Poro-Elastic Theory with Applications to Transport in Porous Media

This book treats the subject of porous flow and its applications in three engineering and scientific problems. The first major part of the book is devoted to solute transport in unsaturated porous media. Dynamic hydraulic conductivity and degree of saturation associate with pore pressures are also included in the consolidation-induced solute transport process. The second part of this book focuses on tidal dynamics in coastal aquifers, including shallow water expansion for sloping beaches, two-dimensional problem in estuarine zone and leaky confined aquifers. The final part of the book summarizes the recent development of porous model in the field of liquefaction around marine infrastructures including fundamental mechanisms of momentary and residual seabed liquefaction, two-dimensional and three-dimensional porous models for fluid-seabed interactions around breakwaters, pipelines and piled foundations in marine environments. The authors’ aim is to describe in detail the applications of porous models for several engineering problems. This book will provide academic researchers and industry an overview of recent development in the field of porous models and the applications. Cover Half Title Title Page Copyright Page Contents Preface Acknowledgments Chapter 1: Introduction 1.1. Poro-elastic Theory 1.2. Solute Transport in a Porous Medium 1.3. Tidal Dynamics in Coastal Aquifers 1.4. Porous Models for Fluid-Seabed Interactions around Marine Structures SECTION I: Solute Transport in Porous Media Chapter 2: 1D Small Strain Model for Solute Transport in a Porous Medium 2.1. Introduction 2.2. Theoretical Model 2.2.1. Consolidation equation 2.2.2. Solute transport equation 2.2.3. Non-dimensional analysis of coupled equations 2.3. Application to a Single-Layer Landfill System 2.3.1. Problem considered 2.3.2. Validation of the present model 2.3.3. Dimensionless analysis 2.3.4. Simplification analysis 2.4. Solute Transport in Layered Porous Media 2.4.1. Boundary conditions and initial conditions 2.4.2. Input parameters 2.4.3. Comparison with a single-layer model 2.4.4. Effects of hydraulic conductivity 2.4.5. Effects of shear modulus 2.4.6. Effects of molecular diffusion coefficient 2.4.7. Effects of thickness of each layer 2.4.8. Effects of degree of saturation and Poisson’s ratio 2.4.9. Advective emission and average flow velocity 2.5. Summary 2.6. Appendix: Derivation of Fluid Storage and Solute Transport Equations Chapter 3: 1D Finite Strain Coupled Model for Consolidation and Solute Transport 3.1. Introduction 3.2. Model Formulation 3.2.1. Finite strain consolidation 3.2.2. Solute transport equations 3.2.3. Special cases 3.3. Variations of Parameters in Consolidation and Solute Transport Processes 3.3.1. Soil compressibility 3.3.2. Hydraulic characteristics 3.3.3. Dispersion coefficient 3.3.4. Sorption 3.4. Application to a Landfill Liner 3.4.1. Boundary conditions for consolidation 3.4.2. Boundary conditions for solute transport 3.4.3. Model verification 3.4.4. Correctness of the boundary condition at CCL base 3.5. Numerical Results and Discussions 3.5.1. Effect of consolidation 3.5.2. Effect of degree of saturation 3.5.3. Effect of compressibility of pore-water (CPW) 3.5.4. Effect of dispersion 3.5.5. Effect of finite deformation 3.6. Summary Chapter 4: Solute Transport with Dynamic Hydraulic Conductivity and Compressibility of Pore Fluid 4.1. Introduction 4.2. Dynamic Hydraulic Conductivity and Degree of Saturation 4.2.1. Dynamic hydraulic conductivity 4.2.2. Dynamic degree of saturation 4.3. Theoretical Models 4.3.1. Model configuration 4.3.2. Dynamic model (Kp+Srp) 4.3.3. Dynamic model (Srp) 4.3.4. Dynamic model (Kp) 4.3.5. The conventional model with constant K and Sr 4.4. Numerical Model for a Landfill System 4.4.1. Boundary conditions and initial conditions 4.4.2. Input parameters 4.5. Results and Discussions 4.5.1. Dynamic hydraulic conductivity model (Model Kp) 4.5.2. Dynamic degree of saturation model (Model Srp) 4.5.3. Dynamic hydraulic conductivity and degree of saturation model (Model Kp+Srp) 4.5.4. Average flow velocity and advective emission 4.5.5. Concavity of dynamic degree of saturation function 4.5.6. Parametric study for various air-entry 4.6. Summary 4.7. Appendix: Derivation of solution transport with dynamic hydraulic conductivity and degree of saturation 4.7.1. Derivation of fluid storage equation with dynamic hydraulic conductivity and degree of saturation 4.7.2. Derivation of solute transport equation with dynamic hydraulic conductivity and degree of saturation Chapter 5: Volatile Organic Contamination through Deforming Clay Liner 5.1. Introduction 5.2. Model Formulation 5.2.1. Coordinate systems 5.2.2. Force equilibrium 5.2.3. Moisture and heat energy transfer in the spatial coordinate system (ξ , t) 5.2.3.1. Mass balance for water 5.2.3.2. Mass balance for dry air 5.2.3.3. Heat energy balance 5.2.3.4. Organic solute transfer 5.2.4. Moisture and heat energy transfer in the material coordinate system (z, t) 5.2.5. Constitutive relationships 5.3. Verification of the Proposed Model 5.3.1. Isothermal moisture transport in a deformable soil column 5.3.2. Multi-phase VOC transport 5.4. Application: VOC Transport through an Intact CCL 5.5. Results and Discussions 5.5.1. Geometric non-linearity and soil velocity 5.5.2. Two-way coupling coefficient D* and ρda 5.5.3. Total constitution of the concentration of the VOCs 5.5.4. Longitudinal mechanical dispersion (Dhw and Dhg) 5.5.5. Mechanical consolidation and temperature increase 5.5.6. Contribution of the gaseous phase 5.6. Summary 5.7. Appendix: Coefficients for VOC through deforming clay liner 5.8. Appendix: Coordinate Conversion for the Governing Equations SECTION II: Tidal Dynamics in Coastal Aquifers Chapter 6: Free Surface Flow in Coastal Aquifers: Shallow Water Expansion 6.1. Introduction 6.2. Boundary Value Problem for Free Surface Flow in Coastal Aquifers 6.3. Shallow Water Expansion 6.3.1. Non-dimensional equations 6.3.2. Expansion with the shallow water parameter (ε) 6.4. Previous Solutions 6.4.1. Previous solutions for a vertical beach 6.4.2. Previous solutions for a sloping beach 6.5. Second-Order Shallow Water Expansion 6.5.1. Zeroth-order approximation 6.5.2. First-order approximation 6.5.3. Second-order approximation 6.5.4. Special case: a vertical beach 6.5.5. Comparisons with previous solutions 6.5.6. Effects of the second-order component 6.5.7. Effects of beach slopes (β) 6.6. Higher-Order Shallow Water Expansion 6.6.1. General forms of boundary value problems for zeroth and first-order problem 6.6.2. Semi-analytical approaches 6.6.3. Comparisons with the second-order approximation 6.6.4. Effects of higher-order components 6.6.5. Non-transient components of solutions 6.7. Summary and Remarks 6.8. Appendix: Coefficients for the higher-order solution for tidal dynamics in coastal aquifers Chapter 7: Tidal Dynamics in Coastal Aquifers with Capillarity Effects 7.1. Introduction 7.2. Boundary Value Problem 7.3. Capillarity Correction 7.3.1. Definition of capillarity correction 7.3.2. New definition of capillarity correction 7.4. Approximation I: Complete Solution 7.4.1. The second-order approximation 7.4.2. Special cases 7.4.3. Effects of higher-order components 7.4.4. Effects of the capillarity correction 7.5. Approximation II: Solution with New Definition of Capillarity Corrections 7.5.1. Simplified solution 7.5.2. Comparison of two solutions 7.6. Summary 7.7. Appendix: List of Coefficients for Tidal Dynamics in Coastal Aquifers with Capillarity Effects Chapter 8: Tidal Dynamics in Coastal Aquifers in Estuarine Zone 8.1. Introduction 8.2. Problem Set-up 8.3. Perturbation Approximation 8.3.1. Non-dimensional parameters 8.3.2. Perturbation process 8.3.3. Zeroth-order shallow water expansion 8.3.4. First-order shallow-water expansion 8.3.5. Special cases 8.4. Results and Discussions 8.4.1. Comparison with experimental data 8.4.2. Water table fluctuations for a sandy beach in a temporal domain 8.4.3. Effects of the rhythmic coastline 8.4.4. Effects of beach slopes 8.5. 