R. Allan Freeze
Department of Geological Sciences
University of British Columbia
Vancouver, British Columbia
John A. Cherry
Department of Erth Science
Univerty of Waterloo
" I l 'P HI. Inc.
Groundwater Resource Evalution I C
fact that the variables of the system under study are represented by analog
physical quantities and pieces of equipment is extremely valuable for the purp
of teaching or display, but the cost in time is large. The network, once b
describes only one specific aquifer. In digital modeling, on the other hand, on
general computer program has been prepared, data decks representing a wide
ety of aquifers and aquifer conditions can be run with the same program.
effort involved in designing and keypunching a new data deck is much less t
that involved in designing and building a new resistance-capacitance netw
This flexibility is equally important during the calibration phase of aqi
The advantages of digital simulation weigh heavily in its favor, and with
advent of easy accessibility to large computers, the method is rapidly becoi
the standard tool for aquifer management. However, analog simulation
undoubtedly continue to play a role for some time, especially in developing c
tries where computer capacities are not yet large.
8.10 Basin Yield
Safe Yield and Optimal Yield
of a Groundwater Basin
Groundwater yield is best viewed in the context of the full three-dimensi
hydrogeologic system that constitutes a groundwater basin. On this scale of s
we can turn to the well-established concept of safe yield or to the more rigc
concept of optimal yield.
Todd (1959) defines the safe yield of a groundwater basin as the amou:
water that can be withdrawn from it annually without producing an unde
result. Any withdrawal in excess of safe yield is an overdraft. Domenico (
and Kazmann (1972) review the evolution of the term. Domenico notes tha
"undesired results" mentioned in the definition are now recognized to in(
not only the depletion of the groundwater reserves, but also the intrusion of\
of undesirable quality, the contravention of existing water rights, and the
rioration of the economic advantages of pumping. One might also include exci
depletion of streamflow by induced infiltration and land subsidence.
Although the concept of safe yield has been widely used in ground,
resource evaluation, there has always been widespread dissatisfaction wi
(Thomas, 1951; Kazmann, 1956). Most suggestions for improvement have en
aged consideration of the yield concept in a socioeconomic sense within the o
framework of optimization theory. Domenico (1972) reviews the develop
of this approach, citing the contributions of Bear and Levin (1967), Buras (I
Burt (1967), Domenico et al. (1968), and others. From an optimization view
groundwater has value only by virtue of its use, and the optimal yield mt
determined by the selection of the optimal groundwater management scheme
a set of possible alternative schemes. The optimal scheme is the one that best:
365 GroundwatUr Rasouce Ew lwuon / Ch. 8
a set of economic and/or social objectives associated with the uses to which the
water is to be put. In some cases and at some points in time, consideration of the
present and future costs Ad benefits may lead to optimal yields that involve mining
groundwater, perhaps emn to depletion. In other situations, optimal yields may
reflect the need for complete conservation. Most often, the optimal groundwater
development lies somewhere between these extremes.
The graphical and mathematical methods of optimization, as they relate to
groundwater development, are reviewed by Domenico (1972).
Transient Hydrologic Budgets and Basin Yield
In Section 6.2 we examined the role of the average annual groundwater recharge,
R, as a component in the steady-state hydrologic budget for a watershed. The value
of R was determined from a quantitative interpretation of the steady-state, regional,
groundwater flow net. Some authors have suggested that the safe yield of a ground-
water basin be defined as the annual extraction of water that does not exceed the
average annual groundwater recharge. This concept is not correct. As pointed out
by Bredehoeft and Young (1970), major groundwater development may signif-
icantly change the rechae-discharge regime as a function of time. Clearly, the
basin yield depends both on the manner in which the effects of withdrawal are
transmitted through thd"iquifers and on the changes in rates of groundwater
recharge and discharge iniuced by the withdrawals. In the form of a transient
hydrologic budget for thliaturated portion of a groundwater basin,
,dpQPt) AP ) D(t) +7 (8.72)
where Q(t) = total rate of groundwater withdrawal
R(r) = total rate ofigroundwater recharge to the basin
D(t) = total rate ofagroundWater discharge from the basin
dS/dt = rate of charge of storage in the saturated zone of the basin.
