Theory of Ground Water Movement

Contents\nPreface\nIntroduction\nPart I Steady Flow of Groundwater\nPart II. Unsteady Flows of Groundwaters\nLiterature\nIndex\nPREFACE	5	5\nINTRODUCTION	7	7\nCONTENTS	11	11\nPART I	21	20\nSteady Flow of Groundwater	21	20\nCHAPTER I. PHYSICAL AND MATtiEivlAT L\"CAIJ FUNDAMENTAIJS OF THE THEORY OF GROUNWATER FLOW	21	20\n	§1. Soil Composition	21	20\n	§2. Soil Porosity	24	20\n	§3. Electromolecular Forces in Soils	27	20\n	§4. Various Components of Water in Soil	28	20\n	§5. Seepage Velocity	31	20\n	§6. Experimental Seepage Laws	33	20\n	§7. Seepage Coefficient	35	20\n	§8. Limits of Applicability of the Linear Seepage Law	37	20\n	§9. Capillarity	38	20\n	*§10. Permeability to Water of Incompletely Saturated Soils	39	20\n	§11. Equations of Motion of Groundwaters	41	20\n	*§12. Equations of Motion for Non-Linear Seepage Laws	45	20\nCHAPTER II. TWO-DIMENSIONAL FLOWS IN A VERTICAL PIANE	51	20\n	A. General Considerations	51	20\n		§1. Equations of Motion in a Plane	51	20\n		§2. Boundary Conditions in Two-dimensional Steady Motion	52	20\n		§3. Conditions on the boundary of Two Soils	55	20\n		§4. The Velocity Hodograph	56	20\n		§5. Behaviour of the Velocity in Corner Points of the Flow Region	58	20\n		§6. Examples of Construction of the Velocity Hodograph	60	20\n		§7. The Seepage Triangle [4]	66	20\n		§8. Forces Acting on Soil Particles	67	20\nB. Simplest Examples Of Plane Flows	70	20\n	§9. Preliminary Remarks	70	20\n	§10. Drainage Slit on Impervious Basis	70	20\n	§11. Horizontal Drain in the Absence of an Impervious Basis. Lines of Equal Groundwater Flow	72	20\n	§12. Flat Bottom Weir on a Layer of Infinite Depth	75	20\n	§13. Sheetpile in Pervious Layer of Infinite Depth	81	20\n	§14. Wetted Contour with Drainage Hole	83	20\nCHAPTER III. CONFINED SEEPAGE UNDER HYDRAULIC STRUCTURES	86	20\n	A. Polygonal Regions in Problems of Confined Seepage. Uniqueness Theorem	86	20\n		§1 . Statement of Problem	86	20\n		§2. Conformal Mapping of a Polygon onto a Half Plane	87	20\n		§3. Mapping of a Rectangle onto the Half Plane	91	20\n		§U. Basic Rectangle of Confined Seepage Problems	92	20\n		§5. Uniqueness Theorem	94	20\n	B. Seepage Under Plat-Bottom Foundations	95	20\n		§6. Flat-bottom Foundation on a Layer of Finite Depth	95	20\n		§7. Flat-bottom Foundation on a Drained Stratum	99	20\n		§8. Two Dams with Flat Foundations in Series on a Stratum of Finite Depth	101	20\n	C. Flow About Structures With Cut-off Walls	102	20\n		§9. Mapping onto a Half Plane of a Polygon when All the Sides of this Polygon Converge into One Point	102	20\n		§10. Flow About an Inclined Cut-off Wall	104	20\n		§11. Cut-off for Layer on Impervious Bedrock or on Draining Substratum	105	20\n		§12. Flat Bottom Foundation with Cut-off on a Stratum of Infinite Depth	108	20\n		* §13. Dam with Two Cut-offs On a Pervious Stratum of Finite Depth	113	20\n		* §14. Weir with Two Symmetrical Cut-offs\n		* §15. Embedded Weir	121	20\n		§16. Overfall Weirs	125	20\n	D. Structures with Multiple Cut-offs	126	20\n		§17. The Method of Fragments	126	20\n		§18. Structures with Multiple Cut-offs on a Stratum of Infinite Depth	127	20\n	E. Hydrodynamic Reactions on Weirbases	129	20\n		§19. Resultant Vector of Pressure Forces	129	20\n		§20. Resulting Moment of Pressure Forces	134	20\n		§21. About the Displacement of Boundary Points in Mapped Regions	135	20\n		§22. Application to the Flow of Groundwater Under Dams	138	20\nCHAPTER IV. ZHUKDVSKY\'S FUNCTION AND ITS APPLICATIONS: APPLICATION OF FUNCTIONAL ANALYSIS 140 20\n	A. Direct Methods to Solve Seepage Problems	140	20\n		§1 . Zhukovsky\'s Function	140	20\nCHAPTER IV. (Cont.)	141	20\n	§2. Zhukovsky\'s Cut-off Wall	141	20\n	§3. Single Drain	143	20\n	54. Infiltration and Flow to a Drain	146	20\n	§5. Seepage From a Canal to Symmetrically Disposed Collectors	150	20\n	§6. Seepage From Canal With Collector on One Side	152	20\n	B. Some Unconfined Flows Derived From Confined Flows	153	20\n		§7. Simplified Sketch of Earth Dam on Pervious Layer of Finite Depth	153	20\n		§8. Simplified Scheme of an Earthdam With Cut-off	155	20\n	C. Semi-inverse Method in the Theory of Canal Seepage	157	20\n		§9. Seepage From Canals with Curvilinear Perimeter on Infinitely Deep Stratum	157	20\n		§10. Seepage with Bedrock Conditions at Infinity	159	20\n		§11. Flow to a Drainage Ditch with Curvilinear Profile	161	20\n		§12. Simplified Scheme of Dam with Drain on Soil of Infinite Depth	161	20\n		*§13. Approximate Solution when the Riverbed is Clogged	162	20\n	D. Application of Functional Analysis	164	20\n		§14. Essence of the Method	164	20\n		§15. Groundwater Flow for Inclined Bedrock	165	20\nCHAPTER V. APPLICATION OF THE METHOD OF INVERSION	169	20\n	§1 . Some Inversion Properties	169	20\n	§2. Seepage From a Canal with Trapezoidal Bed	171	20\n	§3. Canal with Triangular Cross-section	178	20\n	§4. Influence of Soil Capillarity on Seepage from Canals	179	20\n	§5. Canal with Trapezoidal Cross-section	180	20\n	§6. Canal with Low Water level [6]	182	20\n	§7. Groundwater Flow to a Drainage Ditch of Trapezoidal Cross-section	186	20\n	§8. Seepage in Soil Overlying Draining or Waterbearing Stratum	195	20\n	§9. Drain or Irrigation Canal in the Case of Evaporation or Infiltration	199	20\n	§10. Semi-inverse Method Applied to Earthdams on Impervious Foundations	202	20\n	§11. Contour of Constant Velocity in Soil of Infinite Depth	205	20\n	§12. Contour of Constant Velocity in Soil of Finite Depth	207	20\n	§13. Contour with Rectilinear Segments and Segments of Constant Velocity	211	20\n	