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Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology : Princeton Series in Geophysics - Herbert F. Wang

Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology

Princeton Series in Geophysics

Hardcover

Published: 16th November 2000
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The theory of linear poroelasticity describes the interaction between mechanical effects and adding or removing fluid from rock. It is critical to the study of such geological phenomena as earthquakes and landslides and is important for numerous engineering projects, including dams, groundwater withdrawal, and petroleum extraction. Now an advanced text synthesizes in one place, with one notation, numerous classical solutions and applications of this highly useful theory.

The introductory chapter recounts parallel developments in geomechanics, hydrogeology, and reservoir engineering that are unified by the tenets of poroelasticity. Next, the theory's constitutive and governing equations and their associated material parameters are described. These equations are then specialized for different simplifying geometries: unbounded problem domains, uniaxial strain, plane strain, radial symmetry, and axisymmetry. Example problems from geomechanics, hydrogeology, and petroleum engineering are incorporated throughout to illustrate poroelastic behavior and solution methods for a wide variety of real-world scenarios. The final chapter provides outlines for finite-element and boundary-element formulations of the field's governing equations. Whether read as a course of study or consulted as a reference by researchers and professionals, this volume's user-friendly presentation makes accessible one of geophysics' most important subjects and will do much to reduce poroelasticity's reputation as difficult to master.

"This book is essential reading for those students who are serious about geomechanics."--Terry Engelder, Journal of Geoscience Education

Prefacep. xi
Introductionp. 3
Chapter Overviewp. 3
Historical Examplesp. 3
Basic Conceptsp. 5
Brief Historyp. 8
Geomechanicsp. 8
Hydrogeologyp. 10
Petroleum Engineeringp. 13
Biot''s Theoryp. 14
Preview of Constitutive Relationsp. 17
Thermoelastic Analogyp. 22
Linear Constitutive Equationsp. 26
Chapter Overviewp. 26
Kinematic Variablesp. 26
Dynamic Variablesp. 30
Constitutive Relationsp. 31
Principal Coordinatesp. 33
Isotropic Stress and Strainp. 34
Nonprincipal Coordinatesp. 37
Anisotropyp. 42
Effective Stressp. 43
3p. 47
Chapter Overviewp. 47
Compressibilityp. 47
Drained versus Undrained Modulip. 53
Storage Capacityp. 55
Hydraulic Diffusivityp. 61
Poroelastic Expansion Coefficientsp. 62
Coefficients of Undrained Pore-Pressure Buildupp. 64
Incompressible or Highly Compressible Constituentsp. 68
Laboratory Datap. 69
Governing Equationsp. 71
Chapter Overviewp. 71
Force Equilibrium Equationsp. 72
Displacement Formulationp. 73
Beltrami-Michell Equationsp. 76
Strain Compatibility Equationsp. 77
Mechanical Boundary and Initial Conditionsp. 78
Darcy''s Lawp. 79
Fluid Continuityp. 83
Comparison of Diffusion Equationsp. 86
Fluid Boundary and Initial Conditionsp. 87
Uncoupling of Stress or Strain from Pore Pressurep. 88
Force Equilibrium for the Solid Matrixp. 91
Unbounded Problem Domainsp. 96
Chapter Overviewp. 96
Poroelastic Displacement Potential in Infinite Domainp. 96
Uniform Fluid Injection in a Spherep. 98
Green''s Functionsp. 101
Center of Dilatationp. 103
Half Space with Traction-Free Boundaryp. 105
Gravity Analogyp. 107
Sudden Injection of Fluid at a Point in Infinite Domainp. 110
Fluid Dipole Equivalence to Body-Force Distributionsp. 112
Uniaxial Strainp. 116
Chapter Overviewp. 116
Constitutive Equationsp. 116
Force Equilibrium Equationp. 118
Fluid Diffusion Equationp. 119
Step Load on Semi-Infinite Columnp. 120
Consolidation of a Finite Layer (Terzaghi''s Problem)p. 124
Uniformly Increasing Load on a Finite Layerp. 129
Sedimentation on Impermeable Basementp. 131
Erosional Unloadingp. 134
Periodic Load on a Half Spacep. 136
Periodic Load on a Finite Layerp. 138
Water Load on a Half Spacep. 140
Plane Strain and Plane Stress in Rectangular Coordinatesp. 150
Chapter Overviewp. 150
Constitutive Equations for Plane Strainp. 151
Governing Equations for Plane Strainp. 151
Mandel''s Problemp. 153
Biot''s Stress Functionp. 157
Periodic Load on a Half Spacep. 158
Displacement Functionsp. 163
Sudden Step Load on a Half Spacep. 165
Undrained Response to a Line Sourcep. 170
Sudden Fault Slipp. 172
Constitutive Equations for Plane Stressp. 183
Plane Strain in Polar Coordinatesp. 187
Chapter Overviewp. 187
Radial Symmetryp. 187
Sudden Pressurization of a Long Cylinderp. 191
Sudden Pressurization of a Boreholep. 201
Sudden Stress Release due to Borehole Excavation in an Anisotropic Stress Fieldp. 203
Hydraulic Fracturingp. 205
Sudden Internal Pressurization of a Hollow Cylinderp. 206
Line Source in Plane Strainp. 211
Axisymmetryp. 215
Chapter Overviewp. 215
Governing Equationsp. 215 i
Pumping from a Wellp. 216
Reverse Water-Level Fluctuationsp. 218
Pulse-Decay Testp. 221
Elastostatic Subsidence of a Half Spacep. 226
Time-Dependent Subsidence of a Half Spacep. 229
Numerical Methodsp. 238
Chapter Overviewp. 238
Finite-Element Methodp. 238
Boundary-Element Methodp. 245
Appendix Ap. 257
Properties of Fourier Transformsp. 257
Properties of Laplace Transformsp. 258
Stehfest Algorithm for Laplace Transform Inversionp. 259
Properties of Hankel Transformsp. 260
Relations Among Poroelastic Constantsp. 262
Representative Poroelastic Constantsp. 265
Symbolsp. 267
Referencesp. 269
Uniited Referencesp. 279
Author Indexp. 283
Subject Indexp. 286
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691037462
ISBN-10: 0691037469
Series: Princeton Series in Geophysics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 304
Published: 16th November 2000
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 2.54
Weight (kg): 0.58