ARTESIAN

I AQUIFERS.' OSCAR EDWARD RIEINZER.z I CONTENTS

Dcti!litiot~ oi tlie problem.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 i':l;ioa. in~estig;ltions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 1:. . i . . , ,(,~ilre of compressibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

li.iilcnce from laboratory tests.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 I!r.i

264 OSCAR EDWARD AIEINZER.

treme cases this hydrostatic force m a y be virtually as great as the weight of the rocks but generally i t is n ~ u c h less. IVllen wells a r e drilled t o the aquifer a n d water i s ~ v i t h d r a ~ ~ n the hydrostat~c pressure is reduced (Fig . I ) .

FIG. 1. Ideal section showing pressure relations in an artesian aquifer. The hydrostatic pressure of the artesian water is measured by means o i a pressure gage in well No. I and hy means of a colu~nn of water in \\.ell No. 2. The watcr exerts an upnard pressure against the overlying- con- fining bed equal to $, which is measured by the weight of a column oi water ac in height. The confining bed exerts a downward pressure P due to its weight. As the specific gravity of the shale that forms the con- fining bed is much greater than that of water, the dorunward pressure P is greater than the upward pressure f . Only the difference, P - j , ii borne by the sandstone that forms the aquifer. When the valve is opened in well KO. I, water escapes and the hydrostatic pressure is reduced. The upward pressure of the watcr is then decreased to the quantity fi', vhich is measured by the weight of a column of water bc in height. The pres. sure upon the s;tiidstooe is arcordinglp increased hy the quantity f-f ' , which is measured by a column of water ob in height.

It has generally been assumed t h a t the formations which consti. tu te the aquifers a r e incompressible a n d inelastic a n d that, there- fore, changes in t h e hydrostatic pressure d o n o t produce an) changes in the pore space of the rock. T h e r e are, howeyer, sec era1 lines of evidence tha t the artesian water, especially in strati of sand o r sof t sandstone, supports a par t of the load of the over lying rock and tha t the aquifers a r e compressed when the artesial

COMPRESSIBILITY O F ARTESIAN AQUIFERS. 265

pressure is decreased and expanded when it is increased. The evidence indicates that there are only very moderate amounts of contraction and expansion as a result of the changes of pressure produced by the operation of wells. Nevertheless, the amounts are more than can be attributed to the elasticity or other volume change in the water itself and they are large enough to affect radically the conclusions in regard to the recharge, movement, and discharge of the water in the artesian aquifers.

PREVIOUS INVESTIGATIONS.

Various investigations have been made of the compressibility of rock materials such as sand, silt, clay, and marl,s and of shrink- age produced by the drainage of such materials.' These shrinkage investigations have been conducted largely in Germany in con- nection 9-ith problems of subsidence of the surface and they have bee11 concerned chiefly with molecular forces in clays and marls.

The specific subject of the compressibility and elasticity of artesian aquifers and their relation t o artesian pressure has re- ceived but little attention, and, so far as the writer has informa- tion, no effort has hitherto been made to study the subject inten- sively by the application of critical data. I n 1890, Hay5 suggested, in a paper which he read before the Kansas Academy oi Science, that the flow of certain artesian wells in that State may be due to "rock pressure," that is, to the pressure of the rocks overlying plastic artesian aquifers upon the water itself. In 1906, Gregory,' adopted the theory of rock pressure as a par-

3 Sarby, H. C., " On the Application of Quantitative Methods to the Study of the Structure and History of Roclir, Geol. Soc. London Quwt. lour., vol. 64, p. zr4, ,908. Terraghi, Charles, "Principles of Soil Mechanics: Elastic Behavior of Sand

ay," Etig. Niws-Recmd, vol. 95, pp. 742, et seq., Igrj. Hedberg, H. D., Effect of Gravitational Compaction on the Structure of Sedimentary Rocks," Assoc. Petrol. Gcol. Bsll., vol. lo, pp. 1035-lo72, 1926. ung. L. E., and Stock, H. H., "Subsidence Resulting from Mining," Univ.

"';"":" Eng. Exper. Sta. Bull. 91, pg. 47-49, 19'6. See also bibliography, pp. 5 . Y, Robert. "Artesian Vv"?lls in Kansas and Causes of their Flow," Amer. kt, "01. 5, pp. 296-301, 1890.

RGre~ory, J. W., "The Dead Heart of Australia," pp. 28&289. John Murray. London. ,906. The various theories relating to artesian water that were advanced

tial explatlation of the flo\ving rvells in central Australia, a1111 emphasized the bearing of the theory upon the question o i tlie depletion of the artesian \vater supply. The principle of coti~prri- sibility and elasticity of artesian aquifers was inferred by Ventch' in 1906, in his discussion of the effects on the head of the artesiar. water produced by ocean tides, the rise of rivers and lakes, the passing of trains, and the erection and burning of buildings. Tile principle of compressibility was more defiuitely stated b!. Fuller.' in 1908, as follows: " Pressure may he exerted [on the artesia!? r a te r ] by virtue of the weight o i the overlying materials aloiie. This is prol,al>ly not a common factor, but extensive sinkings oi the ground have follo~ved the pumping of water from mines and the ~vithdrawal of the support afforded by hydrostatic pressure, indicatiiig that the rock pressure on the water must have beel: considerable, at least locally." Apparently the practical impor- tance of the subject has lint been appreciated except by Grezor!..

EVIDEXCE O F COMPRESSIBILITY.

Eziderice f ror~ i Loborntory Tests.-It is generally reco~oin~l that deposits of fii~e-grained material are greatly compressed a: they become covered by younger formatio~ls through the nntorai processes of sedimentation. It has 'ken sho11.11 by E. W. Sha\;i that much of the newly deposited material of the Mississijilli Delta has a porosity of 80 to go per cent." By the time this ma- terial has beconie buried beneath a thousaild feet of sediments its porosity \\-ill probably be more nearly 35 per cent. Sorby cotl- cluded from his investigations that fine-grained material nliicl~ originally contained as much as go per cent. of water ma!. bars heen made almost solid b.y the sclueezing out of the water, so tl~rt in this book led to considerable cliscussion between the author and E. F. Pittmr \vho held very different views.