§14. \"Streamlined\" Dam Foundation	212	20\n	§15. \"Streamlined\" Cut-off	215	20\nCHAPTER VI. THE MIXED PROBLEM OF THE THEORY OF FUNCTIONS AND ITS APPLICATIONS TO THE SEEPAGE THEORY	218	20\n	A. The Mixed Problem of The Theory of Functions	218	20\n		§l. Definitionof an Analytic Function by its Real Part on the Real Axis	218	20\n		§2. Mixed Problem of the Theory of Functions	221	20\n		§3. Particular Case of the Problem	224	20\n	B. Problems About Drains and Canals	225	20\n		§4. Drain in Stratum on Bedrock with Non-symmetrical Flow	225	20\n		§5. Flow to a Rectangular Trench with Sloping Free Surface in a Stratum of Infinite Depth	231	20\n		§6. About Seepage Towards a Drain or Canal in the Case of Inclined Bedrock	235	20\n	C. Earth Dams	247	20\n		§7. Drained Earth Dam with Trapezoidal Profile on Impervious Bedrock	247	20\n		*§8. Earth Dam with Horizontal Drain on Pervious Stratum of Infinite Depth [3]	267	20\nCHAPTER VII. APPLICATION OF THE ANALYTIC THEORY OF LINEAR DIFFERENTIAL EQUATIONS	281	20\n	A. General Theory	281	20\n		§1. Introductory Remarks	281	20\n		§2. Conditions at the Real Axis for Two Basic Functions	281	20\n		§3. Problem of Determining Two Functions by Conditions at the Real Axis	283	20\n		§4. Equation with Three Regular Singular Points	287	20\n		§5. Hypergeometric Functions and their Properties	288	20\n		*§6. Curvilinear Polygons\n		§7. Case of Real Exponents. Second Derivation of the Characteristic Equation	293	20\n		§8. Exponents for Basic Cases of the Seepage Theory	296	20\n	B. Problem of Seepage Through a Vertical Dam	301	20\n		§.9.Seepage Rate Through a Dam and Discharge of a Well	301	20\n		§10. Construction of the Solution for a Vertical Dam	304	20\n	C. Dams With Rectangular Trapezoidal Cross-Section	318	20\n		§11. Seepage in a Trapezoidal Dam when Evaporation Occurs	318	20\n		§12. Seepage Through a Trapezoidal Dam without Evaporation	321	20\nCHAPTER VIII. SEEPAGE IN HETEROGENEOUS AND ANISOTROPIC SOILS: SEEPAGE OF TWO FLUIDS	329	20\n	A. Heterogeneous Soils	329	20\n		§1. Weir on Two Strata of Same Thickness	329	20\n		§2. Cut-off in Two Strata of Same Depth	341	20\n		§3. Cut-offs without Penetration on Soil with Two Strata	351	20\n		§1*. Point Vortex in Multilayered Region	355	20\n		§5. Simplest Flows in Stratified Soils	360	20\n	B. Anisotropic Soils	363	20\n		§6. Equations of Motion. Boundary Conditions	363	20\n		§7. Flow to a Drain on Impervious Foundation in Anisotropic Soil [8]	368	20\n		§8. Interpretation of Anisotropic Soil by Means of Two Alternating Soils	370	20\n	C. Two Fluids of Different Density	371	20\n		§9. About Flow of Two Liquids of Different Density	371	20\n		§10. Flow About a Cut-off without Penetration	375	20\n		*§11. Diffusion of Dissoluble Matter in Bases of Hydraulic Structures	376	20\n		§12. Heterogeneous Soil with Seepage Coefficient a Continuous Function of Coordinates	378	20\nCHAPTER IX. NATURAL AND MAN-MADE WELLS: HORIZONTAL DRAINS	380	20\n	A. Fully Penetrating Wells	380	20\n		§1. Fully Penetrating Well in the Center of a Stratum	380	20\n		§2. Well Eccentrically Established in a Circular Contour	383	20\n		§3. The Case of the Arbitrary Contour [2]	385	20\n		§4. About the Interference of Wells	388	20\n		§5. Flow to a Fully Penetrating Well in Nonhomogeneous Medium	391	20\n	B. Horizontal Drains	394	20\n		§6. Application of the Method of Sources to Problems About Horizontal Drains	394	20\n		§7. Underground Layer of Weak Transmlssivlty\n	C. Movements in Strata\n		§8. Derivation of Equations [7]	397	20\n		§9. Movement in One Pervious Layer [8]	400	20\n		§10. Fully Penetrating Wells in a Confined Stratum	401	20\n		*§11. Interaction of Pervious Strata\n		§12. About the Form of the Piezometric Surface	410	20\n		§13. unconfined Flow to a Well in a Layer With Poorly Pervious Foundation	412	20\nCHAPTER IX. (cont.)	415	20\n	SOME THREE-DIMENSIONAL PROBLEMS IN THE THEORY OP SEEPAGE	415	20\n		§14. About Three-dimensional Problems	415	20\n		§15. Partially Penetrating W e M s in a Half Space	415	20\n		§16. Source Between Two Horizontal Planes	418	20\n		§17. Partially Penetrating Well in a Stratum of Finite Depth	420	20\n		§18. The Problem of Recharge of Water in the Soil	421	20\nCHAPTER X. HYDRAULIC THEORY OP STEADY FLOW	424	20\n	A. Uhconfined Flow in Strata on Bedrock	424	20\n		§1 . Hydraulic Theory and its Basic Assumptions	424	20\n		§2. Plane Flow in Stratum on Horizontal Impervious Base	427	20\n		§3. Free Surface with Infiltration or Evaporation [9]	429	20\n		§4. Seepage in Soils\n		§5. Seepage for Sloping Bedrock [2]	435	20\n		§6. Change of Variables	438	20\n		§7. Seepage in Two-layered Soil with Inclined Boundary Line [12]	440	20\n	B. Uhconfined and Semi-Confined Three-Dimensional Plows	442	20\n		§8. Connection Between Three-Dimensional Unconfined and Two-Dimensional Confined Flows	442	20\n		§9. About Flow to a Pit with Polygonal Plane Cross-Section	444	20\n		§10. Semi-confined Flows [9]	445	20\n		§11. Seepage Around Structures	446	20\nCHAPTER XI. GRAPHICAL\n	A. Graphical and Numerical Methods	451	20\n		§1. Flownet	451	20\n		§2. Graphical Method for Flownet Construction [2]	452	20\n		§3. Method of Arithmetical Averages. Finite Differences	453	20\n		§4. Axisymmetrical Flownet	456	20\n		§5. Net for Steady Well Recharge (Axial Symmetry)	458	20\n		§6. Construction of an Isobar	461	20\n		§7. Fictitious Flow in the Hodograph Plane	465	20\n		§8. Construction of the Net in the Flowregion	466	20\n		§9. Isoclines and Isotaches of the Fictitious Flow [13]	468	20\n		§10. Graphoanalytlcal Method to Compute Three-Dimensional Flows	471	20\n		