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GEOTECHNICAL

ENGINEERING

For CIVIL ENGINEERING

SYLLABUS Soil Mechanics: Origin of soils, soil structure and fabric; Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability - one dimensional flow, Darcy’s law; Seepage through soils - two-dimensional flow, flow nets, uplift pressure, piping; Principle of effective stress, capillarity, seepage force and quicksand condition; Compaction in laboratory and field conditions; One- dimensional consolidation, time rate of consolidation; Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics of clays and sand. Foundation Engineering: Sub-surface investigations - scope, drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories - Rankine and Coulomb; Stability of slopes - finite and infinite slopes, method of slices and Bishop’s method; Stress distribution in soils - Boussinesq’s and Westergaard’s theories, pressure bulbs; Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity theories, effect of water table; Combined footing and raft foundation; Contact pressure; Settlement analysis in sands and clays; Deep foundations - types of piles, dynamic and static formulae, load capacity of piles in sands and clays, pile load test, negative skin friction.

ANALYSIS OF GATE PAPERS Exam Year 1 Mark Ques. 2 Mark Ques. Total

2003 6 11 28

2004 6 10 26 2005 4 10 24

2006 5 8 21

2007 3 10 23

2008 3 11 25

2009 4 6 16

2010 5 6 17

2011 5 5 15

2012 6 5 16

2013 4 6 16

2014 Set-1 4 4 12

2014 Set-2 4 5 14

2015 Set-1 5 5 15

2015 Set-2 5 5 15

2016 Set-1 3 6 15

2016 Set-2 3 5 13

2017 Set-1 5 4 13

GEOTECHNICAL ENGINEERING

Topics Page No

1. ORIGIN OF SOIL & SOIL WATER RELATIONSHIP

1.1 Definition of Soil 01 1.2 Origin of Soil 01 1.3 Important Definitions 01 1.4 Some Important Relationship 03 1.5 Pycnometer Method 06 1.6 Index Property of Soil 06 1.7 Procedure of Sieve Analysis 07 1.8 Sedimentation Analysis 07 1.9 Particle Size Distribution Curve 08

2. CLASSIFICATION OF SOIL

2.1 Indian standard soil classification System 10 2.2 Classification of Fine Grained Soil 11

3. EFFECTIVE STRESS, CAPILLARITY AND PERMEABILITY

3.1 Permeability 12 3.2 Darcy’s La 12 3.3 Coefficient of permeability 12 3.4 Determination of coefficients of permeability 13 3.5 Constant Head Permeability Test 13 3.6 Capillarity Permeability Test 14 3.7 Permeability of stratified Soil 14 3.8 Salient Point About Flw Net 15 3.9 Use of Flow Net 15 3.10 Seepage in Anisotropic Soil 16

4. COMPRESSIBILITY AND CONSOLIDATION

4.1 Introduction 18 4.2 Effective Stress and Void Ratio Relationship 18 4.3 Compressibility of Clay 19 4.4 Computation of Settlement 20 4.5 Determination of Coefficient of Consolidation 21 4.6 Compression Ratio 21

5. COMPACTION

5.1 Introduction 23

CONTENTS

5.2 Compaction of Cohesionless Soil 23 5.3 Compaction of Cohesive Soil 24 5.4 Proctor Test 24 5.5 Standard Proctor Test 24 5.6 Modified Proctor Test 25 5.7 Importance of Proctor Test 25 5.8 Light Compaction Test (IS : 2720, PART VII-1974) 25 5.9 Heavy Compaction Test (IS : 2720, PART VIII- 1983) 25 5.10 Factors Affecting Compaction 25 5.11 Lambe Explanation 25 5.12 Typical Compaction Curves For Different Soils 26 5.13 Effect of Compaction on Properties of Soils 27

6. VERTICAL STRESSES

6.1 Introduction 29 6.2 Vertical Stresses Due To Concentrated Load 29 6.3 Vertical Stresses Due To Line Load 30 6.4 Vertical Stresses Due To Strip Load 31 6.5 Vertical Stress Under A Circular Area 32 6.6 Vertical Stress Below The Corner Of A Rectangular 33 6.7 Vertical Stress At Any Point Under A Rectangular Area 33

7. SHEAR STRENGTH OF SOIL

7.1 Introduction 35 7.2 Mechanism Of Shear Resistance (Shear Resist-Ance) 35 7.3 Mohr’s Hypothesis 36 7.4 Columb Hypothesis 36 7.5 Procedure For Drawing Mohr Circle 37 7.6 Relation Between Angle Of Failure Plane (𝛉f) and Angle of Shearing Resistance (∅) 38 7.7 Various Laboratory Test Performed To Find Out C & ∅ 38 7.8 Results of the Test 39 7.9 Vane Shear Test 40 7.10 Pore Pressure Coefficients 41 7.11 Shear Strength of Cohesive Soils 41

8. SOIL EXPLORATION

8.1 Introduction 43 8.2 Methods of Exploration 43 8.3 Boring of Holes 43 8.4 Methods of Boring 43 8.5 Soil Samples 45 8.6 Samples 46 8.7 Depth of Exploration 47 8.8 Field Tests 47

