DYNAMIC AND STATIC STUDIES OF SEAWATER INTRUSION L. Stephen Lau Technical Report No. 3 February 1967 Project Completion Report for DEVELOPMENT AND HYDROLOGY OF GROUND WATER BASIN WITH SPECIAL REFERENCE TO SEAWATER ENCROACHMENT IN THE HONOLULU REGION OWRR Project No. A-007-HI, Grant Agreement No. 14-01-0001-581 Principal Investigators: L. Stephen Lau and Doak C. Cox Project Period: April 1 to Sept. 30, 1965 The programs and activities described herein were supported in part by funds provided by the United States Department of the Interior as autho- rized under the Water Resources Act of 1964, Public Law 88-379.
Transcript
DYNAMIC AND STATIC STUDIES OF SEAWATER INTRUSION
~
L. Stephen Lau
Technical Report No. 3
February 1967
Project Completion Report
for
DEVELOPMENT AND HYDROLOGY OF GROUND WATER BASIN WITH SPECIAL
REFERENCE TO SEAWATER ENCROACHMENT IN THE HONOLULU REGION
OWRR Project No. A-007-HI, Grant Agreement No. 14-01-0001-581
Principal Investigators: L. Stephen Lau and Doak C. Cox
Project Period: April 1 to Sept. 30, 1965
The programs and activities described herein were supported in part by funds provided by the United States Department of the Interior as authorized under the Water Resources Act of 1964, Public Law 88-379.
ABSTRACT
A theopetiaal equation Was adapted and modified fop a watep
table aquifep to pelate fpeshwatep flow to the sea, geometpy of the
fpesh watep-sea watep interfaae, and aquifep ahaPaatepistias undep
dynamia equiUbpium. Vepifiaation was obtained in laboratopy expePi
ments aonduated in a hydpaulia sand model.
Othep labopatopy expePiments pevealed speaial flow patterns in
the tpansitional zone of the fpeshwatep-seawatep interfaae. The extent
and the vertiaal density gpadient of the bpaakish water in the tpansi
tional zone wepe examined for their effeats on modifying the aonven
tional Ghyben-Hepzbepg Patio. Groundwatep data aolleated fPOrn a deep
weU on Oahu, Hawaii was disaussed as an illustration.
iii
FIGURES
Figure 1 Definition Sketch for Nomitsu's Formulas ................... 3
2 Definition Sketch for Glover's Formulas .................... 5
3 Location of Interface in a Water Table Aquifer ............. 7
4 Comparison Between Three Theories and Measurements ......... 9
5 Flow Net and Interface for a Pumping Well in a Coastal Area. It ............................ 111 ......................... iii ........................... It .... 11
6 Comparison Between Actual Depth and Ghyben-Herzberg's Depth ...................................................... 14
7 Defi ni ti on Sketch for Equati on 9 ..........................• 15
8 Brackish-Water Zone Related to Ghyben-Herzberg Ratio ....... 18
9 Change in Chloride Content of Water vs. Depth of Test Hole ............................................ ,., ....................................... "' ........... 20
I
vi
INTRODUCTION
The Ghyben-Herzberg lenses underlying the Honolulu-Pearl Harbor
area constitute the most important source of water supply in Hono
lulu. These horizontally interconnected freshwater lenses overlie a
brackish water interface and seawater zones which occur in the inter
stices of the basaltic formations. The water flows in and about the
lens, including natural and artificial recharges and discharges, bring
about disperSion of the underlying seawater, and, hence, salinization
of the freshwater lens.
For five years, several groundwater research projects concerning
the hydrodynamics and dispersion in the lens have been conducted under
the joint sponsorship of the Board of Water Supply of the City and
County of Honolulu, and the College of Engineering of the University
of Hawaii (Lau, 1964). This work is being continued in the Water
Resources Research Center of the University. Projects have included
theory as well as studies of regional groundwater hydrology problems.
Sand-packed hydraulic models and electrical analog models were used in
these projects. This report presents some findings of general interest
with ramifications.