§11. Application of the Method of Flownets to Anisotropic Soils	475	20\nCHAPTER XI. (cont.)	479	20\n	B. Method of Electro-dynamical Analog [EGDA]	479	20\n		§12. Basic Concepts	479	20\n		§13. Application of the EGDA Method to Two-dimensional Problems	483	20\n		§14. Application of the EGDA Method to Determine the Seepage Coefficient	483	20\n	C. Experiments with Parallel Plate Models	485	20\n		§15. The Theory of the Parallel Plate Model	485	20\n		§16. Determination of the Seepage Picture	488	20\n		§17. Modelling of Heterogeneous Soils	490	20\n		*§18. Unsteady Plow	491	20\n		§19. Calculation of the Capillarity of the Soil	493	20\n		§20. Modelling of Anisotropic Soil. Modelling at Distorted Scale	494	20\n		*§21. Remark Concerning Experiments with Parallel Plate Models	496	20\n	D. Observations of Seepage of Water in the Soil	497	20\n		§22. Experiments in Soil Boxes	497	20\n		§23. Observations in Nature	498	20\nPART II.	501	20\nUnsteady Flows of Groundwaters	501	20\nCHAPTER XII. ABOUT INERTIA TERMS IN UNSTEADY FLOWS. CONFINED FLOWS	501	20\n	§1. About Confined Plows with Operating Heads Depending On Time	501	20\n	§2. About the Influence of Waviness On Seepage Under Hydraulic Structures	504	20\n	§3. One-dimensional Vertical Flow for Constant Operating Head	508	20\n	§4. Seepage for a Given Constant Flow Rate	510	20\n	§5. Gradual Filling With Water	511	20\n	§6. Seepage In Two-layered Soil	513	20\nCHAPTER XIII. NON-LINEAR EQUATIONS OF UNSTEADY FLOWS WITH A FREE SURFACE	517	20\n	§1. Derivation of Basic Relations	517	20\n	§2. Derivation of Non-linear Equation	518	20\n	§3. The Method of the Small Parameter	519	20\n	§4. Seepage By Variable Water Level in a Reservoir	520	20\n	§5. Numerical Integration	525	20\nCHAPTER XIII. (cont.)	526	20\n	§6. Seepage Into an Empty Reservoir	526	20\n	§7. Flow In the Soil With Zero Ground Water Level [ 7\n	§8. Construction of Other Curves	531	20\n	§9. Uniform Rise of Water Level in a Canal. Solutions of the Non-linear Equation of the Source Type	533	20\n	§10. Boussinesq\'s Problem	535	20\nCHAPTER XIV. LINEAR EQUATION OF UNSTEADY GROUNDWATER FLOW	538	20\n	A. Seepage From a Canal on Sloping Bedrock	538	20\n		§1 . Seepage from a Canal on Horizontal Bedrock and without Infiltration	538	20\n		§2. Seepage from a Canal When the Underlying Bedrock has a Slight Slope	540	20\n		§3. Seepage from One Canal to Another on Sloping Bedrock	546	20\n	B. Dynamics of Groundwater Spreading	552	20\n		§4. Spreading Strip — Stratum Overlying Impervious Bedrock	552	20\n		§5. Damping of a Groundwater Mound	554	20\n		§6. Account for Evaporation and Transpiration from Plants	556	20\n		§7. Damping of Groundwater Mound in Case of Evaporation [2]	558	20\n	C. Unsteady Flow in Multilayered Medium. Flow of Two Fluids	559	20\n		§8. Unsteady Flow for a Seepage Coefficient\n		§9. Variable Interface Between Two Liquids of Different Density	562	20\n	D. Some Three-dimensional Problems	563	20\n		§10. Example of Three-dimensional Problem [4]	563	20\n		§11 . Unsteady Flow to a Well in Confined Stratum	569	20\n		§12. Irrigation of a Circular Area	571	20\nCHAPTER XV. TWO-DIMENSIONAL UNSTEADY GROUNDWATER FLOW	572	20\n	§1 . Introduction	572	20\n	§2. Conditions at the Free Surface	572	20\n	§3. Problem of the Damping of a Groundwater Mound in the Half-plane	575	20\n	§4. Same Problem for Linearized Condition	579	20\n	§5. Problem of Spreading of a Groundwater Mound in a Layer of Finite Depth	584	20\n	§6. Groundwater Flow to a Drain in a Stratum of Infinite Thickness	575	20\n	*§7. Problem About the Migration of Oil in Hydrostatic Environment	590	20\nCHAPTER XVI. APPROXIMATE NUMERICAL AND GRAPHICAL METHODS IN THE STUDY OP UNSTEADY GROUNDWATER PLOW	592	20\n	§1. Method of Successive Changes of Steady State Values	592	20\n	§2. Method of Finite Differences	597	20\n	§3. Graphical Method to Integrate the Equation of Heat Conduction	599	20\n	§4. A Graphical Method to Compute Plane Unsteady Groundwater Flow	600	20\n	§5. Examples of Graphical Computation	601	20\n	§6. Problem with Axial Symmetry	607	20\nLITERATURE	609	20\nINDEX	629	20\nPREFACE	5	5\nINTRODUCTION	7	7\nCONTENTS	11	11\nPART I	21	20\nSteady Flow of Groundwater	21	20\nCHAPTER I. PHYSICAL AND MATtiEivlAT L\"CAIJ FUNDAMENTAIJS OF THE THEORY OF GROUNWATER FLOW	21	20\n	§1. Soil Composition	21	20\n	§2. Soil Porosity	24	20\n	§3. Electromolecular Forces in Soils	27	20\n	§4. Various Components of Water in Soil	28	20\n	§5. Seepage Velocity	31	20\n	§6. Experimental Seepage Laws	33	20\n	§7. Seepage Coefficient	35	20\n	§8. Limits of Applicability of the Linear Seepage Law	37	20\n	§9. Capillarity	38	20\n	*§10. Permeability to Water of Incompletely Saturated Soils	39	20\n	§11. Equations of Motion of Groundwaters	41	20\n	*§12. Equations of Motion for Non-Linear Seepage Laws	45	20\nCHAPTER II. TWO-DIMENSIONAL FLOWS IN A VERTICAL PIANE	51	20\n	A. General Considerations	51	20\n		§1. Equations of Motion in a Plane	51	20\n		§2. Boundary Conditions in Two-dimensional Steady Motion	52	20\n		§3. Conditions on the boundary of Two Soils	55	20\n		§4. The Velocity Hodograph	56	20\n		§5. Behaviour of the Velocity in Corner Points of the Flow Region	58	20\n		§6. Examples of Construction of the Velocity Hodograph	60	20\n		§7. The Seepage Triangle [4]	66	20\n		§8. Forces Acting on Soil Particles	67	20\nB. Simplest Examples Of Plane Flows	70	20\n	§9. Preliminary Remarks	70	20\n	§10. Drainage Slit on Impervious Basis	70	20\n	§11. Horizontal Drain in the Absence of an Impervious Basis. Lines of Equal Groundwater Flow	72	20\n	§12. Flat Bottom Weir on a Layer of