Strength Analysis in Geomechanics (eBook)

Foreword 5
Foreword to the 2nd Edition 7
Preface 8
Contents 12
1 Introduction: Main Ideas 17
1.1 Role of Engineering Geological Investigations 17
1.2 Scope and Aim of the Subject. Short Historyof Soil Mechanics 17
1.3 Use of the Continuum Mechanics Methods 18
1.4 Main Properties of Soils 20
1.4.1 Stresses in Soil 20
1.4.2 Settling of Soil 22
Phases of Soil State 22
Settling of Earth Layer of Limited Thickness 23
Role of Loading Area 24
Influence of Load on Footing 25
Influence of Time 26
Combined Influence of Time and Loading 27
1.4.3 Computation of Settling Changing in Time 27
Premises of Filtration Consolidation Theory 27
Model of Terzaghi-Gersewanov 27
Differential Equation of Consolidation Due to Filtration 28
1.5 Description of Properties of Soils and Other Materials by Methods of Mechanics 29
1.5.1 General Considerations 29
1.5.2 The Use of the Elasticity Theory 30
Main Ideas 30
Some Solutions Connected with Stability of Bars 31
Bases of Crack Mechanics 32
1.5.3 The Bases of Ultimate Plastic State Theory 33
Main Ideas 33
Ultimate State of Statically Indetermined Beams 34
Ultimate State of Plates in Bending 35
1.5.4 Simplest Theories of Retaining Walls 37
1.5.5 Longtime Strength 40
1.5.6 Eccentric Compression and Determination of Creep Parameters from Bending Tests 42
1.5.7 Fracture of Tunnel Arch 45
2 Main Equations in Media Mechanics 49
2.1 Stresses in Body 49
2.2 Displacements and Strains 51
2.3 Rheological Equations 52
2.3.1 Generalised Hooke's Law 52
2.3.2 Non-linear Equations 53
2.3.3 Constitutive Equations for Anisotropic Materials 54
2.4 Solution Methods of Mechanical Problems 58
2.4.1 General Considerations 58
2.4.2 Basic Equations for Anti-plane Deformation 58
2.4.3 Plane Problem 60
2.4.4 Axisymmetric Problem 62
2.4.5 Spherical Coordinates 63
2.5 Economical Profile of Triangular Dam Under Self-Weight and Laternal Pressure of Water 64
3 Some Elastic Solutions 66
3.1 Longitudinal Shear 66
3.1.1 General Considerations 66
3.1.2 Longitudinal Displacement of Strip 67
3.1.3 Deformation of Massif with Circular Holeof Unit Radius 68
3.1.4 Brittle Rupture of Body with Crack 69
3.1.5 Conclusion 71
3.2 Plane Problem 71
3.2.1 Wedge Under One-Sided Load 71
3.2.2 Wedge Pressed by Inclined Plates 72
General Case 72
Some Particular Cases 75
Case of Parallel Plates 76
3.2.3 Wedge Under Concentrated Force in its Apex: Some Generalizations 77
General Case 77
Case of Distributed Load 78
The First Ultimate Load 79
3.2.4 Beams on Elastic Foundation 80
3.2.5 Use of Complex Variables 83
General Expressions 83
Tension of Plate with Circular Hole 83
3.2.6 General Relations for a Semi-PlaneUnder Vertical Load 85
3.2.7 Crack in Tension 85
3.2.8 Critical Strength 86
3.2.9 Stresses and Displacements Under Plane Punch 88
3.2.10 General Relations for Transversal Shear 89
3.2.11 Rupture due to Crack in Transversal Shear 89
3.2.12 Constant Displacement at Transversal Shear 90
3.2.13 Inclined Crack in Tension 91
3.3 Axisymmetric Problem and its Generalization 92
3.3.1 Sphere, Cylinder and Cone Under External and Internal Pressure 92
3.3.2 Boussinesq's Solution and its Generalization 94
Stresses in Semi-Space Under Concentrated Load 94
Stresses Under Distributed Load 95
Stresses Under Rectangles 96
Displacements in Massif 97
Approximate Methods of Settling Computations 98
3.3.3 Short Information on Bending of Thin Plates 99
General Equations for Circular Plates 99
Ultimate State of Circular Plates 100
Ultimate State of Square Plates 101
3.3.4 Circular Crack in Tension 102
4 Elastic-Plastic and Ultimate State of PerfectPlastic Bodies 104
4.1 Anti-Plane Deformation 104
4.1.1 Ultimate State at Torsion 104
4.1.2 Plastic Zones Near Crack and Punch Ends 105
4.2 Plane Deformation 107
4.2.1 Elastic-Plastic Deformation and Failure of Slope 107
Stresses in Wedge 107
Displacements in Wedge 108
Ultimate State of Slope 108
4.2.2 Compression of Massif by Inclined Rigid Plates 109
Main Equations 109
General Case 110
Cases of Big n and Parallel Plates 111
Addition of Shearing Force 113
4.2.3 Penetration of Wedge and Load-bearing Capacityof Piles Sheet 114
4.2.4 Theory of Slip Lines 116
Main Equations 116
Examples of Slip Lines 117
Construction of Slip Lines Fields 118
Construction of Slip Fields for Soils 118
4.2.5 Ultimate State of Some Plastic Bodies 119
Plate with Circular Hole at Tension or Compression 119
