Elsoufiev Strength Analysis in Geomechanics

2. Auflage 2010
ISBN: 978-3-642-01301-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 258 Seiten

Reihe: Springer Series in Geomechanics and Geoengineering

This book presents a new method for solving geomechanical problems - one that explicitly takes into account deformation and fractures of soils, which create important effects, but are neglected in classical approaches. The method reveals the influence of the form of a structure on its ultimate state. The entire approach takes into account five types of physical as well as geometrical non-linearity, and highlights the simplicity of some non-linear computations against the consequently linear ones.

Autoren/Hrsg.

Elsoufiev, Serguey A.

Inhaltsverzeichnis

1;Foreword;5
2;Foreword to the 2nd Edition;7
3;Preface;8
4;Contents;12
5;1 Introduction: Main Ideas;17
5.1;1.1 Role of Engineering Geological Investigations;17
5.2;1.2 Scope and Aim of the Subject. Short Historyof Soil Mechanics;17
5.3;1.3 Use of the Continuum Mechanics Methods;18
5.4;1.4 Main Properties of Soils;20
5.4.1;1.4.1 Stresses in Soil;20
5.4.2;1.4.2 Settling of Soil;22
5.4.2.1;Phases of Soil State;22
5.4.2.2;Settling of Earth Layer of Limited Thickness;23
5.4.2.3;Role of Loading Area;24
5.4.2.4;Influence of Load on Footing;25
5.4.2.5;Influence of Time;26
5.4.2.6;Combined Influence of Time and Loading;27
5.4.3;1.4.3 Computation of Settling Changing in Time;27
5.4.3.1;Premises of Filtration Consolidation Theory;27
5.4.3.2;Model of Terzaghi-Gersewanov;27
5.4.3.3;Differential Equation of Consolidation Due to Filtration;28
5.5;1.5 Description of Properties of Soils and Other Materials by Methods of Mechanics;29
5.5.1;1.5.1 General Considerations;29
5.5.2;1.5.2 The Use of the Elasticity Theory;30
5.5.2.1;Main Ideas;30
5.5.2.2;Some Solutions Connected with Stability of Bars;31
5.5.2.3;Bases of Crack Mechanics;32
5.5.3;1.5.3 The Bases of Ultimate Plastic State Theory;33
5.5.3.1;Main Ideas;33
5.5.3.2;Ultimate State of Statically Indetermined Beams;34
5.5.3.3;Ultimate State of Plates in Bending;35
5.5.4;1.5.4 Simplest Theories of Retaining Walls;37
5.5.5;1.5.5 Longtime Strength;40
5.5.6;1.5.6 Eccentric Compression and Determination of Creep Parameters from Bending Tests;42
5.5.7;1.5.7 Fracture of Tunnel Arch;45
6;2 Main Equations in Media Mechanics;49
6.1;2.1 Stresses in Body;49
6.2;2.2 Displacements and Strains;51
6.3;2.3 Rheological Equations;52
6.3.1;2.3.1 Generalised Hooke's Law;52
6.3.2;2.3.2 Non-linear Equations;53
6.3.3;2.3.3 Constitutive Equations for Anisotropic Materials;54
6.4;2.4 Solution Methods of Mechanical Problems;58
6.4.1;2.4.1 General Considerations;58
6.4.2;2.4.2 Basic Equations for Anti-plane Deformation;58
6.4.3;2.4.3 Plane Problem;60
6.4.4;2.4.4 Axisymmetric Problem;62
6.4.5;2.4.5 Spherical Coordinates;63
6.5;2.5 Economical Profile of Triangular Dam Under Self-Weight and Laternal Pressure of Water;64
7;3 Some Elastic Solutions;66
7.1;3.1 Longitudinal Shear;66
7.1.1;3.1.1 General Considerations;66
7.1.2;3.1.2 Longitudinal Displacement of Strip;67
7.1.3;3.1.3 Deformation of Massif with Circular Holeof Unit Radius;68
7.1.4;3.1.4 Brittle Rupture of Body with Crack;69
7.1.5;3.1.5 Conclusion;71
7.2;3.2 Plane Problem;71
7.2.1;3.2.1 Wedge Under One-Sided Load;71
7.2.2;3.2.2 Wedge Pressed by Inclined Plates;72
7.2.2.1;General Case;72
7.2.2.2;Some Particular Cases;75
7.2.2.3;Case of Parallel Plates;76
7.2.3;3.2.3 Wedge Under Concentrated Force in its Apex: Some Generalizations;77
7.2.3.1;General Case;77
7.2.3.2;Case of Distributed Load;78
7.2.3.3;The First Ultimate Load;79
7.2.4;3.2.4 Beams on Elastic Foundation;80