Infinite Depth	75	20\n	§13. Sheetpile in Pervious Layer of Infinite Depth	81	20\n	§14. Wetted Contour with Drainage Hole	83	20\nCHAPTER III. CONFINED SEEPAGE UNDER HYDRAULIC STRUCTURES	86	20\n	A. Polygonal Regions in Problems of Confined Seepage. Uniqueness Theorem	86	20\n		§1 . Statement of Problem	86	20\n		§2. Conformal Mapping of a Polygon onto a Half Plane	87	20\n		§3. Mapping of a Rectangle onto the Half Plane	91	20\n		§U. Basic Rectangle of Confined Seepage Problems	92	20\n		§5. Uniqueness Theorem	94	20\n	B. Seepage Under Plat-Bottom Foundations	95	20\n		§6. Flat-bottom Foundation on a Layer of Finite Depth	95	20\n		§7. Flat-bottom Foundation on a Drained Stratum	99	20\n		§8. Two Dams with Flat Foundations in Series on a Stratum of Finite Depth	101	20\n	C. Flow About Structures With Cut-off Walls	102	20\n		§9. Mapping onto a Half Plane of a Polygon when All the Sides of this Polygon Converge into One Point	102	20\n		§10. Flow About an Inclined Cut-off Wall	104	20\n		§11. Cut-off for Layer on Impervious Bedrock or on Draining Substratum	105	20\n		§12. Flat Bottom Foundation with Cut-off on a Stratum of Infinite Depth	108	20\n		* §13. Dam with Two Cut-offs On a Pervious Stratum of Finite Depth	113	20\n		* §14. Weir with Two Symmetrical Cut-offs\n		* §15. Embedded Weir	121	20\n		§16. Overfall Weirs	125	20\n	D. Structures with Multiple Cut-offs	126	20\n		§17. The Method of Fragments	126	20\n		§18. Structures with Multiple Cut-offs on a Stratum of Infinite Depth	127	20\n	E. Hydrodynamic Reactions on Weirbases	129	20\n		§19. Resultant Vector of Pressure Forces	129	20\n		§20. Resulting Moment of Pressure Forces	134	20\n		§21. About the Displacement of Boundary Points in Mapped Regions	135	20\n		§22. Application to the Flow of Groundwater Under Dams	138	20\nCCHAPTER IV. ZHUKDVSKY\'S FUNCTION AND ITS APPLICATIONS: APPLICATION OF FUNCTIONAL ANALYSIS	140	20\n	A. Direct Methods to Solve Seepage Problems	140	20\n		§1 . Zhukovsky\'s Function	140	20\nCHAPTER IV. (Cont.)	141	20\n	§2. Zhukovsky\'s Cut-off Wall	141	20\n	§3. Single Drain	143	20\n	54. Infiltration and Flow to a Drain	146	20\n	§5. Seepage From a Canal to Symmetrically Disposed Collectors	150	20\n	§6. Seepage From Canal With Collector on One Side	152	20\n	B. Some Unconfined Flows Derived From Confined Flows	153	20\n		§7. Simplified Sketch of Earth Dam on Pervious Layer of Finite Depth	153	20\n		§8. Simplified Scheme of an Earthdam With Cut-off	155	20\n	C. Semi-inverse Method in the Theory of Canal Seepage	157	20\n		§9. Seepage From Canals with Curvilinear Perimeter on Infinitely Deep Stratum	157	20\n		§10. Seepage with Bedrock Conditions at Infinity	159	20\n		§11. Flow to a Drainage Ditch with Curvilinear Profile	161	20\n		§12. Simplified Scheme of Dam with Drain on Soil of Infinite Depth	161	20\n		*§13. Approximate Solution when the Riverbed is Clogged	162	20\n	D. Application of Functional Analysis	164	20\n		§14. Essence of the Method	164	20\n		§15. Groundwater Flow for Inclined Bedrock	165	20\nCHAPTER V. APPLICATION OF THE METHOD OF INVERSION	169	20\n	§1 . Some Inversion Properties	169	20\n	§2. Seepage From a Canal with Trapezoidal Bed	171	20\n	§3. Canal with Triangular Cross-section	178	20\n	§4. Influence of Soil Capillarity on Seepage from Canals	179	20\n	§5. Canal with Trapezoidal Cross-section	180	20\n	§6. Canal with Low Water level [6]	182	20\n	§7. Groundwater Flow to a Drainage Ditch of Trapezoidal Cross-section	186	20\n	§8. Seepage in Soil Overlying Draining or Waterbearing Stratum	195	20\n	§9. Drain or Irrigation Canal in the Case of Evaporation or Infiltration	199	20\n	§10. Semi-inverse Method Applied to Earthdams on Impervious Foundations	202	20\n	§11. Contour of Constant Velocity in Soil of Infinite Depth	205	20\n	§12. Contour of Constant Velocity in Soil of Finite Depth	207	20\n	§13. Contour with Rectilinear Segments and Segments of Constant Velocity	211	20\n	§14. \"Streamlined\" Dam Foundation	212	20\n	§15. \"Streamlined\" Cut-off	215	20\nCHAPTER VI. THE MIXED PROBLEM OF THE THEORY OF FUNCTIONS AND ITS APPLICATIONS TO THE SEEPAGE THEORY	218	20\n	A. The Mixed Problem of The Theory of Functions	218	20\n		§l. Definitionof an Analytic Function by its Real Part on the Real Axis	218	20\n		§2. Mixed Problem of the Theory of Functions	221	20\n		§3. Particular Case of the Problem	224	20\n	B. Problems About Drains and Canals	225	20\n		§4. Drain in Stratum on Bedrock with Non-symmetrical Flow	225	20\n		§5. Flow to a Rectangular Trench with Sloping Free Surface in a Stratum of Infinite Depth	231	20\n		§6. About Seepage Towards a Drain or Canal in the Case of Inclined Bedrock	235	20\n	C. Earth Dams	247	20\n		§7. Drained Earth Dam with Trapezoidal Profile on Impervious Bedrock	247	20\n		*§8. Earth Dam with Horizontal Drain on Pervious Stratum of Infinite Depth [3]	267	20\nCHAPTER VII. APPLICATION OF THE ANALYTIC THEORY OF LINEAR DIFFERENTIAL EQUATIONS	281	20\n	A. General Theory	281	20\n		§1. Introductory Remarks	281	20\n		§2. Conditions at the Real Axis for Two Basic Functions	281	20\n		§3. Problem of Determining Two Functions by Conditions at the Real Axis	283	20\n		§4. Equation with Three Regular Singular Points	287	20\n		§5. Hypergeometric Functions and their Properties	288	20\n		*§6. Curvilinear Polygons\n		§7. Case of Real Exponents. Second Derivation of the Characteristic Equation	293	20\n		§8. Exponents for Basic Cases of the Seepage Theory	296	20\n	B. Problem of Seepage Through a Vertical Dam	301	20\n		§.9.Seepage Rate Through a Dam and Discharge of a Well	301	20\n		§10. Construction