Table Of ContentH Mechanics of
Ground Engineering
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“This book will be a useful addition to the professional library of ground- Groundwater in
water modelers and hydrogeologists. Its treatment of the mathematics and
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analysis of groundwater flow is clear and thorough, and it is invaluable in
presenting the fundamentals of groundwater flow through porous media in e Porous Media
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—Martin Preene, Golder Associates
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Engineers, geologists, and hydrologists need to understand groundwater
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movement. This senior undergraduate and the graduate level text covers the
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topic from theory and principles through to practical engineering problems.
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Mechanics of Groundwater in Porous Media is written for engineering
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and science students but the large number of illustrations and worked
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examples should also suit professionals.
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A careful balance is maintained between mathematical rigor and the physical
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aspects of groundwater movement. The core mathematics generally acquired
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during the first two semesters of calculus at the university level is assumed,
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and further skills needed for the analysis of groundwater movement are
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gradually developed throughout the text. It avoids unnecessary mathematical
subtleties and over-simplifications of qualitative descriptions. a
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Muhammad I. Haque is professor of engineering and applied science at r
The George Washington University, Washington, D.C., USA.
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K19071 d
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A SPON PRESS BOOK
K19071 cvr mech.indd 1 6/16/14 12:51 PM
Mechanics of
Groundwater in
Porous Media
Muhammad I. Haque
A SPON PRESS BOOK
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
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Version Date: 20140428
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Dedicated to the memory of my father, Muhammad Abdul Haque,
my mother, Amina Haque, and my brother, Azizul Haque
Contents
Preface xi
Author xiii
1 Introduction 1
1.1 Hydrological cycle 2
1.1.1 Noncyclic water 5
1.2 Vertical moisture profile 5
1.2.1 Soil water zone 6
1.2.2 Intermediate zone 6
1.2.3 Capillary zone 7
1.3 Classification of aquifers 10
1.3.1 Confined aquifer 11
1.3.2 Unconfined aquifer 11
1.3.3 Perched aquifer 11
1.4 River–aquifer interaction 11
1.5 Homogeneity and isotropy of aquifers 13
1.6 Illustrative problems 14
Suggested readings 17
2 Preliminaries 19
2.1 Preliminaries from fluid mechanics 19
2.1.1 Stress vector and its vector resolution
into normal and shearing components 19
2.1.2 Static pressure at a point 21
2.1.2.1 The invariance of static
pressure with direction 23
2.1.2.2 Static pressure at a point not
directly under the free surface 24
v
vi Contents
2.1.3 Bernoulli’s theorem 26
2.1.3.1 Kinetic energy 26
2.1.3.2 Potentials and the potential energy 29
2.1.3.3 Energy equation for steady motion
of an incompressible ideal fluid 34
2.2 Preliminaries from soil mechanics 37
2.2.1 Porosity of soil or porous medium 37
2.2.2 Void ratio, water content, and degree of saturation 39
2.2.3 Total pressure, porewater pressure, and effective
pressure 40
2.3 Continuum concept of a porous medium 41
2.3.1 Notion of porosity in a porous medium 42
2.3.2 Notion of rectilinear flow in a porous medium 44
2.3.3 Specific discharge and seepage velocity 45
2.4 Stagnant groundwater and zero-gradient of piezometric head 47
2.5 Piezometric head in the field 50
2.6 Illustrative problems 51
2.7 Exercises 54
Suggested readings 57
3 Field equations of flow through a porous medium 59
3.1 Darcy’s law 59
3.1.1 Generalization of Darcy’s law 63
3.1.2 Laboratory determination of coefficient of
permeability 66
3.2 Conservation of mass, or continuity, equation 69
3.3 Laplace equation 72
3.4 Two-dimensional anisotropic medium and permeability
matrix (or tensor) 72
3.4.1 Mohr’s circle 78
3.4.2 Physical significance of cross permeability terms 82
3.5 Exercises 85
Suggested readings 86
4 Discharge potentials for two-dimensional flows in
horizontal, shallow aquifers 87
4.1 Horizontal, shallow, confined (artesian) aquifer 87
4.2 Horizontal, shallow, unconfined (phreatic) aquifer 90
4.3 Horizontal, shallow, partly confined aquifer 96
Contents vii
4.4 Applications 99
4.4.1 Flow through horizontal, shallow,
confined (artesian) aquifer 99
4.4.1.1 Case I: Rectilinear flow
through a confined aquifer 99
4.4.1.2 Case II: Radial flow toward a well
in a confined (artesian) aquifer 102
4.4.2 Flow through horizontal, shallow,
unconfined (phreatic) aquifer 105
4.4.2.1 Case I: One-dimensional flow through
an unconfined (phreatic) aquifer 105
4.4.2.2 Case II: Radial flow toward a well
in an unconfined (phreatic) aquifer 109
4.4.3 Flow through horizontal, shallow, partly
unconfined aquifer 110
4.4.3.1 Case I: One-dimensional flow
through partly unconfined aquifer 110
4.4.3.2 Case II: Radial flow toward a well
in partly unconfined aquifer 112
4.5 Illustrative problems 115
4.6 Exercises 118
Suggested readings 120
5 Laplace equation, superposition of harmonic functions,
and method of images 121
5.1 Some important properties of harmonic functions 121
5.2 Method of images 122
5.2.1 Well at a finite distance from an infinitely
long stream 123
5.2.2 Well at a finite distance from an infinitely long
impervious boundary 132
5.2.3 Well operating in the vicinity of combined
impervious and constant-head boundaries 135
5.2.4 Well between two parallel impervious boundaries 140
5.2.4.1 Location of image wells on the
positive x-axis 142
5.2.4.2 Location of image wells on the
negative x-axis 142
5.3 Method of images for circular boundary 143
5.4 Illustrative problems 145
viii Contents
5.5 Exercises 154
Suggested readings 155
6 Flow net 157
6.1 Isotropic case 157
6.1.1 Example of flow-net construction and analysis 163
6.2 Anisotropic case 165
6.2.1 Equivalent permeability in transformed regions 168
6.2.2 Example of flow-net construction in a
homogeneous, anisotropic aquifer 171
6.2.3 Illustrative problem 6.1 174
6.3 Layered heterogeneity 177
6.3.1 Refraction of streamline 182
6.4 Concluding remarks 184
6.5 Exercises 185
Suggested readings 186
7 Determination of aquifer characteristics 187
7.1 Determination of transmissivity or coefficient of
permeability 188
7.1.1 Thiem equation: Confined aquifer 188
7.1.2 Dupuit equation: Unconfined aquifer 189
7.1.3 Illustrative problem 7.1 190
7.2 Theis equation: Transient radial flow to a well
in a confined aquifer 191
7.2.1 Illustrative problem 7.2 194
7.3 Theis method 195
7.3.1 Illustrative problem 7.3 197
7.3.2 Optimization problem 199
7.4 Jacob straight-line method 200
7.4.1 Illustrative problem 7.4 201
7.5 Modification of the Jacob method:
Distance–drawdown method 202
7.5.1 Illustrative problem 7.5 204
7.6 Remarks on the use of the Thiem equation in the
case of unsteady flow condition 204
7.7 Exercises 206
Suggested readings 207
