Advanced soil physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Malabar, Fla.
Krieger
1984
|
| Edition: | Repr. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 534 S. |
| ISBN: | 089874721X |
Staff View
MARC
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| 245 | 1 | 0 | |a Advanced soil physics |c Don Kirkham ; W.L. Powers |
| 250 | |a Repr. ed. | ||
| 264 | 1 | |a Malabar, Fla. |b Krieger |c 1984 | |
| 300 | |a 534 S. | ||
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| adam_text | CONTENTS
Chapter 1 Static Water in Soil
A. Introduction, 1
B. Structure of Water, 2
C. Forces and Energy in Water, 4
1. Van der Waals-London (V-L) forces, 4
2. The double layer, 5
3. The zeta potential, 7
4. The streaming potential, 8
5. The thickness of the double layer, 8
6. Dispersion of soil colloids, 9
7. Surface tension, 11
8. Pressure energy, 14
D. Surface Tension and Energy Effects of Water, 15
1. Pressure under curved water films, 15
2. Height of rise of water in a capillary, 21
3. Tension under a capillary meniscus, 23
E. Potential Energy of Soil Water, 24
1. The capillary potential (matric potential), 24
2. Devices to measure the capillary potential, 27
3. Hysteresis, 33
4. Pressure and gravitational potentials, 34
5. Heads in a soil column, 36
F. Summary, 37
Problems
References
Symbols
Chapter 2 Darcy s Law, Laplace s Equation, and Boundary Value
Problems
A. Introduction, 46
B. Darcy s Law, 46
ix
38
41
44
46
S CONTENTS
C. Laplace s Equation, 49
1. Derivation of Laplace s equation, 49
2. Solutions of Laplace s equation, 52
3. Eider s relation, 57
4. Laplace s equation in cylindrical coordinates, 59
D. Boundary Value Problems, 61
E. Series Approximation of Boundary Conditions, 63
1. Introduction, 63
2. Infinite series of orthonormal functions, 63
3. Fourier series, 66
F. Series Solutions of Laplace s Equation in Cylindrical
Coordinates, 69
1. Bessel functions, 69
2. General solution of Laplace s equation for
cylindrical coordinates in axial symmetry, 71
G. Linear Flow Laws and Laplace s Equation, 74
Problems 75
References 80
Symbols 82
Chapter 3 Physical Artifices for Solving Flow Problems 85
A. Introduction, 85
1. A change in notation, 85
2. Flow nets, 86
B. Dupuit-Forchheimer (DF) Theory, 87
1. The DF assumptions, 87
2. DF theory for ditch drainage, 89
3. A DF soil, 91
4. Streamlines in a DF soil, 92
C. Solution by Fourier Series, 95
1. Fourier series and the boundary value problem, 95
2. Ditch drainage of soil underlain by gravel, 97
3. Tube drainage of soil over a barrier, 111
D. Solution by Bessel Functions and Fourier Series, 120
1. Seepage to an auger hole, 120
2. Boundary conditions, 121
3. The potential function, 122
4. The stream function, 127
E. Summary, 130
Problems 13Q
References 135
Symbols
CONTENTS
XI
Chapter 4 Further Techniques for Solving Flow Problems 140
A. Introduction, 140
B. Generation of Orthonormal Functions:
the Gram-Schmidt Process, 140
C. Water Flow into and Through Water-Saturated
Soil Bedding, 146
1. Boundary conditions, 147
2. The potential function j , 148
3. The stream function yp, 159
4. The flow net, 160
D. Numerical Methods, 161
1. Finite differences, 161
2. Numerical solution to Laplace s equation, 165
3. Numerical solution to ditch drained land, 167
E. Conformai Mapping, 170
1. The complex variable, 170
2. Definition and properties of conformai mapping, 177
3. Solution by conformai mapping of radial flow
into a well, 177
F. Electrical Analogs, 183
G. Drainage Models, 186
H. Summary and Discussion, 187
Problems 188
References 190
Symbols 193
Chapter 5 The Schwarz-Christoffel Transformation 196
A. Introduction, 196
B. The Transformation Differential Equation, 196
1. Walking rule for critical points, 199
C. Flow at a Corner, 200
D. Flow into Ditches, 204
1. Walking rule for streamlines, 206
2. Construction of the w plane, 206
3. Transformation of the z and w planes to
the t plane, 207
4. The modified t plane, 208
5. Elliptic integrals, 208
6. Evaluation of transformation constants, 209
7. Integration of the w to t plane differential
equation, 213
8. The ditch flux Q, 215
