Call number:
9783319252025 (e-book)
In:
Theory and applications of transport in porous media, Volume 27
Description / Table of Contents:
This book treats the mechanics of porous materials infiltrated with a fluid (poromechanics), focussing on its linear theory (poroelasticity). Porous materials from inanimate bodies such as sand, soil and rock, living bodies such as plant tissue, animal flesh, or man-made materials can look very different due to their different origins, but as readers will see, the underlying physical principles governing their mechanical behaviors can be the same, making this work relevant not only to engineers but also to scientists across other scientific disciplines.
Readers will find discussions of physical phenomena including soil consolidation, land subsidence, slope stability, borehole failure, hydraulic fracturing, water wave and seabed interaction, earthquake aftershock, fluid injection induced seismicity and heat induced pore pressure spalling as well as discussions of seismoelectric and seismoelectromagnetic effects. The work also explores the biomechanics of cartilage, bone and blood vessels.
Chapters present theory using 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.
This book provides an excellent introduction to linear poroelasticity and is especially relevant to those involved in civil engineering, petroleum and reservoir engineering, rock mechanics, hydrology, geophysics, and biomechanics.
Type of Medium:
12
Pages:
1 Online-Ressource (893 Seiten)
,
Illustrationen, Diagramme
ISBN:
9783319252025 (e-book)
,
978-3-319-25202-5
ISSN:
2213-6940
,
0924-6118
Series Statement:
Theory and applications of transport in porous media Volume 27
URL:
Fulltext @ Ebook Central (AWI only)
Language:
English
Note:
Contents
1 Introduction
1.1 Porous Material
1.2 Physical Mechanism
1.2.1 Drained and Undrained Responses
1.2.2 Time and Length Scale
1.2.3 Skempton Pore Pressure Effect
1.2.4 Effective Stress for Volumetric Deformation
1.2.5 Effective Stress for Pore Collapse
1.2.6 Fluid Storage
1.2.7 Thermoelasticity Analogy
1.2.8 Coupled Versus Uncoupled Diffusion
1.3 Poroelastic Phenomena
1.3.1 Borehole Failure
1.3.2 Mandel-Cryer Effect
1.3.3 Noordbergum Effect
1.3.4 Land Subsidence
1.3.5 Slope Stability and Fault Slippage
1.3.6 Fluid Induced Seismicity
1.3.7 Outburst of Coal
1.3.8 Hydraulic Fracturing
1.3.9 Water Wave and Seabed Interaction
1.3.10 Tidal and Barometric Efficiency
1.3.11 Biomechanics
1.3.12 Poroviscoelasticity and Anelastic Strain Recovery
1.3.13 Porothermoelasticity and Thermal Fracturing
1.3.14 Poroelastodynamics and Seismoelectric Effect
1.3.15 Swelling of Clay and Shale
1.3.16 Nanoporous Material
References
2 Constitutive Equation
2.1 Physical Versus Phenomenological Approach
2.2 Stress and Strain of Porous Medium
2.2.1 Stress
2.2.2 Strain
2.3 Poroelastic Constitutive Equation
2.3.1 Isotropic Elastic Material
2.3.2 Isotropic Poroelastic Material
2.3.3 Reciprocal Work Theorem
2.3.4 Stress-Strain Relation
2.3.5 Strain-Stress Relation
2.4 Bulk Material Constant
2.4.1 Drained and Undrained Constant
2.4.2 Effective Stress Coefficient
2.4.3 Pore Pressure Coefficient
2.4.4 Storage Coefficient
References
3 Micromechanics
3.1 Micromechanical Analysis
3.1.1 Solid and Pore Volumetric Strain
