Mechanics in the Earth and Environmental Sciences

Portada
Cambridge University Press, 1994 M08 26 - 459 páginas
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.
 

Contenido

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
Index of names
451
Subject index
455
Derechos de autor

Otras ediciones - Ver todas

Términos y frases comunes

Referencias a este libro

Información bibliográfica