9. EARTH PRESSURE AND RETAINING WALLS

9.1 Introduction 50 9.2 Type of Solid Wastes 50 9.3 Active and Passive Earth Pressure 50 9.4 Relationship Between Wall Movement & Lateral Pressure 51 9.5 Earth Pressure Theories 51 9.6 Various Cases Of Earth Pressures 51 9.7 Coulomb’s wedge Theory 53

10. STABILITY OF SLOPES

10.1 Introduction 56 10.2 Stability Of Infinite Slopes 56 10.3 Stability Of Finite Slopes 57

10.4 Swedish Circle Method 57

10.5 Friction Circle Method 59

10.6 Taylor’s Stability Number 60

11. SHALLOW FOUNDATION

11.1 Introduction 62 11.2 Types of Footing 62 11.3 Classification of Foundation 63 11.4 Basic Definition 63 11.5 Bearing Capacity of Shallow Foundation 64 11.6 Analytical Method 64 11.7 Terzaghi’s Bearing Capacity Theory 66 11.8 Skempton’s Bearing Capacity of Soil for Clayey Soil. 68 11.9 Skempton Proposed Following Values Of Nc According to

Various Types And Sapes Of Footings. 68 11.10 Settlement Of Foundation 68

12. PILE FOUNDATION

11.1 Introduction 70

12.2 Classification of Pile 70

12.3 Pile Load Capacity In Compression 72 12.4 Dynamic Formula 73 12.5 Pile Load Test 74 12.6 Penetration Test 74 12.7 Group Action of in piles 74 12.8 Feld’s Rules 75

13. GATE QUESTIONS 77

14. ASSIGNMENT QUESTIONS 149

1.1 DEFINITION OF SOIL

The term ‘soil’ in soil engineering is defined as an unconsolidated material, composed of solid particles, produced by the disintegration of rocks. The void space between the particles may contain air, water or both. The soil particles may organic matter.

1.2 ORIGIN OF SOIL

The Geological Cucle In a broad sense, soil may be thought of

as an incidental material in vestgeological cycle which has been goingon continuously for millions of years ofgeological time.

The geological cycle consists of 3phases, Erosion; Transportation anddeposition & Earth Movement.

1.3 IMPORTANT DEFINITIONS

1.3.1 WATER CONTENT (W)

w

s

Ww ;w 0

W

Water content or moisture content of asoil mass is defined as the ratio ofweight of water to the weight of solids(dry weight) of the soil mass.

w

s

Ww 100

W

It is denoted by the letter symbol w andis commonly expressed as a percentage.e.g. 20%, 40% etc.

The minimum value for water content is 0

There is no upper limit for watercontent.

Generally fine grained soils have higherwater content as compared to coarsegrained soil.

1.3.2 VOID RATIO (E)

v

s

Ve ;e 0

V

Void ratio is defined as ratio of volumeof voids to the volume of solids.

It is denoted by letter symbol (e) andgenerally expressed as a decimalfraction eg 0.20, 0.45 etc.

There is no upper limit of void ratio insoil suspension and in macro-porous

soils like loess, vV could be much

greater than sV .

Void ratio of fine grained soil isgenerally higher than those of coarsegrained soil.

Size of void in coarse grained soil isgenerally larger than that in finegrained soil.

1.3.3 POROSITY (N)

vVn 100;100 n 0

V

Porosity is defined as ratio of volume ofvoids to the total volume expressed as apercentage. It is also known aspercentage voids.

Porosity is denoted by letter symbol (n)& is commonly expressed as a percentage.

v a wV = V +V

a w sV = V +V +V

The porosity of soil cannot exceed100% hence it has a upper limit of100%.

Both porosity & void ratio are measureof denseness (or looseness) of soil.

1 ORIGIN OF SOIL & SOIL WATER RELATIONSHIP

© Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission. 1

Note: Porosity is defined with respect to V while void ratio is defined with

respect to sV . The total volume V is a

variable quantity. But, since solids are

incompressible, sV remains invariant in

the total volume V of the soil. Thus in Engineering studies, void ratio serves as a useful parameter for representing change in volume under compression.

1.3.4 DEGREE OF SATURATION (S)

w

v

VS 100;0 S 100

V

Degree of Saturation of a soil mass isdefined as the ratio of the volume ofwater in the voids to the volume ofvoids.

It is denoted by letter symbol S and iscommonly expressed as a percentage.

v a wV V V

For a fully saturated soil mass v wV V ,

hence for a saturated soil mass S=100 For fully dry soil mass wV =0, hence for

a fully dry soil S=0%. For partially saturated soil mass degree

of saturation varies between 0 – 100%,which is most common condition innature.

1.3.5 PERCENTAGE AIR VOIDS ( an )

va

Vn 100

V

Percentage air voids of a soil mass aredefined as the ratio of the volume of airvoids to the total volume of the soilmass.