2D Model with Capillarity Fringe 8.5.1. Boundary value problems 8.5.2. Analytical solutions 8.5.3. Comparison with previous solutions 8.5.4. Capillarity effects in 2D cases 8.6. Summary Chapter 9: Other Solutions for Tidal Dynamics in Coastal Aquifers 9.1. Steepness expansion for free surface flow in coastal aquifers 9.1.1. Steepness expansion 9.1.2. Results and discussions 9.2. Tidal Fluctuation in a Leaky Confined Aquifer 9.2.1. Boundary value problem 9.2.2. Analytical solution 9.2.3. Special case I: Constant head in the semi-permeable layer 9.2.4. Special case II: no leakage 9.2.5. Leakage effects on tidal fluctuations in the confined and phreatic aquifers 9.2.6. Dynamic effects of the phreatic aquifer on tidal head fluctuations in the confined aquifer 9.2.7. Comparison with our previous approximate solution 9.3. Spring-neap tide-induced beach water table fluctuations in a sloping coastal aquifer 9.3.1. Analytical solution 9.3.2. Comparisons with field data 9.3.3. Results and discussions 9.4. Summary SECTION III: Fluid-Seabed Interactions around Marine Structures Chapter 10: Poro-Elastic Model for Fluid-Seabed Interactions 10.1. Introduction 10.2. Hydrodynamic Models 10.2.1. Linear wave theory 10.2.2. Reynolds-Averaged Navier-Stokes (RANS) Model 10.3. Seabed Models: Oscillatory Mechanism 10.3.1. Biot’s consolidation (quasi-static) model 10.3.2. Yamamoto-Madsen model 10.3.3. Okusa (1985) model 10.3.4. Boundary-layer approximation: Mei and Foda (1981) 10.3.5. Discussion: Comparisons between various models 10.3.6. Discussion: comparison with experimental data 10.4. Seabed Models: Residual Mechanism 10.4.1. 1D Seed-Rahman model 10.4.2. 2D Seed-Rahman model 10.4.3. Discussion: Role of Oscillatory and Residual Mechanisms 10.4.4. Discussion: comparison between 1D and 2D Seed-Rahman models 10.4.5. Discussion: development of liquefaction zones 10.5. Two-way Coupling Model 10.5.1. Comparison with experimental data 10.5.2. Comparison between two-way and one-way coupling models for 2D wave-seabed interactions 10.6. Summary Chapter 11: Ocean Waves over a Porous Seabed with Special Cases 11.1. Overview 11.2. A Non-Cohesive Seabed with Dynamic Permeability 11.2.1. Basic governing equations 11.2.2. Dynamic permeability models 11.2.3. Comparison with cylinder tests under 1D wave loading 11.3. A Non-Darcy Flow Model for a Non-Cohesive Seabed 11.3.1. Nonlinear complementarity problem arising from instantaneous liquefaction 11.3.2. Finding the dual condition complementary to the primal constraint 11.3.3. Weak form by using the penalty method 11.3.4. Reformulating the nonlinear complementarity problem as a non-Darcy flow model 11.3.5. Cylinder tests under 1D wave loading 11.3.6. 2D wave-seabed interactions 11.4. Summary Chapter 12: Liquefaction around Marine Structures: Breakwaters 12.1. Overview: Fluid-Seabed-Structure Interactions 12.2. Numerical Model: PORO-FSSI Model 12.3. Validation of the Model 12.4. Seabed Response around a Composite Breakwater under Ocean Wave Loading 12.4.1. Dynamic response of a seabed 12.4.2. Wave-induced momentary liquefaction 12.5. Water Waves over Permeable Submerged Breakwaters with Bragg Reflection 12.5.1. Numerical example configuration 12.5.2. Pore fluid pressures 12.5.3. Vertical effective normal stresses 12.5.4. Liquefaction potential 12.6. 