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CAVES AND KARST Research in Speleology formerly CAVE NOTES Volume 9, No. 4 July/August 1967 SOLUTION OF LIMESTONE UNDER LAMINAR FLOW BETWEEN PARALLEL BOUNDARIES by ALAN D. HOWARD and BARBARA Y. HOWARD Introduction Although the eq1liiibri1f.m relationships of the major chemical components of carbonate rocks with ground water are fairly well known, knowledge concerning the kin e tics of dissolution of carbonate rocks is almost completely lacking. A few theoretical treatments of such kinetics under simplified assumptions have been offered by Weyl (1958), Howard (1964a) and Curl (1965), and a few simple kinetic exper im ents have been attempted by Weyl (1958) and Kaye (1957). However, these experiments were not directly com parable ro the dissolution of carbonate rocks by ground water flowing through joints and conduits The experiments reported investigate solution kinetics under conditions approaching those of natural ground water flow through joints and fissures in carbonate rocks. The experiments were restricted ro flow within parallel walls of limesrone with narrow gap widths in the size range of sm all, natural fractures and openings ; the experi ments were designed ro represent the initial stage of solution enlargement of small frac tures a nd joints into caves and fissures. As I have pointed out previously (HOWARD, 1964a, p. 48), "the first stages of solution of a cavern are the most critical in its hisrory, for the patterns of ground water flow through the cavern and the resulting pattern of its development are determined to a great extent by the beginnings of solution." Experimental Artificial "joint openings" were constructed by sawing blocks of limestOne into rectang ular pieces which were then lapp ed rogether and cemented with epoxy along two edges ro a predetermined gap width, ro form parallel openings having the dimensions given in Table 1. The solutions were constrained, by the cement edges, ro flow along the long dimension of the blocks. The resulting cavity is described by coordinate axes, x, y, and z whete x is the long dimension (length), y is the intermediate dimension (width), a nd z is the gap width (Figure 1). In the equation below, the variable x refers ro the position a long the path of flow, referred ro an origin a t the point of entry of fresh solutions into the block. In the experiments, the x and y dimensions were oriented in the horizontal plane Two types of limesrone were used ro construct the blocks described above. Blocks A through F were made from a very pure crystalline limesrone the 'Tennessee Marble" of the Holsron or Lenoir formations, and blocks G and H used a pure, black, organicrich, cryprocrystalline limesrone (Srones River formation, West Virginia). Both of these lime srones were a lm ost pure calcium ca rbonate, and yielded negligible concentrations of magnesium or other ions upon dissolution in the "ground waters" described below Bec ause the gap width in all blocks was much smaller that the width of the opening (z y), the effects of the boundary walls in the ydirection were negl ected a nd the mea sure of the discharge through the openings used in all calculations is the actual discharge divided by the ydimensio n of the block, or discharge per uni t width, Qy. The flow was slightly constricted at the ends of the blocks, but these effects were negl ected The hydraulic 'Departments of Geography and Chemist ry, Johns Hopkins University, B a ltimore Maryland 21218 25
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CAVES AND KARST CAVES AND KARST CAVES AND KARST is a publication of Cave Research Associates. Subscriptions are available for $2 .50 per year (six issues) or $6.00 for Volumes 9 through 11. Midyear subscriptions receive the earl ier numbers of the volume. Correspondence, contributions and subscriptions should be addressed to : CAVE RESEARCH ASSOCIATES, 3842 Brookdale Blvd Castro Valley, Calif 94546 Editor: Arthur l. lange Associate Editor : James G Day Editors: Neely H Bostick, R deSaussure, J. F. Quinlan Copyright 1967, Cave Research Associates gradienr, h, was computed by dividing the measured hydraulic head a cting across the block by the l ength of the block All experimenrs were conducted within the laminar flow regime, as verified by the proportional relationship between dis c h arge a nd hydraulic gradienr. Under laminar flow the following formula (after PAD, 1961) describes the relationship between the discharge per unit width, Qy (cc/cm sec), the hydraulic gradienr, h, (dimensionless), and gap wid th, z (em) : hz 3 = 1. 17 X 104 Qy (1) In laminar flow, surface roughness d oes not a ffect the flow characteristics However, it may affec t solution kinetics. Surface roughness of the blocks was not measured, but the surfaces subjected to solution in the experimenrs were exposed to the dissolving action of carbonic acid prior to the actual experimenrs so th at the surfaces would be characteristic of dissolving limestone. Although the ope nings were constructed to approxima te a specified gap width, the percenrage error in the constructed openings was large for the smaller gap widths. There fore Equation 1 was used to obtain a more realistic effective gap width for each block, f rom observed relationships between discharge and hydraulic gradienr Because of the solutional en l argeme nr of the openings during the experimenrs, the gap widths did not remain constanr. The values given in Table 1 are averages, but more precise figures are used in individual experimenrs. Because the ga p width did not incre ase greatly during anyone set of experimenrs o n the same block under differenr hydraulic gradienrs, no apprec i a ble error was inrroduced by considering the gap width to be a constanr The "groundwate r solutions run through the blocks consisted of distilled water charged with a specilied partial pressure of carbon dioxide at one atmosphere total pres sure. In one set of experimenrs the p a rtial pressure o f carbon dioxide pCOl, was one atmosphe re This partial pressure of COl was selec ted to represenr approximately the upper limit of dissolved COl of natural waters This is not unreason able, bec ause partial pressures o f at l east 0.15atm have been measured in soil water. The l ower limit of CO l cClocenrration in grou nd water should be approximately equal to the equilibrium value with respect to atmospheric 1O3 5atm. The compressed air used to approx imate this lower limit h ad a pCO l in the range from 10 2 3 to 1O3.2atm as estimated from limestone satu ration experimenrs (see later discussion) The concenrration of dissolved calcium ion in the solutions was determined by titrati on with N aEDTA (RAINWATER AND THATCHER, 1960, p 127129), and con cenrration values a re reported as panspermillion (ppm) of calcium ion The temperature o f the dissolving solutions in all experimenrs varied from 21 to 24.5 C ave raging about 23.5 C. Pre senration a nd ana lysis of results is tre ated separately for the case of a pCO l of 1 atm and atmosphe ric CO l conrenr. 26
