The author has made efforts to present the fundamentals of the subsurface hydrologic processes in logical order by explaining trivial details to facilitate the learning of the subject by “individual study”. Consequently, he has endeavored to analyze the fate of water and water borne pollutants once they infiltrate the land surface. Thus, the transport of water and solutes in the unsaturated and saturated domains beneath the land surface is the main theme of the book. These subsurface flow processes constitute the necessary elements of the “Fundamentals of Subsurface Hydrology”. The essential mathematical steps with requisite explanations are given throughout the book to assist “individual study”. Knowledge of calculus is a prerequisite for in-depth understanding of the book. Analytic solutions in Chapters 10 and 11 are developed using the Laplace transform technique. The presentation of the “Fundamentals of Subsurface Hydrology” is arranged into twelve chapters. Concept of subsurface flow along with the brief history of the evolution of ideas of saturated and unsaturated flows are described in Chapter 1. Chapters 2, 3 and 4 deal primarily with the water in the porous geologic formation by comprehensively describing the (i) porous geologic matrix, (ii) elements of fluid mechanics, and (iii) water beneath the land surface. Chapters 5, 6, 7, 8, and 9 form the core of the book. They elucidate, in the same order, on (i) groundwater movement, (ii) differential equations of groundwater flow, (iii) water movement in vadose zone, (iv) pollution of subsurface water, and (v) subsurface flow equations in curvilinear coordinates. In these chapters the governing differential equations for water and solute transport in saturated and partially saturated geologic formations are derived using the principle of conservation of mass and the appropriate transport laws. Generalized form of the boundary conditions are written to complete the mathematical formulations of the transport processes in subsurface hydrology. Most of the derivations appearing in these chapters are elucidated with the help of the adequate number of mathematical steps to enable the reader to easily grasp them. Once a physical problem is formulated, it could be solved using different analytical and numerical techniques. Analytic solutions of some simple groundwater flow problems are derived in chapters 10 and 11. They comprise of (i) analytical modeling of unconfined groundwater flow, as well as (ii) hydraulics of wells, in confined and unconfined aquifers. Many of these solutions are utilized for determining the aquifer parameters. Chapter 12, the last chapter of the book, lays the theoretical foundation for the finite region approach for estimating natural groundwater recharge from precipitation and irrigation. It elucidates the principles, methods and structures for artificial groundwater recharge. Land and stream management works which store rain water, modulate runoff, and enhance groundwater recharge are adequately discussed using research data from a 850 ha integrated watershed management project in Madhya Pradesh, and field data from a 476 sq Km catchment area of Arvari river in Rajasthan, India. Improvement in groundwater quality due to recharge is demonstrated using field observations The book is intended to serve the needs of the students, teachers, researchers, and field practitioners in the disciplines of agricultural, civil, hydrologic, and environmental engineering, water resources, soil physics, hydrogeology, and earth sciences, who are interested to learn the fate of water and solutes in the weathered zone constituting the upper mantle of the earth. The author is of the view that the book would meet its basic objective of facilitating in-depth learning of the subject by “individual study”.

