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AN INTEGRATED FRAMEWORK FOR STRUCTURAL GEOLOGY
A modern and practice-oriented approach to structural geology
An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks builds a framework for structural geology from geometrical description, kinematic analysis, dynamic evolution, and rheological investigation of deformed rocks. The unique approach taken by the book is to integrate these principles of continuum mechanics with the description of rock microstructures and inferences about deformation mechanisms. Field, theoretical and laboratory approaches to structural geology are all considered, including the application of rock mechanics experiments to nature.
Readers will also find:
* Three case studies that illustrate how the framework can be applied to deformation at different levels in the crust and in an applied structural geology context
* Hundreds of detailed, two-color illustrations of exceptional clarity, as well as many microstructural and field photographs
* The quantitative basis of structural geology delivered through clear mathematics
Written for advanced undergraduate and graduate students in geology, An Integrated Framework for Structural Geology will also earn a place in the libraries of practicing geologists with an interest in a one-stop resource on structural geology.
A modern and practice-oriented approach to structural geology
An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks builds a framework for structural geology from geometrical description, kinematic analysis, dynamic evolution, and rheological investigation of deformed rocks. The unique approach taken by the book is to integrate these principles of continuum mechanics with the description of rock microstructures and inferences about deformation mechanisms. Field, theoretical and laboratory approaches to structural geology are all considered, including the application of rock mechanics experiments to nature.
Readers will also find:
* Three case studies that illustrate how the framework can be applied to deformation at different levels in the crust and in an applied structural geology context
* Hundreds of detailed, two-color illustrations of exceptional clarity, as well as many microstructural and field photographs
* The quantitative basis of structural geology delivered through clear mathematics
Written for advanced undergraduate and graduate students in geology, An Integrated Framework for Structural Geology will also earn a place in the libraries of practicing geologists with an interest in a one-stop resource on structural geology.
AN INTEGRATED FRAMEWORK FOR STRUCTURAL GEOLOGY
A modern and practice-oriented approach to structural geology
An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks builds a framework for structural geology from geometrical description, kinematic analysis, dynamic evolution, and rheological investigation of deformed rocks. The unique approach taken by the book is to integrate these principles of continuum mechanics with the description of rock microstructures and inferences about deformation mechanisms. Field, theoretical and laboratory approaches to structural geology are all considered, including the application of rock mechanics experiments to nature.
Readers will also find:
* Three case studies that illustrate how the framework can be applied to deformation at different levels in the crust and in an applied structural geology context
* Hundreds of detailed, two-color illustrations of exceptional clarity, as well as many microstructural and field photographs
* The quantitative basis of structural geology delivered through clear mathematics
Written for advanced undergraduate and graduate students in geology, An Integrated Framework for Structural Geology will also earn a place in the libraries of practicing geologists with an interest in a one-stop resource on structural geology.
A modern and practice-oriented approach to structural geology
An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks builds a framework for structural geology from geometrical description, kinematic analysis, dynamic evolution, and rheological investigation of deformed rocks. The unique approach taken by the book is to integrate these principles of continuum mechanics with the description of rock microstructures and inferences about deformation mechanisms. Field, theoretical and laboratory approaches to structural geology are all considered, including the application of rock mechanics experiments to nature.
Readers will also find:
* Three case studies that illustrate how the framework can be applied to deformation at different levels in the crust and in an applied structural geology context
* Hundreds of detailed, two-color illustrations of exceptional clarity, as well as many microstructural and field photographs
* The quantitative basis of structural geology delivered through clear mathematics
Written for advanced undergraduate and graduate students in geology, An Integrated Framework for Structural Geology will also earn a place in the libraries of practicing geologists with an interest in a one-stop resource on structural geology.
Über den Autor
Steven Wojtal is Professor of Geoscience at Oberlin College in Oberlin, Ohio, United States.
Tom Blenkinsop is Professor in Earth Science at Cardiff University, United Kingdom.
Basil Tikoff is Professor of Geoscience at the University of Wisconsin-Madison, United States.