Freeze (1971a) e i the response of R(t) and D(t) to an increase in Q(t)
in a hypothetical basin in Whumid climate where water tables are near the surface.
The response was simulaid with the aid of a three-dimensional transient analysis
of a complete saturated-unsaturated system such as that of Figure 6.10 with a
pumping well added. Figure 8.32 is a schematic representation of his findings.
The diagrams show the time-dependent changes that might be expected in the
various terms of Eq. (8.72) under increased pumpage. Let us first look at the case
shown in Figure 8.32(a),Yin which withdrawals increase with time but do not
become excessive. The initial condition at time to is a steady-state flow system in
which the recharge, Re, equals the discharge, Do. At times t, 2, t,, and t,, new
wells begin to tap the system and the pumping rate Q undergoes a set of stepped
increases. Each increase is initially balanced by a change in storage, which in an
unconfined aquifer takes the form of an immediate water-table decline. At the
366 Gowindweorw RMesow Evw wan I /
0 --t-o R -i. t- t o t* T.'r
0 er imum Ti Im
Q baln nyield- C
decline Wl I"gHnh.
Withdrawal rote,Q below whichaimm rwhichl
--- Recharge rate, R grounder rechorgate ro echal"'ll
------ Discharge rate, D cannolonger be usSwnSd i ,
---. Rate of change of storage, dS/dt
Figure 8.32 Schematic diagram of transient relationships between recharge
rat, dieharratee, end withdrawal rae (after Frea, 1971a).
same time, the basin strives to set up a new equilibrium under conditions d
increased recharge, RA The unsaturated zone will now be induced to deliver greal
flow rates to the water table under the influence of higher gradients in the satu-
rated zone. Concurrently, the increased pumpage may lead to decreased dischuip
rates, D. In Figure 8.32(a), after time t,, all natural discharge ceases and td
' discharge curve rises above the horizontal axis, implying the presence of induced
recharge from a stream that had previously been accepting its baseflow componen
from the groundwater system. At time ts, the withdrawal Q is being fed by tk.
recharge, R, and the induced recharge, D; and there has been a significant decline
in the water table. Note that the recharge rate attains a maximum between t, aadW
4t. At this rate, the groundwater body is accepting all the infiltration that is a
able from the unsaturated zone under the lowered water-table conditions.
In Figure 8.32(a), steady-state equilibrium conditions are reached prior to
each new increase in withdrawal rate. Figure 8.32(b) shows the same sequence of
events under conditions of continuously increasing groundwater devel
over several years. This diagram also shows that if pumping rates are
to increase indefinitely, an unstable situation may arise where the declining
table reaches a depth below which the maxnwdm rate of groundwater recharpi
can no longer be sustained. Afterthis pointfin time the same annual preci
rate no longer provides the same percentage of infiltration to the water
Evapotranspiration during soil-moisture-redistribution periods now takes
of the infiltrated rainfall before it has a chance to percolate down to the
water zone. At t, in Figure 8.32(b), the water table reaches a depth below
no stable recharge rate can be maintained. At t, the maximum available rate
induce charge is attained. From time ts on, it is impossible for the basin to sup*
increased rates of withdrawal. The only source lies in an increased rate of change
storage that manifests itself in rapidly declining water tables. Pumping rates
iCh. 8 367 Grounmdwtw Resowce Evalitedon / Ch. 8
no longer be maintained at their original levels. Freeze (1971a) defines the value
of Q at which instability occurs as the maximum stable basin yield. To develop a
basin to its limit of stability would, of course, be foolhardy. One dry year might
Time cause an irrecoverable water-table drop. Production rates must allow for a factor
of safety and must therefore be somewhat less than the maximum stable basin
The discussion above emphasizes once again the important interrelationships
between groundwater low and surface runoff. If a groundwater basin were devel-
Soble oped up to its maximum yield, the potential yields of surface-water components
h bo of the hydrologic cycle in the basin would be reduced. It is now widely recognized
harge ro that optimal development of the water resources of a watershed depend on the
iied cofnunctivee usof surface water and groundwater. The subject has provided a
fertile field for the application of optimization techniques (Maddock, 1974; Yu
and Haimes, 1974). Young and Bredehoeft (1972) describe the application of digital
computer simulations of the type described in Section 8.8 to the solution of manage-
ment problems involving conjunctive groundwater and surface-water systems.
