Theory of Porous Media

1 Introduction.- 2 The Early Era.- 2.1 The Development of the Principles of Mechanics.- 2.2 The Dynamics of Rigid Bodies.- 2.3 The Theory of Ideal Fluids.- 2.4 Euler's Description of a Porous Body.- 2.5 Coulomb's Earth Pressure Theory.- 2.6 Woltman's Contribution to the Porous Media Theory: The Introduction of the Angle of Internal Friction and the Volume Fraction Concept.- 2.7 Concluding Remarks.- 2.8 Biographical Notes.- 3 The Classical Era.- 3.1 Cauchy's Formulation of the Stress Concept.- 3.2 The Development of the Linear Elasticity Theory.- 3.3 Discovery of Fundamental Laws (Delesse, Fick, Darcy).- 3.4 The Development of the Theory of Viscous Fluids.- 3.5 The Mohr-Coulomb Failure Condition and other Plasticity Theory Studies.- 3.6 Motion of Liquids in Rigid Porous Solids.- 3.7 Foundation of the Mixture Theory.- 3.8 The Foundation of Thermodynamics.- 4 The Modern Era.- 4.1 Discovery of Fundamental Effects of Liquid-Saturated Rigid Porous Solids.- 4.2 The Treatment of the Liquid-Saturated Deformable Porous Solid by von Terzaghi.- 4.3 The Foundation of Modern Porous Media Theory by Fillunger.- 4.4 The Tragic Controversy Between the Viennese Professors Fillunger and von Terzaghi in 1936/37.- 4.5 The Further Development of the Viennese Affair and in Soil Mechanics.- 4.6 Biographical Notes.- 4.7 The Followers of von Terzaghi and Fillunger: Biot, Heinrich and Frenkel.- 4.8 Further Development of the Elasticity and Plasticity Theories..- 4.9 Modern Continuum Mechanics and Mixture Theory.- 4.10 Theories of Immiscible Mixtures.- 5 Current State of Porous Media Theory.- 5.1 Introductory Remarks to Porous Media Theory.- 5.2 The Volume Fraction Concept.- 5.3 Kinematics.- 5.4 Balance Equations.- 5.5 Entropy Inequality.- 5.6 The Closure Problem and the SaturationConstraint.- 5.7 Principle of Virtual Work.- 5.8 Constitutive Theory.- 5.9 Applications.- 6 Conclusions and Outlook.- A Evaluation of the Entropy Inequality.- B Introduction to the Vector- and Tensor Calculus for Engineers.- B 1. Introduction.- B 2. Basic Concepts.- B 2.1 Symbols.- B 2.2 Einstein's Summation Convention.- B 2.3 Kronecker Symbol.- B 3. Vector Algebra.- B 3.1 Vector Notion and Vector Operations.- B 3.2 Base System.- B 3.3 Reciprocal Base System.- B 3.4 Covariant and Contravariant Coefficients of the Vector Components.- B 3.5 Physical Coefficients of a Vector.- B 4. Tensor Algebra.- B 4.1 Tensor Notion (Linear Mapping).- B 4.2 Algebra in Base Systems.- B 4.3 Scalar Product of Tensors.- B 4.4 Tensor Product.- B 4.5 Special Tensors and Operations.- B 4.5.1 Inverse Tensor..- B 4.5.2 Transposed Tensor.- B 4.5.3 Symmetrical and Skew-Symmetrical Tensors..- B 4.5.4 Orthogonal Tensor.- B 4.5.5 Trace of the Tensor.- B 4.6 Decomposition of the Tensor.- B 4.6.1 Additive Decomposition.- B 4.6.2 Multiplicative Decomposition (Polar Decomposition).- B 4.7 Change of the Base.- B 4.8 Higher-Order Tensors.- B 4.8.1 Introduction of Higher-Order Tensors...- B 4.8.2 Special Operations and Tensors.- B 4.8.3 Algebra in Base Systems.- B 4.9 Cross Product.- B 4.9.1 Cross Product of Vectors.- B 4.9.2 Cross Tensor Product of Vector and Tensor..- B 4.9.3 Cross Tensor Product of Tensors.- B 4.9.4 Cross Vector Product of Tensors.- B 4.9.5 Special Tensors and Operations.- B 4.10 Fundamental Tensors.- B 5. Vector and Tensor Analysis.- B 5.1 Functions of Scalar Parameters.- B 5.2 Field Theory.- B 5.2.1 Gradient.- B 5.2.2 Derivatives of Higher-Order.- B 5.2.3 Special Operations (Divergence, Rotation, and the Laplace-Operator).- B 5.3 Functions of Vector and Tensor Variables.- B 5.4Integral Theorems.- B 5.4.1 Transformation of Surface Integrals into Volume Integrals.- B 5.4.2 Transformation of Line Integrals into Surface Integrals.- C Geometric Representation of the Principal Stresses, the Stress Invariants and the Mohr-Coulomb Theory.- C 1. Preliminaries.- C 2. Triaxial Plane.- C 3. Octahedral Plane.- C 4. Geometric Representation of Yield Functions.- C 5. Subspace of the Stress State.- C 6. Mohr-Coulomb Theory.- C 6.1 Coulomb's Strength Hypothesis for Arbitrarily Oriented Surfaces.- C 6.2 Failure Surfaces.- C 7. Failure Condition in Invariant Formulation.- References.- Author Index.