Inhaltsverzeichnis
Acknowledgements xvii
Website xix
1 A Framework for Structural Geology 1
1.1 Introduction 1
1.1.1 Deformation 1
1.1.2 Empirical vs. Theoretical Approaches 1
1.1.3 Continuum Mechanics and its Applicability to Structural Geology 6
1.1.4 How to use this Book 6
References 8
2 Structures Produced by Deformation 10
2.1 Geological Structures 10
2.1.1 Structural Fabrics 10
2.1.2 Folds and Boudinage 12
2.1.3 Fractures and Stylolites 15
2.1.4 Faults and Fault Zones 17
2.1.5 Shear Zones 22
2.2 Additional Considerations 25
3 Microstructures 26
3.1 Introduction 26
3.1.1 Overview 26
3.1.2 Framework 27
3.1.3 Imaging of Microstructures 27
3.2 Fractures 28
3.3 Fault Rocks 30
3.4 Overgrowths, Pressure Shadows and Fringes, and Veins 33
3.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 37
3.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 38
3.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 40
3.8 Deformation Twins 43
3.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 43
3.10 Porphyroblasts 47
3.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 49
3.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 49
3.12.1 Asymmetric Pressure Shadows and Fringes 53
3.12.2 Foliation Obliquity and Curvature 55
3.12.3 SC, SC', and SCC' Fabrics 55
3.12.4 Porphyroclast Systems 56
3.12.5 Precautions with Shear Sense Determination 59
3.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60
References 65
4 Displacements 66
4.1 Overview 66
4.2 Chapter Organization 66
4A Displacements: Conceptual Foundation 67
4A.1 Specifying Displacements or Individual Particles 67
4A.1.1 Basic Ideas 67
4A.1.2 Geological Example 69
4A.2 Particle Paths and Velocities 70
4A.2.1 Particle Paths 70
4A.2.2 Velocities 71
4A.3 Displacements of Collections of Particles - Displacement Fields 74
4A.3.1 Displacement Fields 74
4A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 76
4A.3.3 Classes of Displacement Fields 77
4A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 79
4A.5 Idealized, Two-Dimensional Displacement Fields 85
4A.5.1 Simple Shear 87
4A.5.2 Pure Shear 88
4A.6 Idealized, Three-Dimensional Displacement Fields 89
4A.7 Summary 90
4B Displacements: Comprehensive Treatment 90
4B.1 Specifying Displacements for Individual Particles 90
4B.1.1 Defining Vector Quantities 90
4B.1.2 Types of Vectors 92
4B.1.3 Relating Position and Displacement Vectors 94
4B.1.4 Characterizing Vector Quantities 95
4B.2 Particle Paths and Velocities 97
4B.2.1 Incremental Displacements for Particles 97
4B.2.2 Particle Paths and Movement Histories 98
4b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 99
4B.3 Displacements of Collections of Particles - Displacement Fields 101
4B.3.1 Concept of a Displacement Field 101
4B.3.2 Field Quantities 103
4b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 103
4B.3.4 Idealized Versus True Gradients of the Displacement Field 104
4B.4 The Displacement Gradient Tensor - Relating Position and Displacement Vectors 106
4b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 107
4B.4.2 Translation Displacement Fields 107
4B.4.3 Rigid Rotation Displacement Fields 107
4B.4.4 Pure Strain Displacement Fields 109
4B.4.5 Total Displacement Fields 110
4b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 110
4B.5 Idealized, Two- dimensional Displacement Fields 111
4B.5.1 Simple Shear Displacement Fields 111
4B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 113
4B.5.3 Pure Shear Displacement Fields 115
4B.5.4 General Shear Displacement Fields 117
4B.6 Idealized, Three-Dimensional Displacement Fields 117
4B.6.1 Three-Dimensional Simple Shear Displacement Fields 119
4b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 121
4B.6.3 Pure Shearing Displacement Fields 121
4B.6.4 Constrictional Displacement Fields 122
4B.6.5 Flattening Displacement Fields 123
4B.6.6 Three-Dimensional General Shearing Displacement Fields 124
4B.7 Summary 124
Appendix 4-I: Vectors 124
4-I.1 Simple Mathematical Operations with Vectors 124
4-I.2 Vector Magnitudes 126
4-I.3 Properties of Vector Quantities 126
4-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 127
4-I.5 Vector Products 129
Appendix 4-II: Matrix Operations 130
4-II.1 Defining Matrices 130
4-II.2 Matrix Addition and Subtraction 130
4-II.3 Matrix Multiplication 131
4-II.3.1 Multiplying Two "2 × 2" Matrices 132
4-II.3.2 Multiplying Two "3 × 3" Matrices 132
4-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 133
4-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 133
4-II.3.5 Scalar Multiplication 134
4-II.4 Transpose of a Matrix 134
4-II.5 Determinant of a Square Matrix 135
4-II.6 Inverse of a Square Matrix 135
4-II.7 Rotation Matrices 136
References 137
5 Strain 138
5.1 Overview 138
5.2 Chapter Organization 139
5A Strain: Conceptual Foundation 139
5A.1 Specifying Strain in Deformed Rocks 139
5A.2 One-dimensional Manifestations of Strain 141
5A.2.1 Basic Ideas 141
5A.2.2 Geological Example 142
5A.3 Two-dimensional Manifestations of Strain 143
5A.3.1 Longitudinal Strains in Different Directions 143
5A.3.2 Shear Strain 147
5A.4 Relating Strain to Displacements 151
5A.5 Homogeneous and Inhomogeneous Strain 153
5A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 154
5A.6.1 Finite Strain Ellipse 154
5A.6.2 Finite Strain Ellipsoid 159
5A.7 States of Strain and Strain Paths 163
5A.7.1 States of Strain 163
5A.7.2 Strain Paths and Dated Strain Paths 163
5A.7.3 Coaxial Versus Non-Coaxial Strain Paths 164
5A.8 Instantaneous Strains and Strain Rates 166
5A.9 Infinitesimal Strains 166
5A.10 Summary 167
5A.11 Practical Methods for Measuring Strain 167
5A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 167
5A.11.2 Types of Methods for Measuring Strain in Two Dimensions 168
5A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 169
5B Strain: Comprehensive Treatment 176
5B.4 Relating Strain to Displacements 176
5B.4.1 Longitudinal Strains and Displacement Gradients 177
5B.4.2 Longitudinal Strains and Position Gradients 179
5B.4.3 Relating Displacement Gradients and Position Gradients 179
5B.4.4 Longitudinal Strain in Continuous Deformation 179
5B.4.5 Consequences of Longitudinal Strains 181
