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Hydrogeologic Properties of Earth Materials and Principles of Groundwater Flow

William W. Woessner and Eileen P. Poeter

Cover of the book Hydraulic Properties of Earth Materials and Principles of Groundwater Flow

Publication year: 2020
Number of pages: 207
ISBN: 978-1-7770541-2-0

Authors:
William W. Woessner – University of Montana, USA
Eileen P. Poeter – Colorado School of Mines, USA

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Book Description

This book emphasizes the need for groundwater scientists to have a solid understanding of the occurrence and behavior of groundwater in a variety of conditions and settings. Knowledge of how porous media store, yield, and transmit water, and the factors that control groundwater flow rates and directions are highlighted. Eight Boxes present more detailed discussion of concepts introduced in the main text. Sixteen exercises and their solutions are also provided.

Groundwater is water found below the water table in the zone of saturation within the pores and cracks of a wide variety of earth materials. Groundwater occurrence in porous material is described in terms of total porosity, effective porosity, void ratio, volumetric moisture content, specific yield, and specific retention. Interconnected pore space provides for storage and transmission of groundwater.

The movement of groundwater is described by Darcy’s Law which states that the discharge of groundwater is directly proportional to the saturated area perpendicular to the direction of flow, the hydraulic gradient and the transmission capacity (hydraulic conductivity) of the earth material. Groundwater flow rates and directions are controlled by: forces on water within pore spaces and fractures; hydraulic heads; and the hydraulic conductivity of earth materials.

Unconfined, perched, and confined aquifers are groundwater systems that provide groundwater for water supplies. Properties of aquifers are described by transmissivity and storativity. In addition to zones that freely transmit groundwater, some materials inhibit flow and are described as confining units, leaky beds, and aquitards.

Groundwater flow conditions can be described using general equations called governing equations. These partial differential equations are derived and the conditions they describe are presented. Flow in earth materials where the transmission properties vary at every point and location are described by equations representing anisotropic and heterogeneous conditions. When constant values of hydraulic conductivity are representative of earth materials, anisotropic homogeneous or isotropic homogeneous equations are used.

The groundwater flow equations are applied to simple groundwater settings using prescribed boundary conditions. The application of the governing equations in more complex numerical models is also discussed.

The principles used to measure groundwater head in the field, assign physical and hydraulic boundary conditions, and determine groundwater flow directions in uniform and heterogeneous hydrogeologic settings are presented.

Case studies examine flow in: a regional groundwater system, a confined aquifer used for municipal water supply, and a local system associated with groundwater contamination from a smelter.

Contents

1 INTRODUCTION

2 DEFINING GROUNDWATER

3 GROUNDWATER OCCURRENCE IN EARTH MATERIALS

Porous Media
Representative Sample Scales

3.1 Total Porosity

Measuring Porosity
Values of Total Porosity

3.2 Effective Porosity

Measuring Effective Porosity
Values of Effective Porosity

3.3 Primary and Secondary Porosity

Primary Porosity
Secondary Porosity

3.4 Void Ratio

3.5 Volumetric Moisture Content

3.6 Specific Yield and Specific Retention

3.7 Interrelationship of Effective Porosity, Specific Yield and Specific Retention

4 DARCY’S LAW, HEAD, GRADIENT AND HYDRAULIC CONDUCTIVITY

4.1 Darcy’s Law

Specific Discharge
Average Linear Velocity

4.2 Hydraulic Head

Representing Hydraulic Head Distributions

4.3 Hydraulic Gradient

Transient Changes in Gradients

4.4 Hydraulic Conductivity

Intrinsic Permeability
Fluid Properties

4.5 Applicability of Darcy’s Law

4.6 Further Investigation of Darcy’s Law, Head, Gradient and Hydraulic Conductivity

5 HYDRAULIC CONDUCTIVITY VALUES

5.1 Conditions Effecting Hydraulic Conductivity Values

Primary and Secondary Hydraulic Conductivity

5.2 Methods to Estimate Hydraulic Conductivity

5.3 Hydraulic Conductivity Values for Earth Materials

5.4 Spatial and Directional Variation of Hydraulic Conductivity

5.5 Hydraulic Conductivity of Homogeneous and Heterogeneous Materials

Equivalent Hydraulic Conductivity

5.6 Hydraulic Conductivity in Fractured Rocks

6 AQUIFERS AND AQUIFER PROPERTIES

6.1 Unconfined Aquifers

6.2 Perched Aquifers

6.3 Confined Aquifers

6.4 Properties of Aquifers and Confining Units

Transmissivity
Storativity

7 EQUATIONS OF GROUNDWATER FLOW

7.1 Basis for Flow Equation Development

7.2 Governing Equations for Confined Transient Groundwater Flow

One-dimensional Flow
Three-dimensional Flow

7.3 Governing Equations for Unconfined Groundwater Flow

7.4 Steady State Equations Describing Confined and Unconfined Flow

7.5 Applying Governing Equations

The Role of a Water Budget in Formulating Models
Boundary Value Problems
Methods for Solving Groundwater Problems
Boundary Conditions
Application of Flow Equations (Unconfined Aquifer Flow Between Water Bodies)
Example Numerical Application of Flow Equations to a Dewatering Problem

8 INTERPRETING GROUNDWATER FLOW

8.1 Mapping The Head Distribution

8.2 Determining Groundwater Flow Directions

Gradient and Flow Directions in Isotropic Material
Flow Directions in Anisotropic Materials
Flow Directions at Interfaces of Differing Hydraulic Conductivity

8.3 The Influence of Boundary Conditions

Physical Boundaries
Boundaries at Subsurface Features
Hydraulic Boundaries
Flow Systems with Distant Boundaries

8.4 Analysis of Groundwater Flow Systems

Developing Potentiometric Maps and Cross Sections
Putting the Concepts Together

8.5 Examples of Flow Systems

High Plains Aquifer in Wyoming, USA
Memphis Sand Aquifer, Memphis Tennessee, USA
Unconfined Aquifer in East Helena, Montana, USA
Summary of Flow System Examples

9 CONCLUSION

10 EXERCISES

11 REFERENCES

12 BOXES

Box 1 Density of Common Minerals, Rock Types and Soils

Box 2 Analyzing Grain-size Distribution

Box 3 Foundation for Understanding Hydraulic Head and Force Potentials

Box 4 Methods for Estimating Hydraulic Conductivity

Box 5 Equation Derivation for Equivalent K and a 4-layer Application

Box 6 Adding Recharge to the Unconfined Aquifer System

Box 7 Axis Transformation for 2-D Flow in an Anisotropic Medium

Box 8 Deriving the Tangent Law of Refraction

13 EXERCISE SOLUTIONS

About The Authors

Interview with Authors