CONTENTS
E. Well Flow by the Schwarz-Christoffel
Transformation, 216
F. Richmond s Method: The z, W, w, and t Planes, 219
1. Seepage to a slotted well liner, 219
2. Transformation of the z plane to the W plane, 220
3. Transformation of the W plane to the t plane, 223
4. Transformation of the w plane to the t plane, 225
5. The flow QB forn rows of slots, 227
G. Hodographs, 229
Problems
References
Symbols
229
230
232
Chapter 6 Fundamental Concepts of Unsaturated Flow 235
A. Introduction, 235
B. Validity of Darcy s Law for Unsaturated Water Flow, 236
C. A Simple Equation for the Advance of a Wetting Front
in a Horizontal Soil Column, 237
D. Development of the Differential Equation of
Unsaturated Flow, 239
1. The water diffusivity D, 242
2. Introduction of diffusivity D into the
differential equation, 244
E. Mathematical Concepts Applicable to Diffusion
Equations, 245
1. Introduction, 245
2. Boundedness, boundary, and initial conditions, 245
3. Laplace transforms, 246
F. Solution to the One-Dimensional Diffusion Equation
for a Constant Diffusivity, 251
G. Measurement of the Diffusivity, 256
1. Introduction, 256
2. Diffusivity by the method of Bruce and Klute,
Boltzmann s transformation, 257
3. Diffusivity by the pressure plate outflow method, 264
4. Discussion of methods for measuring diffusivity, 274
H. Boltzmann s Transformation and a Wetting Front, 275
I. Summary, 276
Problems 278
References 279
Symbols 283
CONTENTS
XU1
Chapter 7 Solutions to Some Unsaturated Flow Problems 286
A. Introduction, 286
B. Philip s Solutions for Horizontal and
Vertical Infiltration, 286
1. Introduction, 286
2. Horizontal infiltration, 287
3. Vertical infiltration, 320
4. Quantity of infiltration, 342
5. Infiltration rate, 344
C. A Numerical Solution for Infiltration, 346
1. Introduction, 346
2. Horizontal infiltration by Ashcroft et al., 346
3. Vertical infiltration by Hanks and Bowers, 354
D. Evaporation from Horizontal Soil Columns,
Gardner (1959), 359
1. Introduction, 359
2. Solution, 360
E. Summary, 364
Problems 365
References 373
Symbols 376
Chapter 8 Miscible Displacement 379
A. Introduction, 379
B. Experimental Information, 380
1. Physical processes of the movement of solutes
in fluids, 380
2. Types of fluid flow through porous media, 382
3. Hypothetical breakthrough curves, 385
4. Experimental breakthrough curves, 386
C. Mathematical Models for Miscible Displacement, 388
1. Introduction, 388
2. Differential equation for longitudinal dispersion, 389
3. General solution for the one-dimensional
dispersion equation, 391
4. Solution for the dispersion of a displacing front, 397
5. Solution for the dispersion of a slug of fluid, 402
6. Numerical calculations using dispersion formulas, 405
7. Summary on dispersion models, 413
8. Differential equation for diffusion and mass flow, 413
9. Solution for diffusion and mass transfer of a
displacing front, 415
10. Summary on mathematical models, 418
BV
CONTENTS
D. Some Miscible Displacement Research, 419
E. Summary, 420
Problems
References
Symbols
421
423
425
Chapter 9 Gaseous Diffusion in Soils 428
A. Introduction, 428
B. Fick s Law and the Differential Equation of
Caseous Diffusion, 429
C. A General Solution to the Diffusion Equation for
Soil Air, 431
D. The Diffusion Equation in Mole Fractions and
Partial Pressures, 432
E. The Diffusion Coefficient D in Terms of Da, 434
F. Measurement of the Gaseous Diffusion Coefficient D
for Soils, 435
1. Taylor s method for measuring D, 435
2. Loschmidi s method for measuring D, 437
G. Steady State Diffusion in Soils, 440
1. Introduction, 440
2. Diffusion of C02 in soil when a and D are
constant, 441
3. Diffusion of 00% when a and D are functions
of depth, 442
H. Transient State Diffusion of Oxygen in Soil, 445
I. Summary and Some Other Work on Diffusion of
Gases in Porous Media, 454
Problems 455
References 456
Symbols 459
Chapter 10 Soil Temperature
462
A. Introduction, 462
B. Terminology and Fourier s Heat Flow Law, 463
1. Terminology, 463
2. Fourier s heat flow law, 464
CONTENTS
XV
C. Mathematical Equation for Heat Flow by
Conduction, 464
1. Introduction, 464
