Analytic methods in geomechanics. (2012)

• Record Type: Book
• Further Information: Note: Kam-tim Chau.
• Other Names: Chau, Kam-Tim, 1960-
• Contents: Elementary Tensor Analysis; Introduction; General Tensors, Cartesian Tensors, and Tensor Rank; A Brief Review of Vector Analysis; Dyadic Form of Second Order Tensors; Derivatives of Tensors; Divergence and Stokes Theorems; Some Formulae in Cylindrical Coordinates; Some Formulae in Spherical Coordinates; Summary and Further Reading; Problems; ; Elasticity and Its Applications ; Introduction; Basic Concepts for Stress Tensor; Piola–Kirchhoff Stresses; Coordinate Transformation of Stress; Basic Concepts for Strain Tensor; Rate of Deformation; Compatibility Equations; Hill’s Work-conjugate Stress Measures; Constitutive Relation; Isotropic Solids; Transversely Isotropic Solids; Equations of Motion and Equilibrium; Compatibility Equation in Terms of Stress Tensor; Strain Energy Density; Complementary Energy; Hyperelasticity and Hypoelasticity; Plane Stress, Plane Strain and the Airy Stress Function; Stress Concentration at a Circular Hole; Force Acting at the Apex of a Wedge; Uniform Vertical Loading on Part of the Surface; Solution for Indirect Tensile Test (Brazilian Test); Jaeger’s Modified Brazilian Test; Edge Dislocation; Dislocation Pile-up and Crack; Screw Dislocation and Faulting; Mura Formula for Curved Dislocation; Summary and Further Reading; Problems; ; Complex Variable Methods for 2-D Elasticity ; Introduction; Coordinate Transformation in Complex Variable Theory; Homogeneous Stresses in Terms Analytic Functions; A Borehole Subject to Internal Pressure; Kirsch Solution by Complex Variable Method; Definiteness and Uniqueness of the Analytic Function; Boundary Conditions for the Analytic Functions; Single-valued Condition for Multi-connected Bodies; Multi-connected Body of Infinite Extend; General Transformation of Quantities; Elastic Body with Holes; Stress Concentration at a Square Hole; Mapping Functions for Other Holes; Summary and Further Reading; Problems ; Three-Dimensional Solutions in Elasticity ; Introduction; Displacement Formulation; Stress Formulations; Some 3-D Solutions in Geomechanics; Harmonic Functions and Indirect Method; Harmonic Functions in Spherical Coordinates; Harmonic Functions in Cylindrical Coordinates; Biharmonic Functions; Muki’s Formulation in Cylindrical Coordinates; Summary and Further Reading; Problems ; Plasticity and Its Applications ; Introduction; Flow Theory and Deformation Theory; Yield Function and Plastic Potential; Elasto-plastic Constitutive Model; Rudnicki–Rice (1975) Model; Drucker’s Postulate, PMPR, and Il’iushin’s Postulate; Yield Vertex; Mohr–Coulomb Model; Lode Angle or Parameter; Yield Criteria on the π-Plane; Other Soil Yield Models; Cap Models; Physical Meaning of Cam-Clay Model; Modified Cam-Clay; A Cam-Clay Model for Finite Strain; Plasticity by Internal Variables; Viscoplasticity; Summary and Further Reading; Problems; ; Fracture Mechanics and Its Applications ; Introduction; Stress Concentration at a Elliptical Hole; Stress Concentration at a Tensile Crack; Stress Field near a Shear Crack; The General Stress and Displacement Field for Mode I Cracks; The General Stress and Displacement Field for Mode II Cracks; The General Stress and Displacement Field for Mode III Cracks; The Energy Release Rate at Crack Tips; Fracture Toughness for Rocks; J -integral and the Energy Release Rate; Westergaard Stress Function and Superposition; Growth of Slip Surface in Slopes; Energy Release Rate for Earthquake; Wing Crack Model under Compressions; Bazant’s Size Effect Law via J -integral; Continuum Damage Mechanics; Solids Containing Microcracks; Rudnicki–Chau (1996) Multiaxial Microcrack Model; Summary and Further Reading; Problems; ; Viscoelasticty and Its Applications ; Introduction; Boltzmann’s Integral Form of Stress and Strain; Stieltjes Convolution Notation; Stress-Strain Relation in Differential Equation Form; Stress-strain Relation in Laplace Transform Space; Correspondence Principle; Creeping and Relaxation Tests; Calibration of the Viscoelastic Model; Viscoelastic Crack Models for Steam Injection; Summary and Further Reading; Problems; ; Linear Elastic Fluid-Infiltrated Solids and Poroelasticity ; Introduction; Biot’s Theory of Poroelasticity; Biot–Verruijt Displacement Function; McNamee–Gibson–Verruijt Displacement Function; Schiffman–Fungaroli–Verruijt Displacement Function; Schiffman–Fungaroli Displacement Function; Laplace–Hankel Transform Technique; Point Forces and Point Fluid Source in Half-space; Cleary’s Fundamental Solution of Point Forces in Full Space; Rudnicki’s Fundamental Solutions in Full Space; Thermoelasticity vs. Poroelasticity; Summary and Further Reading; Problems; ; Dynamics and Waves In Geomaterials; Introduction; Seismic Waves; Waves in Infinite Elastic Isotropic Solids; Helmholtz Theorem and Wave Speeds; Rayleigh Waves; Love Waves; Stoneley Waves; Elastic-plastic Waves; Waves in Viscoelastic Solids; Dynamic Fracture Mechanics; Vibrations and Soil Dynamics; Summary and Further Reading; Problems; ; Appendices; Appendix A: Nanson Formula; Appendix B: Laplace Transform; Appendix C: Legendre Transform and Work Increments; ; Selected Biographies; ; References; ; Author Index; ; Subject Index
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2012
• Extent: 1 online resource (457 pages), (177 illustrations)
• Subjects: 624.15136; Soil mechanics; Rock mechanics
• Languages: English
• ISBNs: 9781466555891; 1466555890
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.