7 Ventch, A. C.. "Fluctuations of the Water Levcl in Wells, with Special R::. erence to Long Island, N. Y.," U. S. Geol. Survey Water-Supply Paper ~ j i . p 62, 6 3 . 65-69. 74-75. 1906.

fi Fuller, h.1. L., "Summary of the Controlling Factors of Artesian Flo~vs." I i Geal. Survey Bull. 319, p. 33, 1908. '

n Meinrer, 0. E., "The Occurrence of Grouud Water in the United Stater, n:~l a Discussion of Principles," U. S. Geol. Surrey IVater-Supply Paper 489, p. 8, lo:<

CO.1IPRESSIBILITY O F ARTESIA'V AQUIFERS. 267

in extreme cases shales and slates may occupy only one tenth of the volume 11-liich they possessed immediately after they had been rieposited. '

Tests made by different investigators have shown that in gen- eral sand is much less compressible than clay. This difference is due in part to thegreater size of the grains but largely to their better rounding. The compressibility is least in materials con- sisting of uniformly well-rounded grains and greatest in materials of irregular, angular, ant1 elongated particles. I t has been sho\vn h? Terzaghi lo that sand ~vi th admixture o i mica has compres- sibility comparable to that of clay, and he has, moreover, pro- iluced evidence from various sources to show that many clays do contain a considerable percentage of mica or other scalelike par- ticles. In general, the grains of very fine materials are not so ~vell rou~lded as those of coarser materials, for the reason that the cl~ief natural agencies that produce rounding are not effective on very small particles. This principle has been recognized by Daubre6 and others, and was verified by Goldman in his studies of the Catahoula sandstone. Evidence along the same line is iurnished by several samples of very fine sand recently obtained irom a stratum of the Dakota sandstone in which the grains are largely angular."

The compressibility of sand has been demonstrated by labora- tory tests. An experiment was described by Icing l3 in \vhich an upriglit cylinder was filled with saturated sand. In this experi- ille~lt some of the mater mas squeezed out of the interstices by the pressure 'produced by the settling of the sand and v a s forced Ihroagh a pipe at the bottom of the cylinder and through an at-

10 Terzaghi, Charles, " Principles of Final Soil Classification," Massachusetts Inrt. Technology Publications, vol. 63, pp. 4'-43, 1927. Also published in Public Rods, vol. 8, No. 3, May, r937. n Goldman. M.'I., "Petrographic Evidence on the Origin of the Catahoula Sand-

stone of Texas," Amcr. lour. Sci., vol. 29, pp. 271, 272. ,915. See also references given in this paper to Daubre@, Ziegler, Worth, Mackie, Udden, and Friih.

I?Xleinzer, 0. E., "Problems of the Soft-water Supply in the Dakota Sand- stone, xith Sp~ci2.1 Reference to Conditions in Canton. S. Dak., U . 5. Geol. Survey Water-Supply Paper. (In preparation.)

13Kiag. F. H., "Principles and Conditions of the Movements of Ground Water,.' C. S. Ceol. Survey, 19th Ann. Rept., Pt. 11.. pp. 78-80, 189%

268 OSCAR EDWARD A ~ F I I N Z E R

tached hose to a level 6 inches above the water level in the cylinder from which it came. The results of a test recently made by Terzaghi "are shown in Figure 2. In this test, pressure \\,as ap-

PRESSURE IN POUNDS PER SOUARE lhCH

FIG. 2. Diagram showing compressibility and elasticity of compacted sand, according to experiments by Terzaghi (Redrawn from diagram in 1 Esgineering News-Record, vol. 95, p. 987, 1925). The portion of the , curve between n and b represents approximately the change in pressure upon the Dakota sandstone which resulted from the decline in artesian pressure.

plied to a sample of compacted sand u p t o about I,Z jo pou~ids per squarc inch, and the porosity of the sand was decreased by this pressure from about 40 to 34 per cent.

Em.dedelzce from Szibsidei~ce of Surface.-Subsidei~ce amounting to a maximum of more than 3 feet has recently been described by Prat t and Jolu~so~i,'~ in the Goose Creek oil field, on the Gulf Coast in Texas, and has been attributed by them to the extensive extraction of oil, water, gas, and sand from berieath the affected

14 Terzaghi, Charles, Eng. News-Record, "01. 9 5 , pp. 987-990, rg25. 16 Pratt, \V. E., and Johnson, D. W., "Local Subsidence of the Goose Creak O i

Field." lour. Geol., vol. 3 4 , pp. 577-590, 1926.

COMPRESSIBILITY O F ARTESIAV AQUIFERS. 269

area. In a critical paper on the same subject, Snider '' accepts the explanation that the subsidence was caused by the removal of oil, gas, water, and sand, but shows that the removal of sand mas only a very small factor in producing the subsidence and also that drainage of water from the clay strata interbedded with the p r e ducing sands can not have been effective in causing shrinkage and subsidence.

Er.idcfzce front E x c e s s of Discharge over Recharge.-This subject was first forcibly brought to the attention of the writer in connection with a quantitative study that was made, in colab- oration with Herbert A. Hard and Howard E. Simpson, of the artesian water in the upper horizon of the Dakota sandstone in Sorth Dakota." I t v a s estimated in 1923 that in the east-west row of townships under spcial investigation (T. 129 N.) the rate of discharge from all the artesian wells averaged close to 3.000 gallons a minute in the 38 years since the first well was drilled in 1886. The rate of disclmrge was estimated to be nearly 10,000 gallons a minute during the peak period at some time be- trreen 19oj and 1910, about 5,000 gallons in 1915, and about 2,000 gallons in 1920. A detailed survey made under the direc- tion of Professor Simpson showed that it v a s almost exactly rlooo gallons in 1923.

KO accurate estimate could be made of the rate of recharge. that is, of the rate of eastward percolation from the intake area into the area of artesian flow in the 6-mile segment of sandstone underlying this row of townships. I t was assumed that no ap- preciable contribution \\-as received from the townships to the north and south, in which there was comparable artesian-well developnient. According to a rough computation based on in- adequate data it appeared that the recharge was much less than the average discharge of nearly 3,000 gallons a minute.

16 Snider, L. C., " A Suggested Explanation for the Surface Subsidence in the Goose Creek Oil and Gas Field, Texas," Amer. Assoc. Petrol. Gcol. BILII., 11, pp. 729-745, ,927.

17 hfeinzer, 0. E., and Hard, H. A,, "The Artesian-\Vater Supply of the Dakota Sandstone in North Dakota, vith Special Reference to the Edgely Quadrangle," 1'. S. Geol. Survey Water-Supply Paper jzo-E, pp. 90-93, 1925.