1. Introduction 1

1.1 Subsurface Hydrology 1

1.2 Hydrologic Cycle and Subsurface Water 2

1.3 A Brief History 2

1.3.1 Fourier and Ohm’s Laws 2

1.3.2 Flow through Saturated Geologic Materials: Evolution of Concepts 2

1.3.3 Unsaturated Flow through Porous Materials: Development of Ideas 6

2. Porous Geologic Matrix 9

2.1 Weathering of Rocks and Formation of Regolith 9

2.2 The Porous Medium 10

2.3 Representative Elementary Volume 11

2.4 Soil Texture 13

2.5 Particle Size Distribution 14

2.5.1 Sieve Analysis 15

2.5.2 Sedimentation Analysis 16

2.5.3 Measures of Gradation of Particles 18

2.5.4 Effective Grain Diameter: D10 19

2.6. The Soil Resources of India 20

2.7 Volume, Mass and Surface Area Relationships 22

2.8 Structure of Granular Materials 27

3. Elements of Fluid Mechanics 31

3.1 Newton’s Law of Viscosity 32

3.2 Pressure Intensity at a Point in a Fluid Continuum 33

3.3 Pressure-intensity Variation along a Vertical Line 34

3.4 Pressure-intensity Variation along a Horizontal Line 35

3.5 Osmotic Pressure 36

3.6 Bulk Modulus of Elasticity of Fluids 37

3.7 Classification of Flow 38

3.8 Streamline 39

3.9 Continuity Equation 41

3.10 Energy of Surface and Subsurface Waters 43

3.10.1 Basic Energy Equation along a Streamline 43

3.10.2 Gravitational, Pressure, and Velocity Heads 46

3.10.3 Bernoulli’s Equation for Viscous Fluids 47

3.10.4 Energy of Water in Geologic Formations 47

3.11 Flow Nets 48

3.12 Manometers 51

4. Water beneath the Land Surface 55

4.1 Soil Moisture and Groundwater 55

4.2 Vertical Distribution of Water in the Regolith 55

4.3 Water Retention in the Unsaturated Zone 58

4.3.1 Surface Tension 58

4.3.2 Work of Cohesion and Adhesion, and Contact Angle 59

4.3.3 Pressure Difference across a Curved Water- Air Interface 60

4.3.4 Capillary Rise of Water in a Circular Tube 62

4.3.5 Capillary Pressure of Water in Interstices 63

4.3.6 Water Retention Characteristic of a soil 64

4.4 Saturated Zone and Aquifers 67

4.4.1 Aquifer, Aquiclude, Aquifuge and Aquitard 67

4.4.2 Type of Aquifers 68

4.4.3 Hydraulic Properties of Aquifers 70

4.4.3.1 Permeability, Hydraulic Conductivity, and Transmissivity 70

4.4.3.2 Specific Yield and Specific Retention 70

4.4.3.3 Specific storage and Storage Coefficient 71

4.5 The Hydrogeological Setup of India 73

4.5.1 Aquifer Systems of India 73

5. Groundwater Movement 81

5.1 Darcy’s Law 82

5.2 Differential Form of Darcy’s Law 85

5.3 Homogeneous and Isotropic Formation 86

5.4 Darcy’s Law for Multidimensional Flow 86

5.5 Deviation from Darcy’s Law 87

5.6 Layered Geologic Materials 89

5.6.1 Flow Parallel to Layers 89

5.6.2 Flow Normal to Layers 90

5.6.3 Refraction of Flow Lines Across the Interface 92

5.7 Laboratory Measurement of Hydraulic Conductivity 93

5.7.1 Constant Head Permeameter 93

5.7.2 Falling Head Permeameter 94

5.8 Derivation of Darcy’s Law 95

5.8.1 The Bundle of Capillary Tubes Model 96

5.8.2 The Hydraulic Radius Model 100

5.8.2.1 Computation of Specific Surface Area from PSD Data 103

5.8.2.2 Matching Parameter of the Hydraulic Radius Model 104

5.8.2.3 Comparison with Capillary Tube Models 111

5.8.3 The Drag Resistance Model 112

5.8.3.1 Evaluation of the Matching Parameter, Cd 115

5.8.3.2 Dependence of Matching Parameter of the Drag Resistance Model on Soil Properties 116