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Distilled water reservoir VOLUME 9 NO.4 //v=======CO2 or Air T Hydraulic head B CO2 or Air C Figure 1. Experimental apparatus as described in text. 27
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CAVES AND KARST One atmosphere partial pressure of carbon dioxide: Two types of experiments were conducte d a t o n e at m osphere peo2 In the first o f these distilled water ch a rged with carbo n di o xide at o n e at m p a rti a l press ur e was run throug h the various blocks a s a closed sys t e m under different h yd r a ulic gradients using the app a ratus shown in Figure 1. In th e second typ e of experiment, the "groundwat e r" so lutions were repeatedly passed t h ro u gh the sa m e bl o ck as a se micl osed system a nd sampled a t intervals to find the functional dependence o f the a m ount a nd r a te of solution upon the tOtal length of flow ( Figure 1.) In the first t ype o f experiment, the co ncentr a ti o n o f calcium ion being discharged f ro m th e bl o cks was determine d The initial concentration of calcium ion was negligible. For eac h experiment the discharge was measured, and in some cases the hydraulic head a l so was measured In cases where the hydr a uli c he a d was mea s ured, the effective gap wid th of th e blocks was computed by substitution into Equation 1. When the hydraulic h ead was tOO s m all to b e m eas ured effective diameters were assumed from the calculatio ns for known h ydra uli c he a ds. In s uch cases, Equ at i o n 1 was then used to calculate the h ydrau lic gra di e nt. F o r ea ch experiment, computa ti o n s were made of Qy velocity, and residence time o f the solutions within the blocks. These were plotted aga inst ppm of calcium It was f o und that, within the experimenta l erro r all plo ts o n a loglog sca le relating ppm to Q y were p a r a llel straight l ines. H owever, the p o siti on o f the lines f o r blocks of approxi m a tely the same gap width was depend ent upon the l e ngth of the block Plots for blocks o f th e same gapwidth were m a de nea rly coincident by plotting the partspermillion in creas e o f ca lcum i o n per unit length of flow (ppm/ x ) versus Q y The resulting plots described the f a mily o f curves = K Q 0 .75 X Y (2) where K is a constant. The experimental d a ta ar e plo tted in F igure 2 and values of K f o r the individu a l bl o ck s are given in T a ble 1. The const ant K may be calculated approxi m a tely fr o m th e following relationship: K = 0.0956 Z 0.2 (3) This equation s hould be assumed to b e v a lid only over a range o f gap width from about 1O2.5cm to a b out lOlcm, the range of the experimental values. The rel ationship given by Equation 2 d oe s not hold true for value s of Qy greater than a b out 0 .6c m2/ se c or ppm/x less th a n a b o ut 0.2. The rel a tionship replacing (2) for values o f Qy g re a ter than, a nd ppm/x les s th a n the above values i s approximately 7= 0.159 QyO" (4) Few data p oints w ere t ake n in this region and the relati o nship must be considered tenuous From experi m ents run under known hydr au lic he a d a nd disch a r ge, it was found that the tra n s iti o n f o und l aminar to turbul ent flow within the blocks bega n a t a Qy of about 2 6 c m2 / sec. It would thus appear that the t ra n s iti o n between ( 2 ) and (4) is not associated G ap w i d th B lock Width (em) L e ngth (em ) (em x 10 2 ) K A 2 .34 6.43 0.50 0 .20 0 B 2.36 6.43 1.21.4 0 .22 5 C 1.71 1 2.54 1.3 2.4 0.205 D 1.37 6 18 2.8 0.196 E 1.70 12. 7 0 5.1 0 158 F 2.58 12.50 8.9 0.133 G 2.10 1 3.2 5 1.2 0.210 H 1.6 3 1 3.2 5 8 9 0 159 TABLE 1. Block Dimensions and Experimental Values of the Constant K 28
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VOLUME 9, NO.4 2r,,,.. o Gopwidth (z, in em ): A 5 .0_103 0_ B C o F G H 1.2 _102 *1.3 _102 .<>. 2 B _102 .@. 5 I _102 oQ.. 8 .9_102 ". 0'1.2_102 _.0. 8 .9_102 _. = 0.159 QY" Log Qy (ee/ em sec) Figure 2. Relationship between log(ppm/x} and log Qy for singlerun experiments with peo2 = 1 atm. Equations fitted to the experimental data are also shown. with a change in flow regime. It may be that at a low concentration of dissolved calcite a different mechanism may be active, giving a higher rate of dissolution than wo uld be expected from (2). A relationship simi l ar ro (4) was found for atmospheric CO2 con tent (Equation 13), for which the calcium ion concentration was within the same range of values. On the other hand, the data do nor rule Out the possibility that higher velocity rather than higher concentration of calcium ion is the facror determining the transition from (2) to (4). In the second type of experiment, run with a pC02 of latm, the carbon dioxide charged water was successively run through the same block under an approximately con stant hydraulic head. This experiment was run with block C, to investigate the dependence of rate of solution on length of flow for lengths greater than the l ongest of the individual blocks, about 13cm. Under the experimental setup, the water was passed through the block with a falling head Because of the high parrical pressure of dissolved carbon dioxide, it was necessary to rech arg e the solution with carbon di oxi de continuous l y except when passing through the block. Thus the experimental conditions could not exactly duplicate the closed system of continuous circulation over l o ng distances Additionally the average hydraulic head decreased slightly as the experiment progressed, due to the removal of samples from the solution reservoir Because of the l a rge vo lum e of solution passed through the block during each successive run (about 500cc) the gap width of the block increased from about 1.7 x 102 ro 2 5 x 1O2c m during the course of the experiment. There fore, the derived relationship given below must be considered approximate. The experi mental dependence of ppm on the toral length of flow is given by the points in Figure 3. Two of the points were selected as the basis for the fining of an exponential decay curve 29