5B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 182
5B.4.7 Position Gradients and Longitudinal Strains in Different Directions 184
5B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 185
5B.4.9 Area Ratios in Two-Dimensional Deformation 186
5B.4.10 Discontinuous Deformation in Two Dimensions 186
5B.4.11 Displacement Gradients and Shear Strains 187
5B.4.12 Shear Strains and Position Gradients 188
5B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 188
5B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 195
5B.5 Homogeneous and Inhomogeneous Deformation 197
5B.5.1 Homogeneous Deformation 197
5B.5.2 Inhomogeneous Deformation 198
5B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 200
5B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 200
5B.6.2 Working with Strain Markers 200
5B.6.3 Finite Strain Ellipsoid 205
5B.7 States of Strain and Strain Paths 205
5B.7.1 States of Strain 205
5B.7.2 Strain Paths 206
5B.7.3 Velocity Gradient Tensor and Decomposition 207
5B.8 Vorticity 210
5B.8.1 Vorticity Vector 211
5B.8.2 Kinematic Vorticity Number 213
5B.9 Summary 213
Appendix 5-I 214
References 216
6 Stress 217
6.1 Overview 217
6A Stress: Conceptual Foundation 218
6A.1 Forces, Tractions, and Stress 220
6A.1.1 Accelerations and the Forces that Act on Objects 220
6A.1.2 Forces Transmitted Through Objects 221
6A.1.3 Traction - A Measure of "Force Intensity" within Objects 221
6A.1.4 Stress 223
6A.2 Characteristics of Stress in Two Dimensions 225
6A.2.1 Normal and Tangential Stress Components 225
6A.2.2 Stresses on Planes with Different Orientations 227
6A.2.3 Principal Stresses and Differential Stress 227
6A.2.4 The Fundamental Stress Equations 231
6A.3 State of Stress in Two Dimensions 233
6A.3.1 The Stress Matrix 233
6A.3.2 The Stress Ellipse 234
6A.3.3 The Mohr circle 235
6A.3.4 Hydrostatic vs. Non-hydrostatic Stress 246
6A.3.5 Homogeneous vs. Inhomogeneous Stress 248
6A.4 Stress in Three Dimensions 248
6A.4.1 The Stress Ellipsoid 251
6A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 251
6A.5 Pore-fluid Pressure and Effective Stress 253
6A.6 Three-dimensional States of Stress 254
6A.7 The State of Stress in Earth 255
6A.8 Change of Stress: Paleostress, Path, and History 256
6A.9 Comparison of Displacements, Strain and Stress 257
6A.10 Summary 259
6A.11 Practical Methods for Measuring Stress 261
6A.11.1 In situ Stress Measurements 261
6A.11.2 Paleostress 268
6B Stress: Comprehensive Treatment 272
6B.1 Force, Traction, and Stress Vectors 272
6B.1.1 Accelerations and Forces 272
6B.1.2 Traction or Stress Vectors 273
6b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 274
6B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 277
6b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 279
6B.1.6 An Alternative Way to Define Traction or Stress Vectors 281
6B.1.7 Determining Stress Principal Directions and Magnitudes 282
6B.1.8 Stress Invariants 284
6B.1.9 Spatial Variation in Stress 285
Appendix 6-I 289
References 291
7 Rheology 292
7.1 Overview 292
7A Rheology: Conceptual Foundation 293
7A.1 Moving Beyond Equilibrium 293
7A.1.1...
Website xix
1 A Framework for Structural Geology 1
1.1 Introduction 1
1.1.1 Deformation 1
1.1.2 Empirical vs. Theoretical Approaches 1
1.1.3 Continuum Mechanics and its Applicability to Structural Geology 6
1.1.4 How to use this Book 6
References 8
2 Structures Produced by Deformation 10
2.1 Geological Structures 10
2.1.1 Structural Fabrics 10
2.1.2 Folds and Boudinage 12
2.1.3 Fractures and Stylolites 15
2.1.4 Faults and Fault Zones 17
2.1.5 Shear Zones 22
2.2 Additional Considerations 25
3 Microstructures 26
3.1 Introduction 26
3.1.1 Overview 26
3.1.2 Framework 27
3.1.3 Imaging of Microstructures 27
3.2 Fractures 28
3.3 Fault Rocks 30
3.4 Overgrowths, Pressure Shadows and Fringes, and Veins 33
3.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 37
3.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 38
3.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 40
3.8 Deformation Twins 43
3.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 43
3.10 Porphyroblasts 47
3.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 49
3.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 49
3.12.1 Asymmetric Pressure Shadows and Fringes 53
3.12.2 Foliation Obliquity and Curvature 55
3.12.3 SC, SC', and SCC' Fabrics 55
3.12.4 Porphyroclast Systems 56
3.12.5 Precautions with Shear Sense Determination 59
3.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60
References 65
4 Displacements 66
4.1 Overview 66
4.2 Chapter Organization 66
4A Displacements: Conceptual Foundation 67
4A.1 Specifying Displacements or Individual Particles 67
4A.1.1 Basic Ideas 67
4A.1.2 Geological Example 69
4A.2 Particle Paths and Velocities 70
4A.2.1 Particle Paths 70
4A.2.2 Velocities 71
4A.3 Displacements of Collections of Particles - Displacement Fields 74
4A.3.1 Displacement Fields 74
4A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 76
4A.3.3 Classes of Displacement Fields 77
4A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 79
4A.5 Idealized, Two-Dimensional Displacement Fields 85
4A.5.1 Simple Shear 87
4A.5.2 Pure Shear 88
4A.6 Idealized, Three-Dimensional Displacement Fields 89
4A.7 Summary 90
4B Displacements: Comprehensive Treatment 90
4B.1 Specifying Displacements for Individual Particles 90
4B.1.1 Defining Vector Quantities 90
4B.1.2 Types of Vectors 92
4B.1.3 Relating Position and Displacement Vectors 94
4B.1.4 Characterizing Vector Quantities 95
4B.2 Particle Paths and Velocities 97
4B.2.1 Incremental Displacements for Particles 97
4B.2.2 Particle Paths and Movement Histories 98
4b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 99
4B.3 Displacements of Collections of Particles - Displacement Fields 101
4B.3.1 Concept of a Displacement Field 101
4B.3.2 Field Quantities 103
4b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 103
4B.3.4 Idealized Versus True Gradients of the Displacement Field 104
4B.4 The Displacement Gradient Tensor - Relating Position and Displacement Vectors 106
4b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 107
4B.4.2 Translation Displacement Fields 107
