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Hydraulics of Groundwater
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Hydraulics of Groundwater

by Jacob Bear

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This text explores the laws and equations that govern the flow and storage of groundwater in aquifers. It provides groundwater hydrologists, as well as engineers and planners who deal with the development and management of groundwater resources, with all the necessary tools to forecast the behavior of a regional aquifer system.
Following an introduction to the role


This text explores the laws and equations that govern the flow and storage of groundwater in aquifers. It provides groundwater hydrologists, as well as engineers and planners who deal with the development and management of groundwater resources, with all the necessary tools to forecast the behavior of a regional aquifer system.
Following an introduction to the role and management of groundwater in water resource systems, the text examines groundwater balance and motion, mathematical statements of the groundwater forecasting problem, flow in the unsaturated zone, and groundwater quality problems. Additional topics include hydraulics of pumping and recharging wells, fresh and salt water interface in coastal aquifers, modeling of aquifer systems, identification of aquifer parameters, and the use of linear programming in aquifer management. Helpful appendixes and a set of problems corresponding to selected chapters conclude the text.

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Dover Publications
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Dover Books on Engineering
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Hydraulics of Groundwater

By Jacob Bear

Dover Publications, Inc.

Copyright © 1979 Jacob Bear
All rights reserved.
ISBN: 978-0-486-13616-5



In this book we intend to treat only groundwater, referring to both its quantity and quality. Obviously, dividing the water resources of a region into surface water and groundwater is often artificial, or questionable (and unwise from the management point of view). For example, where should spring water be placed? It is groundwater emerging at the ground surface and becoming surface runoff, yet by an appropriate groundwater management policy, water levels in the aquifer in the vicinity of a spring can be maintained below the spring's outlet such that the spring will dry up. The water previously emerging from the spring will now be stored in the aquifer. The same is true when an aquifer is in hydraulic contact with a river, or a lake. By manipulating water levels in the aquifer, we may affect the flow in the river and vice versa. In spite of these comments, we shall focus our attention on groundwater only, as our primary objective is to discuss the hydraulics of groundwater.

The main goal of the groundwater hydrologist, water resources engineer, or planner (or planning team), who deals with a groundwater system, or with a water resource system of which groundwater is a component, is the management of the groundwater system. Simply stated, and using the terminology of systems analysis only loosely, management of a system means making various decisions (that is, assigning numerical values to decision variables) aimed at modifying the state of a considered system. Location, rate, and time of pumping, or artificially recharging an aquifer, are examples of decision variables. Water levels, depth of land subsidence, and solute concentrations, as functions of location and time are examples of state variables. Our reason for modifying the state of a considered system, that is, to bring it from its existing state to another, more desirable one, is to achieve certain goals and objectives. We also wish to do so by the best set of decisions (= policy). This implies the existence of some criteria for comparing the outputs of the system (e.g., costs, pumping) and selecting the best policy. We may refer to this activity as solving the management problem.

However, in order to solve the management problem, we must be able to predict the response of the system to any proposed operation policy, and to obtain from it the new state of the system, given its initial one. Once the new state is known we can check whether it is feasible at all, that is, does not violate any of the constraints imposed on the system. Then we can compare outputs and responses in order to select, according to some criteria, the best policy. Referring now to a groundwater system, we have to be able to forecast water levels, salinities, spring discharges, land subsidence, etc., that is, the system's state variables resulting from any proposed operation policy, say, of pumping and artificial recharge. We may refer to this problem of forecasting the state of the ground-water system as the forecasting problem. No groundwater management problem can be solved without solving first the groundwater forecasting problem for feasible operation policies, in order to select the best solution by comparing the corresponding responses. In the more advanced management procedures, the two problems—the forecasting problem and the management—are solved simultaneously.

In this introductory chapter we shall identify the role played by ground-water in a water resource system and discuss what is involved in the management of such a system when it is based soley or partly on groundwater. The discussion itself will be rather superficial as its sole objective is to set the stage for the chapters which follow.

The last section defines the objectives and scope of this book and describes how we intend to achieve the stated objectives.

We shall assume here, as in the entire book, that the reader is familiar with general hydrology, of both surface and groundwater, at least at an introductory level, and that he knows the hydrologic cycle and the place of groundwater in it.


In order to discuss the role that groundwater may play in the management of regional water resources, let us assume that both kinds of water—surface water and groundwater—are present in relatively significant quantities in a region.