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CAVES AND KARST through the experimental points (so lid line in Figure 3). Ie is evident that the fit of the curve to the data is quite good The equation of this curve is ppm = 235 [1 exp (1. 43 X lO2x ) ] (5) where x is given in centimeters. The slope, or tangent, to this curve at a ny point is dppm = 3.36 exp(1.43 x lO2x ) (6) dx In the following analysis, it is assumed that recirculation runs (in each of the blocks) would approach the s a me a symptote with a path describable by an exponential decay curve Thus, in the gene ral case Equations 5 and 6 become, respectively: ppm = 235 [ 1 exp( Cx) ] (7) a nd dppm = 235 C exp (Cx) (8) dx where C has a functional dependence upon hydraulic gradient and block diameter Because the exponential decay curve is nearly linear for very small values of the exponent, Equation 2 may be assumed to represent the relationship between ppm and x for very small values of x. Thefore, the value of Equation 8 for x = 0.0 can be equated with the deriv a tive of Equ a tion 2, giving KQ 0.75 C = (9) The coefficient C was introduced without specific reference to the actual experimental va lues of z, h and Qy in the experiment yielding Equation 5 As a check on the validity of the assumptions giving (7), (8), and (9), the block diameter used in the recirculation runs can be u sed to estimate the ave r age hydraulic gradient during the runs. For the 300 + 2 u E Q. Q. Total length of Flow, ><, in em Figure 3. Experimental data and fitted curve showing the dependence of ppm of calcium ion to length of flow, x, in the recirculation experiment with pC02 = 1 atm. 30
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VOLUME 9, NO.4 recirculation experiment, the value of C was 1.43 x 102 The average value of z durmg the experiment was about 2.2 x 1O2cm. Using (9), Q y may be found to be 2 37 x 1O2cm2 / sec. Because it took about 5 hours for 500cc of solution to pass through the block, this figure is quite reasonable From (1) the average hydraulic gradient would be 0 .26. The median hydraulic gradient during the runs was about OA, but the time average of the hydraulic gradient was probably very close to the value predicted by (9), inasmuch as the head and corresponding discharge decreased during the progression of each run. The rate of increase of gap width may be equated with the rate of increase of calcium ion in solution by the equation dz = dppm 100 (10) dt dx 2.72X40 where 2 .72 is the density of limestone, the ratio 100/40 corrects partspermillion of calcium ion to the equivalent concentration of dissolved calcite, and the factor 106 con verts partspermilli o n to gramspercm3 The units of dz/dt are em/sec. Equation 10 is valid for any point along the path of flow The final equation relating the rate of increase of gap width to the discharge and position along the p at h of flow relative to the origin is obtained by substitution of (S) and (9) into (10 to give = 9.2X107 KQyD_2Sexp(4.27X103KxQy0 .75). ( 11) Equation 1 may be used to eliminate Qy, giving = 8. 85X10o Kz D .7S h D 2S exp(4.77X100Kxz2 .2S hD 7S ) (12) These equations indicate that the rate of enlargement of the openings decreases in the direction of the flow This means th a t after a finite time the walls of the conduit will no longer be parallel. Thus (11) and (12) are valid only during the initial stages of solution while the channel walls remain of essentially uniform gap width along the direction of flow Also (11) and (12) should not be assumed to be valid for values of Q y greater than 0.7 cm2 / sec or less than 3 x 1O3cm2 / sec, or for values of z outside of the experimental range of 5 0 x 103 to 1O1cm. In the above experiments CO 2 was introduced into the reacting solutions by bubbling the contents of a commercial cylinder of CO l through the solutions at one atmosphere pressure The CO 2 in the gas cylinder was specified to be 99 5 % pure, and should have equilibrated with the solutions to a partial pressure of essentially one atmosphere The equilibrium const a nts given by G a rrels a nd Christ (1965) predict an open system satura tion value of calcium ion at 23. 5 C of 400ppm for a pC02 of one atmosphere The cor responding saturation value for water first equilibrated with respect to one atmosphere pC02 in the absence of limestone and then saturated with respect to limestone in the absence of a gas phase (closed system saturation) would be 3 1Sppm Experiment a l determination of open a nd closed system saturation with respect to limestone using CO 2 from the cylinder as described above and the "Tennessee M a rble yielded low equilibrium values of 305ppm and 256ppm, respectively These values are consistent with a pe02 of 1Oo .37atm (OA7atm) using the equilibrium constants of Garrells and Christ Several factors might account for the lower experimental values relative to the theoreticallypredicted values: 1) The various solutions may not have equilibrated completely with the carbon dioxide bubbling through the system 2) The carbon dioxide may not have been as pure as specified 3) Errors in the equilibrium constants may have been great enough to give the 24 % error between predicted and experimental results. 4) The titration solutions may have had a standardization error of this magnitude 5) Diffusional loss of CO 2 from the circulating solutions subsequent to recharging 31
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CAVES A N D KARST I I I B 1.4 10' C 2.4 _10' o F 8.9 _10' G 1.2 10' o 01H 8.910' * /0., ppm 00508 0 0. x y HI I Log Oy (ee/em sec) Figure 4 Relationship between log(ppm/x) and log Qy for singlerun experiments with peol = I Q 1.8atm. Equ ations fitted to the experimental data are a l so shown. a nd while pass in g to and from th e lime sro ne blocks may have limited the amount of so lu tio n o r caused reprec ipit at i o n of c a lcite w ithin the apparatus. 6) The a ctu a l t empera ture during the experiments m ay h a ve been a few degrees diff erent from the measured temperatures. 7 ) Surface effec t s o n the f ace of th e di sso lving limesrone blocks may have limited the solubility o f th e limesrone. Prec ipit at ion of organic material onto the limesrone (d. CHAVE, 1965) or presence o f s mall concentrat i o ns o f copper, l ead, and other i o ns in the dissolving so luti o n s (d. T ERJEsEN et aI., 1960 ) h a v e been suggested as inhibirory mechan isms in t h e so luti o n of calcit e The o r ga nic materi a l or inhibirory i o ns m ay ha v e derived e i ther fr o m the distilled water o r the dissolved limesron e Facrors 1 a nd 5 above would be expected ro produce rand o m e rrors changi n g from experim ent ro experiment. The co nsistency of borh the saturation experiments and the c i rculat i on experim e nt s a rgue agai n st th e importa nce of these f a ctors In addition, f ac ror 5 d oes n or account f o r the l ow value for th e o pen system saturation. Saturati o n experi )'ents w i t h respect ro atmospheric co ntent o f Cal predi cted from the equilibrium relation ships values o f pCOl 210 times g r eate r than "normal" atmospheric contene. This renders l ess I ikely th e importance o f f acrors 3 a nd 4. The ease o f obraining nearly pure Cal and t he manufacturer's purity specificat i o n r ed uce the probability of the importance of factor 2. Temperature effects upon so lubility are lik ew ise ruled out as the o nl y contribution by the m agnitude o f the de viatio n betwe e n experimental and theoretical saturation values; temperature variation from 20 C ro 25 C (encompassing th e temperature range during the experiments) acco unts f o r only a 10 % change in the s olubility of limesrone Surface effects upo n th e diss o lving Iimesrone thus are the most suspect fac ror causing the discrepancy betwee n exp e rimental a nd theoretical saturation values. The asymptotic 32