4B.4.3 Rigid Rotation Displacement Fields 107
4B.4.4 Pure Strain Displacement Fields 109
4B.4.5 Total Displacement Fields 110
4b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 110
4B.5 Idealized, Two- dimensional Displacement Fields 111
4B.5.1 Simple Shear Displacement Fields 111
4B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 113
4B.5.3 Pure Shear Displacement Fields 115
4B.5.4 General Shear Displacement Fields 117
4B.6 Idealized, Three-Dimensional Displacement Fields 117
4B.6.1 Three-Dimensional Simple Shear Displacement Fields 119
4b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 121
4B.6.3 Pure Shearing Displacement Fields 121
4B.6.4 Constrictional Displacement Fields 122
4B.6.5 Flattening Displacement Fields 123
4B.6.6 Three-Dimensional General Shearing Displacement Fields 124
4B.7 Summary 124
Appendix 4-I: Vectors 124
4-I.1 Simple Mathematical Operations with Vectors 124
4-I.2 Vector Magnitudes 126
4-I.3 Properties of Vector Quantities 126
4-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 127
4-I.5 Vector Products 129
Appendix 4-II: Matrix Operations 130
4-II.1 Defining Matrices 130
4-II.2 Matrix Addition and Subtraction 130
4-II.3 Matrix Multiplication 131
4-II.3.1 Multiplying Two "2 × 2" Matrices 132
4-II.3.2 Multiplying Two "3 × 3" Matrices 132
4-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 133
4-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 133
4-II.3.5 Scalar Multiplication 134
4-II.4 Transpose of a Matrix 134
4-II.5 Determinant of a Square Matrix 135
4-II.6 Inverse of a Square Matrix 135
4-II.7 Rotation Matrices 136
References 137
5 Strain 138
5.1 Overview 138
5.2 Chapter Organization 139
5A Strain: Conceptual Foundation 139
5A.1 Specifying Strain in Deformed Rocks 139
5A.2 One-dimensional Manifestations of Strain 141
5A.2.1 Basic Ideas 141
5A.2.2 Geological Example 142
5A.3 Two-dimensional Manifestations of Strain 143
5A.3.1 Longitudinal Strains in Different Directions 143
5A.3.2 Shear Strain 147
5A.4 Relating Strain to Displacements 151
5A.5 Homogeneous and Inhomogeneous Strain 153
5A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 154
5A.6.1 Finite Strain Ellipse 154
5A.6.2 Finite Strain Ellipsoid 159
5A.7 States of Strain and Strain Paths 163
5A.7.1 States of Strain 163
5A.7.2 Strain Paths and Dated Strain Paths 163
5A.7.3 Coaxial Versus Non-Coaxial Strain Paths 164
5A.8 Instantaneous Strains and Strain Rates 166
5A.9 Infinitesimal Strains 166
5A.10 Summary 167
5A.11 Practical Methods for Measuring Strain 167
5A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 167
5A.11.2 Types of Methods for Measuring Strain in Two Dimensions 168
5A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 169
5B Strain: Comprehensive Treatment 176
5B.4 Relating Strain to Displacements 176
5B.4.1 Longitudinal Strains and Displacement Gradients 177
5B.4.2 Longitudinal Strains and Position Gradients 179
5B.4.3 Relating Displacement Gradients and Position Gradients 179
5B.4.4 Longitudinal Strain in Continuous Deformation 179
5B.4.5 Consequences of Longitudinal Strains 181
5B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 182
5B.4.7 Position Gradients and Longitudinal Strains in Different Directions 184
5B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 185
5B.4.9 Area Ratios in Two-Dimensional Deformation 186
5B.4.10 Discontinuous Deformation in Two Dimensions 186
5B.4.11 Displacement Gradients and Shear Strains 187
5B.4.12 Shear Strains and Position Gradients 188
5B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 188
5B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 195
5B.5 Homogeneous and Inhomogeneous Deformation 197
5B.5.1 Homogeneous Deformation 197
5B.5.2 Inhomogeneous Deformation 198
5B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 200
5B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 200
5B.6.2 Working with Strain Markers 200
5B.6.3 Finite Strain Ellipsoid 205
5B.7 States of Strain and Strain Paths 205
5B.7.1 States of Strain 205
5B.7.2 Strain Paths 206
5B.7.3 Velocity Gradient Tensor and Decomposition 207
5B.8 Vorticity 210
5B.8.1 Vorticity Vector 211
5B.8.2 Kinematic Vorticity Number 213
5B.9 Summary 213
Appendix 5-I 214
References 216
6 Stress 217
6.1 Overview 217
6A Stress: Conceptual Foundation 218
6A.1 Forces, Tractions, and Stress 220
6A.1.1 Accelerations and the Forces that Act on Objects 220
6A.1.2 Forces Transmitted Through Objects 221
6A.1.3 Traction - A Measure of "Force Intensity" within Objects 221
6A.1.4 Stress 223
6A.2 Characteristics of Stress in Two Dimensions 225
6A.2.1 Normal and Tangential Stress Components 225
6A.2.2 Stresses on Planes with Different Orientations 227
6A.2.3 Principal Stresses and Differential Stress 227
6A.2.4 The Fundamental Stress Equations 231
6A.3 State of Stress in Two Dimensions 233
6A.3.1 The Stress Matrix 233
6A.3.2 The Stress Ellipse 234
6A.3.3 The Mohr circle 235
6A.3.4 Hydrostatic vs. Non-hydrostatic Stress 246
6A.3.5 Homogeneous vs. Inhomogeneous Stress 248
6A.4 Stress in Three Dimensions 248
6A.4.1 The Stress Ellipsoid 251
6A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 251
6A.5 Pore-fluid Pressure and Effective Stress 253
6A.6 Three-dimensional States of Stress 254
6A.7 The State of Stress in Earth 255
6A.8 Change of Stress: Paleostress, Path, and History 256
6A.9 Comparison of Displacements, Strain and Stress 257
6A.10 Summary 259
6A.11 Practical Methods for Measuring Stress 261
6A.11.1 In situ Stress Measurements 261
6A.11.2 Paleostress 268
6B Stress: Comprehensive Treatment 272
6B.1 Force, Traction, and Stress Vectors 272
6B.1.1 Accelerations and Forces 272
6B.1.2 Traction or Stress Vectors 273
6b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 274
6B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 277
6b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 279
6B.1.6 An Alternative Way to Define Traction or Stress Vectors 281
6B.1.7 Determining Stress Principal Directions and Magnitudes 282
6B.1.8 Stress Invariants 284
6B.1.9 Spatial Variation in Stress 285
Appendix 6-I 289
References 291
7 Rheology 292
7.1 Overview 292
7A Rheology: Conceptual Foundation 293
7A.1 Moving Beyond Equilibrium 293
7A.1.1...