greater 8.11 Artificial Recharge and Induced Infiltration
scharge In recent years, particularly in the more populated areas of North America where
ind the water resource development has approached or exceeded available yield, there
nduced has been considerable effort placed on the management of water resource systems.
iponent Optimal development usually involves the conjunctive use of groundwater and
by the surface waterjand the reclamation and reuse of some portion of the available water
decline resources. Inmany cases, it involves the importation of surface water from areas
1 and of plenty toams of scarcity, or the conservation of surface water in times of plenty
is avail- for use in times of scarcity. These two approaches require storage facilities, and
there is oftemadvantage to storing water underground where evaporation losses
irior to are minimized. Underground storage may also serve to replenish groundwater
ence of resources in areas of overdraft.
opment Any process by which man fosters the transfer of surface water into the
allowed groundwater,.system can be classified as artificial recharge. The most common
g water method involves infiltration from spreading basins into high-permeability, uncon-
large R fined, alluvial aquifer. In many cases, the spreading basins are formed by the
citation construction of dikes in natural channels. The recharge process involves the growth
r table. of a groundwater mound beneath the spreading basin. The real extent of the mound
s more and its rate of growth depend on the size and shape of the recharging basin, the
,round- duration and rate of recharge, the stratigraphic configuration of subsurface forma-
which tions, and the saturated and unsaturated hydraulic properties of the geologic
rate of materials. Figure 8.33 shows two simple hydrogeological environments and the
supply type of groundwater mound that would be produced in each case beneath a circular
range of spreading basin. In Figure 8.33(a), recharge takes place into a horizontal uncon-
tes can fined aquifer bounded at the base by an impermeable formation. In Figure 8.33(b),
Groundwater Resaorce Evaluation / Ch. 8
Figure 8.33 Growth of a groundwater mound beneath a circular recharge
recharge takes place through a less-permeable formation toward a high-permeabil-
ity layer at depth.
Both cases have been the subject of a large number of predictive analyses,
not only for circular spreading basins but also for rectangular basins and for
recharge from an infinitely long strip. The latter case, with boundary conditions
like those shown in Figure 8.33(b), also has application to canal and river seepage.
It has been studied in this context by Bouwer (1965), Jeppson (1968), and Jeppson
and Nelson (1970). The case shown in Figure 8.33(a), which also has application
to the development of mounds beneath waste disposal ponds and sanitary landfills,
has been studied in even greater detail. Hantush (1967) provides an analytical
solution for the prediction of h(r, t), given the initial water-table height, he, the
diameter of the spreading basin, a, the recharge rate, R, and the hydraulic conduc-
tivity and specific yield, K and S,, of the unconfined aquifer. His solution is limited
to homogeneous, isotropic aquifers and a recharge rate that is constant in time and
space. In addition, the solution is limited to a water-table rise that is less than or
equal to 50% of the initial depth of saturation, ho. This requirement implies that
R < K. Bouwer (1962) utilized an electric-analog model to analyze the same prob-
I I IMP
Groundwate Resorce Eveluation / Ch. 8
lem, and Marino (1975a, 1975b) produced a numerical simulation. Al three of
these analyses have two additional limitations. First, they neglect unsaturated flow
by assuming that the recharge pulse traverses the unsaturated zone vertically and
reaches the water table unaffected by soil moisture-conditions above the water
table. Second, they utilize the Dupuit-Forchheimer theory of unconfined flow
(Section 5.5) which neglects any vertical flow gradients that develop in the saturated
zone in the vicinity of the mound. Numerical simulations carried out on the com-
plete saturated-unsaturated system using the approaches of Rubin (1968), Jeppson
and Nelson (1970), and Freeze (1971a) would provide a more accurate approach
to the problem, but at the expense of added complexity in the calculations.