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VOLUME 9, NO.4 concenrration of 235ppm given by (5) f or infinite path length of flow bears further upon this question. The asymptotic calcium ion concenrration of closed system circulation should be equal to the closed system saturation va lue, and for the recirculation apparatus used to approxi mate closed system circulation the asymptote shou ld be greater, due to the recharging of the solutions with CO2 before each recirculation. In actuality it was less. One difference between the saturatio n experimenrs and the recirculation experimenr was the volume of dissolving water, being approximately 80cc for the sat ur ation experimenrs and 500cc f or the re circulation run. The difference between the asymptotic co ncentration and the closed sys tem saturation would be exp lain ed by a sur f ace inhibitory mechanism if the so urce of the inhibitanr were the dissolving limestone and if the aCtion of the inhibitanr were pro portional to its total quantity in the dissolving so luti ons r elative to the surface a r ea of dissolving limestone (as opposed to its concentration) If surface effects are responsible for the experimental saturation a n omalies, they should be relatively important at high concentrations of dissolved limestone ( l o n g path lengths of flow), and should have little effect at low concentrations of dissolved limestone. Atmospberic partial pressure of carbon dioxide: The experiments for this case were run under conditions identical to those run with a partial pressure o f latm of pC02 except that air from a compressor was bubbled through the water. Results were less consistenr than for those with a pC02 of latm. Three possible reasons for this lie in the higher ex perimental errors at low concentrations of calcium ion, variations in the partial pressure of carbon dioxide in the compressed air, and introduction of variable quantities of acidic components into the solutions by the compress e d air. Assuming that this third source of error was of negliglibible importance, the approximate partial pressure of CO2 in the compressed air was estimated by open system saturatio n of aircharged water with lime stone, using the equilibrium constants of Garrel s and Christ ( 1965), giving a pC02 of 1O3.25atm A closed system saturat i on of aircharged water with limeston e gave an esti mated pC02 of 1O2.32atm These values are not unusual for l a bor atory air. Results of the singlerun experimenrs with the various blocks under different hydrau lic gradients are shown in Figure 4 as the relationship between Qy and ppm/x. An ap proximate relationship fitting these Jata is given by the equation of the line constructed in Figure 4: (13 ) A closedsystem recirculation run was made for this partial pressure of CO2 (Figure 5). Two exponenrial decay curves arc shown in this figure. Neither curve fits the data as well as in the case of a pC02 of btm. The following relationship will be us ed in the mathematical development, with acknowledgement of the error in the approximation: ppm = 8 .20 [ 1 exp(4. 04XlO2x) ] (14) Using (l3) and (14) with the assumptions of identical asymptotes f or all blocks a nd that all recirculation runs follow an exponentia l decay curve in ppm vs. len gt h the equivalenrs of (11) and (12) for the lower pC02 become and respectively. Discussion dz dt dz = 4 .68XIOS Qyo.6exp(6.2XlO3xQyO.4) dt (15 ) (16) The experimenral results given in Equations 11, 12, 15 and 16 arc similar in form to the theoretical derivation based upon masstransfer theory given by Weyl (1958) and 33
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CAVES AND KARST to the simplified model treated by Howard (1964a). Weyl's equations are not in the functional form of the experimenral equations, but may be changed ro this form (see Appendix), giving dz = 5.40XlOsCs z1.oexp(1.75X10axh1.0 Z4.0) (17) dt where C, is the molar saruration (asymptotic) concenrration of calcium ion Note that the powers of hydraulic gradienr and gap width differ significanrly from those of (12) and (16) although the agreemenr is closest with (12). In add irion, Weyl's derivation does nor predict the observed differences in the form of the rate equations depending on the original concenrration of CO, in solution. By use of (10), Equation 17 can be used to predier values of ppm of calcium ion given length of flow, discharge per unit width, hydraulic gradienr, gap width and the saturation concenrration of calcium ion These may then be compared to the experimenral values of ppm as a test of the validiry of Weyl's model. It was found that within the experimenral range of Qy and z, Equation 17 predicted a much more rapid approach to saturation than was observed, with a greater discrepancy at lower values of Qy and z. Therefore, it would appear 'that the acrual solution process is not very accurately represenred by Weyl's diffusion model of one limiting componenr. The rate equation given by Howard (1964a) in the presenr notation, is dz = M exp(Nxh1.0 Z3.0) (18) dt where M and N are unspecified constanrs. This model also shows a large discrepancy from the experimentallyderived equations The asymptotic approach to saturation of the solutions flowing through the joinr openings means that little significanr solution will occur after a finite length of flow. Weyl (1958) defines a "penetration distance" to an arbitrary degree of saturation which may be used to approximate the limit of significanr solution along the path of flow. Weyl selected the penetration distance to 90 % saruration as this measure. This penetration distance for 34 Tolal Lenglh of Flow, x, in em Figure 5. Experimental data and fitted curves showing the dependence of ppm of calcium ion to length of flow, x, in the recirculation experiment with peo, = lO1.8atm.