2. The partial differential equation of heat flow, 465
3. The sine wave approximation of soil temperature, 466
4. A sine wave solution to the heat flow equation, 468
5. Other solutions to the heat flow equations, 473
D. Determination of Heat Flux in Soil, 476
1. Introduction, 476
2. Determination of heat flux by solutions to the
heat flow equation, 476
3. Heat flux determination from heat flux meters
and temperature data, 478
E. Determination of Thermal Conductivity and
Diffusivity of Soil, 480
F. Simultaneous Heat and Moisture Flow, 481
G. Frozen Soil and Frost Heaving, 483
H. Summary, 484
Problems
References
Symbols
Appendix 1. Derivation of the Cauchy-Riemann Relations and
Proof that Equipotentials and Streamlines Intersect Each
Other Orthogonally
Appendix 2. A Table of Expressions for Approximating
a Function/(x)
Appendix 3. Proof of Certain Elliptic Integral Formulas
Appendix 4. Derivation of (7-54) of Chapter 7
Appendix 5. Proof of (7-75), (7-75a), and (7-78)
Appendix 6. Proof of the Fundamental Lemma of
Partial Differentiation
Appendix 7. Diffusion Equation Transformations
484
486
489
491
496
504
508
515
523
526
Index
529
|
| adam_txt |
CONTENTS
Chapter 1 Static Water in Soil
A. Introduction, 1
B. Structure of Water, 2
C. Forces and Energy in Water, 4
1. Van der Waals-London (V-L) forces, 4
2. The double layer, 5
3. The zeta potential, 7
4. The streaming potential, 8
5. The thickness of the double layer, 8
6. Dispersion of soil colloids, 9
7. Surface tension, 11
8. Pressure energy, 14
D. Surface Tension and Energy Effects of Water, 15
1. Pressure under curved water films, 15
2. Height of rise of water in a capillary, 21
3. Tension under a capillary meniscus, 23
E. Potential Energy of Soil Water, 24
1. The capillary potential (matric potential), 24
2. Devices to measure the capillary potential, 27
3. Hysteresis, 33
4. Pressure and gravitational potentials, 34
5. Heads in a soil column, 36
F. Summary, 37
Problems
References
Symbols
Chapter 2 Darcy's Law, Laplace's Equation, and Boundary Value
Problems
A. Introduction, 46
B. Darcy's Law, 46
ix
38
41
44
46
S CONTENTS
C. Laplace's Equation, 49
1. Derivation of Laplace's equation, 49
2. Solutions of Laplace's equation, 52
3. Eider's relation, 57
4. Laplace's equation in cylindrical coordinates, 59
D. Boundary Value Problems, 61
E. Series Approximation of Boundary Conditions, 63
1. Introduction, 63
2. Infinite series of orthonormal functions, 63
3. Fourier series, 66
F. Series Solutions of Laplace's Equation in Cylindrical
Coordinates, 69
1. Bessel functions, 69
2. General solution of Laplace's equation for
cylindrical coordinates in axial symmetry, 71
G. Linear Flow Laws and Laplace's Equation, 74
Problems 75
References 80
Symbols 82
Chapter 3 Physical Artifices for Solving Flow Problems 85
A. Introduction, 85
1. A change in notation, 85
2. Flow nets, 86
B. Dupuit-Forchheimer (DF) Theory, 87
1. The DF assumptions, 87
2. DF theory for ditch drainage, 89
3. A DF soil, 91
4. Streamlines in a DF soil, 92
C. Solution by Fourier Series, 95
1. Fourier series and the boundary value problem, 95
2. Ditch drainage of soil underlain by gravel, 97
3. Tube drainage of soil over a barrier, 111
D. Solution by Bessel Functions and Fourier Series, 120
1. Seepage to an auger hole, 120
2. Boundary conditions, 121
3. The potential function, 122
4. The stream function, 127
E. Summary, 130
Problems 13Q
References 135
Symbols
CONTENTS
XI
Chapter 4 Further Techniques for Solving Flow Problems 140
A. Introduction, 140
B. Generation of Orthonormal Functions:
the Gram-Schmidt Process, 140
C. Water Flow into and Through Water-Saturated
Soil Bedding, 146
1. Boundary conditions, 147
2. The potential function j , 148
3. The stream function yp, 159
4. The flow net, 160
D. Numerical Methods, 161
1. Finite differences, 161
2. Numerical solution to Laplace's equation, 165
3. Numerical solution to ditch drained land, 167
E. Conformai Mapping, 170
1. The complex variable, 170
2. Definition and properties of conformai mapping, 177
3. Solution by conformai mapping of radial flow
into a well, 177