5.8.3.3 Comparison of Hydraulic Radius and Drag Resistance Models 117

5.9 Springs 118

5.9.1 Occurrence of Springs 118

5.9.2 Classification of Springs 118

5.9.3 Sustainability of Spring Flow 121

6. Differential Equations of Groundwater Flow 125

6.1 Groundwater Storage in Confined and Unconfined Aquifers 125

6.1.1 Effect of Atmospheric Pressure on Piezometric Level 129

6.2. Mass Conservation in Saturated Consolidating Geologic Formation 130

6.3 Mass Conservation in Nondeformable Formation Having Source and Sink 134

6.4 Confined Aquifer between Horizontal Aquitards 136

6.5 Vertical Integration for Reducing Spatial Dimension 138

6.5.1 Confined Aquifer between Tilted Aquicludes 142

6.5.2 Confined Aquifer between Tilted Aquitards 143

6.5.3 Integration in the Phreatic Zone 144

6.6 Dupuit-Forchheimer Asumptions and Boussinesq’s Equation 144

6.6.1 Dupuit-Forchheimer Asumptions 145

6.6.2 Boussinesq’s Equation 145

6.6.3 Linearization of Boussinesq’s Equation 148

6.7 Initial and Boundary Conditions 151

6.7.1 Boundary of Specified Hydraulic Head 152

6.7.2 Boundary of Specified Flux 152

6.7.3 Impervious Layer 153

6.7.4 Boundary Specified with the Combination of Head and it’s Derivative 153

6.7.5 Boundary Condition on the Free Surface 154

6.7.6 Seepage Face 157

6.7.7 Initial Condition 157

7. Water Movement in Vadose Zone 159

7.1 Introduction 159

7.2. Darcy-Buckingham Law 160

7.3 Mass Conservation in Vadose Zone – Richards’ Equation 162

7.4 Capillary Potential – Air Humidity Relationship 166

7.5 Infiltration, Evaporation, and Capillary Rise 167

7.5.1 Infiltration 167

7.5.2 Evaporation and Evapotranspiration 168

7.5.3 Capillary Rise from the Water Table 169

7.6 Boundary Value Problems Involving Richards equation 170

7.7 Water Retention Characteristic of Porous Geologic Materials 172

7.7.1 Functional Regression Models 173

7.7.1.1 Brooks and Corey Model 173

7.7.1.2 van Genuchten Model 174

7.7.1.3 Kosugi Model 174

7.7.1.4 Durner Multi-modal Model 175

7.7.1.5 Seki Multi-modal Model 175

7.7.2 Discrete Matric Potential Regression Models 176

7.7.3 Semi-physical Models 177

7.7.3.1 Arya and Paris Model 177

7.7.3.2 Andersson and Jauhiainen Model 177

7.7.3.3 Singh and Verma Model 182

7.7.3.4 Other Semi-physical Models 195

7.8 Relative Hydraulic Conductivity of Partially Saturated Soils 196

7.8.1 Burdine’s and Mualem’s Models 197

7.8.2 Relative Hydraulic Conductivity from the PSD Data 200

7.8.3 Relative Hydraulic Conductivity of Some UNSODA Soils 202

7.9 Hydraulic Conductivity of Sodic Soils 205

7.10 In Situ Measurement of Unsaturated Hydraulic Conductivity 205

7.10.1 Internal Drainage of a Soil Profile 206

7.10.2 Controlled Infiltration in Soils 208

7.10.2.1 Controlled Infiltration by Sprinkling 210

7.10.2.2 Infiltration through an Impeding Layer 210

7.10.3 Other Methods to Measure Unsaturated Conductivity 210

8. Pollution of Subsurface Water 213

8.1. Introduction 213

8.2. Hydrodynamic Dispersion in Porous Media 219

8.2.1 Mechanical dispersion 219

8.2.2 Molecular Diffusion 221

8.3. A Dispersion Experiment and the Breakout Curve 222

8.4. Solute Transport Law 224

8.4.1 Dispersion Coefficients 224

8.5. Tracer Mass Conservation and Convection Dispersion Equation 226

8.6 Initial and Boundary Conditions 231

8.7 Analytic Solutions 233

8.7.1 Continuous Injection of Solute into an Infinite Saturated Medium 233