7.2.5;3.2.5 Use of Complex Variables;83
7.2.5.1;General Expressions;83
7.2.5.2;Tension of Plate with Circular Hole;83
7.2.6;3.2.6 General Relations for a Semi-PlaneUnder Vertical Load;85
7.2.7;3.2.7 Crack in Tension;85
7.2.8;3.2.8 Critical Strength;86
7.2.9;3.2.9 Stresses and Displacements Under Plane Punch;88
7.2.10;3.2.10 General Relations for Transversal Shear;89
7.2.11;3.2.11 Rupture due to Crack in Transversal Shear;89
7.2.12;3.2.12 Constant Displacement at Transversal Shear;90
7.2.13;3.2.13 Inclined Crack in Tension;91
7.3;3.3 Axisymmetric Problem and its Generalization;92
7.3.1;3.3.1 Sphere, Cylinder and Cone Under External and Internal Pressure;92
7.3.2;3.3.2 Boussinesq's Solution and its Generalization;94
7.3.2.1;Stresses in Semi-Space Under Concentrated Load;94
7.3.2.2;Stresses Under Distributed Load;95
7.3.2.3;Stresses Under Rectangles;96
7.3.2.4;Displacements in Massif;97
7.3.2.5;Approximate Methods of Settling Computations;98
7.3.3;3.3.3 Short Information on Bending of Thin Plates;99
7.3.3.1;General Equations for Circular Plates;99
7.3.3.2;Ultimate State of Circular Plates;100
7.3.3.3;Ultimate State of Square Plates;101
7.3.4;3.3.4 Circular Crack in Tension;102
8;4 Elastic-Plastic and Ultimate State of PerfectPlastic Bodies;104
8.1;4.1 Anti-Plane Deformation;104
8.1.1;4.1.1 Ultimate State at Torsion;104
8.1.2;4.1.2 Plastic Zones Near Crack and Punch Ends;105
8.2;4.2 Plane Deformation;107
8.2.1;4.2.1 Elastic-Plastic Deformation and Failure of Slope;107
8.2.1.1;Stresses in Wedge;107
8.2.1.2;Displacements in Wedge;108
8.2.1.3;Ultimate State of Slope;108
8.2.2;4.2.2 Compression of Massif by Inclined Rigid Plates;109
8.2.2.1;Main Equations;109
8.2.2.2;General Case;110
8.2.2.3;Cases of Big n and Parallel Plates;111
8.2.2.4;Addition of Shearing Force;113
8.2.3;4.2.3 Penetration of Wedge and Load-bearing Capacityof Piles Sheet;114
8.2.4;4.2.4 Theory of Slip Lines;116
8.2.4.1;Main Equations;116
8.2.4.2;Examples of Slip Lines;117
8.2.4.3;Construction of Slip Lines Fields;118
8.2.4.4;Construction of Slip Fields for Soils;118
8.2.5;4.2.5 Ultimate State of Some Plastic Bodies;119
8.2.5.1;Plate with Circular Hole at Tension or Compression;119
8.2.5.2;Penetration of Wedge;120
8.2.5.3;Pressure of Massif through Narrowing Channel;121
8.2.5.4;Tension of Plane with Crack;122
8.2.6;4.2.6 Ultimate State of Some Soil Structures;124
8.2.6.1;Conditions of Beginning of Plastic Shear;124
8.2.7;4.2.7 Pressure of Soils on Retaining Walls;128
8.2.8;4.2.8 Stability of Footings;130
8.2.9;4.2.9 Elementary Tasks of Slope Stability;132
8.2.9.1;Soil Has Only Internal Friction;132
8.2.10;4.2.10 Some Methods of Appreciation of Slopes Stability;134
8.3;4.3 Axisymmetric Problem;137
8.3.1;4.3.1 Elastic-plastic and Ultimate Statesof Thick-walled Elements;137
8.3.2;4.3.2 Compression of Cylinder by Rough Plates;140
8.3.3;4.3.3 Flow of Material within Cone;141
8.3.3.1;Common Case;141
8.3.3.2;Case of Big n;142
8.3.3.3;Approximate Approach;143
8.3.4;4.3.4 Penetration of Rigid Cone and Load-bearingCapacity of Circular Pile;143
8.4;4.4 Intermediary Conclusion;144
9;5 Ultimate State of Structures at Small Non-Linear Strains;146
9.1;5.1 Fracture Near Edges of Cracks and Punch at Anti-Plane Deformation;146
9.1.1;5.1.1 General Considerations;146
9.1.2;5.1.2 Case of Crack Propagation;147
9.1.3;5.1.3 Plastic Zones Near Punch Edges;149
9.2;5.2 Plane Deformation;149
9.2.1;5.2.1 Generalization of Flamant's Problem;149
9.2.1.1;Common Solution;149
9.2.1.2;Particular Cases;150
9.2.1.3;Comparison of Results;150
9.2.1.4;Case of Horizontal Force;151
9.2.2;5.2.2 Slope Under One-Sided Load;152
9.2.2.1;General Relations;152