Practical research on spreading basins has shown that the niceties of predictive
analysis are seldom reflected in the real world. Even if water levels in spreading
ponds are kept relatively constant, the recharge rate almost invariably declines
with time as a result of the buildup of silt and clay on the basin floor and the growth
of microbial organisms that clog the soil pores. In addition, air entrapment between
the wetting front and the water table retards recharge rates. Todd (1959) notes
that alternating wet and dry periods generally furnish a greater total recharge
than does continuous spreading. Drying kills the microbial growths, and tilling
and scraping of the basin floor during dry periods reopens the soil pores.
There are several excellent case histories that provide an account of specific
projects involving artificial recharge from spreading basins. Seaburn (1970)
describes hydrologic studies carried out at two of the more than 2000 recharge
basins that are used on Long Island, east of New York City, to provide artificial
recharge of storm runoff from residential and industrial areas. Bianchi and Haskell
(1966, 1968) describe the piezometric monitoring of a complete recharge cycle
of mound growth and dissipation. They report relatively good agreement between
the field data and analytical predictions based on Dupuit-Forchheimer theory.
They note, however, that the anomalous water-level rises that'accompany air
entrapment (Section 6.8) often make it difficult to accurately monitor the growth
of the groundwater mound.
While water spreading is the most ubiquitous form of artificial recharge,
it is limited to locations with favorable geologic conditions at the surface. There
have also been some attempts made to recharge deeper formations by means of
injection wells. Todd (1959) provides several case histories involving such diverse
applications as the disposal of storm-runoff water, the recirculation of air-condi-
tioning water, and the buildup of a freshwater barrier to prevent further intrusion
of seawater into a confined aquifer. Most of the more recent research on deep-well
injection has centered on utilization of the method for the disposal of industrial
wastewater and tertiary-treated municipal wastewater (Chapter 9) rather than for
the replenishment of groundwater resources.
The oldest and most widely used method of conjunctive use of surface water
and groundwater is based on the concept of induced infiltration. If a well produces
water from alluvial sands and gravels that are in hydraulic connection with a
P i I:~P.~P~C~P ~ 4
;^. ** ***
370 Groundwater Resource Evaluation / Ch. 8
stream, the stream will act as a constant-head line source in the manner noted in
Figures 8.15(d) and 8.23(d). When a new well starts to pump in such a situation,
the pumped water is initially derived from the groundwater zone, but once the cone
of depression reaches the stream, the source of some of the pumped water will be
streamflow that is induced into the groundwater body under the influence of the
gradients set up by the well. In due course, steady-state conditions will be reached,
after which time the cone of depression and the drawdowns within it remain con-
stant. Under the steady flow system that develops at such times, the source of all
the pumped groundwater is streamflow. One of the primary advantages of induced
infiltration schemes over direct surface-water utilization lies in the chemical and
biological purification afforded by the passage of stream water through the alluvial
8.12 Land Subsidence
In recent years it has become apparent that the extensive exploitation of ground-
water resources in this century has brought with it an undesired environmental
side effect. At many localities in the world, groundwater pumpage from uncon-
solidated aquifer-aquitard systems has been accompanied by significant land sub-
sidence. Poland and Davis (1969) and Poland (1972) provide descriptive summaries
of all the well-documented cases of major land subsidence caused by the withdrawal
of fluids. They present several case histories where subsidence has been associated
with oil and gas production, together with a large number of cases that involve
groundwater pumpage. There are three cases-the Wilmington oil field in Long
Beach, California, and the groundwater overdrafts in Mexico City, Mexico, and
in the San Joaquin valley, California-that have led to rates of subsidence of the
land surface of almost I m every 3 years over the 35-year period 1935-1970. In
the San Joaquin valley, where groundwater pumpage for irrigation purposes is
to blame, there are three separate areas with significant subsidence problems.