It is denoted by letter symbol ( an ) and

commonly expressed as a percentage.

1.3.6 AIR CONTENT c(a )

ac

v

Va =

V

Air content of a soil mass is defined as aratio of volume of air voids to the total

volume of voids. It is denoted by letter symbol ca and commonly expressed as a

percentage.

1.3.7 BULK UNIT WEIGHT ( t )

s wt

s w a

W WW

V V V V

Bulk unit weight of soil mass is definedas the weight per unit volume of soilmass.

It is denoted by letter or γ or t and is

generally expressed as 3 3 3

kN N kgf, ,

m m cm

Note: Density (γ) is mass per unit volume

1.3.8 UNIT WEIGHT OF SOLIDS ( s )

ss

s

W

V

Unit weight of solids is the weight ofsoil solids per unit volume of solidsalone. It is also called as “absolute unitweight” of a soil.

It is denoted by letter s .

1.3.9 UNIT WEIGHT OF WATER ( wγ )

ww

w

W

V

Unit weight of water is the weight perunit volume of water.

It is denoted by letter symbol wγ .

Note: The value of wγ changes with

temperature but usually we take wγ =9.813kN m which is at 4°C

1.3.10 DRY UNIT WEIGHT ( dγ )

s dd

W Wγ = =

V V

The saturated unit weight of soil isdefined as bulk unit weight of soil massin saturated condition.

It is denoted by symbol satγ and has unit 3kN m .

© Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.

Origin Of Soil & Soil Water Relationship

2

1.3.11 SUBMERGED (BUOYANT) UNIT WEIGHT ( subγ )

s subsub

(W )γ =

V

Submerged unit weight is defined as submerged unit weight of soil solids per unit of total volume.

It is denoted by symbol subγ and has unit 3kN m .

When the soil exists below ground water i.e. in submerged condition, a buoyant force acts on the soil solids.

Hence it is obvious that net weight of saturated soil solids has been reduced and this reduced mass is known as Submerged Unit Weight or Buoyant Unit Wt.

sat wγ=γ -γ

Note: Soil in Submerged condition will be in saturated state but soil in saturated condition need not to be submerged. For example, soil mass below water table is in submerged as well as saturated condition whereas soil mass incapillary zone is in saturated condition only. 1.3.12 SPECIFIC GRAVITY OF SOLIDS (G)

s

w

γG=

γ

The specific gravity of solids is defined

as the ratio of the unit weight of solids (absolute unit weight of soil) to the unit weight of water of water. It is denoted by letter G and is a Unit less quantity.

This is also known as “Absolute specific gravity” or “Grain specific gravity”.

1.3.13 MASS SPECIFIC GRAVITY OF SOIL ( mG )

tm

w

G

Mass specific gravity is defined as the ratio of bulk unit weight of soil to unit weight of water.

It is denoted by letter symbol mG and is

a unit less quantity.

1.3.14 RELATIVE DENSITY ( rD )

maxr

max min

e e(D )

e e

The relative density is a parameter used in sandy and gravelly soils.

The value of max mine &e represents the

soil in very dense and loose conditions, respectively, and are determined by a standard laboratory test.

Loose soil have values of rD , while

dense soils high values. The theoretically lowest possible value

of rD is 0% and highest theoretical

possible value is 100%. Thus rD , is

often more useful than void ratio (e) because we can easily compare the field value to the lowest and highest possible values. According to relative density, the soil is classified as: Relative density Classification

0 – 15 Very loose 15 – 35 Loose 35 – 65 Medium dense 65 – 85 Dense 85 – 100 Very dense

1.4 SOME IMPORTANT RELATIONSHIPS Abbreviations w = Water Content

sW = Weight of solid

W = Total weight of soil

sV = Volume of solid

V = Total volume of soil S = Degree of Saturation

wW = Weight of water

vV = Volume of voids

wV = Volume of water



3

S

WW

1 w

SW W (1 w)

S

WW

1 w

S

VV

1 e

SV (1 e) V

S

VV

1 e

e

n1 e

S S S

S S S S

V eV eV en

V V V V eV 1 e

en

1 e

SeS wG

w

S S S w

SS S S

S

W

V V V 1e

WV V V S

w wS

S S

W1 1e wG

S W S

SeS wG

eS wG

s

t w

G Se

1 e

ws

ss wt

s v vs

s

WW 1

WW WW

V V V VV 1

V

s

s

W (1 w)

V (1 e)

s w st w

G (1 w) G Se

1 e 1 e

st w

G Se

1 e

Alternatively

S W

t

S V

W W

V V

S w wG Se

1 e

2t w

G Se

1 e

Ssat w

G e

1 e

In the expression St w

G e

1 e



4

by putting S = 1 for saturated condition

ssat w

G e

1 e

s ws w wsat

G eG e

1 e 1 e

S wsat

G

1 e

In the expression St w

G Se

1 e

by putting S = 0 for completely dry condition

s wd

G

1 e

s wd

G

1 e

sw

G 1'