Penetration of Wedge 120
Pressure of Massif through Narrowing Channel 121
Tension of Plane with Crack 122
4.2.6 Ultimate State of Some Soil Structures 124
Conditions of Beginning of Plastic Shear 124
4.2.7 Pressure of Soils on Retaining Walls 128
4.2.8 Stability of Footings 130
4.2.9 Elementary Tasks of Slope Stability 132
Soil Has Only Internal Friction 132
4.2.10 Some Methods of Appreciation of Slopes Stability 134
4.3 Axisymmetric Problem 137
4.3.1 Elastic-plastic and Ultimate Statesof Thick-walled Elements 137
4.3.2 Compression of Cylinder by Rough Plates 140
4.3.3 Flow of Material within Cone 141
Common Case 141
Case of Big n 142
Approximate Approach 143
4.3.4 Penetration of Rigid Cone and Load-bearingCapacity of Circular Pile 143
4.4 Intermediary Conclusion 144
5 Ultimate State of Structures at Small Non-Linear Strains 146
5.1 Fracture Near Edges of Cracks and Punch at Anti-Plane Deformation 146
5.1.1 General Considerations 146
5.1.2 Case of Crack Propagation 147
5.1.3 Plastic Zones Near Punch Edges 149
5.2 Plane Deformation 149
5.2.1 Generalization of Flamant's Problem 149
Common Solution 149
Particular Cases 150
Comparison of Results 150
Case of Horizontal Force 151
5.2.2 Slope Under One-Sided Load 152
General Relations 152
Results of Computation 153
Simple Solution 155
5.2.3 Wedge Pressed by Inclined Rigid Plates 156
Engineering Relations for Particular Case 156
Flow of Material Between Immovable Plates 157
Some Particular Cases 160
5.2.4 Penetration of Wedge and Load-bearing Capacity of Piles Sheet 161
5.2.5 Wedge Under Bending Moment in its Apex 162
5.2.6 Load-bearing Capacity of Sliding Supports 166
5.2.7 Propagation of Cracks and Plastic Zones near Punch Edges 168
Transversal Shear 170
5.3 Axisymmetric Problem 171
5.3.1 Generalization of Boussinesq's Solution 171
5.3.2 Flow of Material within Cone 173
Common Equations 173
5.3.3 Cone Penetration and Load-bearing Capacityof Circular Pile 177
5.3.4 Fracture of Thick-walled Elements due to Damage 178
Stretched Plate with Hole 178
Sphere 180
Cylinder 180
Cone 181
Conclusion 182
6 Ultimate State of Structures at Finite Strains 183
6.1 Use of Hoff's Method 183
6.1.1 Tension of Elements Under Hydrostatic Pressure 183
6.1.2 Fracture Time of Axisymmetrically Stretched Plate 185
6.1.3 Thick-Walled Elements Under Internaland External Pressures 186
6.1.4 Final Notes 188
6.2 Mixed Fracture at Unsteady Creep 188
6.2.1 Tension Under Hydrostatic Pressure 188
6.2.2 Axisymmetric Tension of Variable Thickness Plate with Hole 189
General Case and that of Constant Thickness 189
Curved Profile 189
Optimal Profile 190
6.2.3 Thick-Walled Elements Under Internaland External Pressures 191
Sphere 191
Cylinder and Cone 193
6.2.4 Deformation and Fracture of Thin-Walled ShellsUnder Internal Pressure 194
General Relations 194
Some Approximate Solutions 195
Another Approximate Approach 196
Torus of Revolution 196
6.2.5 Thin-Walled Membranes Under Hydrostatic Pressure 198
General Expressions and Cylindrical Membrane 198
Spherical Membrane 199
Comparison with Test Data 200
6.2.6 Two other Problems 200
Tension of Limited Length Tube 200
Compression of Cylinder 201
Final Notes 202
6.2.7 Ultimate State of Anisotropic Platein Biaxial Tension 202
General Considerations 202
Basic Expressions 202
Ultimate State 202
Ultimate State of Plastic Materials 203
Ultimate State of Brittle Materials 205
Conclusion 206
References 208
Appendices 211
A Computation of p for Brittle Materials Which do not Resist Tension 212
B Values of Ks in (3.127) 214
C Values of K' in (3.128) 215
D Values of b1,b2 in Fig 4.33 and factors A, B in (4.88) 216
E Flow of Ideal Plastic Material in Cone 217
F Computation of Stresses at Anti-plane Deformation of Massif with Crack and Moving Punch 219
G Some Computations on Bending of Wedge 222
H Bases of Applied Creep Theory 225
I Inelastic Zones Near Crack in Massif at Tensionand Pressed Punch 228
J Inelastic Zones Near Crack and Punch Endsat Transversal Shear 230
K Flow of Material in Cone 232
L The Use of Hypotheses of Creep 234
M Use of the Coulomb's Law for Description of Some Elastic-Plastic Systems at Cycling Loading 236
N Investigation of Gas Penetrationin Polymers and Rubbers 241
O Fracture of Optimal Profile Rotating Disk 245
P Strength of Anisotropic Tubes at Different Loadings. Construction of Potential Function 250
Index 258