9.2.2.2;Results of Computation;153
9.2.2.3;Simple Solution;155
9.2.3;5.2.3 Wedge Pressed by Inclined Rigid Plates;156
9.2.3.1;Engineering Relations for Particular Case;156
9.2.3.2;Flow of Material Between Immovable Plates;157
9.2.3.3;Some Particular Cases;160
9.2.4;5.2.4 Penetration of Wedge and Load-bearing Capacity of Piles Sheet;161
9.2.5;5.2.5 Wedge Under Bending Moment in its Apex;162
9.2.6;5.2.6 Load-bearing Capacity of Sliding Supports;166
9.2.7;5.2.7 Propagation of Cracks and Plastic Zones near Punch Edges;168
9.2.7.1;Transversal Shear;170
9.3;5.3 Axisymmetric Problem;171
9.3.1;5.3.1 Generalization of Boussinesq's Solution;171
9.3.2;5.3.2 Flow of Material within Cone;173
9.3.2.1;Common Equations;173
9.3.3;5.3.3 Cone Penetration and Load-bearing Capacityof Circular Pile;177
9.3.4;5.3.4 Fracture of Thick-walled Elements due to Damage;178
9.3.4.1;Stretched Plate with Hole;178
9.3.4.2;Sphere;180
9.3.4.3;Cylinder;180
9.3.4.4;Cone;181
9.3.4.5;Conclusion;182
10;6 Ultimate State of Structures at Finite Strains;183
10.1;6.1 Use of Hoff's Method;183
10.1.1;6.1.1 Tension of Elements Under Hydrostatic Pressure;183
10.1.2;6.1.2 Fracture Time of Axisymmetrically Stretched Plate;185
10.1.3;6.1.3 Thick-Walled Elements Under Internaland External Pressures;186
10.1.4;6.1.4 Final Notes;188
10.2;6.2 Mixed Fracture at Unsteady Creep;188
10.2.1;6.2.1 Tension Under Hydrostatic Pressure;188
10.2.2;6.2.2 Axisymmetric Tension of Variable Thickness Plate with Hole;189
10.2.2.1;General Case and that of Constant Thickness;189
10.2.2.2;Curved Profile;189
10.2.2.3;Optimal Profile;190
10.2.3;6.2.3 Thick-Walled Elements Under Internaland External Pressures;191
10.2.3.1;Sphere;191
10.2.3.2;Cylinder and Cone;193
10.2.4;6.2.4 Deformation and Fracture of Thin-Walled ShellsUnder Internal Pressure;194
10.2.4.1;General Relations;194
10.2.4.2;Some Approximate Solutions;195
10.2.4.3;Another Approximate Approach;196
10.2.4.4;Torus of Revolution;196
10.2.5;6.2.5 Thin-Walled Membranes Under Hydrostatic Pressure;198
10.2.5.1;General Expressions and Cylindrical Membrane;198
10.2.5.2;Spherical Membrane;199
10.2.5.3;Comparison with Test Data;200
10.2.6;6.2.6 Two other Problems;200
10.2.6.1;Tension of Limited Length Tube;200
10.2.6.2;Compression of Cylinder;201
10.2.6.3;Final Notes;202
10.2.7;6.2.7 Ultimate State of Anisotropic Platein Biaxial Tension;202
10.2.7.1;General Considerations;202
10.2.7.2;Basic Expressions;202
10.2.7.3;Ultimate State;202
10.2.7.4;Ultimate State of Plastic Materials;203
10.2.7.5;Ultimate State of Brittle Materials;205
11;Conclusion;206
12;References;208
13;Appendices;211
13.1;A Computation of p for Brittle Materials Which do not Resist Tension;212
13.2;B Values of Ks in (3.127);214
13.3;C Values of K' in (3.128);215
13.4;D Values of b1,b2 in Fig 4.33 and factors A, B in (4.88);216
13.5;E Flow of Ideal Plastic Material in Cone;217
13.6;F Computation of Stresses at Anti-plane Deformation of Massif with Crack and Moving Punch;219
13.7;G Some Computations on Bending of Wedge;222
13.8;H Bases of Applied Creep Theory;225
13.9;I Inelastic Zones Near Crack in Massif at Tensionand Pressed Punch;228
13.10;J Inelastic Zones Near Crack and Punch Endsat Transversal Shear;230
13.11;K Flow of Material in Cone;232
13.12;L The Use of Hypotheses of Creep;234
13.13;M Use of the Coulomb's Law for Description of Some Elastic-Plastic Systems at Cycling Loading;236
13.14;N Investigation of Gas Penetrationin Polymers and Rubbers;241
13.15;O Fracture of Optimal Profile Rotating Disk;245
13.16;P Strength of Anisotropic Tubes at Different Loadings. Construction of Potential Function;250
14;Index;258