Taken together, there is a total area of 11,000 km2 that has subsided more than
0.3 m. At Long Beach, where the subsiding region is adjacent to the ocean, sub-
sidence has resulted in repeated flooding of the harbor area. Failure of surface struc-
tures, buckling of pipe lines, and rupturing of oil-well casing have been reported.
Remedial costs up to 1962 exceeded $100 million.
Mechanism of Land Subsidence
The depositional environments at the various subsidence sites are varied, but
there is one feature that is common to all the groundwater-induced sites. In each
case there is a thick sequence of unconsolidated or poorly consolidated sediments
forming an interbedded aquifer-aquitard system. Pumpage is from sand and gravel
aquifers, but a large percentage of the section consists of high-compressibility
clays. In earlier chapters we learned that groundwater pumpage is accompanied by
vertical leakage from the adjacent aquitards. It should come as no surprise to find
Groundwater Resource Evaluation I Ch. 8
that the process of aquitard drainage leads to compaction* of the aquitards just as
the process of aquifer drainage leads to compaction of the aquifers. There are two
fundamental differences, however: (1) since the compressibility of clay is 1-2
orders of magnitude greater than the compressibility of sand, the total potential
compaction of an aquitard is much greater than that for an aquifer; and (2) since
the hydraulic conductivity of clay may be several orders of magnitude less than the
hydraulic conductivity of sand, the drainagelprocess, and hence the compaction
process, is much slower in aquitards than in aquifers.
Consider the vertical cross section shown in Figure 8.34. A well pumping at
.. :. .
t i '.. -.. :'
Figure 8.34 One-dimensional consolidation of an aquitard.
a rate Q is fed by two aquifers separated by an aquitard of thickness b. Let us
assume that the geometry is radially symmetric and that the transmissivities in the
two aquifers are identical. The time-dependent reductions in hydraulic head in the
aquifers (which could be predicted from leaky-aquifer theory) will be identical
at points A and B. We wish to look at the hydraulic-head reductions in the aquitard
along the line AB under the influence of the head reductions in the aquifers at A
and B. If hA(t) and h,(t) are approximated by step functions with a step Ah (Figure
8.34), the aquitard drainage process can be viewed as the one-dimensional, transient
boundary-value problem described in Section 8.3 and presented as Eq. (8.21).
The initial condition is h = ho all along AB, and the boundary conditions are
*Following Poland and Davis (1969), we are using the term "compaction" in its geological
sense. In engineering jargon the term is often reserved for the increase in soil density achieved
through the use of rollers, vibrators or other heavy machinery.
__ F ',77 _7
372 Groundwater Resource Evaluation / Ch. 8
h = he Ah at A and at B for all t > 0. A solution to this boundary-value prob.
lem was obtained by Terzaghi (1925) in the form of an analytical expression for
h(z, t). An accurate graphical presentation of his solution appears as Figure 8.17.
The central diagram on the right-hand side of Figure 8.34 is a schematic plot of his
solution; it shows the time-dependent decline in hydraulic head at times to, tl,...,
t. along the line AB. To obtain quantitative results for a particular case, one must
know the thickness b', the vertical hydraulic conductivity K', the vertical compress-
ibility a', and the porosity n' of the aquitard, together with the head reduction Ah
on the boundaries.
In soil mechanics the compaction process associated with the drainage of a
clay layer is known as consolidation. Geotechnical engineers have long recognized
that for most clays a > nf, so the latter term is usually omitted from Eq. (8.21).