F. Electrical Analogs, 183
G. Drainage Models, 186
H. Summary and Discussion, 187
Problems 188
References 190
Symbols 193
Chapter 5 The Schwarz-Christoffel Transformation 196
A. Introduction, 196
B. The Transformation Differential Equation, 196
1. Walking rule for critical points, 199
C. Flow at a Corner, 200
D. Flow into Ditches, 204
1. Walking rule for streamlines, 206
2. Construction of the w plane, 206
3. Transformation of the z and w planes to
the t plane, 207
4. The modified t plane, 208
5. Elliptic integrals, 208
6. Evaluation of transformation constants, 209
7. Integration of the w to t plane differential
equation, 213
8. The ditch flux Q, 215
CONTENTS
E. Well Flow by the Schwarz-Christoffel
Transformation, 216
F. Richmond's Method: The z, W, w, and t Planes, 219
1. Seepage to a slotted well liner, 219
2. Transformation of the z plane to the W plane, 220
3. Transformation of the W plane to the t plane, 223
4. Transformation of the w plane to the t plane, 225
5. The flow QB forn rows of slots, 227
G. Hodographs, 229
Problems
References
Symbols
229
230
232
Chapter 6 Fundamental Concepts of Unsaturated Flow 235
A. Introduction, 235
B. Validity of Darcy's Law for Unsaturated Water Flow, 236
C. A Simple Equation for the Advance of a Wetting Front
in a Horizontal Soil Column, 237
D. Development of the Differential Equation of
Unsaturated Flow, 239
1. The water diffusivity D, 242
2. Introduction of diffusivity D into the
differential equation, 244
E. Mathematical Concepts Applicable to Diffusion
Equations, 245
1. Introduction, 245
2. Boundedness, boundary, and initial conditions, 245
3. Laplace transforms, 246
F. Solution to the One-Dimensional Diffusion Equation
for a Constant Diffusivity, 251
G. Measurement of the Diffusivity, 256
1. Introduction, 256
2. Diffusivity by the method of Bruce and Klute,
Boltzmann's transformation, 257
3. Diffusivity by the pressure plate outflow method, 264
4. Discussion of methods for measuring diffusivity, 274
H. Boltzmann's Transformation and a Wetting Front, 275
I. Summary, 276
Problems 278
References 279
Symbols 283
CONTENTS
XU1
Chapter 7 Solutions to Some Unsaturated Flow Problems 286
A. Introduction, 286
B. Philip's Solutions for Horizontal and
Vertical Infiltration, 286
1. Introduction, 286
2. Horizontal infiltration, 287
3. Vertical infiltration, 320
4. Quantity of infiltration, 342
5. Infiltration rate, 344
C. A Numerical Solution for Infiltration, 346
1. Introduction, 346
2. Horizontal infiltration by Ashcroft et al., 346
3. Vertical infiltration by Hanks and Bowers, 354
D. Evaporation from Horizontal Soil Columns,
Gardner (1959), 359
1. Introduction, 359
2. Solution, 360
E. Summary, 364
Problems 365
References 373
Symbols 376
Chapter 8 Miscible Displacement 379
A. Introduction, 379
B. Experimental Information, 380
1. Physical processes of the movement of solutes
in fluids, 380
2. Types of fluid flow through porous media, 382
3. Hypothetical breakthrough curves, 385
4. Experimental breakthrough curves, 386
C. Mathematical Models for Miscible Displacement, 388
1. Introduction, 388
2. Differential equation for longitudinal dispersion, 389
3. General solution for the one-dimensional
dispersion equation, 391
4. Solution for the dispersion of a displacing front, 397
5. Solution for the dispersion of a slug of fluid, 402
6. Numerical calculations using dispersion formulas, 405
7. Summary on dispersion models, 413
8. Differential equation for diffusion and mass flow, 413
9. Solution for diffusion and mass transfer of a
displacing front, 415
10. Summary on mathematical models, 418
BV
CONTENTS
D. Some Miscible Displacement Research, 419
E. Summary, 420
Problems
References
Symbols
421
423
425
Chapter 9 Gaseous Diffusion in Soils 428
A. Introduction, 428
B. Fick's Law and the Differential Equation of
Caseous Diffusion, 429
C. A General Solution to the Diffusion Equation for
Soil Air, 431
D. The Diffusion Equation in Mole Fractions and
Partial Pressures, 432
E. The Diffusion Coefficient D in Terms of Da, 434
F. Measurement of the Gaseous Diffusion Coefficient D
for Soils, 435