Equilibrium Position of Seawater Wedge for Water Table Aquifers
Through displacement, a freshwater-seawater interface can be formed
in a permeable medium. While there can be large scale motions in these
waters: horizontal, vertical, absolute, and relative, the discussion in
this section will be concerned with a stationary seawater body under
dynamic equilibrium. Seasonal and tidal oscillations and trends are not
considered and the degree of mixing of the two waters is considered
,
2
negligible. Also, the flow is two-dimensional and steady I and th.e aquifer
material is homogenous and isotropic.
Most previous studies have been theoretical and laboratory inyes-
tigations of the above are idealized cases rather than site investigations
and probably do not occur in the field. However, these theoretical equa-
tions provide some insight into the complicated phenomena.
A general theoretical treatment of the subject was advanced by
Hubbert, including application of the "law" of Badon Ghyben and Herzberg
(1940, p. 924). Studies which were made primarily for confined aquifers*
include those by Harder et aZ. (1953), Henry (1959), Brooks (1960) and
Rumer and Harleman (1963). Studies which were made for water table aqui
fers include an early study by Nomitsu et at. (1927), Glover (1959), and
Lau (1960).
This report is primarily concerned with water table aquifers. A
brief review of Nomitsu's and Glover's studies is given prior to presenting
Lau's findings. Selected results of confined aquifer studies are cited
wherever suitable.
Nomitsu's study employed Dupuit-Forchheimer's approximations and
assumed validity of the Ghyben-Herzberg principle. Using the symbol con-
vention of this report Nomitsu's Equation reads as follows** :
K 2L w -w s f 2L S-l - = = q h2_h2 w h2_h2 S (1)
0 s 0
*According to Todd, confined aquifers, also known as artesian or pressure aquifers, occur where groundwater is confined under pressure greater than atmospheric by overlying, relatively impermeable strata (1959, p. 28). Suggestion has been made that confined aquifers may be limited to those with confinements top and bottom and that the ones with top confinement only may be called artesian. This finer differentiation is not made here.
**A list of symbols is included as Appendix A.
Nomitsu suggested deletion of the h2 term in Equation (1) whenever o 2 2* h may be considered small when compared with h . This results in o
where q = K =
w -w s f
w s = 2L
h 2
seaward flow rate of freshwater
coefficient of permeability.
S-l
S
per unit width of aquifer,
(2)
L = hOl'izontal distance from the coastal line to a point on the
fresh-salt water interface,
h = freshwater head or height of groundwater table above sea
level,**
w == specific s weight of salt water in aquifer,
wf = specific weight of freshwater in the aquifer, and
S = W /wf s .
A definition sketch is given in Figure 1.
=-1U-__ -~!c.----1GROUND WATER TABLE
1· h
_.w__-r---I1--- - -1-LEQU,- H
SEA
q
POTENTIAL LINE Wf
....... --L
C· --~::-----L-FRESH-SALT WATER
INTERFACE
FIGURE I: DEFINITION SKETCH FOR NOMlTSU'S FORMULAS
*Nomitsu recognized that it was "inadmissible to consider h = H = 0 at the shoreline as in the figure of Herzberg because it makes the velocity there at such locations infinitely great". p. 285.
**Sea level is used as datum for heads and depths in the report.
4
Nomitsu expressed the Ghyben-Herzberg principle in two alternative
forms:
H wf
1
Ji = w -w = 5-1 s f
Ws S H+h=--h=--h ws-Wf 5-1
(3)
Equations (2) and (3) can be combined and rearranged as Equation
(4) .
K 5 h2 K H2 q = 2" 5-1 L = 2" S(5-1) L (4)
It is necessary to emphasize that the flow direction was assumed
to be horizontal and uniform everywhere through a cross section of the
freshwater, as Nomitsu himself pointed out. These assumptions are parts
of the Dupuit-Forchheimer assumptions. Further, points C and C' are the
two ends of a vertical line.
Glover's study was restricted to theories and was basically an
adaptation of a mathematical solution obtained by Kozeny for flow through
a semi-infinite underdrained earthdam resting on horizontal bedrock
(Kozeny, p. 410). The mathematical procedure dealt with complex potential
and hodograph by conformal mapping. In his analysis, the flow through
the seepage surface above sea level was assumed to be neglible, possibly
because, in part, there was no such counterpart in Kozeny's problem.
