Poro-Elastic Theory with Applications to Transport in Porous Media

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