1. Taylor's method for measuring D, 435
2. Loschmidi's method for measuring D, 437
G. Steady State Diffusion in Soils, 440
1. Introduction, 440
2. Diffusion of C02 in soil when a and D are
constant, 441
3. Diffusion of 00% when a and D are functions
of depth, 442
H. Transient State Diffusion of Oxygen in Soil, 445
I. Summary and Some Other Work on Diffusion of
Gases in Porous Media, 454
Problems 455
References 456
Symbols 459
Chapter 10 Soil Temperature
462
A. Introduction, 462
B. Terminology and Fourier's Heat Flow Law, 463
1. Terminology, 463
2. Fourier's heat flow law, 464
CONTENTS
XV
C. Mathematical Equation for Heat Flow by
Conduction, 464
1. Introduction, 464
2. The partial differential equation of heat flow, 465
3. The sine wave approximation of soil temperature, 466
4. A sine wave solution to the heat flow equation, 468
5. Other solutions to the heat flow equations, 473
D. Determination of Heat Flux in Soil, 476
1. Introduction, 476
2. Determination of heat flux by solutions to the
heat flow equation, 476
3. Heat flux determination from heat flux meters
and temperature data, 478
E. Determination of Thermal Conductivity and
Diffusivity of Soil, 480
F. Simultaneous Heat and Moisture Flow, 481
G. Frozen Soil and Frost Heaving, 483
H. Summary, 484
Problems
References
Symbols
Appendix 1. Derivation of the Cauchy-Riemann Relations and
Proof that Equipotentials and Streamlines Intersect Each
Other Orthogonally
Appendix 2. A Table of Expressions for Approximating
a Function/(x)
Appendix 3. Proof of Certain Elliptic Integral Formulas
Appendix 4. Derivation of (7-54) of Chapter 7
Appendix 5. Proof of (7-75), (7-75a), and (7-78)
Appendix 6. Proof of the Fundamental Lemma of
Partial Differentiation
Appendix 7. Diffusion Equation Transformations
484
486
489
491
496
504
508
515
523
526
Index
529 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kirkham, Don |
| author_facet | Kirkham, Don |
| author_role | aut |
| author_sort | Kirkham, Don |
| author_variant | d k dk |
| building | Verbundindex |
| bvnumber | BV021874445 |
| classification_rvk | RB 10160 |
| ctrlnum | (OCoLC)633966832 (DE-599)BVBBV021874445 |
| discipline | Geographie |
| discipline_str_mv | Geographie |
| edition | Repr. ed. |
| format | Book |
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| id | DE-604.BV021874445 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:03:32Z |
| indexdate | 2024-07-09T20:46:28Z |
| institution | BVB |
| isbn | 089874721X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015090161 |
| oclc_num | 633966832 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 534 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Krieger |
| record_format | marc |
| spelling | Kirkham, Don Verfasser aut Advanced soil physics Don Kirkham ; W.L. Powers Repr. ed. Malabar, Fla. Krieger 1984 534 S. txt rdacontent n rdamedia nc rdacarrier Bodenmechanik (DE-588)4007385-3 gnd rswk-swf Bodenphysik (DE-588)4432839-4 gnd rswk-swf Bodenphysik (DE-588)4432839-4 s DE-604 Bodenmechanik (DE-588)4007385-3 s 1\p DE-604 Powers, William L. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015090161&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kirkham, Don Advanced soil physics Bodenmechanik (DE-588)4007385-3 gnd Bodenphysik (DE-588)4432839-4 gnd |
| subject_GND | (DE-588)4007385-3 (DE-588)4432839-4 |
| title | Advanced soil physics |
| title_auth | Advanced soil physics |
| title_exact_search | Advanced soil physics |
| title_exact_search_txtP | Advanced soil physics |
| title_full | Advanced soil physics Don Kirkham ; W.L. Powers |
| title_fullStr | Advanced soil physics Don Kirkham ; W.L. Powers |
| title_full_unstemmed | Advanced soil physics Don Kirkham ; W.L. Powers |
| title_short | Advanced soil physics |
| title_sort | advanced soil physics |
| topic | Bodenmechanik (DE-588)4007385-3 gnd Bodenphysik (DE-588)4432839-4 gnd |
| topic_facet | Bodenmechanik Bodenphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015090161&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kirkhamdon advancedsoilphysics AT powerswilliaml advancedsoilphysics |