of the Solution for a Vertical Dam	304	20\n	C. Dams With Rectangular Trapezoidal Cross-Section	318	20\n		§11. Seepage in a Trapezoidal Dam when Evaporation Occurs	318	20\n		§12. Seepage Through a Trapezoidal Dam without Evaporation	321	20\nCHAPTER VIII. SEEPAGE IN HETEROGENEOUS AND ANISOTROPIC SOILS: SEEPAGE OF TWO FLUIDS	329	20\n	A. Heterogeneous Soils	329	20\n		§1. Weir on Two Strata of Same Thickness	329	20\n		§2. Cut-off in Two Strata of Same Depth	341	20\n		§3. Cut-offs without Penetration on Soil with Two Strata	351	20\n		§1*. Point Vortex in Multilayered Region	355	20\n		§5. Simplest Flows in Stratified Soils	360	20\n	B. Anisotropic Soils	363	20\n		§6. Equations of Motion. Boundary Conditions	363	20\n		§7. Flow to a Drain on Impervious Foundation in Anisotropic Soil [8]	368	20\n		§8. Interpretation of Anisotropic Soil by Means of Two Alternating Soils	370	20\n	C. Two Fluids of Different Density	371	20\n		§9. About Flow of Two Liquids of Different Density	371	20\n		§10. Flow About a Cut-off without Penetration	375	20\n		*§11. Diffusion of Dissoluble Matter in Bases of Hydraulic Structures	376	20\n		§12. Heterogeneous Soil with Seepage Coefficient a Continuous Function of Coordinates	378	20\nCHAPTER IX. NATURAL AND MAN-MADE WELLS: HORIZONTAL DRAINS	380	20\n	A. Fully Penetrating Wells	380	20\n		§1. Fully Penetrating Well in the Center of a Stratum	380	20\n		§2. Well Eccentrically Established in a Circular Contour	383	20\n		§3. The Case of the Arbitrary Contour [2]	385	20\n		§4. About the Interference of Wells	388	20\n		§5. Flow to a Fully Penetrating Well in Nonhomogeneous Medium	391	20\n	B. Horizontal Drains	394	20\n		§6. Application of the Method of Sources to Problems About Horizontal Drains	394	20\n		§7. Underground Layer of Weak Transmlssivlty\n	C. Movements in Strata\n		§8. Derivation of Equations [7]	397	20\n		§9. Movement in One Pervious Layer [8]	400	20\n		§10. Fully Penetrating Wells in a Confined Stratum	401	20\n		*§11. Interaction of Pervious Strata\n		§12. About the Form of the Piezometric Surface	410	20\n		§13. unconfined Flow to a Well in a Layer With Poorly Pervious Foundation	412	20\nCHAPTER IX. (cont.)	415	20\n	SOME THREE-DIMENSIONAL PROBLEMS IN THE THEORY OP SEEPAGE	415	20\n		§14. About Three-dimensional Problems	415	20\n		§15. Partially Penetrating W e M s in a Half Space	415	20\n		§16. Source Between Two Horizontal Planes	418	20\n		§17. Partially Penetrating Well in a Stratum of Finite Depth	420	20\n		§18. The Problem of Recharge of Water in the Soil	421	20\nCHAPTER X. HYDRAULIC THEORY OP STEADY FLOW	424	20\n	A. Uhconfined Flow in Strata on Bedrock	424	20\n		§1 . Hydraulic Theory and its Basic Assumptions	424	20\n		§2. Plane Flow in Stratum on Horizontal Impervious Base	427	20\n		§3. Free Surface with Infiltration or Evaporation [9]	429	20\n		§4. Seepage in Soils\n		§5. Seepage for Sloping Bedrock [2]	435	20\n		§6. Change of Variables	438	20\n		§7. Seepage in Two-layered Soil with Inclined Boundary Line [12]	440	20\n	B. Uhconfined and Semi-Confined Three-Dimensional Plows	442	20\n		§8. Connection Between Three-Dimensional Unconfined and Two-Dimensional Confined Flows	442	20\n		§9. About Flow to a Pit with Polygonal Plane Cross-Section	444	20\n		§10. Semi-confined Flows [9]	445	20\n		§11. Seepage Around Structures	446	20\nCHAPTER XI. GRAPHICAL\n	A. Graphical and Numerical Methods	451	20\n		§1. Flownet	451	20\n		§2. Graphical Method for Flownet Construction [2]	452	20\n		§3. Method of Arithmetical Averages. Finite Differences	453	20\n		§4. Axisymmetrical Flownet	456	20\n		§5. Net for Steady Well Recharge (Axial Symmetry)	458	20\n		§6. Construction of an Isobar	461	20\n		§7. Fictitious Flow in the Hodograph Plane	465	20\n		§8. Construction of the Net in the Flowregion	466	20\n		§9. Isoclines and Isotaches of the Fictitious Flow [13]	468	20\n		§10. Graphoanalytlcal Method to Compute Three-Dimensional Flows	471	20\n		§11. Application of the Method of Flownets to Anisotropic Soils	475	20\nCHAPTER XI. (cont.)	479	20\n	B. Method of Electro-dynamical Analog [EGDA]	479	20\n		§12. Basic Concepts	479	20\n		§13. Application of the EGDA Method to Two-dimensional Problems	483	20\n		§14. Application of the EGDA Method to Determine the Seepage Coefficient	483	20\n	C. Experiments with Parallel Plate Models	485	20\n		§15. The Theory of the Parallel Plate Model	485	20\n		§16. Determination of the Seepage Picture	488	20\n		§17. Modelling of Heterogeneous Soils	490	20\n		*§18. Unsteady Plow	491	20\n		§19. Calculation of the Capillarity of the Soil	493	20\n		§20. Modelling of Anisotropic Soil. Modelling at Distorted Scale	494	20\n		*§21. Remark Concerning Experiments with Parallel Plate Models	496	20\n	D. Observations of Seepage of Water in the Soil	497	20\n		§22. Experiments in Soil Boxes	497	20\n		§23. Observations in Nature	498	20\nPART II.	501	20\nUnsteady Flows of Groundwaters	501	20\nCHAPTER XII. ABOUT INERTIA TERMS IN UNSTEADY FLOWS. CONFINED FLOWS	501	20\n	§1. About Confined Plows with Operating Heads Depending On Time	501	20\n	§2. About the Influence of Waviness On Seepage Under Hydraulic Structures	504	20\n	§3. One-dimensional Vertical Flow for Constant Operating Head	508	20\n	§4. Seepage for a Given Constant Flow Rate	510	20\n	§5. Gradual Filling With Water	511	20\n	§6. Seepage In Two-layered Soil	513	20\nCHAPTER XIII. NON-LINEAR EQUATIONS OF UNSTEADY FLOWS WITH A FREE SURFACE	517	20\n	§1. Derivation of Basic Relations	517	20\n	§2. Derivation of Non-linear Equation	518	20\n	§3. The Method of the Small Parameter	519	20\n	§4. Seepage