8.7.2 Determination of Longitudinal Dispersivity 234

8.8 Numeric Approaches 236

8.8.1 Mathematical Formulation for the Removal of Solutes by Tube Drains 236

8.8.2 Subsurface Flow in Tube-Drained Soil System 241

8.8.2.1 Water Movement in Unsaturated Zone 241

8.8.2.2 Water Movement to Drains in Saturated Zone 242

8.8.3 Semi-Analytic Solution of the Problem for the Removal of Solutes by Tube Drains 244

8.9 Magnitudes of Dispersivities 245

8.10 Occurrence of Saline Waters in Aquifers 245

8.10.1 Sea Water Intrusion in Coastal Aquifers 246

8.10.2 Ghyben-Herzberg Relation 246

8.11 Transition Zone between Fresh and Saline Waters 247

8.12 Reduction of Pollution in Subsurface Water 248

9. Subsurface Flow Equations in Curvilinear Coordinates 251

9.1 Mass Conservation in a Cylindrical Region 251

9.2 Transformation to General Curvilinear Coordinates 254

9.3 Saturated Flow Equations in Cylindrical and Polar Coordinates 257

9.3.1 Specific Discharge in Cylindrical Coordinates 258

9.3.2 Groundwater Flow Equation in Consolidating Aquifer 259

9.3.3 Confined Flow between Horizontal Aquitards 259

9.3.4 Boussinesq’s Equation in Polar Coordinates 260

9.4 Groundwater Flow Equation in Spherical Coordinates 261

9.4.1 Specific Discharge in Spherical Coordinates 262

9.4.2 Three Dimensional Groundwater Flow in Consolidating Aquifer 262

9.5 Richards Equation in Cylindrical and Spherical Coordinates 263

9.6 Convection Dispersion Equation in Cylindrical and Spherical Coordinates 264

10. Analytical Modeling of Unconfined Groundwater Flow 269

10.1 Steady Unconfined Flow with Recharge between Water Bodies 269

10.1.1 Water Table Height between Water Bodies with Equal Water Levels 271

10.2 Unsteady Unconfined Flow between Two Channels 273

10.2.1 Superposition Principle 273

10.2.2 Unconfined Aquifer over a Horizontal Impervious layer 274

10.2.3 Phreatic Aquifer over a Sloping Impervious Layer 280

10.2.4 Solutions of Some Groundwater Flow Problems 281

10.2.4.1 Horizontal Basis Layer: Constant Auxiliary Conditions 281

10.2.4.2 Sloping Basis Layer: Constant Auxiliary Conditions 285

10.3 Stream-Aquifer Interaction in Semi-infinite Flow Domain 287

10.3.1 Seepage from a Canal 289

10.3.2 Seepage to an Effluent Stream 293

10.4 Estimation of Aquifer Diffusivity in Stream-Aquifer System: an Inverse Problem 294

10.4.1 Evaluation of Hydraulic Gradient 299

10.5 Aquifer Parameters from Measurements in Drain-Aquifer System 299

10.5.1 Estimation of the Product of Aquifer Parameters, K D Sy 301

10.5.2 Determination of Aquifer Diffusivity, Specific Yield, and Transmissivity 302

10.5.3 Estimation of Equivalent Depth to Impervious Layer 305

10.6 Groundwater Dynamics in an Infinite Aquifer Underlying a Spreading Strip 306

10.6.1 Development of a Long Groundwater Mound 307

10.6.2 Dissipation of a Long Rectangular Groundwater Mound 310

10.7 Growth and Decay of Rectangular and Circular Groundwater Mounds 312

10.7.1 Dynamics of Groundwater beneath a Rectangular Percolation Pond 312

10.7.2 Water Table Fluctuation beneath a Circular Percolation Tank 316

11. Hydraulics of Wells 323

11.1 Steady Flow to a Fully Penetrating Well 324

11.1.1 Well in a Confined Aquifer 324

11.1.2 Well in an Unconfined Aquifer 328

11.1.3 Well in an Unconfined Aquifer with Uniform Recharge 331