270 OSCAR EDWARD M P I S Z G R

The problem o i recharge was then al>proachcd I>!- another line of reasoning, as folio\\-s: During the period from 1915 to 19'3, 174th progressive decrease in the rate of discharge, there was pro- gressive decline in pressure head, indicating that depletion n-as going on. I11 1923, ~vith a discharge of only 1,000 gallons a minute, the head was apparently still declining, TI-hich ~~-ould seem to iudicate that the recharge was less than ~,ooo'gallons a minute. It can not be argued that the rate of recharge decreased on accouut of decrease in the hydraulic gradient, because the evidence seems to show that at the elltrance to the area of artesian flow the hydraulic gradient actually increased from 191 j to 1923. For example, the pressure head dropped farther during this period at Ellendale, N. Dak., than at the margin of the area of artesian flow 10 to 13 miles farther ~ \~es t .

If the rate of discharge in the area of artesian flow has been more rapid than the rate at which water percolated into the sand- stone underlying this area, some of the water discharged must have been derived from storage in the sandstone underlying the area. This withdra\val from storage requires a reduction in the interstitial space occupied by water. As will be shown later, the vacated space can not be accounted for by the slight expansio~~ of the water itself nor by any changes in volume that might have resulted from chemical precipitation with the release of pressure. Either the water \%.as replaced in some of the interstices by gas, or else the sandstone was to some extent buoyed up by the ar- tesian pressure within the sandstone, and when this ~ v a s relieved the sandstone underwent a certain amount of compression in which its total interstitial space was reduced by a volume approxi- mately equal to the volume of the stored water that was dis- charged. The theory of gas accumulation is believed to be un- tenable. In his unpublished report Hard states that the gas discharged by some of the wells seems to occur as un unsaturated solution in the artesian waters of the Dakota sandstone and a p parently is released from solution by the reduction of pressure incident to the rise of the water to the surface. There is no indication that gas occurs in the sandstone in the gaseous state

CO~WPRESSIBILITY OF ARTESIA.\- AQUIFERS. 271

at the present time. The conclusion, therefore, seems to be in- evitable that most of the artesiat~ water that has been discharged irom the Dakota sandstone through the flowing n.ells in this row o i to~vnships was taken out of storage in the sandstone underly- i t~g the area of artesian flo\v and that there was a corresponding shrinkage in the total volume of interstitial space. As this is a typical row of toumships the same conclusion will prol)abl!. hold for the rest of North and South Dakota.

Ezidefzce fronz lag iqz tlze decline i g z $lead nfzd local clznracter of clzanges iiz /zydrat,~lic grndirl~t.-If a perfectly tight and inelastic tank 11-ere filled with water under great pressure and were then tapped, only a minute quantity of water, equal to the expansion of the water itself, would have to be discharged in order to re- lieye all the pressure. On the other hand, if the tank were made oi elastic material, such as rubber, the discharge mould continue, at a constantly diminishing rate, until the strain of the xh-alls of the tank would be almost completely relieved. For this reason pressure tanks used in waterworks are all\-ays kept partly filled with air, which furuishes the necessary elasticity.

If the Dakota sandstone were perfectly incompressible ally con- siderable withdrawal of water ought to have resulted in a rapid drop in head and a prompt readjustment of the hydraulic gradi- ent all the way from the area of artesian flow to the outcrop from \~hich the water is derived, hundreds of miles away. This read- justment ought to have occurred with only slight movement of the artesian water. After the readjustment had been made con- ditions ought to have remained nearly constant, or if the water lerel at the outcrop had declined there ought to hare been a gradual flattening of the hydraulic gradient.

The changes that actually took place seem to have been of very different character. The head did not drop suddenly, hut has been declining gradually for about 40 years. The surrey made in 1923 showed that there has been much less decline in the water levels in the wells near the western margin of the area of artesian How than a few miles farther east, suggesting that in all these years there has not been much readjustment of the hydraulic

272 OSCAR EDWARD MEI.I'ZER.

gradient beyond the area in which artesian water was withdrawn (Fig. 3). Moreover, near the west margin of the area of ar- tesian flow, for which data are available, the hydraulic gradient has not flatteAed out but instead has become steeper.

FIG. 3. General east-west section of the area of artesian flow from the Dakota sandstone in the Edgeley quadrangle, N. Dak., showing approxi- mately the original hydraulic gradient, and the gradient in 1915 and 1923. (After Meinzer and Hard, U. S . Geol. Survey Water-Supply Paper 520, Fig. 8.)

In order to reach conclusive results more data are needed as to the head in the large region between the area of flow and the outcrop, but the data at hand certainly point to the co~iclusioli that the Dakota sandstone has not behaved like an incompresslhle reservoir; that the water discharged by the flowing wells has largely been derlved locally from storage and not by transfer of water all the way from the outcrop.

Ez,idence frorn Tides in Wells Produced by Ocean Tides.-I numerous places along the sea coast, fluctuations in water lev1 in \\ells have been observed that are definitely related to the tide in the ocean." In many of these there is no connection betwee

1s Ventch, A. C., op. at., pp. 63-69.

COJIPRESSIBILITY OF ARTES1A.V AQUIFERS. 273

foot 8 mil iron?

10 I, Yorks' 9" ?.

[lie sea water and the water in the formation that is tapped by the well or else the connection is too indirect to produce the ob- served fluctuations. As early as 1817 Inglis'%xplained the tidal fluctuation of the head in an artesian well at Bridlington, England, as due to the alternate loading and unloading of ocean water upon the flexible clay bed that overlies the artesian water. This same explanation was given by Veatch for many wells with tidal fluctuations that came under his observation.

An excellent example of such a tidal effect is afforded by a non- tlowing ~vell, about 800 feet deep, a t 1-ongport, N. J., about 5 miles southwest o i Atlantic City, which has been given detailed study by Thomp~on. '~ The well is tightly cased and passes through a few hundred feet of impermeable clay into a coarse water-bearing sand that is about 80 ieet thick. A continuous record for many months, obtained by means of an automatic n-ater-stage recorder over this well, sho\vs that even slight varia- tions and irregularities in the ocean tide are faithfully recorded, sit11 but little lag, in the fluctuations o i the lvater level in the well (Fig. 4).