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VOLUME 9, NO.4 a pC02 of latm within the range of conditions limiting the applicability of (11) and (12) is (19) and for a pC02 of 1O1.8atm is (20) If the penetration distance is of the order of magnitude of, or larger than, the total length of flow of ground water in the natural joint, then enlargement of the original joints and fractures into cavern passages by virtue of solutional attack of the limestone by dissolved CO2 should be expected. If the penetration distance is much shorter than the length of the unenlarged joints and fractures, then this mechanism cannot be responsible for the initial stages of development of any cavern passages Length of the path of groundwater flow through limestone, original joint diameters, and hydraulic gradients through limestone vary greatly depending upon the stratigraphy, structure, and physiographic situation. Two hypothetic a l groundwater flow pattenrs will be introduced to test for the feasibility of joint enlargement by the mechanisms investi gated in this paper. The first situation represents a favorable extreme for groundwater flow through limestone in which the path length of flow is assumed to be short (10m) and the hydraulic gradient is postulated to be high (101.). Assuming further that pC02 is 1 atm, the gap width of unenlarged joint th at would give a penetration distance of 10m is 6.8 x 1O2cm from the criterion of (19). Because natural joints a nd fractures under favorable circumstances might reach such a gap width, initiation of cavern development by solution attack by dissolved CO2 is not unreasonable under favorable conditions of high hydraulic gradienr and short distance of groundwater flow through limestone. On the other hand, under a less favorable hydraulic regime in which the hydraulic gradient is only 103 and the length of flow is 1000m, an origin a l gap width of 0.89cm would be required to give a penetration distance of 1000m. Because such a gap width seems unlikely, the present mech a nism alone could not account for the initial stages of cavern development under the assumed hydraulic regime. In fact, cavern development does take place under hydraulic siruations as extreme or more extreme than the unfavorable" situation postulated above. Cavern development in the Black Hills of South Dakota, described by Howard (1964b), takes place under such low hydraulic gradients and long paths of subterranean flow. F A Swenson (personal communication) describes an artesian ground water system through limestone in South Dakota in which the hydraulic gradient is about 3 x 104 and the path of groundwater flow is about 240km. Swenson asserts that significant limestone solution is taking place at presenr and has taken place in the past along the length of this flow Thus it would appear that mechanisms other than solution by virtue of original unders a turation with respect to CO2 are active in cavern development in certain cases. Such mechanisms might include convergence of flow, addition of fresh solutions along the path of flow, M i schtmgskor rosion effects, addition of CO2 or other acids along the path of flow, systematic changes of pressure or temperature along the path of flow, control of pH in the ground water by species other th a n those involving calcium and carbonate radicals. Of the innumerable joints and fractures within limestone of karst areas only a few are ultimately enlarged to form cavern passages. Therefore, it is relevanr to ask whether the mechanism discussed in this paper promotes differential enlargement of one initial frac ture relative to another because of an initial advantage in fracture diameter or hydraulic gradient acting across it. In order for differential enlargement to occur, the ratio of the larger to the smaller passages being compared must increase with time. For this to be true, then the rate of change of the rate of increase of gap width with time, d2z/dt2 must be a positive, increasing function of gap width. Equations 12 and 16 give complicated acceleration functions, in which it is impossible to tell by inspection whether or not the 35
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CAVES AND KARST Length of A B flow, x (em) z =lOl em z=lO' em z=10' em =lOlem z=lO'em z=10' em 0 1.0 x 10 5 3.6 x 106 1.3 x 106 6.0 x 10 6 3.8 x 10 7 2.4 x 10 6 5 0 4.8 x 106 1.3 x 106 7.6 x 109 3.4 x 107 2.4 x 106 10 0 5.2 x 106 1.3 x 106 4.4 x 1010 3.2 x 107 2.4 x 106 20 0 5.6 x 10 6 1.3 x 106 6.0 x 1013 2.5 x 107 2.4 x 106 50 0 4.0 x 106 1.3 x 196 0 1.1 x 107 2 3 x 706 100 0 1.3 x 106 1.3 x 106 0 2.1 x 108 2.2 x 106 200 0 8.0 x 108 1.3 x 106 0 6.0 x 1010 1.9 x 106 500 0 4.4 x 1012 1.4 x 106 0 5.6 x 1015 9.6 x 107 1000 0 0 1.3 x 106 0 0 4 8 x 107 TABLE 2. Acceleration of Passage Gap Width, d2z/dt2 for h = 1. above criterion is met. Therefore numerical values of the acceleration functions of (12) and (16) are given in Table 2. In Table 2A the accelerations are given for an arbitrary hydraulic gradient and selected values of gap width and position along the path of flow for the case governed by (12). Similar numerical examples are given in Table 2B for accelerations derived from (16). In Table 2B the acceleration is at all points a positive, increasing function of passage diameter, indicating differential enlargement. In Table 2A, however, at the entrance region of the flow path the acceleration is a positive but decreasing func tion of passage diameter, indicating that all joints of different gap widths are competitive. Note that although the acceler ation for the entrance region in Table 2A decreases with increasing gap width (12) shows that the r ate of increase of passage gap width increases with increasing gap width if the hydraulic gradient is constant. For points farther from the entrance region of the passage (large x), the inverse relationship between gap width and acceleration in Table 2A changes to a direct relationship, indicating that selective enlargement of originally larger joints will occur. This is related to the penetration distance discussed earlier. A table similar to Table 2 might be made in which the gap width is assigned an arbitrary value and the hydraulic gradient is allowed to vary. This would show that in the entrance re gion no selective enlargement of passages with originally