Details
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Geologie |
| Genre: | Geowissenschaften |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 608 |
| Inhalt: | 608 S. |
| ISBN-13: | 9781405106849 |
| ISBN-10: | 1405106840 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Tikoff, Basil
Wojtal, Steven Blenkinsop, Tom |
| Hersteller: | John Wiley & Sons Inc |
| Maße: | 233 x 186 x 31 mm |
| Von/Mit: | Basil Tikoff (u. a.) |
| Erscheinungsdatum: | 21.07.2022 |
| Gewicht: | 1,214 kg |
Über den Autor
Steven Wojtal is Professor of Geoscience at Oberlin College in Oberlin, Ohio, United States.
Tom Blenkinsop is Professor in Earth Science at Cardiff University, United Kingdom.
Basil Tikoff is Professor of Geoscience at the University of Wisconsin-Madison, United States.
Inhaltsverzeichnis
Acknowledgements xvii
Website xix
1 A Framework for Structural Geology 1
1.1 Introduction 1
1.1.1 Deformation 1
1.1.2 Empirical vs. Theoretical Approaches 1
1.1.3 Continuum Mechanics and its Applicability to Structural Geology 6
1.1.4 How to use this Book 6
References 8
2 Structures Produced by Deformation 10
2.1 Geological Structures 10
2.1.1 Structural Fabrics 10
2.1.2 Folds and Boudinage 12
2.1.3 Fractures and Stylolites 15
2.1.4 Faults and Fault Zones 17
2.1.5 Shear Zones 22
2.2 Additional Considerations 25
3 Microstructures 26
3.1 Introduction 26
3.1.1 Overview 26
3.1.2 Framework 27
3.1.3 Imaging of Microstructures 27
3.2 Fractures 28
3.3 Fault Rocks 30
3.4 Overgrowths, Pressure Shadows and Fringes, and Veins 33
3.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 37
3.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 38
3.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 40
3.8 Deformation Twins 43
3.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 43
3.10 Porphyroblasts 47
3.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 49
3.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 49
3.12.1 Asymmetric Pressure Shadows and Fringes 53
3.12.2 Foliation Obliquity and Curvature 55
3.12.3 SC, SC', and SCC' Fabrics 55
3.12.4 Porphyroclast Systems 56
3.12.5 Precautions with Shear Sense Determination 59
3.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60
References 65
4 Displacements 66
4.1 Overview 66
4.2 Chapter Organization 66
4A Displacements: Conceptual Foundation 67
4A.1 Specifying Displacements or Individual Particles 67
4A.1.1 Basic Ideas 67
4A.1.2 Geological Example 69
4A.2 Particle Paths and Velocities 70
4A.2.1 Particle Paths 70
4A.2.2 Velocities 71
4A.3 Displacements of Collections of Particles - Displacement Fields 74
4A.3.1 Displacement Fields 74
4A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 76
4A.3.3 Classes of Displacement Fields 77
4A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 79
4A.5 Idealized, Two-Dimensional Displacement Fields 85
4A.5.1 Simple Shear 87
4A.5.2 Pure Shear 88
4A.6 Idealized, Three-Dimensional Displacement Fields 89
4A.7 Summary 90
4B Displacements: Comprehensive Treatment 90
4B.1 Specifying Displacements for Individual Particles 90
4B.1.1 Defining Vector Quantities 90
4B.1.2 Types of Vectors 92
4B.1.3 Relating Position and Displacement Vectors 94
4B.1.4 Characterizing Vector Quantities 95
4B.2 Particle Paths and Velocities 97
4B.2.1 Incremental Displacements for Particles 97
4B.2.2 Particle Paths and Movement Histories 98
4b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 99
4B.3 Displacements of Collections of Particles - Displacement Fields 101
4B.3.1 Concept of a Displacement Field 101
4B.3.2 Field Quantities 103
4b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 103
4B.3.4 Idealized Versus True Gradients of the Displacement Field 104
4B.4 The Displacement Gradient Tensor - Relating Position and Displacement Vectors 106
4b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 107
4B.4.2 Translation Displacement Fields 107
4B.4.3 Rigid Rotation Displacement Fields 107
4B.4.4 Pure Strain Displacement Fields 109
4B.4.5 Total Displacement Fields 110
4b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 110
4B.5 Idealized, Two- dimensional Displacement Fields 111
4B.5.1 Simple Shear Displacement Fields 111
4B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 113
4B.5.3 Pure Shear Displacement Fields 115
4B.5.4 General Shear Displacement Fields 117
4B.6 Idealized, Three-Dimensional Displacement Fields 117
4B.6.1 Three-Dimensional Simple Shear Displacement Fields 119
4b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 121
4B.6.3 Pure Shearing Displacement Fields 121
4B.6.4 Constrictional Displacement Fields 122
4B.6.5 Flattening Displacement Fields 123
4B.6.6 Three-Dimensional General Shearing Displacement Fields 124
4B.7 Summary 124
Appendix 4-I: Vectors 124
4-I.1 Simple Mathematical Operations with Vectors 124
4-I.2 Vector Magnitudes 126
4-I.3 Properties of Vector Quantities 126
4-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 127
4-I.5 Vector Products 129
Appendix 4-II: Matrix Operations 130
4-II.1 Defining Matrices 130