Glover's equation of the fresh-salt water interface is given in
Equation (5) in terms of the notation used here.
2q' (5-1)K x (5)
5
GR~D SURFACE
---.....---.,..."...-::::-------+Z-----.-------- SEA LEVEL DATUM
I q
--...r. ___ FRESH-SALT WATER INTERFACE
FIGURE 2: DEFINIl10N SKETCH FOR GLOVER'S FORMULAS
from which H = q' 0 (5-1) K (6)
and x = -q' 0 2(5-1)K (7)
Glover and Nomitsu's results may be compared in spite of some
basic difference in assumptions. Glover's Equation (5) and Nomitsu's
Equation (1) may be re-written as:
Nomitsu: (la)
6
Glover:
Other things being equal, q shOUld be larger than q' as suggested
in the two definition sketches. Comparison of Equations (la) and (Sa)
verifies this and further shows that Nomitsu's q is larger than Glover's
q' by a factor of the specific gravity of seawater S which is often taken
to be 1.025.
Lau conducted a laboratory investigation for the Board of Water
Supply to examine the behavior of the Ghyben-Herzberg lenses in Hawaii.
Considering the idealized case in which the flow is two-dimensional and
steady in a homogenous and isotropic medium, neglecting both the disper-
sion at the salt-fresh interface and the motion of the underlying salt
water, and noting flatness of some water tables (say I foot per mile),
except close to points of discharges and recharges, he obtained an equa-
tion by applying Harder's potential function to an unconfined aquifer
boundary condition (1960).* The equation may be written as Equation (8).
= ~ (S-l) M2 q 2L
Equation (8) was experimentally verified for the realm of low
~)
hydraulic gradient illustrated by the close agreement between the theo-
retical line and experimental points in Figure 3. Experiments were
conducted in a sand-packed hydraulic model, and data were recorded when
dynamic equilibrium was reached.
Toward the higher flow rates, the deviation of experimental results
from theory became noticeable. It was largely due to the fact that as
the groundwater table became steeper for higher flow rates, the assump-
*A brief summary of Harder's approach together with a review given by Brooks (1960) is given in Appendix B.
q KM
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Sea I.vel
Theory -----_
..9.... _ !.:.!. hi KM - 2 T
Experiment points
(a}O At toe of wedQe
(b)A At Intermediate points (c)O
7
Ground- water table
4----q
q: Fresh water flow ratl per unit width
L: Dlstanc. from coalt to interfaCI
hi: Thickn... of fresh - water saturated lo"e S: S.a water Ip. gravity
1<: Coefficient of permlability
o ~----~------~------~----~~----~------~------~---o 0.01 0.02 0.03 0.04 0.05 0.06 0.07
(S-I) • M 2 L
FIGURE 3: LOCATION OF INTERFACE IN A WATER TABLE AQUIFIER (AFTER LAU. 1960)
tion required by the theory, i.e., flatness of water table, was no
longer realized in experimental conditions.
A comparison of the three theories by Lau, Nomitsu and Glover may
be made by utilizing typical experimental data such as the intermediate
points b in Figure 3. Figure 4 depicts such a comparison and shows
clearly that agreement between theory and experiments is achieved best
by Lau's Equation (8), next by Nomitsu's Equation (la) and then by
Glover's Equation (Sa).
Freshwater-Seawater Dispersion and the Brackish Water Zone
Dispersion of solutes in fluids in a porous medium results from
variations of microscopic velocity and molecular diffusion, but the
latter is considered to be insignificant CRifai, 1956). When a miscible
liquid contaminant is introduced on the surface of a liquid moving
through a permeable medium, dispersion of the contaminent will occur
logitudinally and laterally with greater dispersion in the former direc
tion.