By Variable Water Level in a Reservoir	520	20\n	§5. Numerical Integration	525	20\nCHAPTER XIII. (cont.)	526	20\n	§6. Seepage Into an Empty Reservoir	526	20\n	§7. Flow In the Soil With Zero Ground Water Level [ 7\n	§8. Construction of Other Curves	531	20\n	§9. Uniform Rise of Water Level in a Canal. Solutions of the Non-linear Equation of the Source Type	533	20\n	§10. Boussinesq\'s Problem	535	20\nCHAPTER XIV. LINEAR EQUATION OF UNSTEADY GROUNDWATER FLOW	538	20\n	A. Seepage From a Canal on Sloping Bedrock	538	20\n		§1 . Seepage from a Canal on Horizontal Bedrock and without Infiltration	538	20\n		§2. Seepage from a Canal When the Underlying Bedrock has a Slight Slope	540	20\n		§3. Seepage from One Canal to Another on Sloping Bedrock	546	20\n	B. Dynamics of Groundwater Spreading	552	20\n		§4. Spreading Strip — Stratum Overlying Impervious Bedrock	552	20\n		§5. Damping of a Groundwater Mound	554	20\n		§6. Account for Evaporation and Transpiration from Plants	556	20\n		§7. Damping of Groundwater Mound in Case of Evaporation [2]	558	20\n	C. Unsteady Flow in Multilayered Medium. Flow of Two Fluids	559	20\n		§8. Unsteady Flow for a Seepage Coefficient\n		§9. Variable Interface Between Two Liquids of Different Density	562	20\n	D. Some Three-dimensional Problems	563	20\n		§10. Example of Three-dimensional Problem [4]	563	20\n		§11 . Unsteady Flow to a Well in Confined Stratum	569	20\n		§12. Irrigation of a Circular Area	571	20\nCHAPTER XV. TWO-DIMENSIONAL UNSTEADY GROUNDWATER FLOW	572	20\n	§1 . Introduction	572	20\n	§2. Conditions at the Free Surface	572	20\n	§3. Problem of the Damping of a Groundwater Mound in the Half-plane	575	20\n	§4. Same Problem for Linearized Condition	579	20\n	§5. Problem of Spreading of a Groundwater Mound in a Layer of Finite Depth	584	20\n	§6. Groundwater Flow to a Drain in a Stratum of Infinite Thickness	575	20\n	*§7. Problem About the Migration of Oil in Hydrostatic Environment	590	20\nCHAPTER XVI. APPROXIMATE NUMERICAL AND GRAPHICAL METHODS IN THE STUDY OP UNSTEADY GROUNDWATER PLOW	592	20\n	§1. Method of Successive Changes of Steady State Values	592	20\n	§2. Method of Finite Differences	597	20\n	§3. Graphical Method to Integrate the Equation of Heat Conduction	599	20\n	§4. A Graphical Method to Compute Plane Unsteady Groundwater Flow	600	20\n	§5. Examples of Graphical Computation	601	20\n	§6. Problem with Axial Symmetry	607	20\nLITERATURE	609	20\nINDEX	629	20\nPREFACE	5\nINTRODUCTION	7\nCONTENTS	11\nPART I. Steady Flow of Groundwater	21\nCHAPTER I. PHYSICAL AND MATtiEivlAT L\"CAIJ FUNDAMENTAIJS OF THE THEORY OF GROUNWATER FLOW	21\n	§1 . Soil Composition	21\n	§2. Soil Porosity	24\n	§3. Electromolecular Forces in Soils	27\n	§4. Various Components of Water in Soil	28\n	§5. Seepage Velocity	31\n	§6. Experimental Seepage Laws	33\n	§7. Seepage Coefficient	35\n	§8. Limits of Applicability of the Linear Seepage Law	37\n	§9. Capillarity	38\n	*§10. Permeability to Water of Incompletely Saturated Soils	39\n	§11. Equations of Motion of Groundwaters	41\n	*§12. Equations of Motion for Non-Linear Seepage Laws	45\nCHAPTER II. TWO-DIMENSIONAL FLOWS IN A VERTICAL PIANE	51\n	A. General Considerations	51\n		§1. Equations of Motion in a Plane	51\n		§2. Boundary Conditions in Two-dimensional Steady Motion	52\n		§3. Conditions on the boundary of Two Soils	55\n		§4. The Velocity Hodograph	56\n		§5. Behaviour of the Velocity in Corner Points of the Flow Region	58\n		§6. Examples of Construction of the Velocity Hodograph	60\n		§7. The Seepage Triangle [4]	66\n		§8. Forces Acting on Soil Particles	67\n	B. Simplest Examples Of Plane Flows	70\n		§9. Preliminary Remarks	70\n		§10. Drainage Slit on Impervious Basis	70\n		§11. Horizontal Drain in the Absence of an Impervious Basis. Lines of Equal Groundwater Flow	72\n		§12. Flat Bottom Weir on a Layer of Infinite Depth	75\n		§13. Sheetpile in Pervious Layer of Infinite Depth	81\n		§14. Wetted Contour with Drainage Hole	83\nCHAPTER III. CONFINED SEEPAGE UNDER HYDRAULIC STRUCTURES	86\n	A. Polygonal Regions in Problems of Confined Seepage. Uniqueness Theorem	86\n		§1 . Statement of Problem	86\n		§2. Conformal Mapping of a Polygon onto a Half Plane	87\n		§3. Mapping of a Rectangle onto the Half Plane	91\n		§4. Basic Rectangle of Confined Seepage Problems	92\n		§5. Uniqueness Theorem	94\n	B. Seepage Under Plat-Bottom Foundations	95\n		§6. Flat-bottom Foundation on a Layer of Finite Depth	95\n		§7. Flat-bottom Foundation on a Drained Stratum	99\n		§8. Two Dams with Flat Foundations in Series on a Stratum of Finite Depth	101\n	C. Flow About Structures With Cut-off Walls	102\n		§9. Mapping onto a Half Plane of a Polygon when All the Sides of this Polygon Converge into One Point	102\n		§10. Flow About an Inclined Cut-off Wall	104\n		§11. Cut-off for Layer on Impervious Bedrock or on Draining Substratum	105\n		§12. Flat Bottom Foundation with Cut-off on a Stratum of Infinite Depth	108\n		* §13. Dam with Two Cut-offs On a Pervious Stratum of Finite Depth	113\n		* §14. Weir with Two Symmetrical Cut-offs\n		* §15. Embedded Weir	121\n		§16. Overfall Weirs	125\n	D. Structures with Multiple Cut-offs	126\n		§17. The Method of Fragments	126\n		§18. Structures with Multiple Cut-offs on a Stratum of Infinite Depth	127\n	E. Hydrodynamic Reactions on Weirbases	129\n		§19. Resultant Vector of Pressure Forces	129\n		§20. Resulting Moment of Pressure Forces	134\n		§21. About the Displacement of Boundary Points in Mapped Regions	135\n		§22. Application to the Flow of Groundwater Under Dams	138\nCHAPTER IV. ZHUKDVSKY\'S FUNCTION AND