4-II.2 Matrix Addition and Subtraction 130
4-II.3 Matrix Multiplication 131
4-II.3.1 Multiplying Two "2 × 2" Matrices 132
4-II.3.2 Multiplying Two "3 × 3" Matrices 132
4-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 133
4-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 133
4-II.3.5 Scalar Multiplication 134
4-II.4 Transpose of a Matrix 134
4-II.5 Determinant of a Square Matrix 135
4-II.6 Inverse of a Square Matrix 135
4-II.7 Rotation Matrices 136
References 137
5 Strain 138
5.1 Overview 138
5.2 Chapter Organization 139
5A Strain: Conceptual Foundation 139
5A.1 Specifying Strain in Deformed Rocks 139
5A.2 One-dimensional Manifestations of Strain 141
5A.2.1 Basic Ideas 141
5A.2.2 Geological Example 142
5A.3 Two-dimensional Manifestations of Strain 143
5A.3.1 Longitudinal Strains in Different Directions 143
5A.3.2 Shear Strain 147
5A.4 Relating Strain to Displacements 151
5A.5 Homogeneous and Inhomogeneous Strain 153
5A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 154
5A.6.1 Finite Strain Ellipse 154
5A.6.2 Finite Strain Ellipsoid 159
5A.7 States of Strain and Strain Paths 163
5A.7.1 States of Strain 163
5A.7.2 Strain Paths and Dated Strain Paths 163
5A.7.3 Coaxial Versus Non-Coaxial Strain Paths 164
5A.8 Instantaneous Strains and Strain Rates 166
5A.9 Infinitesimal Strains 166
5A.10 Summary 167
5A.11 Practical Methods for Measuring Strain 167
5A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 167
5A.11.2 Types of Methods for Measuring Strain in Two Dimensions 168
5A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 169
5B Strain: Comprehensive Treatment 176
5B.4 Relating Strain to Displacements 176
5B.4.1 Longitudinal Strains and Displacement Gradients 177
5B.4.2 Longitudinal Strains and Position Gradients 179
5B.4.3 Relating Displacement Gradients and Position Gradients 179
5B.4.4 Longitudinal Strain in Continuous Deformation 179
5B.4.5 Consequences of Longitudinal Strains 181
5B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 182
5B.4.7 Position Gradients and Longitudinal Strains in Different Directions 184
5B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 185
5B.4.9 Area Ratios in Two-Dimensional Deformation 186
5B.4.10 Discontinuous Deformation in Two Dimensions 186
5B.4.11 Displacement Gradients and Shear Strains 187
5B.4.12 Shear Strains and Position Gradients 188
5B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 188
5B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 195
5B.5 Homogeneous and Inhomogeneous Deformation 197
5B.5.1 Homogeneous Deformation 197
5B.5.2 Inhomogeneous Deformation 198
5B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 200
5B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 200
5B.6.2 Working with Strain Markers 200
5B.6.3 Finite Strain Ellipsoid 205
5B.7 States of Strain and Strain Paths 205
5B.7.1 States of Strain 205
5B.7.2 Strain Paths 206
5B.7.3 Velocity Gradient Tensor and Decomposition 207
5B.8 Vorticity 210
5B.8.1 Vorticity Vector 211
5B.8.2 Kinematic Vorticity Number 213
5B.9 Summary 213
Appendix 5-I 214
References 216
6 Stress 217
6.1 Overview 217
6A Stress: Conceptual Foundation 218
6A.1 Forces, Tractions, and Stress 220
6A.1.1 Accelerations and the Forces that Act on Objects 220
6A.1.2 Forces Transmitted Through Objects 221
6A.1.3 Traction - A Measure of "Force Intensity" within Objects 221
6A.1.4 Stress 223
6A.2 Characteristics of Stress in Two Dimensions 225
6A.2.1 Normal and Tangential Stress Components 225
6A.2.2 Stresses on Planes with Different Orientations 227
6A.2.3 Principal Stresses and Differential Stress 227
6A.2.4 The Fundamental Stress Equations 231
6A.3 State of Stress in Two Dimensions 233
6A.3.1 The Stress Matrix 233
6A.3.2 The Stress Ellipse 234
6A.3.3 The Mohr circle 235
6A.3.4 Hydrostatic vs. Non-hydrostatic Stress 246
6A.3.5 Homogeneous vs. Inhomogeneous Stress 248
6A.4 Stress in Three Dimensions 248
6A.4.1 The Stress Ellipsoid 251
6A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 251
6A.5 Pore-fluid Pressure and Effective Stress 253
6A.6 Three-dimensional States of Stress 254
6A.7 The State of Stress in Earth 255
6A.8 Change of Stress: Paleostress, Path, and History 256
6A.9 Comparison of Displacements, Strain and Stress 257
6A.10 Summary 259
6A.11 Practical Methods for Measuring Stress 261
6A.11.1 In situ Stress Measurements 261
6A.11.2 Paleostress 268
6B Stress: Comprehensive Treatment 272
6B.1 Force, Traction, and Stress Vectors 272
6B.1.1 Accelerations and Forces 272
6B.1.2 Traction or Stress Vectors 273
6b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 274
6B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 277
6b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 279
6B.1.6 An Alternative Way to Define Traction or Stress Vectors 281
6B.1.7 Determining Stress Principal Directions and Magnitudes 282
6B.1.8 Stress Invariants 284
6B.1.9 Spatial Variation in Stress 285
Appendix 6-I 289
References 291
7 Rheology 292
7.1 Overview 292
7A Rheology: Conceptual Foundation 293
7A.1 Moving Beyond Equilibrium 293
7A.1.1...