In the experimental work described in the preceding section, the
interface between the miscible freshwater and seawater was observed as
a sharp surface with negligible dispersion in the flow patterns in
laboratory tests. However, with other flow patterns, particularly
patterns involving oscillatory motions perpendicular to the interface,
such as may be generated by pumping, tidal, effects, or seasonal varia
tions in recharge, substantial dispersion can occur at the interface,
creating a thick zone of brackish water. In the Pearl Harbor area on
Oahu, the transitional zone of brackish water was as thick as 1,300
feet, attributed primarily to pumping, and secondarily, to tidal fluc-
0.15
a'
1 _ 0.10
a E o o
0.05
.05
(;) LAU
A NOMITSU
o GLOVER
Li ne of perfect
aQreement between
0.10
Measured q
A
EI
A
EJ
9
Data: intermediate point b
in Fig. :3
0.15
FIGURE 4: COMPARISON BETWEEN THREE THEORIES
AND MEASUREMENTS
10
tuations (Visher and Mink, 1964).1
Reported here are laboratory tests involving observations on dis-
persion along an interface caused by vertical velocity components in a
flow converging upwards 'toward a pumping well. Tests and observations
were also made for other purposes in the same study CLau, 1960).
Figure 5 shows the front view of a model that is sand-packed in
the center section and fed by a constant-head contrqlled freshwater
source from the right end and seawater from the left end below a simu-
lated "caprock." The model "caprock," an impermeable boundary, was
penetrated by a pumping well. The results of different pumping rates
were observed with this configuration. After all discernible transitory
phenomena had passed, flow with the attendant interface was steady or
time-independent. The well draft rate in this experiment was such that
the freshwater discharge initially escaping into the sea from beneath
the caprock, was completely diverted. In fact, the well pumpage was
found to contain about 0.2% of sea water.
The freshwater body was divided in two by a tongue of very brack-
ish water (AWM in Figure 5), rising to the caprock about one-third the
distance from the well to the original discharge point and presumably
following the base of the caprock from there to the well. In the essen-
tially static freshwater body seaward of this salt water tongue, the
salt-fresh contact zone was practically horizontal. The zone of mixture
of salt and freshwater was thick, and the~e were some noticeable finer
brackish water streaks in the freshwater in addition to the major salt
water tongue. Although these streaks were presumably drawn toward the
IRumer and tlarleman studied theoretical dispersion of an interface caused by tidal fluctuation (1963).
v
Sea
water
v Sea
Equipotential Flow line
line------~
~ \l I
L--- \ 1 Fresh \ water
source
FIGURE 5: FLOW NET AND INTERFACE FOR A PUMPING WELL
IN A COASTAL AREA (LAU, 1960, EXP. C-I- e )
f-' f-'
.......
/
12
well from the underlying sea water, the velocity was practically un-
measureable by inj action of a dye spot.
In contrast, the interfac.e landward of the salt water tongue ~ form-
ing seaward boundaries of the portion of the freshwater through which
essentially all the discharge was taking place, was steep and sharp. It
was curvilinear, as shown in Figure 5, following closely streamlines in
the freshwater indicated by dye streaks. The thinness of the brackish
water zone fs believed to be due to the flushing return of the strongly
flowing freshwater.
The piezometric measurements and subsequent calculations indicated
that the simple static Ghyben-Herzberg principle was inapplicable to the
parts of the model with appreciable vertical components of flow.
Within the main seawater body, there was undoubtedly some movement
inland and toward the well to supply the salt water dispersing into the
freshwater and being discharged from the well, although this flow was
not measured. The isolated seaward freshwater body was gradually becom-
ing salinized although measurements were not continued to prove this. It
would probably have lost its identity with time.
Modification of the Ghyben-Herzberg Ratio in the Presence of the Brackish Water Zone
The ratio of 40:1, known as the Ghyben-Herzberg ratio, comes from
the Ghyben-Herzberg principle, an explanation that salt water underlying
the coast with a seawater density and salinity occurred at a depth of
approximately 40 times the height of freshwater above sea level. The
pressures of any point at the fresh-salt interface must be the same on
either side of the interface. Then by hydrostatics, the freshwater
being lighter must stand higher to create the pressure. If the specific
13
gravity of seawater were taken to be 1.025, the freshwater would stand
at two and a half hundredths of a foot higher than each foot of seawater,
or one foot higher for each forty feet of seawater. Should the specific
gravity of seawater S differ from 1.025, a corresponding ratio may be
computed by the expression l/(S-I). Recognition of the variation of the
specific gravity of seawater with local temperature and depth has been
amply demonstrated by Wentworth (1939).
