This book gives a comprehensive coverage of the mechanics of porous materials infiltrated with a fluid (poromechanics), with a focus on its linear theory (poroelasticity). Porous materials can be found in nature as inanimate bodies such as sand, soil, and rock, as living bodies such as plant tissue and animal flesh, or as man-made materials. These materials can look much different in their appearances due to their origin, but the underlying physical principles governing their mechanical behaviors can be the same. The theory is presented both from an intuitive, phenomenological approach at the bulk continuum level, and a thermodynamics based variational energy approach at the micromechanical level. The physical mechanisms covered extend from the quasi-static theory of poroelasticity to poroelastodynamics, poroviscoelasticity, porothermoelasticity, and porochemoelasticity. Closed form analytical solutions are derived in details. Physical phenomena discussed include soil consolidatio
n, land subsidence, slope stability, borehole failure, hydraulic fracturing, water wave and seabed interaction, earthquake aftershock and fluid injection induced seismicity, heat induced pore pressure spalling, seismoelectric and seismoelectromagnetic effect, and biomechanics of cartilage, bone, and blood vessel.
1 Introduction 1.1 Porous Material 1.2 Physical Mechanism 1.3 Poroelastic Phenomena 2. Constitutive Equation 2.1 Physical versus Phenomenological Approach 2.2 Stress and Strain of Porous Medium 2.3 Poroelastic Constitutive Equation 2.4 Bulk Material Constant 3. Micromechanics 3.1 Micromechanical Analysis 3.2 Ideal Porous Medium 3.3 Effective Modulus 3.4 Nonlinear Model 3.5 Laboratory Test 3.6 Table of Poroelastic Constants 4. Variational Energy Formulation 4.1 Internal and external stress and strain4.2 Thermodynamic Principles4.3 Variational Formulation4.4 Constitutive Equation4.5 Intrinsic Material Constant4.6 Link with Phenomological Model4.7 Deviation from Ideal Porous Medium4.8 Limiting Material Properties4.9 Material Stability and Energy Diagram4.10 Semilinear Model 4.11. Laboratory Measurement of Intrinsic Constant5. Anisotropy5.1 Anisotropic Constitutive Equation5.2 Material Symmetry5.3 Micromechanics5.4 Ideal Porous Medium5.5 Example6. Governing Equ
ation6.1 Darcy"s Law6.2 Other Physical Laws6.3 Governing Equation6.4 Degenerated Governing Equation6.5 Boundary Value Problem6.6 Field Equation7. Analytical Solution 8. Fundamental Solution and Integral Equation8.1 Reciprocal Theorem8.2 Somigliana Integral Equation8.3 Fredholm Integral Equation8.4 Stress Discontinuity Method8.5 Displacement Discontinuity Method8.6 Dislocation Method8.7 Galerkin Integral Equation8.8 Fundamental Solution8.9 Poroelasticity Fundamental Solution8.10 Fluid Source8.11 Fluid Dipole8.12 Fluid Dilatation8.13 Fluid Force8.14 Fluid dodecapole8.15 Total Force8.16 Solid Quadrupole and Hexapole8.17 Solid Center of Dilatation8.18 Displacement Discontinuity8.19 Edge Dislocation8.20 Fundamental Solution Relation Based on Reciprocity9. Poroelastodynamics9.1 Dynamic Equilibrium Equation9.2 Dynamic Permeability9.3 Governing Equation9.4 Wave Propagation9.5 Phase Velocity and Attenuation9.6 One-Dimensional Wave Problem9.7 Thermoelast
icity Analogy9.8 Poroelastodynamics Fundamental Solution9.9 Integral Equation Representation9.10 Plane Wave Reflection and Refraction10. Poroviscoelasticity 10.1 Viscoelasticity10.2 Poroviscoelasticity10.3 Borehole Problem10.4 Cylinder Problem10.5 Poroviscoelastodynamics11. Porothermoelasticity11.1 Constitutive Equation11.2 Balance Law11.3 Nonequilibrium Thermodynamics and Transport Law11.4 Governing Equation11.5 Uniaxial Strain11.6 Heating off a Half Space11.7 Axial Symmetry11.8 Borehole Problem11.9 Cylinder Problem11.10 Spherical Symmetry11.11 Cavity Problem11.12 Sphere Problem11.13 Porothermoelasticity Fundamental Solution12. Porochemoelasticity12.1 Electrochemical Effect12.2 Micromechanical Analysis12.3 Constitutive Equation12.4 Balance and Transport Law12.5 Governing Equation12.6 Uniaxial Strain Problem 12.7 Axial Symmetry Problem 12.8 Spherical Symmetry Problem Appendices Index
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"The volume on Poroelasticity by Professor Alex Cheng is a comprehensive and authoritative study that is bound to become a standard work on the subject. It gives the essential developments and advances in poroelasticity taking into consideration both historical and modern perspectives. It is written in a readable style that will enable both researchers and practitioners to take advantage of the conceptual and mathematical developments and the extensive list of usable solutions to problems in poroelasticity ... ." (A.P.S. Selvadurai, William Scott Professor and James McGill Professor, McGill University, Canada) "A very comprehensive and well written textbook that addresses the physical concept, mathematical formulation, analytical solutions, and applications of the theory of poroelasticity. This book is a must for students and researchers learning this subject." (Younane Abousleiman, Larry W. Brummett/ONEOK Chair in Poromechanics, Director of PoroMechanics Institute, University of Oklahoma, USA) "This is a very impressive book, containing a wealth of information on the development of the theory of poroelasticity, to which Professor Cheng has himself contributed many