Surface Water Versus Groundwater

Actually surface water (in lakes and streams) and groundwater (in aquifers) are not necessarily separate and independent water resources. Consider, for example, the interrelations between a river (or a lake) and an adjacent aquifer, or a river passing through a region under which a phreatic aquifer exists. If the river (or lake) bed is not completely clogged, water will flow through it from the river into the aquifer when water levels in the former are higher than in the latter, and vice versa. Base flow in streams is provided by groundwater. In this way, rivers and lakes in direct continuous hydraulic contact with adjacent, or underlying aquifers serve as boundaries to the flow domain in the latter. By controlling water levels in them, we can control the flow of water through them into or out of an aquifer.

Spring discharge is another example of groundwater emerging under certain conditions at the ground surface and becoming surface runoff. By controlling groundwater levels in the vicinity of a spring, its discharge is controlled, or even stopped completely.

The above considerations apply not only to water quantity, but also to water quality, defined, for example, by some chemical species or bacteria carried with the water. Polluted surface water may easily reach and pollute groundwater.

It is thus obvious that the management of regional water resources should always include both resources simultaneously, incorporating each of them in the overall system according to its individual features. In one way or another, any control of one resource will eventually, if not immediately, affect the other. The possible time lag may be due to storage and/or the relatively slow movement of groundwater and of pollutants carried by it. One should note, however, that the water divide delineating a groundwater basin and that delineating a surface one are not necessarily geographically identical and that depending on the geographical boundaries of any considered region, management may include transfer of water from one basin to another within the framework of regional conjunctive use.

Although it seems obvious that groundwater, when present in a region, should be used conjunctively with surface water within the framework of any development and management scheme, one finds in many parts of the world a certain degree of reluctance to include groundwater in the development and management of water resources.

Perhaps in part, this attitude stems from the fact that unlike water in streams and lakes, one cannot actually see groundwater in aquifers. However, in trying to rationalize this attitude, the following reasons are often given (Wiener, 1972):

(a) Exploitation of groundwater is energy consuming and expensive, especially when the water table, or the piezometric surface, is deep.

(b) Planning the development of groundwater resources requires long-term data, which usually are not available.

(c) Evaluation and planning groundwater resources requires highly trained personnel which are not available.

(d) It is difficult to predict the response of an aquifer (in terms of both water quantity and quality) to proposed activities.

(e) Groundwater projects are usually single purpose ones, namely, to supply water (whereas most surface water projects have multiple purposes).

Obviously in order to examine these arguments and to compare surface water with groundwater, one must know the local conditions. In general, however, it seems that at least in part, these arguments are based on lack of knowledge. For example:

(a) It is true that when pumping heads are large, energy costs may be significant (whereas energy may be produced from surface water). However, if one includes in the annual expenditures also the relatively high investments required for hydraulic structures, such as storage dams diversions, canals, and pipes, the overall economic picture may show a clear advantage of groundwater.

(b) Because of the large storage and slow motion involved, groundwater levels at any instant reflect the accumulated effect of a rather long period of time; changes are relatively small and slow, in comparsion with those of surface water. Hence, in general, shorter groundwater records give sufficient information for planning purposes, whereas much longer records are required in order to obtain a complete picture of the more frequent and rapid fluctuating behavior of surface water.

(c) It is true that a certain amount of knowledge is required which often is not part of the usual training of engineers. Most of this knowledge has been developed in the last two to three decades. Nowadays, however, this information is included more and more in the ordinary training of hydrologists and civil and agricultural engineers, or in special courses of continuing education. Most of the necessary theory is also included in the present text, as a contribution to the dissemination of information on groundwater. Consequently, the lack of skilled personnel can easily be overcome, even in regions where this subject has been neglected in the past.

(d) With modern hydrological tools, there is no difficulty in modeling the behavior of a groundwater system and forecasting its response (both quantity and quality wise). In general, the forecasts are reliable. Digital computers are often used when the complexity of the system warrants it.

(e) One can certainly not use groundwater for recreation, as one does in a large storage reservoir. Nevertheless, and perhaps to a more limited extent, groundwater projects may also serve multiple purposes. For example, in addition to water supply, drainage and reclamation of land may be achieved. We have already mentioned above the control of base flow in streams which may be achieved by controlling groundwater levels in adjacent aquifers. Artificial recharge can be used for disposal of reclaimed sewage water, using the purifying and mixing properties of the aquifer for augmenting the exploitable groundwater quantity.

Characteristics of Groundwater

Our main purpose in bringing these arguments is not to show that groundwater utilization is always superior and more advantageous, but to emphasize again that whenever the two resources are present, they should be used conjunctively according to their individual features. Following are some of the main characteristics of groundwater (Wiener, 1972).