The remaining parameters are often grouped into a single parameter c,, defined by
c, = (8.73)
The hydraulic head h(z, t) can be calculated from Figure 8.17 with the aid of Eq.
(8.23) given c,, Ah, and 6.
In order to calculate the compaction of the aquitard given the hydraulic head
declines at each point on AB as a function of time, it is necessary to recall the effec-
tive stress law: or = o, + p. For oT = constant, do, = -dp. In the aquitard,
the head reduction at any point z between the times t, and t2 (Figure 8.34) is dh
= h (z, t ) h2(z, tz). This head drop creates a fluid pressure reduction: dp = pg dp
= pgd(h z)= pg dh, and the fluid pressure reduction is reflected by an
increase in the effective stress do, = -dp. It is the change in effective stress, acting
through the aquitard compressibility a', that causes the aquitard compaction
Ab'. To calculate Ab' along AB between the times t, and t2, it is necessary to divide
the aquitard into m slices. Then, from Eq. (2.54),
Ab-',. = b' Y pga' dh, (8.74)
where dh, is the average head decline in the ith slice.
For a multiaquifer system with several pumping wells, the land subsidence
as a function of time is the summation of all the aquitard and aquifer compactions.
A complete treatment of consolidation theory appears in most soil mechanics texts
(Terzaghi and Peck, 1967; Scott, 1963). Domenico and Mifflin (1965) were the
first to apply these solutions to cases of land subsidence.
It is reasonable to ask whether land subsidence can be arrested by injecting
groundwater back into the system. In principle this should increase the hydraulic
heads in the aquifers, drive water back into the aquitards, aid cause an expansion
of both aquifer and aquitard. In practice, this approach is not particularly effec-
tive because aquitard compressibilities in expansion have only about one-tenth
the value they have in compression. The most successful documented injection
Groundwater Resource Evaluation / Ch. 8
scheme is the one undertaken at the Wilmington oil field in Long Beach, California
(Poland and Davis, 1969). Repressuring of the oil reservoir was initiated in 1958
and by 1963 there had been a modest rebound in a portion of the subsiding region
and the rates of subsidence were reduced elsewhere.
Field Measurement of Land Subsidence
If there are any doubts about the aquitard-compaction theory of land subsidence,
they should be laid to rest by an examination of the results of the U.S. Geological
Survey subsidence research group during the last decade. They have carried out
field studies in several subsiding areas in California, and their measurements pro-
vide indisputable confirmation of the interrelationships between hydraulic head
declines, aquitard compaction, and land subsidence.
Figure 8.35 is a contoured map, based on geodetic measurements, of the land
subsidence in the Santa Clara valley during the period 1934-1960. Subsidence is
Figure 8.35 Land subsidence in feet, 1934-1960, Santa Clara valley, Cali-
fornia (after Poland and Davis, 1969).
confined to the area underlain by unconsolidated deposits of alluvial and shallow-
marine origin. The centers of subsidence coincide with the centers of major pump-
ing, and the historical development of the subsidence coincides with the period
of settlement in the valley and with the increased utilization of groundwater.
Quantitative confirmation of the theory is provided by results of the type
shown in Figure 8.36. An ingeniously simple compaction-recorder installation
[Figure 8.36(a)] produces a graph of the time-dependent growth of the total
-.7-T-7-T- -T. -MRIM, TTT
11 04 "
..^ -1^ .. ,^^ ^ ^ ^ *^ .11.: .
Groundwater Resource Evaluation / Ch. 8
1960 1961 1962
Figure 8.36 (a) Compaction-recorder installation; (b) compaction meas-
urement site near Sunnyvale, California; (c) measured com-
pactions, land subsidence, and hydraulic head variations at the
Sunnyvale site, 1960-1962 (after Poland and Davis, 1969).
compaction of all material between the land surface and the bottom of the hole.
