID = 0. When the natural deposit is in the densest state, e = emin and hence ID = 1. For any intermediate state, the density index varies between zero and one. 2.3 FUNCTIONAL RELATIONSHIPS

(i) Relation between e, G, w and Sr

In Fig. 10, ew represents volume of water, e represents the volume of voids, and the volume of solids is equal to unity.

Now, Hence, ew = e Sr ------------- (i) The term ew is known as the water voids ratio. For a fully saturated sample, ew = e.

Fig.12 Soil element in terms of ew and e

Now, But,





or ew = wG ----------------(ii)

Equating eqns (i) and (ii), we get,

For a fully saturated sample, Sr = 1 and w = wsat

e = wsat G

(ii) Relation between e, Sr and na

Fig.4, Va = Vv – Vw = e – ew and V = Vs + Vv = 1 + e

But ew = e Sr

(iii)

(iii) Relation between 𝛶d, G and e (or n)

or Now from Fig. 3(a), Vs = 1 and V = (1 + e) But 𝛶s = G 𝛶w





(iv) Relation between 𝛶sat, G and e (or n)

From Fig.3 (a), Vs = 1, Vw = e and V = 1 + e

or

(v) Relation between 𝛶 ‘, G and e

𝛶 ‘ = 𝛶sat - 𝛶w

(vi) Relation between 𝛶d, 𝛶 and w

Water content

Now





2.4 METHODS OF DETERMINING INSITU DENSITY

The following methods are generally used for the determination of mass density. 1) Core cutter method. 2) Sand replacement method. 3) Water balloon method. 4) Radiation method.

1) Core cutter method: -

It is a field method for determination of mass density. A core cutter consists of an open, cylindrical barrel, with a hardened, sharp cutting edge as shown in fig.11. A dolly is placed over the cutter and it is rammed into the soil. The dolly is to prevent burring of the edges of the cutter. The cutter containing the soil is taken out of the ground. Any soil extruding above the edges of the cutter is removed. The mass of the cutter filled with soil is taken. A representative sample is taken for water content determination.

Fig.13 Core cutter with dolly. Bulk mass density

Where,

M2 = mass of cutter, with soil, M1 = mass of empty cutter. V = volume of cutter.

This method is quite suitable for soft, fine grained soil. It cannot be used for stoney, gravelly soils. The method is practicable only at the places where the surface of the soil is exposed and the cutter can be easily driven.





2) Sand replacement method:-

Fig. 14 shows a sand pouring cylinder, which has a pouring cone at its base. The cylinder shown is placed with its base at ground level. There is shutter between the cylinder and the cone. The cylinder is first calibrated to determine the mass density of sand. For good results, the sand used should be uniform, dry and clean, passing a 600 micron sieve and retained on a 300micron sieve.

(a) Calibration of apparatus:-

The cylinder is filled with sand and weighted. A calibrating container is then placed below the cylinder and shutter is opened. The sand fills the calibrating container and cone. The shutter is closed, and the mass of the cylinder is again taken. The mass of the sand in the container and the cone is equal to the difference of the observations.

The pouring cylinder is again filled to the initial mass. The sand is allowed to run out of the cylinder, equal to the volume of the calibrating container and the shutter is closed. The cylinder is placed over a plain surface and the surface is opened. The sand runs out of the cylinder and fills the cone. The shutter is closed when no further movement of the sand takes place. The cylinder is removed and the sand filling the cone is collected and weighed (M2).

The mass density of the sand is determined as under:

Where, M1 = initial mass of the container with sand, M2 = mass of sand in cone only, M3 = mass of cylinder after pouring sand into the cone and the container. Vc = Volume of the container.

(b) Measurement of Volume of Hole:-

A tray with a central hole is placed on the prepared ground surface which has been cleaned and properly leveled. A hole about 100 mm diameter and 150 mm deep is excavated in the ground, using the hole in the tray as a pattern. The soil removed is carefully collected and weighted.

The sand pouring cylinder is then placed over the excavated hole as shown in fig. 6. The shutter is opened and the sand is filled in the cone and the hole. When the sand stops running out, the shutter is closed. The cylinder is removed and weighed. The volume of the hole is determined from the mass of sand filled in the hole and the unit mass density of sand.

Volume of hole =





Where, M1 = mass of cylinder and sand before pouring into the hole,

M2 = mass of sand in core only, M4 = mass of cylinder after pouring sand into the hole, ρs = mass density of sand, as found from calibration.

The bulk mass density of the in – situ soil is determined from the mass of soil excavated and the volume of the hole. The method is widely used for soils of various particle sizes, from fine – grained to coarse – grained.

Fig. 14 Sand Replacement Method.

MANGALWARI BAZAAR ROAD, SADAR, NAGPUR - 440001. … · 1. Introduction : Formation of soil,...

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