It shows that the semi-daily range hetween high and lo~v water in the n-ell varies iron1 about I to 3 feet at different times of the month and is a little more than 50 per cent. of the range in the ocean tide.

The facts presented by Thonlpson show that the increase in artesian pressure in the 800-foot sand \\.hen the tide rises is not due to direct co~nmunication of the sea water with the artesian mter t h r o ~ ~ g h crevices or interstices in the intervening strata. or as a result o i submarine outcrop of this formation. For many years large supplies of water have 'been pumped from the 800-

irells in this vicinity, and in 1925 the pumpage averaged about lion gallons a day. In a pBeriod of 31 years the head dropped 20 to 2 j ieet above sea level to as much as 65 feet below

wlis, Gavin, " O n the Cause of Ebbing and Flowing Springs [at Bridlington, hire]." Phil. Mag., vol. 50, pp. 81-81. 1817. hompson, D. G., " Ground-Water Problems an the ~arr i er Beaches of N e w ." Geol. Soc. Anlerico Bull., vol. 37, p. 466, and Fiz. q, ,926. Also un- bed data.

sea level. A t Atlautic City and Longport the 800-foot sand is the 0111)- formatioll to the depth of 2,300 feet t o \\-hich drilliny has been carried that !-ields a large supply of fresh ~vater. Thc strata that lie nearer tlie surface contain onl!- brackish or salty

FIG. 4. Diagram showing fluctuation of water level in the 800-foo: well near the seashore at Longport, N. J., in relatioil to the tide in thr ocean. These records \\.ere made Jan. 22, 1926, when the rising tide ma! interrupted by a strong northwest wind. (After diagram prepared b! Paul Schureman, Gcogr. Rcoiercf, p. 481, 1926.)

water, which is effectively shut out from the goo-foot sand b y a layer of diatomaceous clay 300 feet thick, as is shown by tbt fact that the water from the goo-foot veils contaiils on]!. 6 to 1 1 parts per million of chloride. Several of these wells h a ~ e yielded salty water, hut it has been prol-ed in each instance thar tlie salty water ca~iie through a defective casing from the overlv. ing formations, for \\-hen the casitigs were repaired the sellr

I CO.IIPRESSIBILITY O F A R T B S I A S .-IQCIPERS. '75 again furnished fresh water of normal lo\v chloride conteilt. If there were free communication between the sea water and the lvater in the 800-ioot sand through openings in the intervening strata, a noticeable amount of salty water ~ ~ o u l d have bee11 drawn ilito the Soo-foot sand by the protracted and heavy pu~llping and tlie consequent great drawdo\vn of the head in the Soo-ioot sand. \loreover, the salty water in tlie overlying strata has uot suf- fered much drawdo\\:n and now has a much higher head than the water in the Soo-foot sand. I t is difficult to conceive o i any con- ditiou that ~ ~ o u l d permit free enough con~munication of water tlirou~h the intervening beds to produce the tidal fluctuations in the wells aud still maintain this difference in head. The rapitl dying out of the tidal fluctuation in the landward direction from the coast, even where the water level in wells is still be1 .o~ sea level, indicates that the fluctuation is not transmitted through the rvater from some submarine outcrop but i s clue to local yielding of the overlying clay beds.

There can he no reasonable doubt that a large part of tlie ]Ires- sure on the sea bottom produced by the loading of the s'ea water at high tide is transmitted through the intervening strata upon

1 tile water in the Soo-foot sand. The tidal fluctuations in the water level in the well record the l~ressure tliat is thus transmitted. 'Iliey indicate tliat only a part of the pressure pro~luced by the high tide is borne by the sand and overlyi~lg strata and that the rest is borne 1)y the water itself.

The water that is squeezed out of the sand bet~veen low and high tide to cause the rise in the water level in tlie Longport and other wells is negligible in cluailtity. The increased pressure on the water shows that the sand is incompetent to support even a slight additional load without conil>ressio~l but it gives no meas- lire of the compressibility. However, to lower the Ivater l e \ d in the well at high tide to its position a t lo\v tide would probablv reouire the removal of a large volurlie of water, and this volume

11d give sonic sort o i measure of the compression tliat ~vould ~ l t i i the sand itself had to support the entire load prqduced

. he rise in sea level. The \yell at Eridlington was described

276 OSCAR ED WARD M E I N Z E R .

as overflo~ving vigorously for 5 hours during each period of high tide, thus indicating considerable compressioll of the water-bear. ing material.

Evide~zce f i . 0 9 1 ~ F l ~ ~ c f z ~ n t i o ~ z s ifz Artcs in?~ Pressz~re Prodzlced by Rnilroad Trains.-Many years ago Icing" discovered that in one of his observation wells situated near a railroad the water level rose \vhenever a train went by but fell again as soon as the train had passed. H e found that a heavy freight train produced a greater rise than a lighter and swifter passenger train and that a locomotive alone did not produce any noticeable effect. This subject is no\v under investigation by the Geological Survey on wells near railroads in California, Utah, New Mexico, and New Jersey. I t is hoped that a quantitative method based on such fluctuations can be developed that will be of use in investigating artesian-water problems and perhaps also in solving other engi- neering and geophysical problems. I n California, H. T. Stearns and T. TY. Robinson obtained fluctuations caused by trains in

FT

MARCH

FIG. j. Automatic record of water .level in the Preszler well (200 ft. deep), near Lodi, Calif., March 4 to 11, 1927, showing daily fluctuations due to pumping and abrupt fluctuations due to the passing of train! a railroad 117 feet from the well. There are two daily trains (( Sundays) ; one arrives a t Lodi at 10 A.M., the other leaves Lodi at P.M. Record furnished by H. T. Stearns and T. W. Robinson.

21 King, F. H., " Observations and Experiments on the Fluctuations in tht and Rate of Movement of Ground Water on the Wisconsin Agricultural I ment Station Farm, and a t Whitewater, Wisconsin," U. S. Weather Bur. I p p 67-69, 1892.

: Level {xperi. >..I1 ,

CO.WPRESSZBI.LITY OF A R T E S I A N AQL'IFERS. 277

three ~vells that are artesian in character (Fig. s), but obtained no fluctuations in a well sunk just to the water table.