3.1.2 Fluid Volumetric Strain
3.1.3 Link Among Material Constants
3.2 Ideal Porous Medium
3.3 Effective Modulus
3.3.1 Mackenzie Model
3.3.2 Walsh Model
3.3.3 Budiansky and O’Connell Model
3.3.4 Bounds on Material Constants
3.4 Nonlinear Model
3.4.1 Effective Stress Dependent Pore Compressibility
3.4.2 Compaction Induced Permeability Change
3.5 Laboratory Test
3.5.1 Drained Test
3.5.2 Undrained Test
3.5.3 Unjacketed Test
3.6 Table of Poroelastic Constants
References
4 Variational Energy Formulation
4.1 Internal and External Stress and Strain
4.1.1 Porosity
4.1.2 Volume and Surface Averaging of Elastic Material
4.1.3 Volume and Surface Averaging of Porous Material
4.1.4 Linkage Between Internal and External Strains
4.2 Thermodynamic Principles
4.3 Variational Formulation
4.3.1 Virtual Work
4.3.2 Internal Energy
4.3.3 Porosity Equilibrium
4.4 Constitutive Equation
4.4.1 Linear Material Model
4.4.2 Linear Model
4.5 Intrinsic Material Constant
4.5.1 Effective Solid Bulk Modulus
4.5.2 Fundamental Deformation Mode
4.5.3 Microisotropy and Microhomogeneity: Ideal Porous Medium
4.6 Link with Phenomenological Model
4.6.1 Link with Bulk Continuum Model
4.6.2 Link with Micromechanics Model
4.7 Deviation from Ideal Porous Medium
4.8 Limiting Material Properties
4.8.1 Ideal Porous Medium
4.8.2 Granular Material
4.8.3 Soil Mechanics Model: Saturated
4.8.4 Soil Mechanics Model: Nearly Saturated
4.8.5 Highly Compressible Solid
4.8.6 Highly Compressible Fluid
4.9 Material Stability and Energy Diagram
4.10 Semilinear Model
4.10.1 Geometric Nonlinearity
4.10.2 Structural Nonlinearity
4.11 Laboratory Measurement of Intrinsic Constant
References
5 Anisotropy
5.1 Anisotropic Constitutive Equation
5.1.1 Elasticity
5.1.2 Poroelastic Stress-Strain Relation
5.1.3 Poroelastic Strain-Stress Relation
5.2 Material Symmetry
5.2.1 Orthotropy
5.2.2 Transverse Isotropy
5.2.3 Isotropy
5.3 Micromechanics
5.4 Ideal Porous Medium
5.5 Example
References
6 Governing Equation
6.1 Darcy’s Law
6.1.1 Darcy’s Empirical Law
6.1.2 Homogenization Theory
6.1.3 Intrinsic Permeability and Mobility Coefficient
6.1.4 Irreversible Thermodynamics Process
6.2 Other Physical Laws
6.2.1 Mass Conservation
6.2.2 Force Equilibrium
6.3 Governing Equation
6.3.1 Navier-Cauchy Equation
6.3.2 Diffusion Equation
6.3.3 Compatibility Equation
6.3.4 Harmonic Relation
6.3.5 Orthotropy
6.3.6 Transverse Isotropy
6.4 Degenerated Governing Equation
6.4.1 Drained and Undrained State
6.4.2 Soil Mechanics Model
6.4.3 Irrotational Displacement Field
6.4.4 Uncoupling of Diffusion Equation
6.5 Boundary Value Problem
6.5.1 Existence and Uniqueness
6.5.2 Boundary Condition
6.6 Field Equation
6.6.1 Biot Function
6.6.2 Biot Decomposition
6.6.3 McNamee-Gibson Displacement Function
References
7 Analytical Solution
7.1 Review of Early Work
7.2 Uniaxial Strain
7.2.1 Isotropy
7.2.2 Transverse Isotropy
7.3 One-Dimensional Consolidation Problem
7.3.1 Terzaghi’s Consolidation Problem
7.3.2 Loading by Fluid Pressure
7.3.3 Variable Rete Loading
7.3.4 Harmonic Excitation
7.4 Plane Strain
7.4.1 Orthotropy
7.4.2 Isotropy
7.4.3 Volumetric Strain and Rotation Formulation
7.5 Generalized Plane Strain
7.5.1 Definition of Generalized Plane Strain
7.5.2 Pure Shear
7.5.3 Warping
7.5.4 Torsion
7.5.5 Plane Strain
