Mechanics in the Earth and Environmental SciencesThe 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. |
Contents
Introduction | 1 |
12 Definition of a continuum | 5 |
13 Governing equations | 7 |
14 Vectors and tensors | 10 |
15 Solving the equations | 11 |
16 The art of modeling | 12 |
Review of elementary mechanics | 14 |
22 Newtons laws | 15 |
68 Flow nets | 211 |
69 Numerical solution of the Laplace equation | 214 |
610 Dispersion by flow | 215 |
611 Refraction of groundwater flow | 217 |
flow near a topographic surface | 220 |
the freshwater lens | 221 |
614 Effect of groundwater on sliding on an infinite slope | 222 |
615 Theory of consolidation | 224 |
23 Vectors coordinates and components | 17 |
24 Position and velocity vectors | 20 |
25 Cylindrical and spherical coordinates left and righthanded Cartesian axes | 22 |
26 Vector statistics | 24 |
27 Example of the use of coordinates | 25 |
28 Numerical solution of the equations of motion | 29 |
29 Work energy and power | 31 |
210 Application to meteorite impact | 36 |
211 Application to fluid drag and lift | 37 |
212 Stream power | 40 |
213 The equations of motion including drag | 41 |
214 Rotation using the vector product | 45 |
215 The vector product crossproduct | 47 |
216 Rotation of vectors about an axis | 48 |
217 Moments and torque | 52 |
218 Angular momentum and moment of inertia | 53 |
219 Centrifugal and tidal forces | 54 |
220 Coriolis forces | 56 |
221 Review problems | 59 |
222 Suggested reading | 66 |
Dimensional analysis and the theory of models | 69 |
32 Dimensions and dimensional homogeneity | 70 |
33 Dimensionless products and the pi theorem | 72 |
34 Scale models | 83 |
35 More on modeling | 86 |
36 Uses of dimensional analysis | 89 |
37 Review problems | 91 |
38 Suggested reading | 98 |
Stress | 100 |
42 Friction | 102 |
43 Rock falls and avalanches | 106 |
44 Strength | 109 |
45 Experimental results for rock friction | 116 |
46 Definition of stress | 117 |
47 Notation and sign convention | 118 |
48 Symmetry of stress components | 120 |
49 Equilibrium of a small prism | 122 |
410 The stress ellipsoid | 124 |
411 The Mohr circle of stress | 126 |
the NavierCoulomb criterion | 128 |
413 Friction and faulting in the earths crust | 131 |
414 Stress fields and trajectories | 133 |
415 State of stress beneath a level ground surface | 134 |
416 Sliding on slopes | 136 |
417 Tensor components of stress | 142 |
418 Why stress is a tensor | 152 |
419 Review problems | 153 |
420 Suggested reading | 160 |
Pressure buoyancy and consolidation | 162 |
52 Pressure in a solid geostatic pressure | 164 |
53 Buoyancy | 165 |
54 Is buoyancy a surface or a body force? | 167 |
55 Isostasy | 170 |
56 Rise and intrusion of magma in the crust | 172 |
57 Forces on settling grains | 175 |
58 Buoyancy in debris flows | 177 |
59 Effective and neutral stress | 178 |
510 Consolidation | 180 |
511 Geopressured zones | 183 |
512 Effect of neutral stresses on shear strength | 185 |
513 Review problems | 186 |
514 Suggested reading | 192 |
Flow through porous media | 193 |
62 Hydraulic head | 195 |
63 Hydraulic conductivity | 198 |
relation to porosity tortuosity and specific surface area | 201 |
65 Gradient and curl and their application to Darcys law and other diffusion equations | 203 |
66 Divergence and the conservation of mass | 207 |
67 Flow to a well | 209 |
616 Review problems | 228 |
617 Suggested reading | 233 |
Strain | 234 |
72 Measures of strain | 236 |
73 Plane strain | 238 |
74 Approach through Taylors theorem | 244 |
75 Generalization to three dimensions | 247 |
76 Measurement of strain | 248 |
78 Review problems | 251 |
79 Suggested reading | 254 |
Elasticity | 255 |
82 Hookes law | 256 |
83 Generalized Hookes law | 258 |
84 Rigidity modulus | 261 |
85 Bulk modulus | 262 |
86 Lames constants | 263 |
87 Measurement of stress in rocks | 265 |
88 Hydraulic fracturing of petroleum reservoir rocks | 267 |
89 State of stress in the crust of the earth | 270 |
810 Flexure of plates | 271 |
Naviers equation | 280 |
812 Application to seismic waves | 284 |
813 Review problems | 289 |
814 Suggested reading | 295 |
Viscous fluids | 296 |
92 Equation of motion | 301 |
93 Kinematics of flow and material acceleration | 304 |
94 NavierStokes equation | 307 |
the Euler and Bernoulli equations | 312 |
96 Irrotational flows | 315 |
97 Boundary layers | 317 |
98 Steady uniform viscous flow between parallel plates | 320 |
99 Flow through a tube | 324 |
911 Viscous flow past a sphere or cylinder | 331 |
912 Review problems | 333 |
913 Suggested reading | 335 |
Flow of natural materials | 337 |
102 Mechanical models of natural materials | 338 |
103 Flow of materials down slopes | 344 |
104 Ice | 348 |
105 Debris | 353 |
106 Lava | 356 |
107 Rock rheology and sedimentary basins | 357 |
108 Review problems | 360 |
109 Suggested reading | 363 |
Turbulence | 365 |
112 Origin of turbulence | 371 |
113 Boundary layers and flow separation | 373 |
114 Reynolds stresses | 378 |
115 Diffusion | 382 |
116 Velocity distribution in a turbulent boundary layer | 387 |
117 Review problems | 391 |
118 Suggested reading | 393 |
Thermal convection | 395 |
122 Conduction | 396 |
123 Thermal instability | 398 |
124 Geometry of convection | 400 |
125 Equations of motion | 403 |
126 Lorenz equations | 404 |
127 Numerical simulation of convection | 407 |
129 Suggested reading | 408 |
List of symbols and vector notation | 410 |
Properties of common fluids and rocks | 416 |
Sets of linear equations | 422 |
Appendix D Partial derivatives and differential equations | 430 |
References | 438 |
451 | |
455 | |
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Mechanics in the Earth and Environmental Sciences Gerard V. Middleton,Peter R. Wilcock No preview available - 1994 |
Common terms and phrases
acceleration angle applied assume asthenosphere axes axis body boundary layer buoyancy Chapter coefficient components compression consider constant constitutive equations convection coordinates cylinder Darcy's law debris flows defined deformation density depth derived diffusion dimensional analysis dimensionless dimensions direction displacement earth elastic energy equal equations of motion example flow fluid mechanics force acting fractures friction given grains gravity groundwater heat horizontal hydraulic Laplace's equation linear lithosphere magma magnitude mantle mass material matrix measured Navier-Stokes equation Newtonian fluid non-Newtonian fluid normal stress notation obtain permeability physical plane plastic plate pore pressure porous principal stresses problem produced result Reynolds number rock rotation scale Section sediment sedimentary sedimentary basins shear strain shear stress shown in Figure sliding slope solid solution strain tensor strength surface temperature tensor theory turbulent variables vector velocity vertical viscosity viscous fluid volume x-direction zero ди ду дх