The correct application of the above principle is limited to a
static condition of two bodies of water in contact (Hubbert, 1940). Re-
cognizing the motion of both waters, Hubbert advanced an extensive theory
for a redefined problem. Further, under the combined conditions of
steady seaward flow of freshwater, stationary interface, and motionless
saltwater in the aquifer, the Ghyben-Herzberg ratio was actually applica-
ble between the two ends of an equipotential line such as AB in the fresh-
water region, rather than the two ends of a vertical line AC (Figure 6).
Field measurement of the head is ordinarily made in a test hole extending
to a depth not far below the groundwater table such as point A. The
measured head hA when multiplied by the appropriate ratio, such as 40
gives a depth that falls short of reaching point C of the interface. The
actual depth to the interface is therefore greater than that given by the
Ghyben-Herzberg ratio.
Hubbert also advanced for the condition of a sharp interface with-
out a zone of transition and for anywhere ,on the interface such as point
B, a general relationship rewritten here as Equation (9) among five
variables defined graphically in Figure 7 and as shown below:
Z = (9)
14
Ground IIIrfoc:t
I __ ~H-=Y===--Ground wot., tobt.
G,.ol.r thon <40 h.
FIGURE 6: COMPARtSON BETWEEN ACTUAL DEPTH AND GHYBEN - HERZBERG'S DEPTH. (AfTER HU88ERT)
where Z = depth to a point of the interface below sea level,
hf = freshwater head as ~easured at that point of interface,
h = seawater head as measured at that point of the interface, s
wf ::: specific weight of freshwater, and
w ::: specific weight of seawater. s 1
The heads in Equation (9) should be measured in wells tapping the
same point defined by the depth Z on the interface. The well tapping the
freshwater side should be filled with freshwater and the well tapping the
saltwater side should be filled with salt water. This condition corres-
ponds to the so-called point water head introduced by Lusczynski (1961).
Hubbert's equation is intended, as also pointed out by Lusczynski,
for a sharp interface without the presence of a zone of transition. In
cases where the salt water below the interface is motionless, seawater
head hs becomes zero and Equation (9) is reduced to:
FIGURE 7
GROLND WATER TABLE
hf
,
'" I u b . I L- ",",,""-_DA_JUM (SEA LEVEL) -----I ~
/ !
/
/ z
'----t---EQUIPOTENTIAL LINE
DEFINITION SkETCH -FOR EQ. (9)
15
e9a)
While freshwater head hf is for point B on the interface, it is
the same as that for point A on the groundwater table because both A and
B are points of the same equipotential line. This special case corres-
ponds to Figure 6, the ramification of which has already been described.
Interfaces seldom occur in nature as sharp surfaces. Rather, there
16
occurs frequently a zone of transition in which. the water is a mixture of
the two in varying proportions at different locations, and likewise, the
salinity such as chloride would increase with depth from the freshwater
to the saltwater zone. Such a zone of transition is found, for example,
at Long Island, N. Y. by Perlmutter (1959), and at Pearl Harbor, Hawaii
by Visher and Mink (1964). Equation (9) was used to estimate the depth
to the fresh-sea water interface at the two localities. The computed
elevation Z by Perlmutter was shown to fall within the zone of transition.
The computed depth by Visher and Mink was 775 feet, which was also in the
zone of transition, and water at that depth had only 43% of the chloride
concentration (17,500 ppm) of water found at a depth of 1,300 feet. Sup
ported by another similar instance, Visher and Mink noted that the point
where salinity is 50% 'that of seawater would likely be at a depth equal
to about 40 times the head above sea level.
Recognizing these uncertainties, Lusczynski developed an equation
for determining the depth to the contact zone of freshwater with diffused
water, L e., the top of the transitional zone. However, the application
of his equation is not simple and direct; it requires estimations of
several variables (Lusczynski, 1961).