ITS APPLICATIONS: APPLICATION OF FUNCTIONAL ANALYSIS	140\n	A. Direct Methods to Solve Seepage Problems	140\n		§1. Zhukovsky\'s Function	140\nCHAPTER IV. (Cont.)	141\n	§2. Zhukovsky\'s Cut-off Wall	141\n	§3. Single Drain	143\n	§4. Infiltration and Flow to a Drain	146\n	§5. Seepage From a Canal to Symmetrically Disposed Collectors	150\n	§6. Seepage From Canal With Collector on One Side	152\n	B. Some Unconfined Flows Derived From Confined Flows	153\n		§7. Simplified Sketch of Earth Dam on Pervious Layer of Finite Depth	153\n		§8. Simplified Scheme of an Earthdam With Cut-off	155\n	C. Semi-inverse Method in the Theory of Canal Seepage	157\n		§9. Seepage From Canals with Curvilinear Perimeter on Infinitely Deep Stratum	157\n		§10. Seepage with Bedrock Conditions at Infinity	159\n		§11. Flow to a Drainage Ditch with Curvilinear Profile	161\n		§12. Simplified Scheme of Dam with Drain on Soil of Infinite Depth	161\n		*§13. Approximate Solution when the Riverbed is Clogged	162\n	D. Application of Functional Analysis	164\n		§14. Essence of the Method	164\n		§15. Groundwater Flow for Inclined Bedrock	165\nCHAPTER V. APPLICATION OF THE METHOD OF INVERSION	169\n	§1 . Some Inversion Properties	169\n	§2. Seepage From a Canal with Trapezoidal Bed	171\n	§3. Canal with Triangular Cross-section	178\n	§4. Influence of Soil Capillarity on Seepage from Canals	179\n	§5. Canal with Trapezoidal Cross-section	180\n	§6. Canal with Low Water level [6]	182\n	§7. Groundwater Flow to a Drainage Ditch of Trapezoidal Cross-section	186\n	§8. Seepage in Soil Overlying Draining or Waterbearing Stratum	195\n	§9. Drain or Irrigation Canal in the Case of Evaporation or Infiltration	199\n	§10. Semi-inverse Method Applied to Earthdams on Impervious Foundations	202\n	§11. Contour of Constant Velocity in Soil of Infinite Depth	205\n	§12. Contour of Constant Velocity in Soil of Finite Depth	207\n	§13. Contour with Rectilinear Segments and Segments of Constant Velocity	211\n	§14. \"Streamlined\" Dam Foundation	212\n	§15. \"Streamlined\" Cut-off	215\nCHAPTER VI. THE MIXED PROBLEM OF THE THEORY OF FUNCTIONS AND ITS APPLICATIONS TO THE SEEPAGE THEORY	218\n	A. The Mixed Problem of The Theory of Functions	218\n		§l. Definitionof an Analytic Function by its Real Part on the Real Axis	218\n		§2. Mixed Problem of the Theory of Functions	221\n		§3. Particular Case of the Problem	224\n	B. Problems About Drains and Canals	225\n		§4. Drain in Stratum on Bedrock with Non-symmetrical Flow	225\n		§5. Flow to a Rectangular Trench with Sloping Free Surface in a Stratum of Infinite Depth	231\n		§6. About Seepage Towards a Drain or Canal in the Case of Inclined Bedrock	235\n	C. Earth Dams	247\n		§7. Drained Earth Dam with Trapezoidal Profile on Impervious Bedrock	247\n		*§8. Earth Dam with Horizontal Drain on Pervious Stratum of Infinite Depth [3]	267\nCHAPTER VII. APPLICATION OF THE ANALYTIC THEORY OF LINEAR DIFFERENTIAL EQUATIONS	281\n	A. General Theory	281\n		§1. Introductory Remarks	281\n		§2. Conditions at the Real Axis for Two Basic Functions	281\n		§3. Problem of Determining Two Functions by Conditions at the Real Axis	283\n		§4. Equation with Three Regular Singular Points	287\n		§5. Hypergeometric Functions and their Properties	288\n		*§6. Curvilinear Polygons\n		§7. Case of Real Exponents. Second Derivation of the Characteristic Equation	293\n		§8. Exponents for Basic Cases of the Seepage Theory	296\n	B. Problem of Seepage Through a Vertical Dam	301\n		§9. Seepage Rate Through a Dam and Discharge of a Well	301\n		§10. Construction of the Solution for a Vertical Dam	304\n	C. Dams With Rectangular Trapezoidal Cross-Section	318\n		§11. Seepage in a Trapezoidal Dam when Evaporation Occurs	318\n		§12. Seepage Through a Trapezoidal Dam without Evaporation	321\nCHAPTER VIII. SEEPAGE IN HETEROGENEOUS AND ANISOTROPIC SOILS: SEEPAGE OF TWO FLUIDS	329\n	A. Heterogeneous Soils	329\n		§1. Weir on Two Strata of Same Thickness	329\n		§2. Cut-off in Two Strata of Same Depth	341\n		§3. Cut-offs without Penetration on Soil with Two Strata	351\n		§4. Point Vortex in Multilayered Region	355\n		§5. Simplest Flows in Stratified Soils	360\n	B. Anisotropic Soils [8]	363\n		§6. Equations of Motion. Boundary Conditions	363\n		§7. Flow to a Drain on Impervious Foundation in Anisotropic Soil [8]	368\n		§8. Interpretation of Anisotropic Soil by Means of Two Alternating Soils	370\n	C. Two Fluids of Different Density	371\n		§9. About Flow of Two Liquids of Different Density	371\n		§10. Flow About a Cut-off without Penetration	375\n		*§11. Diffusion of Dissoluble Matter in Bases of Hydraulic Structures	376\n		§12. Heterogeneous Soil with Seepage Coefficient a Continuous Function of Coordinates	378\nCHAPTER IX. NATURAL AND MAN-MADE WELLS: HORIZONTAL DRAINS	380\n	A. Fully Penetrating Wells	380\n		§1. Fully Penetrating Well in the Center of a Stratum	380\n		§2. Well Eccentrically Established in a Circular Contour	383\n		§3. The Case of the Arbitrary Contour [2]	385\n		§4. About the Interference of Wells	388\n		§5. Flow to a Fully Penetrating Well in Nonhomogeneous Medium	391\n	B. Horizontal Drains	394\n		§6. Application of the Method of Sources to Problems About Horizontal Drains	394\n		§7. Underground Layer of Weak Transmlssivlty\n	C. Movements in Strata\n		§8. Derivation of Equations [7]	397\n		§9. Movement in One Pervious Layer [8]	400\n		§10. Fully Penetrating Wells in a Confined Stratum	401\n		*§11. Interaction of Pervious Strata\n		§12. About the Form of the Piezometric Surface	410\n		§13. unconfined Flow to a Well in a Layer