Website xix
1 A Framework for Structural Geology 1
1.1 Introduction 1
1.1.1 Deformation 1
1.1.2 Empirical vs. Theoretical Approaches 1
1.1.3 Continuum Mechanics and its Applicability to Structural Geology 6
1.1.4 How to use this Book 6
References 8
2 Structures Produced by Deformation 10
2.1 Geological Structures 10
2.1.1 Structural Fabrics 10
2.1.2 Folds and Boudinage 12
2.1.3 Fractures and Stylolites 15
2.1.4 Faults and Fault Zones 17
2.1.5 Shear Zones 22
2.2 Additional Considerations 25
3 Microstructures 26
3.1 Introduction 26
3.1.1 Overview 26
3.1.2 Framework 27
3.1.3 Imaging of Microstructures 27
3.2 Fractures 28
3.3 Fault Rocks 30
3.4 Overgrowths, Pressure Shadows and Fringes, and Veins 33
3.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 37
3.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 38
3.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 40
3.8 Deformation Twins 43
3.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 43
3.10 Porphyroblasts 47
3.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 49
3.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 49
3.12.1 Asymmetric Pressure Shadows and Fringes 53
3.12.2 Foliation Obliquity and Curvature 55
3.12.3 SC, SC', and SCC' Fabrics 55
3.12.4 Porphyroclast Systems 56
3.12.5 Precautions with Shear Sense Determination 59
3.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60
References 65
4 Displacements 66
4.1 Overview 66
4.2 Chapter Organization 66
4A Displacements: Conceptual Foundation 67
4A.1 Specifying Displacements or Individual Particles 67
4A.1.1 Basic Ideas 67
4A.1.2 Geological Example 69
4A.2 Particle Paths and Velocities 70
4A.2.1 Particle Paths 70
4A.2.2 Velocities 71
4A.3 Displacements of Collections of Particles - Displacement Fields 74
4A.3.1 Displacement Fields 74
4A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 76
4A.3.3 Classes of Displacement Fields 77
4A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 79
4A.5 Idealized, Two-Dimensional Displacement Fields 85
4A.5.1 Simple Shear 87
4A.5.2 Pure Shear 88
4A.6 Idealized, Three-Dimensional Displacement Fields 89
4A.7 Summary 90
4B Displacements: Comprehensive Treatment 90
4B.1 Specifying Displacements for Individual Particles 90
4B.1.1 Defining Vector Quantities 90
4B.1.2 Types of Vectors 92
4B.1.3 Relating Position and Displacement Vectors 94
4B.1.4 Characterizing Vector Quantities 95
4B.2 Particle Paths and Velocities 97
4B.2.1 Incremental Displacements for Particles 97
4B.2.2 Particle Paths and Movement Histories 98
4b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 99
4B.3 Displacements of Collections of Particles - Displacement Fields 101
4B.3.1 Concept of a Displacement Field 101
4B.3.2 Field Quantities 103
4b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 103
4B.3.4 Idealized Versus True Gradients of the Displacement Field 104
4B.4 The Displacement Gradient Tensor - Relating Position and Displacement Vectors 106
4b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 107
4B.4.2 Translation Displacement Fields 107
4B.4.3 Rigid Rotation Displacement Fields 107
4B.4.4 Pure Strain Displacement Fields 109
4B.4.5 Total Displacement Fields 110
4b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 110
4B.5 Idealized, Two- dimensional Displacement Fields 111
4B.5.1 Simple Shear Displacement Fields 111
4B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 113
4B.5.3 Pure Shear Displacement Fields 115
4B.5.4 General Shear Displacement Fields 117
4B.6 Idealized, Three-Dimensional Displacement Fields 117
4B.6.1 Three-Dimensional Simple Shear Displacement Fields 119
4b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 121
4B.6.3 Pure Shearing Displacement Fields 121
4B.6.4 Constrictional Displacement Fields 122
4B.6.5 Flattening Displacement Fields 123
4B.6.6 Three-Dimensional General Shearing Displacement Fields 124
4B.7 Summary 124
Appendix 4-I: Vectors 124
4-I.1 Simple Mathematical Operations with Vectors 124
4-I.2 Vector Magnitudes 126
4-I.3 Properties of Vector Quantities 126
4-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 127
4-I.5 Vector Products 129
Appendix 4-II: Matrix Operations 130
4-II.1 Defining Matrices 130
4-II.2 Matrix Addition and Subtraction 130
4-II.3 Matrix Multiplication 131
4-II.3.1 Multiplying Two "2 × 2" Matrices 132
4-II.3.2 Multiplying Two "3 × 3" Matrices 132
4-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 133
4-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 133
4-II.3.5 Scalar Multiplication 134
4-II.4 Transpose of a Matrix 134
4-II.5 Determinant of a Square Matrix 135
4-II.6 Inverse of a Square Matrix 135
4-II.7 Rotation Matrices 136
References 137
5 Strain 138
5.1 Overview 138
5.2 Chapter Organization 139
5A Strain: Conceptual Foundation 139
5A.1 Specifying Strain in Deformed Rocks 139
5A.2 One-dimensional Manifestations of Strain 141
5A.2.1 Basic Ideas 141
5A.2.2 Geological Example 142