In Utah, TV. N. White did not get even a trace of a rise in a rrcll which he sank just to tlie water table at a point very tiear the railroad. In New Mexico, A. G. Fiedler failed to get any rise in a deep artesian well situated near a railroad. Further study will be required before these data can be adequately interpreted. 'Io~vever, they seem to indicate that the rise in the water levels is an artesian phenomenon, and that, beyond a certain limit, neither the artesian aquifers nor the overlying strata are com- petent to support the weight of the trains but allom the weight to be borne in part by the artesian water itself. If the support giren by the water xere removed compression of the aquifer ivould obviously occur.

EVIDENCES O F ELASTICITY.

In testing the pressure in flowing wells in the Dakota artesian basin, Hard 22 found that after a \I-ell was closed the pressure, recorded on the gage, would run up quickly at first and \\.auld then continue to illcrease for some time at a'constantly diminishing rate. These observations confirmed the reports of earlier investiga- tors. Xettlet~n,'~ in his investigations in 1890 and 1891, found that the wells differed greatly in regard to the time required for them to recover their full head. In some the recovery was very prompt but in others it was notably slow. I n regard to the well at Frederick, S. Dak., Nettleton stated that " the pressure in- creases for several hours or even days after tlie flow is shut off, and when opened the flow decreases in the same way until the normal flonr is reached, which corresponds somewhat to the time required to gain its maximum pressure." In regard to several other n.ells with slo~v recovery he made the following comments:

Plankington, S. Dak.: "When the flow is shut off the pressure quickly mns up to 50 pounds and in three hours it reaches its maximum, 91 pounds

??l\leinzer, 0. E., and Hard, H. A,, op. cit., p. gr . ?3Fettleton, E. S., "Artesian and Underflow Investigation." ~ z d Cong., 1st sess.,

S. E r Doe. qr, pt. 2, pp. 40-74, 1892.

278 OSCrlR EDWARD dlEl.\lZl~R.

per square inch." Wolsey, S. Dak.: " I f the well has been discliargiiig ireel? for some time it takes about 18 liours for it to reach its maximum pressure after the water is shut off." IVoonsocket, S. Dak.: "The pres- sure is 12j pounds per square inch \%,hen tlie flow is shut off. . . . The \\-ell was allowed to flow freely for 48 hours and mas then closed, when it showed a pressure of 8s pounds. . . . A fe\v liours afterwards the closed pressure was 93 pounds." Ellendale, N. Dak. : "\i~\'hen the flow is shut off the pl-essure rises quickly to 80 pounds and in a few hours it rcaclies its maximum, which is 115 pounds."

The explanation of the slow 'recovery seems to be that the i water-bearing bed has a certain amount of volun~e elasticity, that

l it becomescompressed \?,hen the artesian pressure is relieved, and that before the pressure in the well can again reach the pressure 1 that is general in the, formation sufficient time has to elapse to 1 allow the water to percolate into the depleted and compressed ' part of the formation surrounding the well and to expand the interstitial space. So long as the pressure in the shut-down well

ent fro111 all directions toward the well-a cone of depression

I has not reached the maximum there is oln~iously a hydraulic gradi- 1

I in the piezon~etric surface (Fig. 6) . Eut nrherever there is a

FIG. 6. Ideal section showing gradual recovery of head when an ar- tesian well is closed. The lines ~b and rb s11o\r- the liead of tlie water in the aquifer at all points along the section while the well is flowing. They show that there is a hydraulic gradient froni all directions toward thc \\-ell, as a result of which water percolates toward the well. The liner ob' and rb' show the head some time after the well has heen closed. Thcy show that water is still percolating toward the well frolu all directions although it has no outlet. The lines ob" and cb" show the head at a stiil later time when complete recovery has occurred and there is no longer concentric percolation toward the well.

COMPRESSIBILITY OF ARTESIAN AQUIFERS. *79

llydraulic gtadient in the water in a permeable rock there is movenient of the water in the direction of the gradient. Through- out the period of recovery \vater is therefore percolating to\\-ard the well. But if the well is tightly cased this water has no means of escape. It must be stored in the interstices of the fo rmat io~~ in the vicinity of the well. If there are no unfilled interstices at the beginning of the period of recovery, as the conditions seen1 to require, the inflowing water must, it seems, be stored in space made available by the expansion of the sandstone. If the sand- stone were perfectly inelastic the recovery would be nearly in- stantaneous and ~vould occur 11-ithout the transfer of any appre- ciable quantity of water toward the well.

The phenonienon of gradual recovery of head has been ob- served not only in the wells eliding in the Dakota sandstone but to some degree in those of practically every arlesian aquifer in regard to which informatio~l is available. In Fig. 7 is shown the gradual recovery of the artesian head in the Roswell Artesian

k <

0 W PM M PM N. PK M PU M, PM U PU M PM. M. PM M PM M PM M PM SUNDAY MONDAY TTUESDll WDNtlOAY THURSDAY FIIIDAI SPTUROAI SUNOW MONDAY IUFSDkY

MARCH 7 8 9 10 1 1 11 13 lb iS 16

FIG. 7. Automatic record on an ohservation well, showing fluctuatio~~s in head in the Roswell Artesian Basin,.N. Mex., produced by variations in the rate o f pumping. (After A. G. Fiedler, New Mexico State Engi- neer, 7th Biennial Rept., PI. 5, p. 38.) As the pumps that are not op- crated throughout the night are usually shut down in the evening, the persistent rise in pressure until morning seems to indicate replenishment of storage tliroughout the night. (The depths below bench mark shown in this diagram range from 2o . j to 26.0 it., the onlission of decimal points being an error.)

19

280 OSCA4R EDWARD I I IEISZER

Basin at night after certain of tlic \yells have been shut do\\-11 and a still further recovery on Sundays, when many of tlie wells are not operated. This seems to prove that there is considerab!e volunie elasticity ex.en in the aquifer of this hasin, ~\rhicli con- sists largely of ca\-ernous lii~iestone.~' The wells that are not operated throughout the night are generally shut down in the evening. Hence, if there \\-ere no elasticity the head should run up about to a maximum long before midnight. The deep well at the Atlantic City waterworks was pumped at approximately uniform rate fiom the middle of May, 1925, until March 22. 1926, when it was shut' down. From hlarcli 22 the water level in this T\-ell continued to rise for several xveelis although there was no declii~e in pumpage it1 other 'parts of the Atlantic City area."

