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Mechanics in the Earth and Environmental Sciences - Gerard V. Middleton

Mechanics in the Earth and Environmental Sciences

Paperback

Published: 28th November 1994
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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.

'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

Prefacep. xiii
Introductionp. 1
What this book is aboutp. 1
Definition of a continuump. 5
Governing equationsp. 7
Vectors and tensorsp. 10
Solving the equationsp. 11
The art of modelingp. 12
Review of elementary mechanicsp. 14
Introductionp. 14
Newton's lawsp. 15
Vectors, coordinates, and componentsp. 17
Position and velocity vectorsp. 20
Cylindrical and spherical coordinates; left- and right-handed Cartesian axesp. 22
Vector statisticsp. 24
Example of the use of coordinatesp. 25
Numerical solution of the equations of motionp. 29
Work, energy, and powerp. 31
Application to meteorite impactp. 36
Application to fluid drag and liftp. 37
Stream powerp. 40
The equations of motion including dragp. 41
Rotation using the vector productp. 45
The vector product (cross-product)p. 47
Rotation of vectors about an axisp. 48
Moments and torquep. 52
Angular momentum and moment of intertiap. 53
Centrifugal and tidal forcesp. 54
Coriolis forcesp. 56
Review problemsp. 59
Suggested readingp. 66
Dimensional analysis and the theory of modelsp. 69
Introductionp. 69
Dimensions and dimensional homogeneityp. 70
Dimensionless products and the pi theoremp. 72
Scale modelsp. 83
More on modelingp. 86
Uses of dimensional analysisp. 89
Review problemsp. 91
Suggested readingp. 98
Stressp. 100
Introductionp. 100
Frictionp. 102
Rock falls and avalanchesp. 106
Strengthp. 109
Experimental results for rock frictionp. 116
Definition of stressp. 117
Notation and sign conventionp. 118
Symmetry of stress componentsp. 120
Equilibrium of a small prismp. 122
The stress ellipsoidp. 124
The Mohr circle of stressp. 126
Failure: the Navier-Coulomb criterionp. 128
Friction and faulting in the earth's crustp. 131
Stress fields and trajectoriesp. 133
State of stress beneath a level ground surfacep. 134
Sliding on slopesp. 136
Tensor components of stressp. 142
Why stress is a tensorp. 152
Review problemsp. 153
Suggested readingp. 160
Pressure, buoyancy, and consolidationp. 162
Concept of pressure in a fluidp. 162
Pressure in a solid (geostatic pressure)p. 164
Buoyancyp. 165
Is buoyancy a surface or a body force?p. 167
Isostasyp. 170
Rise and intrusion of magma in the crustp. 172
Forces on settling grainsp. 175
Buoyancy in debris flowsp. 177
Effective and neutral stressp. 178
Consolidationp. 180
Geopressured zonesp. 183
Effect of neutral stresses on shear strengthp. 185
Review problemsp. 186
Suggested readingp. 192
Flow through porous mediap. 193
Darcy's lawp. 193
Hydraulic headp. 195
Hydraulic conductivityp. 198
Nature of permeability: relation to porosity, tortuosity, and specific surface areap. 201
Gradient and curl and their application to Darcy's law and other diffusion equationsp. 203
Divergence and the conservation of massp. 207
Flow to a wellp. 209
Flow netsp. 211
Numerical solution of the Laplace equationp. 214
Dispersion by flowp. 215
Refraction of groundwater flowp. 217
The water table: flow near a topographic surfacep. 220
Fluids of different densities: the freshwater lensp. 221
Effect of groundwater on sliding on an infinite slopep. 222
Theory of consolidationp. 224
Review problemsp. 228
Suggested readingp. 233
Strainp. 234
Definitionsp. 234
Measures of strainp. 236
Plane strainp. 238
Approach through Taylor's theoremp. 244
Generalization to three dimensionsp. 247
Measurement of strainp. 248
Strain ellipse, Mohr circle of strainp. 248
Review problemsp. 251
Suggested readingp. 254
Elasticityp. 255
Constitutive equationsp. 255
Hooke's lawp. 256
Generalized Hooke's lawp. 258
Rigidity modulusp. 261
Bulk modulusp. 262
Lame's constantsp. 263
Measurement of stress in rocksp. 265
Hydraulic fracturing of petroleum reservoir rocksp. 267
State of stress in the crust of the earthp. 270
Flexure of platesp. 271
Equations of motion: Navier's equationp. 280
Application to seismic wavesp. 284
Review problemsp. 289
Suggested readingp. 295
Viscous fluidsp. 296
Constitutive equationsp. 296
Equation of motionp. 301
Kinematics of flow and material accelerationp. 304
Navier-Stokes equationp. 307
Inviscid flows: the Euler and Bernoulli equationsp. 312
Irrotational flowsp. 315
Boundary layersp. 317
Steady, uniform viscous flow between parallel platesp. 320
Flow through a tubep. 324
Geological applicationsp. 324
Viscous flow past a sphere or cylinderp. 331
Review problemsp. 333
Suggested readingp. 335
Flow of natural materialsp. 337
Introductionp. 337
Mechanical models of natural materialsp. 338
Flow of materials down slopesp. 344
Icep. 348
Debrisp. 353
Lavap. 356
Rock rheology and sedimentary basinsp. 357
Review problemsp. 360
Suggested readingp. 363
Turbulencep. 365
Description of turbulencep. 365
Origin of turbulencep. 371
Boundary layers and flow separationp. 373
Reynolds stressesp. 378
Diffusionp. 382
Velocity distribution in a turbulent boundary layerp. 387
Review problemsp. 391
Suggested readingp. 393
Thermal convectionp. 395
Introductionp. 395
Conductionp. 396
Thermal instabilityp. 398
Geometry of convectionp. 400
Equations of motionp. 403
Lorenz equationsp. 404
Numerical simulation of convectionp. 407
Review problemsp. 407
Suggested readingp. 408
List of symbols and vector notationp. 410
Properties of common fluids and rocksp. 416
Sets of linear equationsp. 422
Partial derivatives and differential equationsp. 430
Referencesp. 438
Index of namesp. 451
Subject indexp. 455
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521446693
ISBN-10: 0521446694
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 476
Published: 28th November 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.88 x 19.1  x 2.52
Weight (kg): 0.83