1 e

We know that γ’ = submerged unit wt =

sat w

= s sw w w

G e G 1

1 e 1 e

sw

G 1'

1 e

td

1 w

s w st d

W W W (1 w)W(1 w)

V V V

td

1 w

w sd

s

G

wG1

S

We know that

s w s wd

s

G G

wG1 e1

S

a w s w sa

w s w

V V V W W1 n 1

V V V G V

= d s d

s w w w s

wW 1w

G V G

a s w

d

s

1 n G

1 wG

w

t

wS

1(1 w)

G

s w

w w

s wv

d

wG

VS

GV1

s

s w w

t t

wG w

G (1 w) (1 w) 11

G

Summary

1. s

WW

1 w

2. s

VV

1 e

3. n

e1 n

4. e

n1 e

5. seS wG

6. st w

G Se

1 e

7. ssat w

G e

1 e



5

8. sd w

G

1 e

9. sw

G 1'

1 e

10. td

1 w

11. a s ws w

ds s

1 n GG

wG 1 wG1

S

1.5 PYCNOMETER METHOD A pycnometer is a glass jar of about 1

litre capacity and fitted with a brass conical cap by means of a screw-type cover. The cap has a small hole 6 mm diameter at its apex.

The pycnometer method for the determination of water content can be used only if the specific gravity of solid (G) particles is known.

First, the weight of the empty

pycnometer is determined ( 1W ) in the

dry condition. Then the sample of moist soil, is placed in the pycnometer and its

weight with the soil is determined ( 2W ).

The remaining volume of the pycnometer is then gradually filled with distilled water or kerosene. The entrapped air should be removed either by gentle heating and vigorous shaking or by applying vaccum. The weight of the pycnometer, soil and water is

obtained ( 3W ) carefully. Lastly, the

bottle is emptied, thoroughly cleaned and filled with distilled water or

kerosene, and its weight taken ( 4W ).

w 2 1 sW W W W

w 2 1

s s

W W Ww 1

W W

s w4 1 3 1 s

s w

WW W W W W

G

3 4 s

s

s

(W W )GW

G 1

2 1

3 4 s

s

W Ww 1

(W W )G

(G 1)

s2 1

3 4 s

G 1W Ww 1

W W G

Removal of entrapped air is difficult from cohesive soil. Hence this method is more suited for cohesionless soil.

1.6 INDEX PROPERTY OF SOIL Those properties which help to access

the engineering behavior of a soil and which assist in determining its classification accurately are termed as index properties. Index properties include indices which help in determining the engineering behavior such as a) strength b) load-bearing capacity c) swelling and shrinkage d) settlement etc. These properties may be relating to 1. Individual soil grain 2. Aggregate soil mass

The properties of individual particles can be determined from a remoulded, disturbed sample. These depend upon the individual grains their mineralogical composition, size and shape of grains and are independent of soil formation. Type of soil Index property

Coarse soil Particle size, Relative density, Grain shape

Fine soil Atterberg’s Limit & Consistency



6

The soil aggregate properties depend upon the mode of soil formation, soil history and soil structure. These properties should be determined from undisturbed samples or preferably from in situ tests.

1.7 PROCEDURE OF SIEVE ANALYSIS The soil sample to be tested is dried,

lumps are broken if necessary, and the sample is passed through the series of sieves by shaking.

The fractions retained on and passing 2 mm IS Sieve are tested separately.

An automatic sieve-shaker, run by an electric motor, may be used; about 10 to 15 minutes of shaking is considered adequate.

Larger particles are caught on the upper sieves, while the smaller ones filter through to be caught on one of the smaller underlying sieves.

The material retained on any particular sieve should naturally include that retained on the sieves on top of it, since the sieves are arranged with the aperture size decreasing from top to bottom.

The weight of material retained on each sieve is converted to a percentage of the total sample.

The percentage material finer than a sieve is obtained by subtracting this from 100.

The material passing the bottom-most sieve, which is usually the 75-μ sieve, is used for conducting sedimentation analysis for the fine fraction.

If the soil is clayey in nature the fine fraction cannot be easily passed through the 75-μ sieve in the dry condition.

In such a case, the material is to be washed through it with water (preferably mixed with 2 gm of sodium hexametaphosphate per liter), until the wash water is fairly clean

The material which passes through the sieve is obtained by evaporation. This is called ‘wet sieve analysis, and may be required in the case of cohesive granular soils’.

The resulting data are conventionally presented as a “Grain-size distribution curve” plotted on semi-log co-ordinates, where the sieve size is on a horizontal ‘logarithmic’ scale, and the percentage by weight of the size smaller than a particular sieve-size is on a vertical ‘arithmetic’ scale.

Logarithmic scales for the particle diameter gives a very convenient representation of the sizes because a wide range of particle diameter can be shown in a single plot.

1.8 SEDIMENTATION ANALYSIS The soil particles less than 75-μ size can

be further analyzed for the distribution of the various grain-sizes of the order of silt and clay by ‘sedimentation analysis’ or ‘wet analysis’.

The soil fraction is kept in suspension in a liquid medium, usually water.