Modifications of the Ghyben-Herzberg ratio for static-equilibrium
cases in which the zone of transition is of significant thickness was
discussed by Lau (1962). The seawater head is assumed to be at mean
sea level. Within the zone of transition. specific weight of water may
increase with depth z in some describable function w(z), The bottom of
the brackish water zone HI can be written by equating pressure caused by
seawater having a depth of H' and pressure caused by all waters above
the bottom of the diffused water up to the groundwater table (Inset of
17
Figure 8). This yields Equation (10).
J H'+ h
H' = 1- w(z)dz w s (10)
where z = depth measured for sea level, positive downward and negative
upward,
d = the incremental depth, and z
w = the specific weight of seawater. s
If the variation of the specific weight with depth w(z) is known,
the depth H' can be computed. To demonstrate the procedure, assume th.e
variation to be linear, changing from freshwater specific weight at the
top of the transitional zone to seawater specific weight at the bottom,
and only freshwater is above the transitional zone. The thickness of the
transitional zone is shown as B. Then, as detailed in Appendix C, Equa-
tion (10) can be readily integrated and reduce to Equation (11).
HI = (11)
Equation (11) may be shown in the dimensionless plot, Figure'8,
for the convenience of examination. The ordinate has been chosen pur-
posely to be the ratio of the depth to the bottom of the transitional
zone HI and the freshwater head h. The abscissa is the thickness of the
transitional zone expressed as a fraction of the depth to the bottom of
the transitional zone.
An extreme case is zero thickness for the transitional zone. Ac-
cording to Figure 8, the corresponding H'/h becomes 40 which is the ex-
pected ratio for a sharp interface.
The other extreme case occurs when the transitional zone extends
18
.tt: h
80
70
60
50
1 GROLNl WATER TABLE
LEVEL DA1U4 ---
FRESH WATER ZONE
HI
I
\It ---} BRACKISH YATER I ZONE ---
llJlllti} ~~A~!~I /
I I
/
/ /
/
/
LINEAR SALINITY ----fj-.....--ASYMMETRICAL SALINITY DISTRIBUTION IN DISTRIBUTION IN BRACKISH BRACKISH WATER WATER ZONE 0-0.465 ZONE SEE APPENDIX D
~ ~~
/ /
/
I /
~Vh: FRESH WATER HEAD ~ H: DEPTH TO BRACKISH-SEA WATER INTERFACE
FIGURE 8 BRACKISH WATER ZONE RELATED TO GHYBEN.,.HERZBERG RATIO (LAU,1962)
19
all the way to the sea level datum. Again? according to Figure 8, the
depth to the bottom of the transitional zone will be 80 feet for each
foot of freshwater head, while by the conventional Ghyben-Herzberg prin
ciple disregarding the presence of a transitional zone. the predicted
depth would be only 40 feet per foot of freshwater head and therefore
only one-half of the actual depth. Further, by the assumed linear
relationship between specific weight and depth and by taking 19,000 mg/l
to be the chloride content of seawater and 250 mg/l that of freshwater,
specific weight at one-half of the actual depth would correspond to 53%
of the chloride content of seawater.
If the salinity-depth curve in the transitional zone is nonlinear,
but symmetrical about its midpoint, Figure 8 is still applicable since
the integral in Equation (10) is geometrically equivalent to the area of
the salinity-depth curve and the areas for a linear case and a symmetrical
curve are identical. Wentworth employed a rinsing theory and yielded a
theoretical symmetrical curve (1948). Cox reported a nearly symmetrical
sigmoidal curve for an experimental well on Maui (1955). Non-symmetrical
curves have been observed and reported such as that by Visher and Mink
for Well T-67 in the Pearl Harbor area of Oahu (Figure 9). Computed depth
to the base of the transitional zone, using observed hydrological data and
the above discussion, was remarkably consistent with observed depth.
(See Appendix C.)
20
0
100
200
300
400
500
600 4) > .!! CJ 700 4)
'" ~ .2 800 4)
.t:l -4) 4) 900 -£:
.. 1000 .t:: -0.