useful parts ... . The book presents fine presentations of the properties of porous media in several chapters, many examples of problems with their solutions, and introductions to such varied topics as poroelastodynamics, poroviscoelasticity, porothermoelasticity and porochemoelasticity, which may further be developed in future ... . With its more than 800 pages the book will remain a valuable source for many researchers for many years to come ... ." (Arnold Verruijt, Emeritus Professor of Soil Mechanics Delft University of Technology, The Netherlands) "This prodigious and scholarly book is a comprehensive treatment of linear poroelasticity. It will be useful as an introduction to the subject as well as a resource for practitioners and researchers. It is destined to be a classic in the field." (John Rudnicki, Professor of Civil and Environmental Engineering and Mechanical Engineering, Northwestern University, USA) "Professor Cheng has written the definitive book on the theory and applications of poroelasticity. This comprehensive book will be an invaluable reference for scientists and engineers dealing with the mechanics of fluid-infiltrated porous solids in biomechanics, geophysics, and geomechanics." (Emmanuel Detournay, Theodore W. Bennett Chair in Mining Engineering and Rock Mechanics, University of Minnesota, USA) "The author declares at the beginning that the goal of this book is limited, focusing largely on the linear theories, such as classical linear elasticity and porous medium flow (Darcy flow); hence the title has been chosen as poroelasticity, rather than the more general poromechanics one. However this limited goal is thoroughly covered in the 12 chapters of the book. Already the introduction contains an abundance of examples which certainly attract the interest of the reader ... . Given the clarity of the text and the large spectrum of topics covered ... the book is a must for all those who want to approach this rather complicated subject." (Bernhard Schrefler, Professor Emeritus, Department of Civil, Environmental and Architectural Engineering, University of Padua, Italy)
1 Introduction1.1 Porous Material1.2 Physical Mechanism1.3 Poroelastic Phenomena2. Constitutive Equation2.1 Physical versus Phenomenological Approach2.2 Stress and Strain of Porous Medium2.3 Poroelastic Constitutive Equation2.4 Bulk Material Constant3. Micromechanics3.1 Micromechanical Analysis3.2 Ideal Porous Medium3.3 Effective Modulus3.4 Nonlinear Model3.5 Laboratory Test3.6 Table of Poroelastic Constants4. Variational Energy Formulation 4.1 Internal and external stress and strain4.2 Thermodynamic Principles4.3 Variational Formulation4.4 Constitutive Equation4.5 Intrinsic Material Constant4.6 Link with Phenomological Model4.7 Deviation from Ideal Porous Medium4.8 Limiting Material Properties4.9 Material Stability and Energy Diagram4.10 Semilinear Model 4.11. Laboratory Measurement of Intrinsic Constant5. Anisotropy5.1 Anisotropic Constitutive Equation5.2 Material Symmetry5.3 Micromechanics5.4 Ideal Porous Medium5.5 Example6. Governing Equation6.1 Darcys Law6.2 Other Physical Laws6.3 Governing Equation6.4 Degenerated Governing Equation6.5 Boundary Value Problem6.6 Field Equation7. Analytical Solution7.2 Uniaxial Strain7.3 One-dimensional Consolidation Problem7.4 Plane Strain7.5 Generalized Plane Strain7.6 Bending of Plate7.7 Mandel Problem7.8 Water Wave over Seabed7.9 Spherical Symmetry7.10 Cryer Problem7.11 Spherical Cavity7.12 Axial Symmetry7.13 Cylinder Problem7.14 Borehole Problem7.15 Borehole and Cylinder Application Problems7.16 Moving Load on Half Plane7.17 Plane Strain Half Space and Layered Problem7.18 Axial Symmetry Half Space Problem8. Fundamental Solution and Integral Equation8.1 Reciprocal Theorem8.2 Somigliana Integral Equation8.3 Fredholm Integral Equation8.4 Stress Discontinuity Method8.5 Displacement Discontinuity Method8.6 Dislocation Method8.7 Galerkin Integral Equation8.8 Fundamental Solution8.9 Poroelasticity Fundamental Solution8.10 Fluid Source8.11 Fluid Dipole8.12 Fluid Dilatation8.13 Fluid Force8.14 Fluid dodecapole8.15 Total Force8.16 Solid Quadrupole and Hexapole8.17 Solid Center of Dilatation8.18 Displacement Discontinuity8.19 Edge Dislocation8.20 Fundamental Solution Relation Based on Reciprocity9. Poroelastodynamics9.1 Dynamic Equilibrium Equation9.2 Dynamic Permeability9.3 Governing Equation9.4 Wave Propagation9.5 Phase Velocity and Attenuation9.6 One-Dimensional Wave Problem9.7 Thermoelasticity Analogy9.8 Poroelastodynamics Fundamental Solution9.9 Integral Equation Representation9.10 Plane Wave Reflection and Refraction10. Poroviscoelasticity10.1 Viscoelasticity10.2 Poroviscoelasticity10.3 Borehole Problem10.4 Cylinder Problem10.5 Poroviscoelastodynamics11. Porothermoelasticity11.1 Constitutive Equation11.2 Balance Law11.3 Nonequilibrium Thermodynamics and Transport Law11.4 Governing Equation11.5 Uniaxial Strain11.6 Heating off a Half Space11.7 Axial Symmetry11.8 Borehole Problem11.9 Cylinder Problem11.10 Spherical Symmetry11.11 Cavity Problem11.12 Sphere Problem11.13 Porothermoelasticity Fundamental Solution12. Porochemoelasticity12.1 Electrochemical Effect12.2 Micromechanical Analysis12.3 Constitutive Equation12.4 Balance and Transport Law12.5 Governing Equation12.6 Uniaxial Strain Problem12.7 Axial Symmetry Problem12.8 Spherical Symmetry Problem AppendicesIndex
