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| Preface | |
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| Introduction | |
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| What this book is about | |
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| Definition of a continuum | |
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| Governing equations | |
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| Vectors and tensors | |
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| Solving the equations | |
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| The art of modeling | |
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| Review of elementary mechanics | |
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| Introduction | |
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| Newton's laws | |
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| Vectors, coordinates, and components | |
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| Position and velocity vectors | |
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| Cylindrical and spherical coordinates; left- and right-handed Cartesian axes | |
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| Vector statistics | |
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| Example of the use of coordinates | |
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| Numerical solution of the equations of motion | |
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| Work, energy, and power | |
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| Application to meteorite impact | |
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| Application to fluid drag and lift | |
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| Stream power | |
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| The equations of motion including drag | |
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| Rotation using the vector product | |
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| The vector product (cross-product) | |
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| Rotation of vectors about an axis | |
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| Moments and torque | |
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| Angular momentum and moment of intertia | |
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| Centrifugal and tidal forces | |
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| Coriolis forces | |
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| Review problems | |
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| Suggested reading | |
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| Dimensional analysis and the theory of models | |
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| Introduction | |
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| Dimensions and dimensional homogeneity | |
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| Dimensionless products and the pi theorem | |
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| Scale models | |
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| More on modeling | |
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| Uses of dimensional analysis | |
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| Review problems | |
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| Suggested reading | |
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| Stress | |
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| Introduction | |
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| Friction | |
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| Rock falls and avalanches | |
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| Strength | |
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| Experimental results for rock friction | |
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| Definition of stress | |
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| Notation and sign convention | |
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| Symmetry of stress components | |
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| Equilibrium of a small prism | |
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| The stress ellipsoid | |
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| The Mohr circle of stress | |
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| Failure: the Navier-Coulomb criterion | |
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| Friction and faulting in the earth's crust | |
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| Stress fields and trajectories | |
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| State of stress beneath a level ground surface | |
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| Sliding on slopes | |
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| Tensor components of stress | |
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| Why stress is a tensor | |
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| Review problems | |
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| Suggested reading | |
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| Pressure, buoyancy, and consolidation | |
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| Concept of pressure in a fluid | |
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| Pressure in a solid (geostatic pressure) | |
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| Buoyancy | |
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| Is buoyancy a surface or a body force? | |
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| Isostasy | |
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| Rise and intrusion of magma in the crust | |
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| Forces on settling grains | |
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| Buoyancy in debris flows | |
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| Effective and neutral stress | |
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| Consolidation | |
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| Geopressured zones | |
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| Effect of neutral stresses on shear strength | |
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| Review problems | |
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| Suggested reading | |
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| Flow through porous media | |
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| Darcy's law | |
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| Hydraulic head | |
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| Hydraulic conductivity | |
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| Nature of permeability: relation to porosity, tortuosity, and specific surface area | |
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| Gradient and curl and their application to Darcy's law and other diffusion equations | |
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| Divergence and the conservation of mass | |
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| Flow to a well | |
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| Flow nets | |
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| Numerical solution of the Laplace equation | |
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| Dispersion by flow | |
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| Refraction of groundwater flow | |
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| The water table: flow near a topographic surface | |
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| Fluids of different densities: the freshwater lens | |
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| Effect of groundwater on sliding on an infinite slope | |
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| Theory of consolidation | |
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| Review problems | |
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| Suggested reading | |
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| Strain | |
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| Definitions | |
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| Measures of strain | |
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| Plane strain | |
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| Approach through Taylor's theorem | |
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| Generalization to three dimensions | |
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| Measurement of strain | |
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| Strain ellipse, Mohr circle of strain | |
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| Review problems | |
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| Suggested reading | |
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| Elasticity | |
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| Constitutive equations | |
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| Hooke's law | |
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| Generalized Hooke's law | |
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| Rigidity modulus | |
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| Bulk modulus | |
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| Lame's constants | |
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| Measurement of stress in rocks | |
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| Hydraulic fracturing of petroleum reservoir rocks | |
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| State of stress in the crust of the earth | |
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| Flexure of plates | |
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| Equations of motion: Navier's equation | |
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| Application to seismic waves | |
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| Review problems | |
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| Suggested reading | |
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| Viscous fluids | |
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| Constitutive equations | |
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| Equation of motion | |
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| Kinematics of flow and material acceleration | |
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| Navier-Stokes equation | |
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| Inviscid flows: the Euler and Bernoulli equations | |
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| Irrotational flows | |
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| Boundary layers | |
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| Steady, uniform viscous flow between parallel plates | |
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| Flow through a tube | |
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| Geological applications | |
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| Viscous flow past a sphere or cylinder | |
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| Review problems | |
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| Suggested reading | |
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| Flow of natural materials | |
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| Introduction | |
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| Mechanical models of natural materials | |
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| Flow of materials down slopes | |
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| Ice | |
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| Debris | |
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| Lava | |
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| Rock rheology and sedimentary basins | |
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| Review problems | |
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| Suggested reading | |
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| Turbulence | |
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| Description of turbulence | |
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| Origin of turbulence | |
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| Boundary layers and flow separation | |
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| Reynolds stresses | |
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| Diffusion | |
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| Velocity distribution in a turbulent boundary layer | |
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| Review problems | |
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| Suggested reading | |
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| Thermal convection | |
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| Introduction | |
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| Conduction | |
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| Thermal instability | |
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| Geometry of convection | |
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| Equations of motion | |
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| Lorenz equations | |
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| Numerical simulation of convection | |
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| Review problems | |
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| Suggested reading | |
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| List of symbols and vector notation | |
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| Properties of common fluids and rocks | |
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| Sets of linear equations | |
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| Partial derivatives and differential equations | |
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| References | |
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| Index of names | |
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| Subject index | |