l arger hydraulic head would occur, but that farther along the path of flow, the hydraulic gradient would become a selective factOr in passage The presence of, or lack of, selective enlargement is a major determinant of the path of ground water flow and the pattern of the resultant caves. However, because the experi ments reported in this paper are subject to refinement and enlargement to cover a greater range of hydrochemical conditions, no inferences as to their significance in this respect are offered. A general discussion of the subject is given in HOWARD (1964a). The experimental results presented in this paper are not regarded as definitive or conclusive, but rather indicative of the solution kinetics of the CO2watercalcite system in the laminar flow regime These experiments were conducted on a limited budget, bur show the feasibility of experimental investigation under conditions approximating natural groundwater flow through limestOne. A few suggestions are offered for possible enlarge ment of th e experiments Bec ause the experiments described show little agreement with Weyl's masstransfer theory of solut ions kinetics, similar experiments might be run on gypsum blocks, whose solution chemistry is simpler than that of the carbonate system. Other carbonate rocks might be employed, to include 1) limestOnes with other physical and chemical characteristics and 2 ) dolomite. The experiments described might be enlarged to include a greater variety of gap widths, a greater range of CO2 partial pressure and, finally, to admit both very slow and very rapid flows. A partieular problem is encountered for very rapid flows, including flows in the turbulent flow regime, in that concentrations of dissolved calcium ion for a reasonable length of flow are very low, so that either more 36
PAGE 13
VOLUME 9. NO. 4 sensitive analytical techniques would have co be employed or recirculation techniques would be required. Finally, the solurion kinetics of passages with nOllparallel walls might be investigated. Acknow Iedgemenrs We wish co thank the Geography Department of the Johns Hopkins University for financial suppOrt for the expe r im e ntal work and Owen P. Bricker and Rane L. Curl for their interest helpful comments in reviewing an earl y draft of this paper. References CHAVE, K. E. ( 1965 ) Carbonates: association with organic matter in surface sea water. S c ience. 148 : 172 3 1724. CURL, R. L. (1965). Solution kinetics of calcite. (Paper presented at the Fourth International Congress of Speleolo gy, Ljubljana, Yugoslavia ) GARRELS, R. M., & C. L. CHRIST (1965). Solutions, Minerals and Equilibria. Harper & Row, New York. 450p. KAYE, C. A. (1957). Effect of solvent motion on limestone solution. journal 0/ Geo logy, 65: 3 546. HOW ARD, A. D. ( 1964a ) Processes of limestone cavern J evtlopment. Ilit ematio nal j01anal 0/ SPeleology, 1: 4760. HOWARD, A. D. (1964b) Model for cavern devel opment under artesian ground water flow with special reference to the Black Hills. Natiollal S/Je/evlogical Society Bu//. 26: 7 16. PAO, R. H. F. (1961). Fluid Mechanics. Wiley & Sons, New York. 502p. RAINWATER, F. H. & L. L. THATCHER (1960). Methods for collection and analysis of water samples. U.S. Geological SUr/'ey, WaterSupply Pap e r no. 1454, 30 I p. TERJESEN, S. G., O ERGA, G. THORSSEN, & A. VE (1960) Inhabitory action of metal i ons on the formation of calcium bicarbonate by the reaction of calcite with aqueous carbon dioxiJe. Chemi cal Engineering Science, 14: 277288. WEYL, P. K. (1958) Solution kinetics of calcite. ,Tournai 0/ Geolo gy. 58: 163176. APPENDIXDERIVATION OF EQUATION (17) Weyl (1958) defines the quantity C, the fractional difference from saturation, as c' = 1 (lA) CS where C is the concentration of solute and C is the saturation concentration of the solute. Weyl gives concentration in molesperliter, and the so l ure of interest is dissolved calcium carbonate Because the author's concern is with the rate of change of concentration with length of flow, Equation lA can be differenriated co give the following relationship: dC _ C dC' dx 5 dx (2A) The concentrations measured in this paper are average concentrations of the outflow which Weyl distinguishes by bars (e.g., C and C'). Wey]'s equation relating C'ro the variables of length of flow, gap width and How v e locity is given as an infinite series. Be cause the series converges rapidly only the coefficients for the fIrst term will be used. Weyl's equation for laminar flow in parallel channels becomes, in the present notation (3A) where V is the average velocity through the channel. Because Vz = Qy, V may be elim inated from (3A), and Qy may be further eliminated by use of ( 1), giving Therefore, by differentiating, dC'= 1.72X10Sh'z4 exp(1.75X10sxh'z4) dx (4A) ( SA) 37
PAGE 14
CAVES AND KARST The relationship between dz/ dt and de' / dx in molar co ncentr ations is dz 101 dC (6A) dt = 2.72 dx Fr o m (5A), (6A), and (2A), dE' / dx can be related ro dz / dt, and Qy can be e limin ated using (1), giving Equation 17. ANNOTATED BIBLIOGRAPHY Edited b y JAMES F. QUINLAN A LP SU, IRrAN ( 1966 ) A hydr olog i c study of water l osses at May Res e rv o ir. CENTO, Symposium. 011 H y tlrolog yanr! I f l ate r Resolirces D erelo pmellt. Ankara, Turkey, reb. 712,1966. p. 119126. (Avail able from Ofiice o f U.S. Economic Coordinator for CENTO Affairs, American Embassy, Ankara) A brief account, with hydtographs and tabu l ated data, of th e failure of a reservoir located on Mesozoic lim estone, near Konya, Turkey. The 28 mhi g h earthfill dam was completed in 1950. Between february and Apri l 1960 the reservoir held water, but by June it had comp letely drained, leaving a bottom c ontaining circu l ar, vertical sinkholes in the alluvium covering the limestone. ALL ASSOCIATION INTERNATIONALE DES HYDROGEOLOGUES (1966). Reun;on de Belgrade 1963, M e m o ires 6: 1407 ( Available from Comite National Yougoslave pour la Geologie de Genie Civi l er nlydrogcologie, Kneza 7/1/1, Belgrade.) More than 25 % of this important volume of proceedings concerns ka r st hydrology The papers a re too numerous t o be cited here. JFQ BIRD, ). BRIAN (1965). Limeston e terrains in southern arctic Canada. [in International Conference on Permafrost, 1 st ( Lafayette, Indiana, Nov. 1963), Proceedin gs 1. National Academy of Sciences