Mechanics in the Earth and Environmental Sciences

ISBN-10: 0521446694

ISBN-13: 9780521446693

Edition: 1994

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Description: 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.

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Book details

List price: $105.00
Copyright year: 1994
Publisher: Cambridge University Press
Publication date: 8/26/1994
Binding: Paperback
Pages: 476
Size: 7.00" wide x 9.75" long x 1.00" tall
Weight: 1.848
Language: English

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