In areas in which there is a seasonal fluctuation in the use of ground water there is likewise a seasonal fluctuation in head. Elasticity is not indicated by the fluctuatio~i itself but 'by the la: of the fluctuation in head after the fluctuation in draft. Such lag has, for example, been observed by Thompson '' in the At- lantic City area.

In Terzaghi's laboratory experiments he invariably found that the sand expanded when the pressure x a s decreased, and he gives approximate values for the exl~ansion coefficient. The expansion was, holyever, generally much less than the compression that re- sulted from the preceding application of tlie pressure (Fig. 2 ) .

QUANTITATIVE ESTIMATES OF COMPRESSION AND EXPAXSIOK.

The foregoing calculations in regard to the Dakota sandstolie afford a basis for computing tlie approximate amount of compres- sioil that has taken place. If in the 38 years prior to the time of the investigation the average rate of discharge from the east-west row of to\vnsliips under consideratioil was 3,000 gallons a minute

z* Fiedler, A. G.. Report on investigations of the Roswell Artesian Basin, Chaves and Eddy counties, N. Mex., during the year ending June 3 0 , rgz6: New 3lerieo State Engineer, 7th Biennial Rept., pp. 34-43, ,926.

2: Thompson, D. G., unpublished dntn. 28 Thompson, D. G., op. rib., p. 468.

COI~IPRESSIBILITY OF ARTESIAZ A@LrlFERS. 28 I

and the average rate of recharge only 500 gallons a minute, the average withdra~val from storage amounted to 2,500 gallons a minute. If the area of depletion consists of the 18 townships rlescribed as T. 129 N., Rs. 484.j W., a withdrawal from storage of 2.500 gallons a minute for 38 years would a~uount to a layer oi n-ater 4.4 inches deep. If the average thickness of the sand- stolie is estimated to be 60 feet, a compression of 4.4 inches amounts to about .6 of I per cent.

The first well a t Ellendale, according to the log, reached the Dakota sandstone at a depth of 1,o3j feet. The strata above the Dakota are chiefly soft shale, which, ~ ~ i t h the water they con- tain, must have a specific gravity of about z. Hence these strata, o~ving to their weight, exert a pressure equal to that of a colum~l oi I\-ater about 2,070 feet high, or 898 pounds to the square inch. According to one report, the original pressure a t the surface in this \yell was 145 pounds to the square inch and according to an- other it was 175 pounds If it was 145 pounds the artesian pres- sure at the top of the Dakota sandstone was 145 pounds plus the ~re id~t of a colun~n of water 1,035 feet high, or 594 pounds to tile square inch. Then, 594 pounds of the pressure exerted by t l ~ e strata that overlie the Dakota sandstone ;\-as supported by the water in the sandstone, and only 304 pounds by the sandstone itseli. If the original artesjan pressure at the surface \\-as 17,; poi~n~ls, the artesian pressure at the top of the sandstone was (124 pounds, and only 2 74 pounds of the overlying strata was sup- lported by the sandstone. If a t any point within the area of ar- lesiail flow the head at the surface was as great as the depth to the Dakota sandstone the artesian pressure must have been great enou::li virtually to float the overl!.ing beds.

In 1923 the water level in the Ellendale well stood almost exactly at the surface. Hence, the head had declined either 145 or 175 pounds to the square inch, according to the report of original pressure that is accepted. If the original pres- sure \\-as 145 pounds the load placed on the sandstone as a result of the decline in head increased from 304 to 449 pounds, I r 47% per cent.; if the original pressure \\.as I jj pounds the

282 OSCAR EDWARD AIEIA'ZER.

load increased from 274 to 449 pounds, or 64 per cent. For the entire area under consideration the average decline in artesian pressure was probably son~ewhat less than that at Ellendale, but it is approximately correct to say that according to the computa- tions the compression amounted to .2 of I per cent. for each de- crease of IOO feet in artesian head.

I n the experiments by Terzaghi it was found that, within a moderate range in pressure, the compression proceeded in grn- era1 about in proportion to the increase in pressure. At least one of Terzaghi's experiments \\,as carried through the range of pressures that are involved in the calculations on the Dakota sandstone. 111 this experiment, as shown by the diagram in Fig. 2, the pressure was increased from zero to about 425 pounds to the square inch, then decreased nearly to zero, and then increased far beyond 42j pounds. During the increase from 304 to 42,; pounds (approximately the increase on the sandstone at Ellen- dale) the sa11d was compressed so as to decrease the porosit!. from about 38.2 to 37.6 per cent.-a decrease in the volume oi the sand of about .6 of I per cent. The close agreement of these laboratory results with the results previously obtained from the computations on the Dakota sandstone is of course accidental. but it shows that the theory of con~pressibility presented in this paper is quantitatively reasonable. When the pressure was de- creased from 425 pounds the sand expanded, but during the de- crease from 425 to 304 pounds the expansiot~ amounted to only about . I of I per cent.

In order to get some idea as to the amount of expansion that is involved in the gradual recovery of head when a flowing well is closed or when pumping on a non-flowing artesian well is stopped, a fe\v rough calculations were made on \veils for mhicll considerable exact information \\,as available. One of these cal. culations \\?as made on the basis of data furnished by Thonlpson" it1 regard to \yells at Avon-by-the-Sea, N. J., which end in a stratum of sand, that lies 420 feet below the surface and is 80 feet thick. On November 12, 1924, Well Ko. 2 , of the city

97 Thompson, D. G., "Ground Water Supplies in the Vicinity of Asbury Park, Pi. J." (unpublished).

COMPRESSIBILITY OF ARTESIAN AQUI!*I~RS. 283

naterworl

284 OSC.4R EDWARD M E I N Z E R

well, 800 feet farther away. A part of the lo~vering ma!, have been due to tidal effect but in part it u-as almost certainly draw d o ~ n due to the pumping in wells Nos. I and 2.

The calculations were based on the simple but somewhat inac- curate assumptions that the area of influence covered one square mile and that the rate of percolation into this area after pumping ceased on November 12, 1924, was in proportion to the dra\vdo\vn in Well No. I . I t \vas estimated fro111 Figure 8, that the avera::: dralvdown in Well No. I during the 2-day period after pumping ceased was 4 feet, or one eighth of the dralvdo~vn when Well Ro. 2 was delivering 300 g'allo~ls a minute. Therefore, the average rate of percolation into the area of influence during the period should have been one eighth of 300 gallons a nlinute, o r 37% gallons a minute. This gives a total inflow of 108,ooo gallons, or an average of 169 gallons an acre, and an average expansion of ,006 inch or ,0006 of I per cent. in the So-foot stratum of sand. I t was estimated, further, that the average tlrawdo\vn for the entire area of influence just before pumping ceased was I foot. Hence, if the expansion were proportional to therecovery in head it would amount to about .o6 of I per cent. ior an increase of roo feet in heatl, or about one third of the compression cdtnputed for a decrease of ~ o o feet in head in the Dakota sandstone.