National R e sear c h Coun c il, P"blic at ioll No. 1 287, p.115121 and discussion, p.552 [19661. ( Available for 535.00 from the Acad e my at Washington, D. C. 20418.) An impo rt a nt review paper. Included is a map showing the distribution of carbonate rocks, a cr itical discussion of chemical and mechanical weathering and its topographic expression, and ground wate r hydrol ogy. Three types of limestone terrain are described: youthful, covered by postglacia l marine landforms and sediments, and covered by glacial deposits. A periglacial limestone cycle of e r os i o n is proposed. In the livel y discussion of this paper, conflicting opinions were expressed con cerning the abundance and age of solution cavities in lar ge bodies of carbonate rock in permafrost regi ons. Several obse rvati ons (unfortunately, not included) indicate that, contrary to Bird 's opinion, large solution openings exist, transmir warer, and are probably susceptible to continu in g enlargmcnt under present permafrost conditions. JFQ BROWN, RICHMOND F. ( 1966). Hydrolo gy of the cavernous limestones of the Mammoth Cave area, Kentucky V. S. Geological Slav e) WaterSupply Paper, 64p. (Available for $.35 from Supt. of D oc uments, Government Printing Office, Washington, D. C. 20402.) Many valuable basic data are interspers ed with occas ional incautious observations and a patent interpretation of cavern development in terms of the classic theories of Davis (1930) and Bretz ( 1942). JFQ CA ILLERE S., & TH. POBEGUIN ( 1956). Considerations generales sur la composition mineralogique et la genese des bauxites du midi d e la France. j"lushml National d Histo;re Nattlrelle, Me,lI o ires n.S., ser. C 12 (4): 125212. A thorough srudy in which results of meticulous laboratory investi ga tion are synthesized with Meld data and used to ex plain the origin and properties of limestonederived bauxites. A brief r eview o f rhe current literature is includ ed JFQ COMMONWEALTH BUREAU OF SOILS ( 1966). Bibliography on terra rossa, 19561965. Bibliograpby, No. 10 37, 1 3p. Available for S 1.20 from rhe Bureau at Rothamsted Experimental Station, Harpc nden, Herrs., Eng land.) An annotated bibliography o f 46 references from the int e rnational literature. JFQ CRIBB A. B. ( 1965). An ecologica l and taxonomic account of the algae of a semimarine cavern P a radise Cave Queensland. Queensland VI/iv., Papers, Dept of Botany, 4 (15): 259282. The cave, approximately 40m long, is penetrated by salt water only during heavy seas. Its algal vege tation is largely dependent o n the occurrence o f fresh water seepage,lrom the roof and walls.JFQ "'Containing only t echnical books and articles in the karst sciences published in non.speleological journals. Contributions to this list, containing the complete reference citation are welcomed. 38
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VOLUME 9 NO.4 DEVDARIANI, A. S. (1966). Geomorfolo g ; ya, no. I Matematicheskie metody. ItOgi nauki ser. geografiya Moskva Institut Nauchnoi Informarsii Akademiya Nauk S.S.S.R., 142p. (Available for $1.50 from VictOr Kamkin, Inc., 1410 Columbia Road N.W., WashingtOn, D. C 20009. Minimum mail order is $2.00). Pages 105 to III analyse the morphology of sinkholes, the stability of c aviry roofs a nd the solvent capacity of karst waters (Mischfmgskor rosion) but they are brief sum maries of work done outside of the U.S.S.R. by Kammerer (1962), Scheidegger (1961), and Lajos (1964). The balance of this book is a review a nd gu ide to the Russian and international literature of mathematical geomorphology. JFQ FISCHER W. A., D. A. DAVIS & T. M. SOUSA (1966). Freshwater springs of Hawaii from infrared images. U. S. Geological Sur vey, H ydrologic ltwestigatio'lls Atlas HA218 Sheet 33x53 inches. ( A va ilable for SO.75 from the Survey at WashingtOn, D. C 20242.) The atlas consists o f a descriptive text an index map, and a series o f 29 aerial phorographs shQw ing th e l ocario n and extent of 219 coastal springs detected by infrar ed images. The shade of an anoma l y on a film indicares whether a spring is hot or cold and the size of the im age indicates rhe magnitude of flow Unfortunately the contrasts were genera lly tOo subtle t o be reproduc ed by halfrone printing, but one fig ure in which the tOnes are more distinct is included. [There is no reason why infrared ima ge ry could not be used to locate submaribe sp rings in karst areas, particularly along the shores of the Medit e rran ea n where ther e are water shortages.Ed.l JFQ GARCIA ROSELL, CESAR (1965). Cavernas, Grittas y Cuevas del Pert; Lima, Talleres Graficas P.L. Villanueva S.A., 54p. (Availab l e for S 1.50 from E. Iturriaga y Cia. S A., Casilla 4640, Lima Peru.) An important first compilation of information o n the caves and rock shelters of Peru many of which are archeological sites. There are no cave maps but there is a map showing cave locations The brief bibliography consists of little more than incomplete citations FENELON, PAUL (1966). Les phenomenes k ars tiques. All11ales de G eographie 75 (408): 1 88196. A summary of the papers present ed at th e Symposium on Karst Phe nomena at the 20th Inter n ationa l Geo g raphical Congress, held in the United Kingdom, 1964. Included is a discussi o n of the field trips in England and a bibli og raphy of th e karst areas visited. HACK, JOHN T. (1966). Interpretati o n of Cumberland Escarpment and Highland Rim, south central Tennessee and northeast Alabama. U. S. Geological Sttrvey, Professiona l Paper 524C, 16p. (Available for $.55 from Superintendent of Documents, Government Printing Office WashingtOn, D. C 20402.) Evidence is presented to refute the classic interpretation of rhe Cumberland Plateau, Highland Rim, a nd Nas hville Basin as tOpographies formed in three cycles of base l eve lin g, each of w hich was followed by periods o f uplift when rhe peneplains were warped a nd partially dissected. The strongly advocate d alternative interprerarion is rhat rhe forms of rhe presenr landscape are adjusted to processes now actin g upon them or that acted on them in the recent geologic past. The landscape is formed by continuous lowering of the surface, a process that involves slope retreat on beds of differin g resistance For example, the Cumberland Escarpment, a solution escarpment, is capped by