The particles descend at velocities, related to their sizes, among other things.

The analysis is based on ‘Stocks Law’. As per this law, if a single sphere is

allowed to fall in an infinite liquid medium without interference, its velocity first increases under the influence of gravity, but soon attains a constant value.

This constant velocity, which is maintained indefinitely unless the boundary conditions change, is known as the ‘terminal velocity’.

The principle is obvious; coarser particles tend to settle faster than finer ones.

By Stokes’ law, the terminal velocity of the spherical particle is given by

2

s l Dv

18



7

Stokes’ Law is considered valid for particle diameters ranging from 0.2 to 0.0002 mm.

For particle sizes greater than 0.2 mm, turbulent motion is set up and for particle sizes smaller than 0.0002 mm, Brownian motion is set up. In both these cases, Stokes’ law is not valid.

The limitations of sedimentation analysis, based on Stokes’ law, are as follows: i) The finer soil particles are never

perfectly spherical. Their shape is plate-like or needle-like. However, the particles are assumed to be spheres, with equivalent diameters (the basis of equivalent being the attainment of the same terminal velocity as that in the case of a perfect sphere.)

ii) Stokes’ law is applicable to a sphere falling freely without any interference, in an infinite liquid medium. The sedimentation analysis is conducted in a one-litre jar, the depth being finite; the walls of the jar could provide a source of interference to the free fall of particles near it. The fall of any particle may be affected by the presence of adjustment particles; thus, the fall may not be really free. However, it is assumed that the effect of these sources of interference is insignificant if suspension is prepared with about 50 g of soil per litre of water.

iii) All the soil grains may not have the same specific gravity. However, an average value is considered all right, since the variation may be insignificant in the case of particles constituting the fine fraction.

iv) Particles constituting to fine soil fraction may carry surface electric charges, which have a tendency to create ‘flocs’. Unless these floces are broken, the sizes calculated may be those of the flocs. Flocs can be

source of erroneous results. A deflocculating agent, such as sodium silicate, sodium oxalate, or sodium hexametaphosphate, is used to get over this difficulty.

The general procedure for sedimentation analysis, which may be performed either with the aid of a pipette or a hydrometer is as follows:

An appropriate quantity of an oven-dried soil sample, finer than 75-μ size, is mixed with a known volume (V) of distilled water in jar.

The sample is pretreated with an oxidizing agent and an acid to remove organic matter and calcium compounds.

Addition of hydrogen peroxide on heating would remove organic matter. Treatment with 0.2 N hydrochloric acid would remove calcium compounds.

Later, a deflocculating or a dispersing agent, such as sodium hexameta phosphate is added to the solution. The mixture is shaken thoroughly by means of a mechanical stirrer and the test is started, keeping the jar vertical.

The soil particles are assumed to be uniformly distributed throughout the suspension, at the instant of commencement of the test.

1.9 PARTICLE SIZE DISTRIBUTION CURVE A soil sample may be either well graded

or poorly (uniformly graded). A soil is said to be well graded when it has good representation of particles of all sizes. On the other hand, a soil is said to be poorly graded if it has an excess of certain size.

For coarse grained soil, certain particle size such as D10, D30 and d60 are important. The d10 represent a size, in mm such that 10% of the particles are finer that this size. Similarly, the soil particles finer than d60 size are 60 per



8

cent of the total mass of the sample. The size d10 is sometimes called the effective diameter.

Coefficient of uniformity The uniformity coefficient Cu (or coefficient of uniformity) is a measure of particle size range and is given by the ratio of d60 and d10 size:

D60Cc

D10

Coefficient of curvature The shape of the particle size cure is represented by the coefficient of the curature Cc given by

Cc = (D30)

D10XD60

Consistency of Soil

Liquid Limit Water content corresponding to arbitrary limit between liquid and plastic stae of soil. Plastic Limit Arbitrary limit between plastic and semi-soiled state of consistency of soil. It is

minimum water content at which soil starts crumbling. Shrinkage Limit Maximum water content at which reduction in water content will not cause decrease in volume of soil mass. Plasticity Index: P L pl W W

Consistency Index: LW w

lp

Liquidity Index: L

w wI

lp

Flow Index: 1 2f

210

1

w wI

nlog

n

Where, WL : water content at liquid limit WP : water content at plastic limit w : natural water content If : low Index w1 : water content corresponding to blows n1

w2 : water content corresponding to blows n2

Shrinkage Limit

1 d

s 1

V V ww w 100

wd

Where, w1 : water content of original sample of

volume V1.

