Mechanics in the Earth and Environmental Sciences

By: Gerard V. Middleton, Peter R. Wilcock

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Paperback | 28 November 1994

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476 Pages

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23.5 x 19.1 x 2.4

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The study of the Earth and the environment requires an understanding of the physical processes within and at the surface of the Earth. This book will allow the student to develop a broad working knowledge of mechanics and its application to the earth and environmental sciences. The mathematics are introduced at a level that assumes only an understanding of first-year calculus. The concepts are then developed to allow an understanding of the basic physics for a wide range of natural processes. These are illustrated by examples from many real situations, such as the application of the theory of flow through porous media to the study of groundwater, the viscosity of fluids to the flow of lava, and the theory of stress to the study of faults. The breadth of topics will allow students and professionals to gain an insight into the workings of many aspects of the Earth's systems.

Industry Reviews

'This is a very good book, and goes a long way in presenting a much-needed dose of mechanics at a level appropriate for many students in the earth sciences. This book should be in any library, and the paperback version is a good buy for personal use.' James P. Evans, Journal of Structural Geology

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Preface	p. xiii
Introduction	p. 1
What this book is about	p. 1
Definition of a continuum	p. 5
Governing equations	p. 7
Vectors and tensors	p. 10
Solving the equations	p. 11
The art of modeling	p. 12
Review of elementary mechanics	p. 14
Introduction	p. 14
Newton's laws	p. 15
Vectors, coordinates, and components	p. 17
Position and velocity vectors	p. 20
Cylindrical and spherical coordinates; left- and right-handed Cartesian axes	p. 22
Vector statistics	p. 24
Example of the use of coordinates	p. 25
Numerical solution of the equations of motion	p. 29
Work, energy, and power	p. 31
Application to meteorite impact	p. 36
Application to fluid drag and lift	p. 37
Stream power	p. 40
The equations of motion including drag	p. 41
Rotation using the vector product	p. 45
The vector product (cross-product)	p. 47
Rotation of vectors about an axis	p. 48
Moments and torque	p. 52
Angular momentum and moment of intertia	p. 53
Centrifugal and tidal forces	p. 54
Coriolis forces	p. 56
Review problems	p. 59
Suggested reading	p. 66
Dimensional analysis and the theory of models	p. 69
Introduction	p. 69
Dimensions and dimensional homogeneity	p. 70
Dimensionless products and the pi theorem	p. 72
Scale models	p. 83
More on modeling	p. 86
Uses of dimensional analysis	p. 89
Review problems	p. 91
Suggested reading	p. 98
Stress	p. 100
Introduction	p. 100
Friction	p. 102
Rock falls and avalanches	p. 106
Strength	p. 109
Experimental results for rock friction	p. 116
Definition of stress	p. 117
Notation and sign convention	p. 118
Symmetry of stress components	p. 120
Equilibrium of a small prism	p. 122
The stress ellipsoid	p. 124
The Mohr circle of stress	p. 126
Failure: the Navier-Coulomb criterion	p. 128
Friction and faulting in the earth's crust	p. 131
Stress fields and trajectories	p. 133
State of stress beneath a level ground surface	p. 134
Sliding on slopes	p. 136
Tensor components of stress	p. 142
Why stress is a tensor	p. 152
Review problems	p. 153
Suggested reading	p. 160
Pressure, buoyancy, and consolidation	p. 162
Concept of pressure in a fluid	p. 162
Pressure in a solid (geostatic pressure)	p. 164
Buoyancy	p. 165
Is buoyancy a surface or a body force?	p. 167
Isostasy	p. 170
Rise and intrusion of magma in the crust	p. 172
Forces on settling grains	p. 175
Buoyancy in debris flows	p. 177
Effective and neutral stress	p. 178
Consolidation	p. 180
Geopressured zones	p. 183
Effect of neutral stresses on shear strength	p. 185
Review problems	p. 186
Suggested reading	p. 192
Flow through porous media	p. 193
Darcy's law	p. 193
Hydraulic head	p. 195
Hydraulic conductivity	p. 198
Nature of permeability: relation to porosity, tortuosity, and specific surface area	p. 201
Gradient and curl and their application to Darcy's law and other diffusion equations	p. 203
Divergence and the conservation of mass	p. 207
Flow to a well	p. 209
Flow nets	p. 211
Numerical solution of the Laplace equation	p. 214
Dispersion by flow	p. 215
Refraction of groundwater flow	p. 217
The water table: flow near a topographic surface	p. 220
Fluids of different densities: the freshwater lens	p. 221
Effect of groundwater on sliding on an infinite slope	p. 222
Theory of consolidation	p. 224
Review problems	p. 228
Suggested reading	p. 233
Strain	p. 234
Definitions	p. 234
Measures of strain	p. 236
Plane strain	p. 238
Approach through Taylor's theorem	p. 244
Generalization to three dimensions	p. 247
Measurement of strain	p. 248
Strain ellipse, Mohr circle of strain	p. 248
Review problems	p. 251
Suggested reading	p. 254
Elasticity	p. 255
Constitutive equations	p. 255
Hooke's law	p. 256
Generalized Hooke's law	p. 258
Rigidity modulus	p. 261
Bulk modulus	p. 262
Lame's constants	p. 263
Measurement of stress in rocks	p. 265
Hydraulic fracturing of petroleum reservoir rocks	p. 267
State of stress in the crust of the earth	p. 270
Flexure of plates	p. 271
Equations of motion: Navier's equation	p. 280
Application to seismic waves	p. 284
Review problems	p. 289
Suggested reading	p. 295
Viscous fluids	p. 296
Constitutive equations	p. 296
Equation of motion	p. 301
Kinematics of flow and material acceleration	p. 304
Navier-Stokes equation	p. 307
Inviscid flows: the Euler and Bernoulli equations	p. 312
Irrotational flows	p. 315
Boundary layers	p. 317
Steady, uniform viscous flow between parallel plates	p. 320
Flow through a tube	p. 324
Geological applications	p. 324
Viscous flow past a sphere or cylinder	p. 331
Review problems	p. 333
Suggested reading	p. 335
Flow of natural materials	p. 337
Introduction	p. 337
Mechanical models of natural materials	p. 338
Flow of materials down slopes	p. 344
Ice	p. 348
Debris	p. 353
Lava	p. 356
Rock rheology and sedimentary basins	p. 357
Review problems	p. 360
Suggested reading	p. 363
Turbulence	p. 365
Description of turbulence	p. 365
Origin of turbulence	p. 371
Boundary layers and flow separation	p. 373
Reynolds stresses	p. 378
Diffusion	p. 382
Velocity distribution in a turbulent boundary layer	p. 387
Review problems	p. 391
Suggested reading	p. 393
Thermal convection	p. 395
Introduction	p. 395
Conduction	p. 396
Thermal instability	p. 398
Geometry of convection	p. 400
Equations of motion	p. 403
Lorenz equations	p. 404
Numerical simulation of convection	p. 407
Review problems	p. 407
Suggested reading	p. 408
List of symbols and vector notation	p. 410
Properties of common fluids and rocks	p. 416
Sets of linear equations	p. 422
Partial derivatives and differential equations	p. 430
References	p. 438
Index of names	p. 451
Subject index	p. 455
Table of Contents provided by Syndetics. All Rights Reserved.

Mechanics in the Earth and Environmental Sciences

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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