Coqx~tat ions on other \\-ells give somewhat co~nparable re- sults. Though the results of these computations are doubtless all greatly in error, they appear to be significant in having the same order of niag~~itude aild one that is entirely reasonable.

I>fPOIIT.4XCE O F CORRELATIVE FACTORS.

Other changes that might be produced by the variations in pressure and might possibly account for the l>I~enomena that hare been discussed are as follo\vs: ( I ) espansion and contractio~l of the water itself; ( 2 ) precipitation of solids out of solution in the water; (3) escape of gases out of solution; (4) removal of sand. silt, and clay through the wells with the water; ( 5 ) leakage through well casings or up through the holes on the outside of the casings, and (6) leakage through. the confining beds. In the

COMPRESSIBILITY OF A R T E S I A . ~ AQUIFERS. 285

following paragraphs all of these possible causes are briefly but critically considered, and the conclusion is reached that they are not adequate to account fully for the phenomena that have been attributed t o the compressibility and elasticity of the artesian aquifers.

Elmticity of t11.c T.Vatrr.-The compressibility of water under moderate pressures, such as are involved in artesian aquifers, a~nounts to about ,015 of I per cent. for each IOO feet of head.'s The \~olume of xvater that could be stored in a sandstone having a porosity of 35 per cent. through compression of the 11-ater by increasing the artesian head ~ o o feet would therefore be ecjual to about .oog of I per cent. of the \volume of the sandstone. As water has \rirtually perfect volunle elasticity, this ~ ~ o u l d also be the increase in volume of water that ~\rould res~trt from a lolvering of head of 100 feet. For the Dakota sandstone in the row of torrnships under consideration the increase in volume due to the drop of approximately 300 feet in artesian head must have amounted t o about ,015 of I per cent. of the volume of the sand- stone, or al~out . I inch. This appears t o be of a different order of magnitude from the depth of 4.4 inches of artesian \\-ater that were talcen from storage according to the previous calculations.

Solids precipitated out of sol~lfioit.-Some solids dissolved in water under pressure are precipitated out of solution when the pressure is decreased and this precipitation ge~lerally causes an increase in aggregate volume of the water and solids. Ten samples of \t7ater from the upper horizon of the Dakota sand- stone, which is here under consideration, were analyzed by Shep- ard '"arly in the history of artesian water development. These samples contained an average of 2.261 parts per million of dis- solved solids, most of I\-hich consisted of soluble sodium salts that would not 11e pt-ecipitated by the change in pressure. They contained an a\.erage of onl!. 27 parts per million of calcium and only 20 parts of magnesium. Even if all of these amounts of calciun~ and magnesium had been precipitaterl as carbonates, the

Fowle, F. E., Slnithsonian physical tables, 7th revised edition, p. r o l l 19~3. Sheparcl, J. H., "The Artesian Waters of South Dakota," South Dakota Agric. and Exp. Sta., Bull, q r , 189j.

286 O S C A R E D l V A R D M E I S Z E R .

volume of the precipitated material would be only about ,002 of I per cent. of the volun~e of the sandstone, or not much more than .OI inch-an amount that is insignificant in comparison with the amount of water that was removed froin storage. More- 01-er, analyses of water from this horizon made in recent years show about the same chemical composition as the earlier analyses, indicating that there has not been much precipitation. Even i f the precipitation of. solids were quantitatively of some conse- quence, the process could not account for most of the phenomena that have been presented as evidences of compressibility and elasticity.

Gmrs Liberated from Sol?~tio>z.-The quantity of any gas that can be held in solution in artesian water decreases with decrease in pressure. If the water in an artesian aquifer is nearly satu- rated with gas some of the gas may escape out of solution \\.hen the artesian pressure is decreased and may occupy some of the interstices of the aquifer in gaseous forill. By such a process large amounts of artesian water might be removed from an in- compressible aquifer and its place might be taken by the liberated . gas. This process may have been operative in some places, but in most artesian aquifers the gas is apparently too meager in quantity to pass out of solution until it approaches the surface in its upward ascent through the well. The available information indicates that release of gas has not been a factor in any of the artesian aquifers that have been considered in this paper, but fuller and more precise data on the quantities of gas delivered by the artesian water would be desirable. At any rate the process of pas liberation would not account for the increase in artesian pressure that occurs when there is loading at the surface, as by ocean tides or railroad trains. As is n-ell known, gas in many wells is liberated from thhwater as it approaches the surface, and this process, like that of an artificial air lift, is effective in bring- ing the water to the surface. HOT\-ever, to account for any of the phenomena cited in this paper as evidences of compressibilitj or elasticity, the gas must be liberated before it reaches the aell. under the high pressures that prevail mithin the aquifers.

COMPRESSIBPLITY O F ARTESIAN AQUIFERS. 287

Sand, Silt, and Clay Removed z&th tlze Water.-Large quan- tities of sand, silt, and clay are in many places brought to the surface by artesian water as it ascends through flowing or pumped wells that end in strata of unconsolidated materials. This has been notably true of some of the mells drilled to the Dakota sand- stone many years ago when the pressure was still great. The re- moval of sand is given by Platt and Johnsoil as one of the proba- ble causes of the subsidence that has been observed at the surface in the Goose Creek Oil Field, in Texas. However, the removal of the solid substance of a formation will tend to increase its storage capacity whereas the problem that has been outlined in regard to the Dakota sandstone is to dispose of the space which has been vacated by the water that was removed from storage. Moreover, removal of sand or other material through wells would not account for any of the other phenomena cited.

