Soil mechanics A ONE DIMENSIONAL INTRODUCTION David Muir Wood

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Contents

Preface page ix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction 1
1.2 Soil mechanics 2
1.3 Range of problems/applications 2
1.4 Scope of this book 10
1.5 Mind maps 11
2 Stress in soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Introduction 12
2.2 Equilibrium 12
2.3 Gravity 13
2.4 Stress 16
2.5 Exercises: Stress 18
2.6 Vertical stress profile 19
2.6.1 Worked examples 21
2.7 Water in the ground: Introduction to hydrostatics 23
2.7.1 Worked example: Archimedes uplift on spherical object 26
2.8 Total and effective stresses 28
2.8.1 Worked examples 32
2.9 Summary 37
2.10 Exercises: Profiles of total stress, effective stress, pore pressure 37
3 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
3.1 Introduction 40
3.2 Units 40
3.3 Descriptions of packing and density 41
3.3.1 Volumetric ratios 43
3.3.2 Water content 44
3.3.3 Densities 44
3.3.4 Unit weights 46
3.3.5 Typical values 46
3.4 Measurement of packing 47
3.4.1 Compaction 50
3.5 Soil particles 52
3.6 Laboratory exercise: particle size distribution and other
classification tests 56
3.6.1 Sieving 56
3.6.2 Sedimentation 57
3.6.3 Particle shape 61
3.6.4 Sand: relative density 61
3.7 Summary 62
3.8 Exercises: Density 64
3.8.1 Multiple choice questions 64
3.8.2 Calculation exercises 65
4 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Introduction 67
4.2 Linear elasticity 67
4.3 Natural and true strain 70
4.4 One-dimensional testing of soils 70
4.4.1 Hooke’s Law: confined one-dimensional stiffness ♣ 72
4.5 One-dimensional (confined) stiffness of soils 74
4.6 Calculation of strains 78
4.6.1 Worked examples: Calculation of settlement 79
4.7 Overconsolidation 82
4.7.1 Worked examples: Overconsolidation 84
4.8 Summary 87
4.9 Exercises: Stiffness 87
5 Seepage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.1 Introduction 90
5.2 Total head: Bernoulli’s equation 90
5.3 Poiseuille’s equation 96
5.4 Permeability 99
5.4.1 Darcy or Forchheimer? 102
5.5 Measurement of permeability 104
5.6 Permeability of layered soil 106
5.7 Seepage forces 108
5.8 Radial flow to vertical drain 111
5.9 Radial flow to point drain 112
5.10 Worked examples: Seepage 113
5.10.1 Example: flow through soil column 113
5.10.2 Example: effect of changing reference datum 116
5.10.3 Example: pumping from aquifer 117
5.10.4 Example: flow into excavation 119
5.11 Summary 121
5.12 Exercises: Seepage 123
6 Change in stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1 Introduction 127
6.2 Stress change and soil permeability 127
6.3 Worked examples 130
6.3.1 Example 1 130
6.3.2 Example 2 131
6.3.3 Example 3 133
6.4 Summary 134
6.5 Exercises: Change in stress 136
7 Consolidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.1 Introduction 138
7.2 Describing the problem 140
7.3 Parabolic isochrones 142
7.4 Worked examples 149
7.4.1 Example 1: Determination of coefficient of consolidation 149
7.4.2 Example 2 152
7.4.3 Example 3 154
7.4.4 Example 4 155
7.5 Consolidation: exact analysis ♣ 155
7.5.1 Semi-infinite layer 159
7.5.2 Finite layer 161
7.6 Summary 165
7.7 Exercises: Consolidation 167
8 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1 Introduction 169
8.2 Failure mechanisms 169
8.3 Shear box and strength of soils 171
8.4 Strength model 173
8.5 Dilatancy 174
8.6 Drained and undrained strength 177
8.7 Clay: overconsolidation and undrained strength 179
8.9 Infinite slope 185
8.9.1 Laboratory exercise: Angle of repose 191
8.10 Undrained strength of clay: fall-cone test 193
8.11 Simple model of shearing ♣ 195
8.11.1 Stiffness 196
8.11.2 Strength 197
8.11.3 Mobilisation of strength 197
8.11.4 Dilatancy 198
8.11.5 Complete stress:strain relationship 199
8.11.6 Drained and undrained response 200
8.11.7 Model: summary 203
8.12 Summary 203
8.13 Exercises: Strength 205
9 Soil-structure interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.1 Introduction 208
9.2.1 Examples 215
9.3 Bending of an elastic beam ♣ 216
9.4 Elastic beam on elastic foundation ♣ 220
9.6 Soil-structure interaction: next steps 226
9.7 Summary 227
9.8 Exercises: Soil-structure interaction 227
10 Envoi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
10.1 Summary 230
10.2 Beyond the single dimension 231
Exercises: numerical answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Index 237