Near Sunnyvale in the Santa Clara valley, three compaction recorders were estab-
lished at different depths in the confined aquifer system that exists there [Figure
Groundwater Resource Evaluation / Ch. 8
8.36(b)]. Figure 8.36(c) shows the compaction records together with the total land
subsidence as measured at a nearby benchmark, and the hydraulic head for the
250- to 300-m-depth range as measured in an observation well at the measurement
site. Decreasing hydraulic heads are accompanied by compaction. Increasing
hydraulic heads are accompanied by reductions in the rate of compaction, but
there is no evidence of rebound. At this site "the land subsidence is demonstrated
to be equal to the compaction of the water-bearing deposits within the depth tapped
by water wells, and the decline in artesian head is proved to be the sole cause of
the subsidence" (Poland and Davis, 1969, p. 259).
Riley (1969) noted that data of the type shown on Figure 8.36(c) can be viewed
as the result of a large-scale field consolidation test. If the reductions in aquitard
volume reflected by the land subsidence are plotted against the changes in effective
stress created by the hydraulic-head declines, it is often possible to calculate the
average compressibility and the average vertical hydraulic conductivity of the
aquitards. Helm (1975, 1976) has carried these concepts forward in his numerical
models of land subsidence in California.
It is also possible to develop predictive simulation models that can relate
possible pumping patterns in an aquifer-aquitard system to the subsidence rates
that will result. Gambolati and Freeze (1973) designed a two-step mathematical
model for this purpose. In the first step (the hydrologic model), the regional hydrau-
lic-head drawdowns are calculated in an idealized two-dimensional vertical cross
section in radial coordinates, using a model that is a boundary-value problem based
on the equation of transient groundwater flow. Solutions are obtained with a
numerical finite-element technique. In the second step of the modeling procedure
(the subsidence model), the hydraulic head declines determined with the hydrologic
model for the various aquifers are used as time-dependent boundary conditions
in a set of one-dimensional vertical consolidation models applied to a more refined
geologic representation of each aquitard. Gambolati et al. (1974a, 1974b) applied
the model to subsidence predictions for Venice, Italy. Recent measurements
summarized by Carbognin et al. (1976) verify the model's validity.
8.13 Seawater Intrusion
When groundwater is pumped from aquifers that are in hydraulic connection with
the sea, the gradients that are set up may induce a flow of salt water from the sea
toward the well. This migration of salt water into freshwater aquifers under the
influence of groundwater development is known as seawater intrusion.
As a first step toward understanding the nature of the processes involved,
it is necessary to examine the nature of the saltwater-freshwater interface in coastal
aquifers under natural conditions. The earliest analyses were carried out indepen-
dently by two European scientists (Ghyben, 1888; Hprzberg, 1901) around the
turn of the century. Their analysis assumed simple hydrostatic conditions in a
homogeneous, unconfined coastal aquifer. They showed [Figure 8.37(a)] that the
376 Groundwater Resource Evaluation / Ch. 8
c spra sa Fresh water
-'''Salt water'^19 1 f
Figure 8.37 Saltwater-freshwater interface in an unconfined coastal aquifer
(a) under hydrostatic conditions; (b) under conditions of steady-
state seaward flow (after Hubbert, 1940).
interface separating salt water of density p, and fresh water of density p, must
project into the aquifer at an angle a < 90*. Under hydrostatic conditions, the
weight of a unit column of fresh water extending from the water table to the inter-
face is balanced by a unit column of salt water extending from sea level to the same
depth as the point on the interface. With reference to Figure 8.37(a), we have
p,gz, = pg(z, + z,) (8.75)
z,= P-. z, (8.76)
For p, = 1.0 and p, = 1.025,
z,= 40z, (8.77)
Equation (8.77) is often called the Ghyben-Herzberg relation.
If we specify a change in the water-table elevation of Az,, then from Eq. (8.77),
Az, = 40Az,. If the water table in an unconfined coastal aquifer is lowered 1 m,
the saltwater interface will rise 40 m.