Leakage of Wells.-Many artesian wells that were improperly constructed or in ~vhich the casing has become corroded, suffer loss of water by underground leakage. A part of the water that is forced into such a Tzrell from the aquifer by artesian pressure escapes through some underground outlet and does not reach the surface. The leakage may occur even in wells that have stopped flowing or have never been flocving wells. Underground leak- age can generally be detected in either flowing or non-flowing vells by abnormally lo^ head of the water in them, and the loca- tion of the leaks and the rate at which the water is escaping can ha +finitely determined by the use of a deep-well current meter.30

e of the phenon~ena that have been cited can, however, be uately explained by assuming leakage from wells. Thus,

..-..~g e does not account for tidal fluctuations, and in so far as it has occurred in the u7ells in the Dakota Artesian Basin it only adds to the disparity between discharge and recharge.

The effect of leakage 011 the rate of recoveiy of head after a flowing well is closed or the pump on a non-flowing artesian well is stopped is somewhat problematical and depends on the condi- tions that exist in the stratum into which the water escapes. It

McCornbs, John, and Fiedler, A. G., "Methods of Exploring and Repairing i Artesian Wells," U. S. Geol. Survey Water-Supply Paper 596-A. rgz7.

288 OSCAR EDWARD AtEISZER

~rould seem that if the head against which the escaping Tvater ii discharged remains constant the leakage will not affect the rate but only the extent of recovery, but that if the head in the upper stratum \vhich receives the escaping water is influenced b!- rlie rate of leakage into it the effect \vill be the same as that of llrc elasticity of the artesian aquifer. I t is possible that the lag ia the nightly recovery in the Roslvell Artesian Basin, shown i ~ : Figure 7, is in part a leakage phenomenon.

Lenl~oge of Colt.finil7.g Ben's.-The confining l>eds in many ar- tesian basins are permeable or leaky to the extent that enough artesian water escapes throrigh them so that even \\.hen the first \\.ell is drilled the artesian w:ater ~vill not rise in the cvell verl- fa; ah77e the water table. If the confining bed is very inconlpetent to prevent leakage the piezometric surface of the artesian acjuifcr even before there is any artesian water development may be 011l.v a few feet or a few inches above the water tabie. Under these conditions upward percolation through the confining bed occurs normally. I t is accelerated whenever there is any rise in artesia~~ head due to decrease in the rate of 1vithdra~3-al of art

COMPRESSIBILITY O F ARTESIAN AQUII;BKS. 289

very nearly so, as is shoxn by the Very high heads that prevailed vheti the first wells were drilled. Leakage into the sandstone could not have occurred through this dense shale or against the artesian pressure, which is still generally suffi'cient to lift the water from the Dakota sandstone above the Tvater table. Leakage out of the sandstone \\-as never great or else the pressure xvould not have been so high \\.hen the first wells were drilled, ant1 at any rate it could not accoulit for the disparity between discharge ant1 recharge. Leakage through the co~~f in ing bed in any basin could not account for such phenon~ena as fluctuations causecl by railroad trains.

SIGKIFICAKCE 01' COMPRESSIRILITI' A N D EI.ASTICITIr I N FROBLEhlS

O F HYDROLOGY.

The amounts o i compressiotl and expansioll that have been computed are so small \\.hen expressed in inches of depth or per- centage of volume that the question may arise as to whether, after all, this discussion has any real significance. The ansn-er is, l~o~vever, near a t hantl. If the con?pression of the sandstone accounts for most of the artesian wafer that has been dischargetl il l the last four decades from ~.j,ooo wells in one of the largest artesian basins in the world, it is oh.iiously o i major importatlce. In the past the principle of elasticity has not been recognized in attempts that ha\-e been made to estimate tlie artesian water supplies from the Dakota sandstone or other artesian aquifers, bnt estimates have generally been based on con~putations of transn~ission capacity, recharge at the intake area, or lowering of tlie xa te r taMe at the intake-all on the assuni]~tion that the artesian aquifer is a perfectly itlcolnpressible and inelastic reser- voir or conduit. I n fact, artesian aquifers are apparently all more or less compressible and elastic though they differ ~videly in the degree and relative imlmrta~lce of these properties. I n general the properties of compressibilit!- and elasticit!. are of the most consequence in aquifers that have Iolv permeability, slow recharge, and high head. In many aquifers these properties are e\.idently importa~lt in supplying water not only by permanent

290 OSCAR EDWARD .MEINZER.

reduction of storage but also by temporary reduction that is replenished when the wells are shut d0n.n or during the season of minimum use. If it were not for the elasticity, the supplies of water that could be recovered through artesian wells for in- termittent or fluctuating needs would be much smaller.

In recent years the United States Geological Survey has con- ducted intensive investigations of four of the largest and most productive artesian basins in the country. The investigation of the Dakota artesian basin in North Dakota has been collducted in cooperation with the State Geologi'cal Survey and has been in charge of Howard E. Simpson, of that Survey, but much inten- sive work has also been done on the project by Herbert A. Hard; the investigation of the artesian aquifers underlying the Coastal Plain of New Jersey has been conducted in cooperation with the New Jersey Department of Conservation and Development 11~1 David G. Thon~pson; the investigation of the Roswell artesian basin, in the Pecos Valley of New RiIexico, has been conducted, in cooperation ~vi th the State Engineer, by Albert G. Fiedler and S. Spencer Nye; and the investigation of the Honolulu artesian basin, in Hawaii, has been conducted, in cooperation with the Territorial Commissioner of Public Lands and the Honolull~ S e ~ ~ e r and Water Commission, by Max H. Carson, John Mc- Combs, and Harold S. Palmer.

In all of these three States and in the Territory of Hawaii, laws have been enacted regulating to some extent the use of the ar- tesian water, thus making headway against the time-honored but disastrous legal fiction that nothing can be known about the source, quantity, or destination of artesian or other ground water and that therefore anyone has the right to use it or waste it as he pleases without regard to the damage that he nlay do to others. If these water supplies are to be fully developed and utilized, more progress must be made in giving legal protection to those who develop them and put them to beneficial use. This can, however, be accomplished only as ground-water geologists and engineers establish a broad, secure, scientific foundation for determining ground-water conditions and estimating ground-water sup

COMPRESSIBILITY OF ARTESIAl\T AQUIFERS. 29I

plies, Most of the quantitative work on ground water has been clone on the non-artesian aquifers ~vhich have water tables, and consecluently methods for intensive work on ar- tesian aquifers have been relatively meager and undeveloped. In the investigations that have been mentioned, however, progress has been made on fundamental principles that will lead to effec- tive methods, ancl it is believed that the theory of compressibility and elasticity of artesian acjuifers expresses one of these funda- mental principles.