Activity of Clay Ratio of plasticity indexes to percentage by weight of ‘clay size’ the particle of size less than 2 microns. Sensitivity of Clay Ratio of unconfined compression strength to that of unconfined compression strength

u

t

u

q undisturbedS

q remouled



9

Topics Page No

1. PROPERTIES OF SOIL 78

2. CLASSIFICATION OF SOIL 82

3. EFFECTIVE STRESS AND PERMEABILITY 86

4. CONSOLIDATION OF SOIL 95

5. SEEPAGE ANALYSIS 106

6. COMPACTION OF SOIL 112

7. STRESS DISTRIBUTION IN THE SOI 116

8. SHEAR STRENGHT OF SOIL 118

9. RETAINING WALLEARTH 122

10. STABILITY ANALYSIS OF SLOPES 128

11. SHALLOW FOUNDATION & BEARING CAPACITY 133

12. DEEP FOUNDATION 140

13. SOIL STABILIZATION & SOIL EXPLORATION 146

GATE QUESTIONS

77

Q.1 The undrained cohesion of a remoulded clay soil is 10kN/N2. If the sensitivity of the clay is 20, the correspondingremoulded compressive strength is a) 5kN/N2 b) 10kN/N2

c) 20kN/N2 d) 200kN/N2

[GATE-2004]

Q.2 The ratio of saturated unit weight of dry unit weight of a soil is 1.25. If the specific gravity of solids (Gs) is 2.65, the void ratio of the soil is a) 0.625 b) 0.663c) 0.944 d) 1.325

[GATE-2004]

Q.3 A saturated soil mass has a total density 22 kN/m3 and a water content of 10%. The bulk density and dry density of this soil are a)12kN/m3 & 20 kN/m3 respectivelyb)22kN/m3 & 20 kN/m3 respectivelyc)19.8kN/m3 & 19.8 kN/m3 respectivelyd)23.2kN/m3 & 19.8 kN/m3respectively

[GATE-2005]

Q.4 The water content of a saturated soil and specific gravity of soil solids were found to be 30% and 2.70 respectively. Assuming the unit wt of water to be 10kN/m3, the saturated unit wt (kN/m3) and the void ratio of the soil are a) 19.4, 0.81 b) 18.5, 0.30c) 19.4, 0.45 d) 18.5, 0.45

[GATE-2007]

Q.5 The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation. a) LL > PL < SL b) LL > PL > SLc) LL < PL < SL d) LL < PL > SL

[GATE-2008]

Q.6 In its natural condition, a soil sample has a mass of 1.980 kg and a

volume of 0.001 3m . After being completely dried in an oven, the mass of the sample is 1.800 kg. Specific gravity G is 2.7. Unit weight

of water is 10 3kN m . The degree of

saturation of the soil is: a) 0.65 b) 0.70c) 0.54 d) 0.61

[GATE-2013]

Q.7 A given cohesionless soil has emax = 0.85 and emax = 0.50. In the field the soil is compacted to a mass density of 1800 kg/m3 at a water content of 8%. Take the mass density of water as 1000kg/m3 and G, as 2.7.The relative density (in %) of the soil is a) 56.43 b) 60.25c) 62.87 d) 65.7

[GATE-2014(1)]

Q.8 A certain soil has the following properties: Gs = 2.71, n = 40% and w = 20%. The degree of saturation of the soil (rounded off to the nearest percent) is _________

[GATE-2014(2)]

Q.9 Which of the following statements is NOT correct? a) Loose sand exhibits contractive

behavior upon shearingb) Dense sand when sheared under

undrained condition, may lead togeneration of negative porepressure

c) Black cotton soil exhibitsexpansive behavior

d) Liquefaction is the phenomenonwhere cohesionless soil near thedownstream side of dams orsheet-piles loses its shearstrength due to high upwardhydraulic gradient

[GATE-2015(1)]

1 PROPERTIES OF SOIL


Q.10 A fine-grained soil has 60% (by weight) silt content. The soil behaves as semi-solid when water content is between 15% and 28%. The soil behaves fluid-like when the water content is more than 40%. The 'Activity' of the soil is a) 3.33 b) 0.42c) 0.30 d) 0.20

[GATE-2015(1)]

Q.11 An earth embankment is to be constructed with compacted cohesion less soil. The volume of the embankment is 5000 m3 and the target dry unit weight is 16.2kN/m3. Three nearby sites (see figure below) have been identified from where the required soil can be transported to the construction site. The void ratios (e) of different sites are shown in the figure. Assume the specific gravity of soil to be 2.7 for all three sites. If the cost of transportation per km is twice the cost of excavation per m3 of borrow pits, which site would you choose as the most economic solution? (Use unit Weight of water =10kN/m3) .

a) Site X b) Site Yc) Site Z d) Any of the sites

[GATE-2015(1)]

Q.12 In the water content of a fully saturated soil mass is 100% the void ratio of the sample is a) Less than specific gravity of soilb) equal to specific gravity of soilc) greater than specific gravity of

soild) independent of specific gravity

of soil[GATE-2015(2)]

Q.13 A 588 cm3 volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of solids, G is 2.67. Assuming density of water as 1 gm/cm3, the void ratio is ________.