5A.3 Two-dimensional Manifestations of Strain 143
5A.3.1 Longitudinal Strains in Different Directions 143
5A.3.2 Shear Strain 147
5A.4 Relating Strain to Displacements 151
5A.5 Homogeneous and Inhomogeneous Strain 153
5A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 154
5A.6.1 Finite Strain Ellipse 154
5A.6.2 Finite Strain Ellipsoid 159
5A.7 States of Strain and Strain Paths 163
5A.7.1 States of Strain 163
5A.7.2 Strain Paths and Dated Strain Paths 163
5A.7.3 Coaxial Versus Non-Coaxial Strain Paths 164
5A.8 Instantaneous Strains and Strain Rates 166
5A.9 Infinitesimal Strains 166
5A.10 Summary 167
5A.11 Practical Methods for Measuring Strain 167
5A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 167
5A.11.2 Types of Methods for Measuring Strain in Two Dimensions 168
5A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 169
5B Strain: Comprehensive Treatment 176
5B.4 Relating Strain to Displacements 176
5B.4.1 Longitudinal Strains and Displacement Gradients 177
5B.4.2 Longitudinal Strains and Position Gradients 179
5B.4.3 Relating Displacement Gradients and Position Gradients 179
5B.4.4 Longitudinal Strain in Continuous Deformation 179
5B.4.5 Consequences of Longitudinal Strains 181
5B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 182
5B.4.7 Position Gradients and Longitudinal Strains in Different Directions 184
5B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 185
5B.4.9 Area Ratios in Two-Dimensional Deformation 186
5B.4.10 Discontinuous Deformation in Two Dimensions 186
5B.4.11 Displacement Gradients and Shear Strains 187
5B.4.12 Shear Strains and Position Gradients 188
5B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 188
5B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 195
5B.5 Homogeneous and Inhomogeneous Deformation 197
5B.5.1 Homogeneous Deformation 197
5B.5.2 Inhomogeneous Deformation 198
5B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 200
5B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 200
5B.6.2 Working with Strain Markers 200
5B.6.3 Finite Strain Ellipsoid 205
5B.7 States of Strain and Strain Paths 205
5B.7.1 States of Strain 205
5B.7.2 Strain Paths 206
5B.7.3 Velocity Gradient Tensor and Decomposition 207
5B.8 Vorticity 210
5B.8.1 Vorticity Vector 211
5B.8.2 Kinematic Vorticity Number 213
5B.9 Summary 213
Appendix 5-I 214
References 216
6 Stress 217
6.1 Overview 217
6A Stress: Conceptual Foundation 218
6A.1 Forces, Tractions, and Stress 220
6A.1.1 Accelerations and the Forces that Act on Objects 220
6A.1.2 Forces Transmitted Through Objects 221
6A.1.3 Traction - A Measure of "Force Intensity" within Objects 221
6A.1.4 Stress 223
6A.2 Characteristics of Stress in Two Dimensions 225
6A.2.1 Normal and Tangential Stress Components 225
6A.2.2 Stresses on Planes with Different Orientations 227
6A.2.3 Principal Stresses and Differential Stress 227
6A.2.4 The Fundamental Stress Equations 231
6A.3 State of Stress in Two Dimensions 233
6A.3.1 The Stress Matrix 233
6A.3.2 The Stress Ellipse 234
6A.3.3 The Mohr circle 235
6A.3.4 Hydrostatic vs. Non-hydrostatic Stress 246
6A.3.5 Homogeneous vs. Inhomogeneous Stress 248
6A.4 Stress in Three Dimensions 248
6A.4.1 The Stress Ellipsoid 251
6A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 251
6A.5 Pore-fluid Pressure and Effective Stress 253
6A.6 Three-dimensional States of Stress 254
6A.7 The State of Stress in Earth 255
6A.8 Change of Stress: Paleostress, Path, and History 256
6A.9 Comparison of Displacements, Strain and Stress 257
6A.10 Summary 259
6A.11 Practical Methods for Measuring Stress 261
6A.11.1 In situ Stress Measurements 261
6A.11.2 Paleostress 268
6B Stress: Comprehensive Treatment 272
6B.1 Force, Traction, and Stress Vectors 272
6B.1.1 Accelerations and Forces 272
6B.1.2 Traction or Stress Vectors 273
6b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 274
6B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 277
6b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 279
6B.1.6 An Alternative Way to Define Traction or Stress Vectors 281
6B.1.7 Determining Stress Principal Directions and Magnitudes 282
6B.1.8 Stress Invariants 284
6B.1.9 Spatial Variation in Stress 285
Appendix 6-I 289
References 291
7 Rheology 292
7.1 Overview 292
7A Rheology: Conceptual Foundation 293
7A.1 Moving Beyond Equilibrium 293
7A.1.1...
Details
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Geologie |
| Genre: | Geowissenschaften |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 608 |
| Inhalt: | 608 S. |
| ISBN-13: | 9781405106849 |
| ISBN-10: | 1405106840 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Tikoff, Basil
Wojtal, Steven Blenkinsop, Tom |
| Hersteller: | John Wiley & Sons Inc |
| Maße: | 233 x 186 x 31 mm |
| Von/Mit: | Basil Tikoff (u. a.) |
| Erscheinungsdatum: | 21.07.2022 |
| Gewicht: | 1,214 kg |
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