Location Springs occur at points. Surface water flows along fixed curved paths. Their utilization usually requires the construction of regulative facilities which will make the water available only along certain portions of their path. Ground-water, on the other hand, underlies (when at all present) extended areas. If these coincide also with demand areas, there is no need for a surface distribution system, as the aquifer acts also as a conduit and each consumer can pump his share directly from the aquifer. This feature is of special interest in regions where development is gradual. More wells are sunk when an increase in pumpage is required. Often control structures for surface water (e.g., dams, or diversions) cannot be built in stages.

Flow and availability Fluctuations in surface flow may be significant. Minimum flows, including zero flow, occur often during the season of highest demand. On the other hand, climatic fluctuations in groundwater levels are usually small relative to the thickness of an aquifer, so that the large volume of water stored in the aquifer may serve as a buffer and also supply water in periods of drought. Whereas the regulation of surface flow requires hydraulic structures which are often rather costly, the regulation of groundwater flow is incorporated in the implementation of management schemes, namely through an appropriate areal and temporal distribution of pumpage and artificial recharge.

The regulation of groundwater flow is, therefore, in general, much less expensive. Base flow in streams and spring flow (including the drying up of streams, which means transforming surface flow into groundwater flow) can be regulated by controlling groundwater levels in their vicinity.

Annual and seasonal variability Annual and seasonal fluctuations are much more pronounced in surface than in groundwater flow. In surface flow, this means large losses of water by spillage in periods of excess water or the need for expensive regulatory structures (e.g., dams). In groundwater flow, storage is provided by the aquifer itself; spillage due to very high water levels near an outlet is relatively small and can easily be avoided by manipulating water levels through pumping.

Energy Energy must always be expended in order to lift groundwater to the ground surface. In general, capital investments in wells are low, but operating costs (i.e., cost of electricity or fuel) are relatively high.

Quality of water In many regions groundwater does not pose major biological or physical quality problems. Surface flow is much more susceptible to man made pollution, which usually requires costly treatment for its removal. This does not mean that groundwater cannot be affected by pollutants. For example, faulty sewage pipes or oil spillage may cause severe pollution of groundwater. In certain formations, pollutants may travel large distances in an aquifer without being modified. As for mineral quality, although the range of concentrations encountered is very large, in general one may observe that groundwater is more liable to pick up minerals in solution. The removal of such minerals is usually very expensive.

When groundwater does get polluted (e.g., by polluting solutes such as leachate from land fills carried down with the water from the ground surface, or by intrusion of groundwater of inferior quality into an aquifer), the restoration of quality and the removal of pollutants by mixing with and leaching by clean groundwater is a very slow hence lengthy, sometimes practically impossible, process (i.e., the process is practically irreversible). This is due to the very slow movement of groundwater especially in layers of very fine material, imbedded in formations of higher permeability, and to adsorption and ion-exchange phenomena on the surface of the solid matrix. These phenomena are especially significant when fine grained materials, such as clay are present in an aquifer. Adsorbed species continue to be fed into the groundwater flow for prolonged periods.

On the other hand, for certain polluting elements carried with the water, the above processes of adsorption and ion exchange are an advantage as they remove them from the water. The aquifer then plays the role of a filter and a purifier, taking advantage of the adsorptive capacity of the solid matrix.

In general, there is always the trend of salinization of groundwater by solutes brought down from the surface. Under natural conditions, an equilibrium is reached by the fact that water leaving the formation carries solutes with it.

However, when a management program calls for a reduction of outflow (i.e., increased pumping) and/or the introduction of more solutes (e.g., when the aquifer is artificially recharged with water of inferior quality, or when more soluble polluting sources are introduced on the ground surface), this equilibrium is destroyed and we observe an inevitable rise in the solute concentration of the groundwater, sometimes beyond permissible limits.

Impact on drainage problems The lowering of the phreatic surface by pumping may solve drainage problems in areas where the latter are produced by a high water table. The application of surface water in such cases may require a drainage system to maintain the water table at the desired depth.

In the case of marshes or of a water table which is close to the ground surface, the lowering of the water table will also reduce evapotranspiration, thus making more water available for beneficial use.

When artificial recharge (Sec. 3-4) is implemented, one should make sure that the rising water table of a phreatic aquifer will not create drainage problems.

Land subsidence When water is pumped out of a confined aquifer the intergranular stress in the solid matrix is increased even without changing the load at the ground surface. When relatively soft layers (e.g., clay, or silt) are present within the aquifer, they are compressed and we observe land subsidence. In certain areas this subsidence is very significant and limits, or even forces the stoppage, of pumping.


Excerpted from Hydraulics of Groundwater by Jacob Bear. Copyright © 1979 Jacob Bear. Excerpted by permission of Dover Publications, Inc..
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