[GATE-2015(2)]

Q.14 The porosity (n) and the degree of saturation (S) of a soil sample are 0.7 and 40%, respectively. In a 100m3 volume of the soil, the volume (expressed in m3) of air is ______

[GATE-2016(1)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14

(c) (b) (b) (a) (b) (c) (d) 81 (d) (c) (b) (b) 0.71 42

ANSWER KEY:

Properties of soil


Q.1 (c) Undrained cohesion of remoulded clay C = 10 kN/m2

Remoulded compressive strength qu = 2C = 20kN/m2

Q.2 (b) Given,

sat

dry

γ=1.25

γ

and Gs 2.65

s

ω

s ω

G +Seγ

1+e=1.25

G γ

1+e

s

s

G +e=1.25

G

(for saturated soil S = 1) 2.65+e

=1.252.65

e = 0.663

Q.3 (b) Saturated soil mass has total density or bulk density, γt = 22 kN/m3

Water content = 10% Dry density

γd = tγ

1+ω

= 22

1 0.1= 20 kN/m3

Q.4 (a) Soil is saturated, so S = 1 Water content, W = 30% Specific gravity, = 2.7

Unit weight of water,

10w kN/m3

We know, Se = wGs

0.3×2.7

e= =0.811

2.7 0.8110

1 0.81

= 19.39 kN/m3

= 19.4 kN/m3

Q.5 (b) Liquid limit > plastic limit > Shrinkage limit

Q.6 (c)

Wt. of water in soil = Wt. of soil sample – wt. of oven dry sample

WW = ( 1.980-1.80)

= 0.18 kg vol of water in soil

Wt.of water=

Unitwt.of water

= -3

3

0.18×9.81×10 kN

10.0kN/m = 0.00018 3m

Now, as we know degree of saturation,

(s) = Vol. of water

Vol.ofvoids

EXPLANATIONS


Q.1 Match List-I (Soil description) with List- II (Coefficient of permeability, mm/s) and Select the correct answer using the codes given below the lists: List-I A. Gravel B. Clay silt admixtures C. Loess D. Homogeneous clays List-II 1. >12. 10-2 to 10-4

3. < 10-6

4. 10-4 to 10-6

Codes: A B C D

a) 4 1 3 2 b) 1 4 3 2 c) 4 1 2 3 d) 1 4 2 3

Q.2 Match Lists-I with List-II and select the correct answer using the codes given below the lists: List-I A. Loess B. Peat C. Alluvial soil D. Marl List-II 1. Deposited from suspension inrunning water 2. Deposits of marine origin3. Deposits by wind4. Organic soilCodes: A B C D a) 3 4 2 1b) 4 3 1 2c ) 4 3 1 2 d) 3 1 4 2

Q.3 According to IS classification, the range of silt size particles is:

a) 4.76 mm to 2.0 mmb) 2.00 mm to 0.425 mmc) 0.425 mm to 0.075 mmd) 0.075 mm to 0.002 mm

Q.4 Match List-I (Range of particle size) with List-II (Type of soil) and select the correct answer using the codes given below the lists: List-IA. Less than 0.002 mm B. 0.075 mm to 0.002 mm C. 80 mm to 4.75 mm D. 4.75 mm to 0.075 mm List-II 1. Gravel2. Sand3. Cobble4. Silt5. ClayCodes:

A B C D a) 4 5 1 3 b) 4 5 2 1 c) 5 4 1 2 d) 5 4 1 2

Q.5 The collect increasing order of the surface area of the given solids is a) silt, sand, colloids, clayb) sand, silt, colloids, clayc) sand, silt, clay, colloidsd) clay, silt, sand, colloids

Q.6 Consider the following statements in the context of aeolian solids: 1. The soil has low density and lowcompressibility. 2. The soil is deposited by wind3. The soil has large permeabilityWhich of these statement are correct ? a) 1, 2 and 3 b) 2 and 3c) 1 and 3 d) 1 and 2

ASSIGNMENT QUESTIONS


Q.7 The collapsible soil is associated with

a) dune sands b) laterite solid c) loess d) black cotton soils Q.8 For a sandy soil with soil grains

spherical in shape and uniform in size, what is the theoretical void ratio ?

a) 0.61 b) 0.71 c) 0.91 d) 0.81 Q.9 A clay sample has a void ratio 0.54

in dry state. The specific gravity of soil solids is 2.7. what is the shrinkage limit of the soil ?

a) 8.5% b) 10.0% c) 17.0% d) 20.0% Q.10 Which one of the following correctly

represents the dry unit weight of a soil sample which has a bulk unit

weight of t at a moisture content of

w% ?

a) twγ

100 b)

t

wγ 1+

100

c) t

100γ

100+w

d) tγ (100-w)

100

Q.11 Select the correct range of Density Index ID a) ID > 0 b) ID ≥ 0 c) 0 < ID < 1 d) 0 ≤ ID ≤ 1

Q.12 The ratio Liquid limit-Watercontent

Plasticlyindex

for a soil mass is called: a) Liquidity index b) Shrinkage ratio c) Consistency index d) Toughness index

Q.13 Which one of the following is the water content of the mixed soil made from 1 kg of Soil (say A) with water content of 100% and 1 kg of soil (say B) with water content of 50% ?