3D Model for Seabed Response around Breakwater Heads 12.6.1. Numerical model set-up 12.6.2. Hydrodynamic process around breakwaters 12.6.3. Dynamic soil responses in the seabed foundation 12.6.4. Soil liquefaction in the seabed foundation 12.7. Seabed Response in the Vicinity of Offshore Detached Breakwaters 12.7.1. Configuration of the breakwaters and input parameters 12.7.2. Hydrodynamics around offshore detached breakwaters 12.7.3. dynamic soil responses around the offshore detached breakwaters 12.7.4. Liquefaction around the offshore detached breakwaters 12.7.5. Parametric study 12.8. Summary Chapter 13: Liquefaction around Marine Structures: Pipelines 13.1. Wave-Seabed Interactions in the Vicinity of Pipelines in a Trench 13.1.1. Theoretical model 13.1.2. Model validations 13.1.3. Hydrodynamic process in the vicinity of the trenched pipeline 13.1.4. Liquefaction around a trench pipeline 13.1.5. Design of a trench layer 13.2. Articulated Concrete Mattresses (ACMs) for Offshore Pipeline Protection 13.2.1. Engineering problem considered 13.2.2. Dual ACMs-pipeline system (DAPS) 13.2.3. Effects of various interaction angles on the seabed liquefaction 13.3. Summary Chapter 14: Liquefaction around Marine Structures: Pile-type foundation 14.1. Seabed Stability around a Single Mono-pile 14.1.1. Theoretical models (PORO-FSSI-FOAM) 14.1.2. Model validation 14.1.3. Wave run-up on a single mono-pile 14.1.4. Development of the wave and current-induced instantaneous liquefaction around the pile 14.1.5. Combined breaking wave and currents-induced instantaneous liquefaction around the pile 14.2. Seabed Instability around the Pile Group 14.3. Application of Protection Mattress around the Pile Group 14.4. Seabed Liquefaction around a Jacket Support Offshore Wind Turbine Foundation 14.4.1. Hydrodynamic process 14.4.2. Dynamic seabed response 14.4.3. Seabed instability around jacket structure 14.5. Summary Bibliography Index This book treats the subject of porous flow and its applications in three engineering and scientific problems. The first major part of the book is devoted to solute transport in unsaturated porous media. Dynamic hydraulic conductivity and degree of saturation associate with pore pressures are also included in the consolidation-induced solute transport process. The second part of this book focuses on tidal dynamics in coastal aquifers, including shallow water expansion for sloping beaches, two-dimensional problem in estuarine zone and leaky confined aquifers. The final part of the book summarizes the recent development of porous model in the field of liquefaction around marine infrastructures including fundamental mechanisms of momentary and residual seabed liquefaction, two-dimensional and three-dimensional porous models for fluid-seabed interactions around breakwaters, pipelines and piled foundations in marine environments. The authors'aim is to describe in detail the applications of porous models for several engineering problems. This book will provide academic researchers and industry an overview of recent development in the field of porous models and the applications.The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons Non Commercial-No Derivatives (CC-BY-NC-ND) 4.0 license. Funded by Qingdao University Technology, China "Poro-elastic theory can be widely applied to numerous engineering and scientific problems involving multi-phase media. This book for graduate students and researchers presents the basic mechanics of poro-elastic theory and explores in detail three particular applications: solute and contaminant transport in compacted clay liner systems with consolidation effects; groundwater table fluctuations in coastal aquifers resulting from tidal dynamics; and basic seabed mechanisms under dynamic loading, affecting marine infrastructures. Most existing books in the field focus on the mechanics of porous flow with applications in environmental science. Open Access from http://www.taylorfrancis.com"-- Provided by publisher Poro-elastic theory has been widely applied in numerous engineering and scientific problem involved in multiphase media. For environmental science and civil related engineering fields, we are interested in static and dynamic response of porous media subject to environmental loading as well as other type of forces, such as those ofthermal and chemical origin. These are generally known as poromechanics, which was first created from the Biot Conference on Poromechanics.