Preface

This book has emerged from a number of stimuli.
There is a view that soils are special: that their characteristics are so extraordinary
that they can only be understood by a small band of specialists. Obviously,
soils do have some special properties: the central importance of density and change
of density merits particular attention. However, in the context of teaching principles
of soil mechanics to undergraduates in the early years of their civil engineering
degree programmes, I believe that there is advantage to be gained in trying to integrate
this teaching with other teaching of properties of engineering materials to
which the students are being exposed at the same time.
It is a fundamental tenet of critical state soil mechanics – with which I grew up
in my undergraduate days – that consideration of the mechanical behaviour of soils
requires us to consider density alongside effective stresses, thus permitting the unification
of deformation and strength characteristics. This can be seen as a broad
interpretation of the phrase critical state soil mechanics. I believe that such a unification
can aid the teaching and understanding of soil mechanics.
There is an elegant book by A. J. Roberts1 which demonstrates in a unified
way how a common mathematical framework can be applied to problems of solid
mechanics, fluid mechanics, traffic flow and so on. While I cannot hope to emulate
this elegance, the title prompted me to explore a similar one-dimensional theme
for the presentation of many of the key concepts of soil mechanics: density, stress,
stiffness, strength and fluid flow.
This one-dimensional approach to soil mechanics has formed the basis for an
introductory course of ten one-hour lectures with ten one-hour problem classes and
one three-hour laboratory afternoon for first-year civil engineering undergraduates
at Bristol University. The material of that course is contained in this book. I have
added a chapter on the analysis of one-dimensional consolidation, which fits neatly
with the theme of the book. I have also included a model of the shearing of soil and
some examples of soil-structure interaction which are capable of theoretical analysis
using essentially one-dimensional governing equations.
1 Roberts, A. J. (1994). A one-dimensional introduction to continuum mechanics. World Scientific.
Simplification of more or less realistic problems leads to differential equations
which can be readily solved: this is the essence of modelling with which engineers
need to engage (and to realise that they are engaging) all the time. A few of these
topics require some modest mathematical ability – a bit of integration, solution of
ordinary and partial differential equations – but nothing beyond the eventual expectations
of an undergraduate engineering degree programme. Sections that might, as
a consequence, be omitted on a first reading, or until the classes in mathematics have
caught up, are indicated by the symbol ♣.
Exercises are given for private study at the end of all chapters and some suggestions
for laboratory demonstrations that could accompany such an introductory
course are sprinkled through the book.
I am grateful to colleagues at Bristol and elsewhere – especially Danuta
Lesniewska, Erdin Ibraim and Dick Clements – who have provided advice and comments
on drafts of this book to which I have tried to respond. Erdin in particular has
helped enormously by using material and examples from a draft of this book in his
own teaching and has made many useful suggestions for clarification. However, the
blame for any remaining errors must remain with me.
I am grateful to Christopher Bambridge, Ross Boulanger, Sarah Dagostino,
David Eastaff, David Nash and Alan Powderham for their advice and help in locating
and giving permission to reproduce suitable pictures.
I thank Bristol University for awarding me a University Research Fellowship
for the academic year 2007–8 which gave me some breathing space after a particularly
heavy four years of administrative duty.
I am particularly grateful to Peter Gordon for his editorial guidance and wisdom
and his intervention at times of stress.
I acknowledge with gratitude Helen’s indulgence and support while I have been
preparing and revising this book.