Serpieri / Travascio Variational Continuum Multiphase Poroelasticity

Theory and Applications
1. Auflage 2017
ISBN: 978-981-10-3452-7
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 207 Seiten

Reihe: Engineering (R0)

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics.The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations.It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the stress tensor work-associated with the macroscopic strain of the solid phase are partitioned according to a relation which, from a formal point of view, turns out to be strictly compliant with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. Moreover, it is shown that some experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi's law, are ordinarily predicted by VMTPM. As a peculiar prediction of VMTPM, the book shows that the phenomenon of compression-induced liquefaction experimentally observed in cohesionless mixtures can be obtained as a natural implication of this theory by a purely rational deduction. A characterization of the phenomenon of crack closure in fractured media is also inferred in terms of macroscopic strain and stress paths.Altogether the results reported in this monograph exemplify the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials.  

Autoren/Hrsg.

Serpieri, Roberto

Travascio, Francesco

Inhaltsverzeichnis

1;Foreword;7
2;Preface;9
3;Contents;11
4;1 Variational Multi-phase Continuum Theories of Poroelasticity: A Short Retrospective;14
4.1;1.1 Introduction;14
4.2;1.2 Variational Theories from the 70s to the 80s;18
4.2.1;1.2.1 Cowin's Theory;19
4.2.2;1.2.2 Mindlin's Variational Single-Phase Theory;19
4.2.3;1.2.3 The Variational Theory of Immiscible and Structured Mixtures by Bedford and Drumheller;20
4.3;1.3 Most Recent Theories;22
4.3.1;1.3.1 Variational Theories by Lopatnikov and Co-workers;22
4.3.2;1.3.2 Variational Higher Gradient Theories by dell'Isola and Co-workers;22
4.4;1.4 Conclusions;24
4.5;References;25
5;2 Variational Macroscopic Two-Phase Poroelasticity. Derivation of General Medium-Independent Equations and Stress Partitioning Laws;29
5.1;2.1 Introduction;29
5.2;2.2 Variational Formulation;33
5.2.1;2.2.1 Basic Configuration Descriptors;34
5.2.2;2.2.2 Variational Formulation;45
5.2.3;2.2.3 Integral Equations;55
5.2.4;2.2.4 Strong Form Equations;59
5.2.5;2.2.5 Additional Solid-Fluid Interaction;66
5.2.6;2.2.6 The Kinematically-Linear Medium-Independent Problem;69
5.2.7;2.2.7 Equations for Static and Quasi-static Problems;72
5.3;2.3 Discussion and Conclusions;79
5.4;References;82
6;3 The Linear Isotropic Variational Theory and the Recovery of Biot's Equations;86
6.1;3.1 Introduction;86
6.2;3.2 Two-Phase Medium-Independent Variational Equations ƒ;88
6.3;3.3 Linear Elastic Isotropic Constitutive Theory ƒ;92
6.4;3.4 Governing PDEs for the Isotropic Linear Problem;96
6.4.1;3.4.1 baru(s)-baru(f) Hyperbolic PDEs with Inertial Terms;96
6.4.2;3.4.2 Analysis of Wave Propagation;97
6.4.3;3.4.3 PDE for Static and Quasi-static Interaction;102
6.5;3.5 Bounds and Estimates of Elastic Moduli;105
6.5.1;3.5.1 Basic Application of CSA;107
6.5.2;3.5.2 Application of CSA to the Extrinsic/Intrinsic Description;110
6.6;3.6 The Limit of Vanishing Porosity;116
6.7;3.7 Comparison with Biot's Theory and Concluding Remarks;121
6.8;References;124
7;4 Stress Partitioning in Two-Phase Media: Experiments and Remarks on Terzaghi's Principle;126
7.1;4.1 Introduction;127
7.2;4.2 Boundary Conditions with Unilateral Contact;134
7.3;4.3 Kinematic and Static Characterization of Undrained Flow Conditions;136
7.3.1;4.3.1 Static Characterization of Undrained Flow;137
7.4;4.4 Stress Partitioning in Ideal Compression Tests;144
7.4.1;4.4.1 Ideal Jacketed Drained Test;149
7.4.2;4.4.2 Ideal Unjacketed Test;151
7.4.3;4.4.3 Ideal Jacketed Undrained Test;155
7.4.4;4.4.4 Creep Test with Controlled Pressure;159
7.5;4.5 Analysis of Nur and Byerlee Experiments;162
7.5.1;4.5.1 Determination of bare(s);165
7.5.2;4.5.2 Estimates of (s);165
7.6;4.6 Domain of Validity of Terzaghi's Principle According to VMTPM;167
7.6.1;4.6.1 Recovery of Terzaghi's Law for Cohesionless Frictional Granular Materials;168
7.6.2;4.6.2 Extensibility of Terzaghi's Effective Stress and Terzaghi's Principle Beyond Cohesionless Granular Materials;170
7.7;4.7 Discussions and Conclusions;172
7.8;References;175
8;5 Analysis of the Quasi-static Consolidation Problem of a Compressible Porous Medium;179
8.1;5.1 Introduction;179
8.2;5.2 Theoretical Background;180
8.2.1;5.2.1 Dimensionless Analysis;180
8.2.2;5.2.2 Semi-analytical Solution of the Stress-Relaxation Problem;182
8.2.3;5.2.3 Numerical Solutions;185
8.3;5.3 Discussion and Conclusions;186
8.4;References;190
9;Appendix A Notation and Identities for Differential Operations;192
10;Appendix B Variation of Individual Terms in Lagrange Function;202