11.2 Steady Flow to a Fully Penetrating Well in a Leaky Confined

Aquifer 333

11.3 Steady Flow to a Fully Penetrating Well with Screens in a

Confined Aquifer 338

11.4 Theis Equation for Unsteady Flow to a Fully Penetrating Well in Confined Aquifer 343

11.4.1 Computation of Well Function 346

11.4.2 Theis Type-Curve Method 346

11.5 Cooper-Jacob Analysis 351

11.6 Chow Method for Estimating Aquifer Parameters 356

11.7 Drawdown Caused by Variable Discharge from a Well in Confined Aquifer 359

11.7.1 Variable Discharge Described by Step Function 362

11.7.2 Theis Recovery Test 363

11.8 Unsteady Flow to Wells in Leaky Confined Aquifers 365

11.8.1 Leaky Confined Aquifer underneath an Aquitard and a Phreatic Aquifer 365

11.8.1.1 Asymptotic Solutions of the Steady Well 368

11.8.1.2 Incompressible Aquitard 372

11.8.1.3 Well in Non-leaky Aquifer 373

11.8.1.4 Infinitely Thick Aquitard 373

11.8.1.5 Drawdown Equation at Steady State 373

11.8.1.6 Share of Aquifer Storage and Induced Leakage in Pumped Water 374

11.8.1.7 Asymptotic Solutions of the Flowing Well 375

11.8.2 Leaky Confined aquifer beneath an Aquitard and an Impermeable Layer 376

11.8.2.1 Asymptotic Solutions of Steady and Flowing wells 378

11.9 Hantush Analysis of Partially Penetrating Wells in Confined Aquifers 380

11.10 Unsteady Flow to a Cavity Well 385

11.10.1 Approximate Solution for the Unsteady Flow to a Spherical Cavity 390

11.11 Neuman’s Analysis for Unsteady Flow to a Well in Unconfined Aquifer 391

11.11.1 Partially Penetrating Well in Water Table Aquifer 392

11.11.2 Fully Penetrating Well in Phreatic Aquifer 398

11.12 Unsteady Flow to Large Diameter Wells 401

11.12.1 A Fully Penetrating Dug-Cum- Bore Well in Confined Aquifer 401

11.12.2 A Partially Penetrating Finite Diameter Well in Unconfined Aquifer 403

11.13 Multiple Well Systems 405

11.13.1 Discharge from the Systems of Two, Three, and Four Interfering Wells 407

11.14 Wells in the Vicinity of Aquifer Boundaries 408

11.14.1 Well Near a Perennial Stream 409

11.14.2 Well Near an Impermeable Boundary 411

11.14.3 Well Near Two Impermeable Boundaries Intersecting at Right Angle 413

11.14.4 Well Near a Stream Intersected by an Impermeable Boundary at Right Angle 414

11.14.5 Well Flow between Parallel Boundaries 415

12. Natural and Artificial Recharge of Groundwater 419

12.1 A Finite Region Approach for Estimating Natural Groundwater Recharge 419

12.2 Recharge from Canal Irrigation System 424

12.3 Artificial Groundwater Recharge 428

12.4 Principles of Artificial Groundwater recharge 429

12.5 Structures for Artificial Recharge 430

12.5.1 Land and Stream Management for Enhancing Surface Infiltration 430

12.5.1.1 Groundwater Recharge Resulting from IWD Interventions 433

12.5.1.2 Transformation of River Flow 437

12.5.2 Recharge Trenches, Pits, and Shafts for Vadose Zone Infiltration 437

12.5.3 Recharge Wells for Injection into Aquifers 439

12.6 Quality Improvement by Recharge 441

12.6.1 Drum Model for Mixing the Native and Recharge Waters 441

12.7 Filtration System for Groundwater Recharge Wells 443

12.7.1 Design of Granular Filter for the Recharge Well 444

12.7.2 Sediment Removal and Hydraulic Properties of Sand Filters 445

12.7.2.1 Rate of Filtration through Vertical Sand Filter 448

12.7.3 Development of Horizontal Filters 449

References 455

Index 475