a) 66% b) 71% c) 75% d) 82% Q.14 A pycnometer is used to determine a) Water content and voids ratio b) specific gravity and dry density c) water content and specific gravity d) voids ratio and dry density Q.15 Match List-I (Symbol) with List-II

(Soil) and select the correct answer using the Codes given below the lists: List-I List-II A. ML 1. Silty sand B. SM 2. Inorganic silt with

large compressibility C. Pt 3. Inorganic silt with

small compressibility D. MH 4. Soil with high

organic content with high compressibility

Codes: A B C D a) 3 2 4 1 b) 4 1 3 2 c) 3 1 4 2 d) 4 2 3 1 Q.16 A soil mass contains 40% gravel,

50% sand and 10% silt. This soil can be classified as a) silty sandy gravel having

coefficient of uniformity less than 60.

b) silty gravelly sand having coefficient of uniformly equal to 10.

c) gravelly silty sand having coefficient of uniformly greater than 60.

d) gravelly silty sand and its coefficient of uniformly cannot be determined.

Q.17 Inorganic soil with low compressibility are represented by a) MH b) SL c) ML d) CH


Assignment Questions

150

Q.1 (d)

Q.2 (d)

Q.3 (d)

Q.4 According to IS grain-size classification Soil Grain size Boulder > 300 mm Cobble 80 – 300 mm Gravel 4.75 – 80 mm Sand 0.075 – 4.75 mm Silt 0.002 – 0.075 mm Clay < 0.002 mm

Q. 5. Finer the particle more the surface area. Silt: 0.002 mm to 0.075 mm Sand: 0.075 mm to 4.75 mm Colloids have size less then clay particles.

Q.6 Aeolian soils are deposited by winds. It consists of uniformly graded particles. The void ratio and permeability of soil are high. They are non-plastic and can withstand deep vertical cuts due to slight cementation between particles. These soils have high compressibility and density is low in natural states. Example: Fine sand in dunes; loess.

Q.7 (c)

Q.8

Cubic element

3

s

πdV =

63

3

V

3

s

πdd -

V 6e= = =0.91πdV

6

Q. 9 At shrinkage limit the soil remains fully saturated,

mins

e 0.54W 100 100 20%

G 2.7

Q. 10 t t

d

100

w (100 w)1

100

Q.11 Density index: maxt

max min

e -eD =

e -e

Q. 12. The consistency index indicates the consistency (firmness) of a soil. It shows the nearness of the water content of the soil to its plastic limit. A soil with a index of zero is at the liquid limit. It is extremely soft and has negligible shear strength. On the other hand, a soil at a water content equal to the plastic limit has a consistency index of 100%, indicating that the soil is relatively firm.

Q. 13. Water content,

W

S

WW= ×100

W

Total weight

S

wW= +1 W

100

Weight of Q.ids in soil A

AS

1000W = =500gm,

1+1

AWW =500gm

Weight of Q.ids in soil B

EXPLANATIONS


BS

1000W = =666.7gm

1.5

BWW =333.3gm

In mixed soil,

WW =500+333.3=833.3gm

SW =500+666.7=1166.7gm

m

833.3W = ×100=71%

1166.7

Q.14 (c) Q.15 (c) Q.16

Particle size

% Retained

% cumulative

%N=100-cum%

Gravel retained 4.75 mm

40% 40% 60%

Sand retained 0.075 mm

50%

90%

10%

Silt retained 0.002 mm

10%

100%

0%

60D =4.75mm

10D =0.075mm

60

u

10

D 4.75C = = =63.33>60

D 0.075

So correct answer is ‘c’ Q.17 In ML; M represent inorganic silt L represent low compressibility

MH. Inorganic silt of high compressibility

SL: Sand of low compressibility CH: Clay with high compressibility Q.18 As 50% of soil is clay. So it will be classified as clay. Q.19 Lower the shrinkage limit greater is

the volume change. For coarse grained soil with fines <5% classification will be GP, GW, SP, and SW. For fines > 12%

classification will be based on plastically chart as GM, GC, SM, and SC. For lines 5 – 12 % dual classification like GP – GM; GP – GC etc., will be used. At liquid limitthe soils possess a certain shear strength which is the smallest value that can bemeasured in a standard procedure. From direct shear tests on different types of clays it is found that liquid limit corresponds to a shearing strength of about 2.7kN/m2.

The shrinkage ratio

1 2

1 2

V V NdSR 100

w w

1 2

d

1 2s

V V 1100 SRV

1w ww

G

It shrinkage limit is less the volume change with change in water content will bemore.

Q. 20 Silica has least plasticity while

Montmorillonite has highest plasticity.

Q. 21 Montro-rillonite has highest

swelling characteristics and kaolinite has lowest swelling characteristics.

Q.22 (c) Q.23 The effect of increasing the amount

of compactive effort is to increase the Maximum dry density and to decrease the optimum water content.

Q.24 (a) Q.25 Unit weight at zero air void

corresponds to dry density of soil.

W

d

Gi.e.

wG1

S


Assignment Questions

161

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