II)
0
1100
1200
1300
1400
1500 0 2 4 6 8 10 12 14 16 18 20
Chloride , in thousand parts per million
FIGURE 9: CHANGE IN CHLORIDE CONTENT OF WATER VS. ,DEPTH OF TEST HOLE (AFTER VISHER AND MINK t 1964)
ACKNOWLEDGEMENTS
Acknowledgement is gratefully extended to the many individuals
and agencies that have contributed discussions ·to portions of this
report. This report has benefited from suggestions by Doak C. Cox,
John F. Mink, Leslie J. Watson and Robert Chuck.
The research was partially supported by the Board of Water Sup
ply of the City & County of Honolulu, the College of Engineering of
the University of Hawaii, and the U. S. Office of Water Resources
Research.
21
This report is a revised version of a paper presented at the 46th
Annual Meeting of the American Geophysical Association (April 1965) in
Washington, D. C.
22
BIBLIOGRAPHY
Brooks, N. H. Review of formulas and derivations for the equilibrium rate of seaward flow in a coastal aquifer with seawater intrusion. Sea Water Intrusion in California, Bulletin No. 63. California State Department of Water Resources, Appendix C, part III. 1960.
Cox, D. C. Current research of the fresh-salt interfaces at the base of the Ghyben-Herzberg lenses in Hawaii, Geological Society of America Bulletin 66(12):1647, pt. 2. Dec. 1955.
Glover, R. E. The pattern of freshwater flow in a coastal aquifer . • T. Geophys. Res. 64(4): 457-459. 1959.
Harder, J. A., et aZ. Laboratory Research on Sea Water Intrusion into Fresh Ground Water Sources and Methods of Prevention~ Final Report. Sanitary Engrg. Res. Lab., Univ. of Calif., Berkeley, 68 p. 1953.
Henry, H. R. Salt intrusion into fresh water aquifers. J. Geophys. Res. 64(11): 1911-1919. 1959.
Hubbert, M. K. The theory of ground water motion. J. Geol. 48(8): 864. 1940.
Kozeny, J. HydrauZik. Springer Verlag, Vienna. 588 p. 1953.
Lau, L. S. Laboratory Investigation of Sea Water Intrusion into Groundwater Aquifers. Honolulu Board of Water Supply. 91 p. 1960.
Lau, L. S. Water Development of KaZauao Basal Springs--Hyd:ruuUc Model- Studies. Honolulu Board of Water Supply. 102 p. 1962.
Lau, L. S. Research in seawater encroachment and groundwater development. Water and Sewage Works 111(7): 308-312. 1964.
Lusczynski, N. J. Head and flow of ground water of variable density. J. Geophys. Res. 66(12): 4247-4256. 1961.
Muskat, M. The FlO1.J of Homogeneous Fluids through Porous Media. McGraw Hill, New York. 763 p. 1937.
Nomitsu, T., Y. Toyohara, and R. Kamimoto. On the contact surface of fresh- and saltwaters near a sandy sea-shore. Mem·. CoUege Sci. Kyoto Imp. Univ. Ser. A, 10(7): 279-302. 1927.
Perlmutter, N. M., et al. The relation between fresh and salty water in southern Nassau and southeastern Queens Counties, Long Island, New York. Econ. Geol. 53(3): 416-435. 1959.
Rifai. M. N. E. Dispersion Phenomena in Laminar Flow Through Porous Media. Sanitary Engrg. Res. Lab., Univ. of Calif., Berkeley. 157 p. 1956.
Rumer, R. R. and D. R. F. Harleman. Intruded saltwater wedge in porous media. .T. HydrauZ. Div., Amer. Soo. of Civil Engineers 89(6): 193-220. 1963.
Todd, O. K. Ground Water Hydrology. John Wiley & Sons, New York. 1959.
Visher, F. N. and J. P. Mink. Groundwater Resouroes in Southern Oahu, Hawaii. Geo1. Survey Water Supply Paper 1778. 133 p. 1964.
23
Wentworth, C. K. The Specifio Gravity of Seawater and Ghyben-Herzberg .Ratio at Honolulu. University of Hawaii. Occasional Paper No. 39. 24 p. 1939.
Wentworth, C. K. Growth of the Ghyben-Herzberg transition zone under a rinsing hypothesis. Transaotions, Amerioan Geophysioal Union 29 (1): 97-98. February 1948.