In most real situations, the Ghyben-Herzberg relation underestimates the
depth to the saltwater interface. Where freshwater flow to the sea takes place, the
hydrostatic assumptions of the Ghyben-Herzberg analysis are not satisfied. A more
realistic picture was provided by Hubbert (1940) in the form of Figure 8.37(b)
for steady-state outflow to the sea. The exact position of the interface can be deter-
mined for any given water-tableconfiguration by graphical flow-net construction,
noting the relationships shown on Figure 8.37(b) for the intersection of equipoten-
tial lines on the water table and on the interface.
The concepts outlined in Figure 8.37 do not reflect reality in yet another way.
Both the hydrostatic analysis and the steady-state analysis assume that the interface
377 Groundwater Resource Evaluation / Ch. 8
separating fresh water and salt water in a coastal aquifer is a sharp boundary.
- In reality, there tends to be a mixing of salt water and fresh water in a zone of
T- diffusion around the interface. The size of the zone is controlled by the dispersive
characteristics of the geologic strata. Where this zone is narrow, the methods of .
solution for a sharp interface may provide a satisfactory prediction of the fresh-
water flow pattern, but an extensive zone Qo diffusion can alter the flow pattern
"_ and the position of the interface, and must be taken into account. Henry (1960)
;' was the first to present a mathematical solution for the steady-state case that
includes consideration of dispersion. Cooper et al. (1964) provide a summary of
the various analytical solutions.
Seawater intrusion can be induced in both unconfined and confined aquifers.
Figure 8.38(a) provides a schematic representation of the saltwater wedge that
would exist in a confined aquifer under conditions of natural steady-state outflow.
Initiation of pumping [Figure 8.38(b)] sets up a transient flow pattern that leads
to declines in the potentiometric surface on the confined aquifer and inland migra-
tion of the saltwater interface. Pinder and Cooper (1970) presented a numerical
mathematical method for the calculation of the transient position of the saltwater
front in a confined aquifer. Their solution includes consideration of dispersion.
~- -- Conrff'ie aquifer
*-~ ~..~r ."::...*: r, **.*. .* *
Interface Fresh water Interface
Figure 8.38 (a) Saltwater-freshwater interface in a confined coastal aquifer
under conditions of steady-state seaward flow; (b) seawater ---
intrusion due to pumping.
One of the most intensively studied coastal aquifers in North America is the
Biscayne aquifer of southeastern Florida (Kohout, 1960a, 1960b). It is an uncon-
fined aquifer of limestone and calcareous sandstone extending to an average depth
of 30 m below sea level. Field data indicate that the saltwater front undergoes
transient changes in position under the influence of seasonal recharge patterns
and the resulting water-table fluctuations. Lee and Cheng (1974) and Segol and
Pinder (1976) have simulated transient conditions in the Biscayne aquifer with
finite-element numerical models. Both the field evidence and the numerical model- _
ing confirm the necessity of considering dispersion in the steady-state and transient
analyses. The nature of dispersion in groundwater flow will be considered more
fully in Chapter 9 in the context of groundwater contamination.
Groundwater Resource Evaluation / Ch. 8
Todd (1959) summarizes five methods that have been considered for control- P
ling seawater intrusion: (1) reduction or rearrangement of the pattern of ground-
water pumping, (2) artificial recharge of the intruded aquifer from spreading
basins or recharge wells, (3) development of a pumping trough adjacent to the coast
by means of a line of pumping wells parallel to the coastline, (4) development of
a freshwater ridge adjacent to the coast by means of a line of recharge wells parallel
to the coastline, and (5) construction of an artificial subsurface barrier. Of these
five alternatives, only the first has been proven effective and economic. Both Todd
(1959) and Kazmann (1972) describe the application of the freshwater-ridge concept
in the Silverado aquifer, an unconsolidated, confined, sand-and-gravel aquifer
in the Los Angeles coastal basin of California. Kazmann concludes that the project
was technically successful, but he notes that the economics of the project remain
a subject of debate.
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