7.5.6 Axial Strain
7.5.7 Pure Bending
7.6 Pure Bending of Plate
7.6.1 Bending of Cantilever Plate
7.6.2 Buckling of Axially Loaded Plate
7.7 Mandel Problem
7.8 Water Wave Over Seabed
7.9 Spherical Symmetry
7.10 Cryer Problem
7.11 Spherical Cavity
7.11.1 Pressurized Cavity
7.11.2 Excavated Cavity
7.11.3 Pore Pressure Meter Problem
7.12 Axial Symmetry
7.13 Cylinder Problem
7.13.1 Solid Cylinder
7.13.2 Hollow Cylinder
7.14 Borehole Problem
7.14.1 Plane Strain Borehole Problem
7.14.2 Inclined Borehole Problem
7.15 Borehole and Cylinder Application Problems
7.15.1 Retrieval of Cylindrical Core
7.15.2 Excavated Borehole
7.15.3 Fluid Extraction and Injection
7.15.4 Borehole Breakdown Pressure
7.15.5 Borehole Stability Analysis
7.16 Moving Load on Half Plane
7.17 Plane Strain Half Space and Layered Problem
7.17.1 General Solution for Layered Problem
7.17.2 Plane Strain Half Space Problem
7.18 Axial Symmetry Half Space Problem
References
8 Fundamental Solution and Integral Equation
8.1 Reciprocal Theorem
8.1.1 Green’s Second Identity
8.1.2 Betti-Maxwell Reciprocal Theorem
8.1.3 Reciprocal Theorem of Poroelasticity
8.2 Somigliana Integral Equation
8.2.1 Green’s Third Identity
8.2.2 Elasticity
8.2.3 Poroelasticity
8.3 Fredholm Integral Equation
8.3.1 Potential Problem
8.3.2 Elasticity
8.3.3 Poroelasticity
8.4 Stress Discontinuity Method
8.5 Displacement Discontinuity Method
8.6 Dislocation Method
8.7 Galerkin Integral Equation
8.8 Fundamental Solution
8.8.1 Elementary Fundamental Solution
8.8.2 Elasticity Fundamental Solution
8.9 Poroelasticity Fundamental Solution
8.10 Fluid Source
8.10.1 Continuous Source
8.10.2 Instantaneous Source
8.11 Fluid Dipole
8.11.1 Continuous Dipole
8.11.2 Instantaneous Dipole
8.12 Fluid Dilatation
8.12.1 Continuous Fluid Dilatation
8.12.2 Instantaneous Fluid Dilatation
8.13 Fluid Force
8.13.1 Continuous Fluid Force
8.13.2 Instantaneous Fluid Force
8.14 Fluid Dodecapole
8.15 Total Force
8.15.1 Continuous Total Force
8.15.2 Instantaneous Total Force
8.16 Solid Quadrupole and Hexapole
8.17 Solid Center of Dilatation
8.18 Displacement Discontinuity
8.19 Edge Dislocation
8.20 Fundamental Solution Relation Based on Reciprocity
References
9 Poroelastodynamics
9.1 Dynamic Equilibrium Equation
9.2 Dynamic Permeability
9.3 Governing Equation
9.4 Wave Propagation
9.4.1 Elastic Wave
9.4.2 Poroelastic Wave
9.5 Phase Velocity and Attenuation
9.5.1 Phase Velocity
9.5.2 Attenuation
9.5.3 Extended Biot Models
9.6 One-Dimensional Wave Problem
9.6.1 Half Space
9.6.2 Finite Thickness Layer
9.7 Thermoelasticity Analogy
9.8 Poroelastodynamics Fundamental Solution
9.8.1 Elastodynamics Fundamental Solution
9.8.2 Helmholtz Decomposition
9.8.3 Three-Dimensional Point Force Solution
9.8.4 Three-Dimensional Fluid Source Solution
9.8.5 Two-Dimensional Fundamental Solution
9.9 Integral Equation Representation
9.10 Plane Wave Reflection and Refraction
9.10.1 Plane Strain Wave Solution
9.10.2 Reflection on Free Surface—Non-Dissipative Medium
9.10.3 Reflection on Free Surface—Dissipative Medium
9.10.4 Impermeable Surface
9.10.5 Fluid and Porous Medium Interface
References
10 Poroviscoelasticity
10.1 Viscoelasticity
10.1.1 Spring and Dashpot Model
10.1.2 Correspondence Principle
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