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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