APPENDICES
APPENDIX A
NOMENCLATURE
B Thickness of a transitional zone containing mixture of fresh and salt water.
27
H Depth of freshwater below sea level to the fresh-salt water interface.
HI Depth of freshwater below sea level to the brackish-salt water interface.
Ho H at the coastline.
h Freshwater head or height of groundwater table above sea level.
hf Freshwater head as measured at a point of the fresh-salt interface.
h h at the coastline. o
h Seawate.r head as measured at a point of the fresh-salt interface. s
K Coefficient of permeability.
L Horizontal distance from the coastal line to a point on the freshsalt water interface.
M Thickness of freshwater zone from groundwater table to fresh-salt water interface.
q Seaward flow rate of freshwater per unit width of aquifer.
q' That portion of a q occurring below the sea level datum.
S Specific gravity. ws/wf .
wf Specific weight of freshwater in the aquifer.
Ws Specific weight of salt water in the aquifer.
Z Depth below the sea level datum to a point of the fresh-salt interface.
z Depth measured from sea level datum.
28
APPENDIX B
Harder recognized the analogy between the problem he studied
and the steady flow problem of seepage through an earth dam, having
vertical upstream and downstream walls, but without tail water. After
identification of the boundaries and the conditions thereof, Harder
adapted an approximate solution given by Muskat to determine the fresh
water head in the region of flow. The freshwater flow q is then deter
mined by int~grating flow across a vertical cross section. The result
is given in Equation (8).
Use of the approximate solution will introduce a theoretical error
in the quantity of freshwater flow q. This was demonstrated by Muskat
(1946, p. 314) for six different cases; however, the error was found to
be less than one percent in all cases.
Because of the constant head condition for the upstream wall in
the seepage problem, Harder's solution inherits the assumption that
freshwater head is uniform along the vertical section passing the "toe"
of the seawater wedge. Further, application of Harder's solution for
water table aquifer will require that at some location inland from the
shore line, the freshwater head will be uniform along a vertical cross
section. These two requirements may be satisfied in a flat fresh-salt
water interface or, correspondingly, a flat water table.
Brooks verified Equation (8) with two other approximate methods:
use of basic parabola and Dupuit-Forchheimer theory. In each case, he
obtained Equation (8).
APPENDIX C
Equation (10) for the prescribed linear variation in specific
weight with depth may be written as:
J z=H'-B +JZ:H' wsH' = wfdz
z=-h z=H'-B
after integration and reduction;
w -w wsH' = wfCH'+ h) + s f B
1-----_ ---------------------
---------
a
: ". ~
J w,
Specific wtlght w
sonnlty
"
•
H'
29
(11)
30
Equation (11) may be rewritten as:
Ola)
The last term of Equation (lla) reflects the area under the
salinity-depth curve for the transitional zone. For linear cases, the
coefficient of the term now denoted as a is ~ according to geometric
relationship as shown in Equation (lla). For nonlinear cases, the
coefficient would assume values in accordance with the comparative areas
of the curve and the straight line. Two different cases are depicted
below.
-- -- --~ o
1
SALINITY
"
ASYMMETRICAL CURVE a>0.5
\ \
STRAIGHT LN:: a- 0.5
~---t-+--ANY SYMMETRICAL CURVE a-0.5
APPENDIX D
The area under Visher and Mink' 5 curve (Figure 9), has been
computed to be 0.93 of the area under the straight line. The value
31
of the coefficient a, Equation ella) of Appendix C is therefore, 0.465.
Using 0.465 instead of 0.5 in Equation (lla), the relation between the
brackish-water zone and the Ghyben-Herzberg ratio has been plotted in
Figure 8.
Visher'and Mink's curve also indicated the measured B/H' to be
1170/1300 = 0.90 (Figure 9); therefore, the corresponding H'/h would
be 68.5 (Figure 5). At Well T-67, the freshwater head taken as an
average of a 6-month period immediately preceed~ng downhole water
sampling was 20.5 feet and taken as current head during sampling was
19.5 feet. It is significant to note then that the compute H' from
the above discussion would be 19.5 X 68.5 or 1,330 feet, a figure