With Poorly Pervious Foundation	412\nCHAPTER IX. (cont.) SOME THREE-DIMENSIONAL PROBLEMS IN THE THEORY OP SEEPAGE	415\n	§14. About Three-dimensional Problems	415\n	§15. Partially Penetrating W e M s in a Half Space	415\n	§16. Source Between Two Horizontal Planes	418\n	§17. Partially Penetrating Well in a Stratum of Finite Depth	420\n	§18. The Problem of Recharge of Water in the Soil	421\nCHAPTER X. HYDRAULIC THEORY OP STEADY FLOW	424\n	A. Uhconfined Flow in Strata on Bedrock	424\n		§1 . Hydraulic Theory and its Basic Assumptions	424\n		§2. Plane Flow in Stratum on Horizontal Impervious Base	427\n		§3. Free Surface with Infiltration or Evaporation [9]	429\n		§4. Seepage in Soils\n		§5. Seepage for Sloping Bedrock [2]	435\n		§6. Change of Variables	438\n		§7. Seepage in Two-layered Soil with Inclined Boundary Line [12]	440\n	B. Uhconfined and Semi-Confined Three-Dimensional Plows	442\n		§8. Connection Between Three-Dimensional Unconfined and Two-Dimensional Confined Flows	442\n		§9. About Flow to a Pit with Polygonal Plane Cross-Section	444\n		§10. Semi-confined Flows [9]	445\n		§11. Seepage Around Structures	446\nCHAPTER XI. GRAPHICAL\n	A. Graphical and Numerical Methods	451\n		§1. Flownet	451\n		§2. Graphical Method for Flownet Construction [2]	452\n		§3. Method of Arithmetical Averages. Finite Differences	453\n		§4. Axisymmetrical Flownet	456\n		§5. Net for Steady Well Recharge (Axial Symmetry)	458\n		§6. Construction of an Isobar	461\n		§7. Fictitious Flow in the Hodograph Plane	465\n		§8. Construction of the Net in the Flowregion	466\n		§9. Isoclines and Isotaches of the Fictitious Flow [13]	468\n		§10. Graphoanalytlcal Method to Compute Three-Dimensional Flows	471\n		§11. Application of the Method of Flownets to Anisotropic Soils	475\nCHAPTER XI. (cont.)	479\n	B. Method of Electro-dynamical Analog [EGDA]	479\n		§12. Basic Concepts	479\n		§13. Application of the EGDA Method to Two-dimensional Problems	483\n		§14. Application of the EGDA Method to Determine the Seepage Coefficient	483\n	C. Experiments with Parallel Plate Models	485\n		§15. The Theory of the Parallel Plate Model	485\n		§16. Determination of the Seepage Picture	488\n		§17. Modelling of Heterogeneous Soils	490\n		*§18. Unsteady Plow	491\n		§19. Calculation of the Capillarity of the Soil	493\n		§20. Modelling of Anisotropic Soil. Modelling at Distorted Scale	494\n		*§21. Remark Concerning Experiments with Parallel Plate Models	496\n	D. Observations of Seepage of Water in the Soil	497\n		§22. Experiments in Soil Boxes	497\n		§23. Observations in Nature	498\nPART II. Unsteady Flows of Groundwaters	501\nCHAPTER XII. ABOUT INERTIA TERMS IN UNSTEADY FLOWS. CONFINED FLOWS	501\n	§1. About Confined Plows with Operating Heads Depending On Time	501\n	§2. About the Influence of Waviness On Seepage Under Hydraulic Structures	504\n	§3. One-dimensional Vertical Flow for Constant Operating Head	508\n	§4. Seepage for a Given Constant Flow Rate	510\n	§5. Gradual Filling With Water	511\n	§6. Seepage In Two-layered Soil	513\nCHAPTER XIII. NON-LINEAR EQUATIONS OF UNSTEADY FLOWS WITH A FREE SURFACE	517\n	§1. Derivation of Basic Relations	517\n	§2. Derivation of Non-linear Equation	518\n	§3. The Method of the Small Parameter	519\n	§4. Seepage By Variable Water Level in a Reservoir	520\n	§5. Numerical Integration	525\nCHAPTER XIII. (cont.)	526\n	§6. Seepage Into an Empty Reservoir	526\n	§7. Flow In the Soil With Zero Ground Water Level [7\n	§8. Construction of Other Curves	531\n	§9. Uniform Rise of Water Level in a Canal. Solutions of the Non-linear Equation of the Source Type	533\n	§10. Boussinesq\'s Problem	535\nCHAPTER XIV. LINEAR EQUATION OF UNSTEADY GROUNDWATER FLOW	538\n	A. Seepage From a Canal on Sloping Bedrock	538\n		§1 . Seepage from a Canal on Horizontal Bedrock and without Infiltration	538\n		§2. Seepage from a Canal When the Underlying Bedrock has a Slight Slope	540\n		§3. Seepage from One Canal to Another on Sloping Bedrock	546\n	B. Dynamics of Groundwater Spreading	552\n		§4. Spreading Strip — Stratum Overlying Impervious Bedrock	552\n		§5. Damping of a Groundwater Mound	554\n		§6. Account for Evaporation and Transpiration from Plants	556\n		§7. Damping of Groundwater Mound in Case of Evaporation [2]	558\n	C. Unsteady Flow in Multilayered Medium. Flow of Two Fluids	559\n		§8. Unsteady Flow for a Seepage Coefficient\n		§9. Variable Interface Between Two Liquids of Different Density	562\n	D. Some Three-dimensional Problems	563\n		§10. Example of Three-dimensional Problem [4]	563\n		§11 . Unsteady Flow to a Well in Confined Stratum	569\n		§12. Irrigation of a Circular Area	571\nCHAPTER XV. TWO-DIMENSIONAL UNSTEADY GROUNDWATER FLOW	572\n	§1 . Introduction	572\n	§2. Conditions at the Free Surface	572\n	§3. Problem of the Damping of a Groundwater Mound in the Half-plane	575\n	§4. Same Problem for Linearized Condition	579\n	§5. Problem of Spreading of a Groundwater Mound in a Layer of Finite Depth	584\n	§6. Groundwater Flow to a Drain in a Stratum of Infinite Thickness	575\n	*§7. Problem About the Migration of Oil in Hydrostatic Environment	590\nCHAPTER XVI. APPROXIMATE NUMERICAL AND GRAPHICAL METHODS IN THE STUDY OP UNSTEADY GROUNDWATER PLOW	592\n	§1. Method of Successive Changes of Steady State Values	592\n	§2. Method of Finite Differences	597\n	§3. Graphical Method to Integrate the Equation of Heat Conduction	599\n	§4. A Graphical Method to Compute Plane Unsteady Groundwater Flow	600\n	§5. Examples of Graphical Computation	601\n	§6. Problem with Axial Symmetry	607\nLITERATURE	609\nINDEX	629