sandstOne a nd shale. Its lower slopes are developed on limestOne and it retr ea t s as a result of sapping of the caprock by solution of the limestOne. JFQ HELLER, FLORIAN ( 1966). Mondmilch oder Montmilch. Geologische Bliitter ifir NordostBayem 16 (1) : 5666. A scholarly histOric a l review of n o m e nclatur e for moonmilk. Included are m ore than 60 references for the period 15461903. JFQ HUSSEY, KEITH M .. & R W. MICHELSON ( 1966 ) Tundra relief f eat ure s near P oi nt B arrow, Alaska. Arctic 19 (2): 1 62184. An illustrated description and interpretation of the orig in o f polygonal grou nd oriented l akes, icecored mounds residual slope features; and the role of g r o und ice in the deve lopment of thermo karsr (ropograp hy p roduced by set tlin g o r cav in g o f ground in re spo nse to the melting of gro und ice) JFQ JATON, C, J. POCHON, J. DELVERT, & M BREDILLET (1966). Etude du Mondmilch de g rottes du Cam badge. An nales de l IlIs titttt Pastell' 110: 912191. A c hemical crystallographic, and biological investigation of th e m oo nmilk of Cambodian caves ha s shown that it is a biotOpe in whic h ammon ifyin g and i ro n reducin g microfloras are particularly active. The study confirms observations pre viously made at the L ascaux Cave in France. JFQ JONES. ROBERT J. (1965). Aspects of th e biological weathering of limest o ne pavement. Geologists' Association Proceedings 76 (4) : 4214 34 A magnificently illu s trated discussion of the development of g rikes (s ub soi l karren) clints ( th e intervening limestone masses), and the role of biological weathering by lichens, soila cids a nd peat forming vegetation. A simple technique is presented for demonstrating h ow the hypha e o f endolithic lichen penetrate several hundred mic rons in to limestone. Recog nition of such cav ities formed by 39
PAGE 16
CAVES AND KARST liche n can be used to distinguish lim estone de nuded o f it s soi l cover from limestone that has nor been den u ded. A very imp ortant paper. JFQ KELLER WALTE R D PRESTON McGRAIN, A. L. REESMAN & N. M. SAUM (1966). tio n s o n the orig in of e nd e llit e in Kentucky and their extension to "indianite'. Clays and Clay Mil/erals 1 3 th National Conference, 1 963, Procee din g s p. 10712 0. P ergamo n Press, New York Beginning p robably during Terti ary time, a n d continuin g today s ulfuric acid from the oxidation of pyr ite pe rcol ated into clayey r es i duu m o f two different pa l eokarsts o f Pa le ozoic age to produce ende lli te and indianite. Eac h residuum had be e n cove red wi th pyritic Pale ozo ic sha l es and sa ndstones. JFQ KOHOUT, F. A ( 1966). Submarine springs : a neglecte d phenomenon of coas t a l hydrol ogy. CENTO, S "11Iposilt11l 011 H y drolog y and Water Resol/rce De v elopmenl. Ankara, Turkey. Feb. 7 12, 1966. p 3 91 4 1 3 [ Same source as ALPSU (1966) abovel An i nt e rest in g r eport o n th e s i gnifica nce of b o th thermal and cold freshwater sp rin gs dischargi n g be n ea th th e sea al o n g th e M ed irerran ca n and Flo ri da coasts. Ac cou nts o f upwellin gs record e d i n R o m a n tim es a r e b o rn ou t by presentday hydrolog i c in vestigatio ns. Non artesian as we ll as a rtesian 1I0ws suppl y th e water from i n lan d so ur ces, w hich by a lt e rin g salinity patterns of the sea 1I00 r p rod u c e bio l ogica l zo n a t ions indicativ e o f th e sp rin gs. Some of rhi s subma rin e water i s now bei ng rapped by we lls Numerou s examples a r e c ited a n d illustrated b y r e m arkab l e photographs. A va lu ab l e bibliogr ap hy is inclu ded. ALL LOVE, COLIN L. ( 1966) A geop hysical study o f a hi g h way probl e m in lim estone terr ain. California Divis i o n of Highwa,'s, ll>fateri als and Res earc h D epartment, R e search Report, No. M&R 6 4273 0 29 p (Availab l e g ratis from th e D epa rtment a t 5900 Folsom Blvd Sacramento, California 95819.) Shallo w r ef r actio n seismic, expanding sp r ead resistivi ty, a nd fixed depth resi s tivity geophysical methods wer e eva l uated in an effo rt to locat e soluti o n cavitie s th a t were potentia l si tes of sink h o l e deve lopment alo n g a hi g h way n ea r Cool, Cali fornia. Onl y the fixed depth resistivity method gave dependab l e resu lts. Seve r a l trend s o f so luti on cavit i es were l oca ted and subsequent to publication of th e r epo rt in Octobe r a sinkh ole deve l oped along o ne o f the tr ends on D e cemb e r 7, 1966. JFQ MAIGNI EN, R ( 1966). R ev i ew o f r esea r c h o n lateries. UNESCO, NatMal Resources R e s earch, IV 148p. ( Availab l e for $5.00 in th e U. S. from UNESCO Public a tions Center 3 1 7 E. 34th St., New York 10016). Al th oug h it o nl y inci de nt ally r efe r s to the weat h erin g of lime s t o n e s thi s m o n og r aph i s a critica l a n d com p r e h e n s i ve r ev i ew o f p r ocesses dnd products of weatherin g and so il f o rmation in the t ropics. Accordin g ly, it pr ov i des val u able in sight int o the natur e and orig in o f soils of many tropic a l kars t s a nd pseudokarsts JFQ MAURIN, VIKTOR, & JOSEF ZbTL (1966). Ein fossi l e r semiarider tropischer Karst auf Ithaka. E rdkllnde 20 (3) : 204208 Paleoclimatic interpre tati ons, dat i ng o f a su rf ace, a nd compa r ison with t h e morphology of recent Austra li an karst forms descr ib ed by J ennings a nd Sweeting ( 1963) suggest that the karst of this I on ian i s l a nd i s a fossi l semiarid tro pica l karst that formed during the Pliocene. This is one of the f ew papers th at discuss ancient k a r sts that deve l o ped in climates that were n o t humid tropical. JFQ MILLS JOSEPH W., & HENRY T. EYRI C H ( 1966 ) The role of unconformiti e s in the l oca l iza ti o n of ep i ge n e t ic mineral deposits in the United St a tes and Canada. Economic Geology 61 (7): 12321257. A survey of th e l i t erature shows th a t unconformities are influential in the l ocalization o f epigenetic mine ral depos it s in at l eas t 68 districts in t h e U S. a nd Canada. In 10 o f these mineral districts epige neti c a r e deposi t s a r e r e l a ted to paleokarst features (espec ially th e ir plumbing system) beneath the overlying sedimentary rocks A par ti a l revi ew and excelle nt synthesis of the literature JFQ WATSON, PATTY JO, & RICHARD A. YARNELL ( 1966). Archaeologica l and p aleoethnobota nical investi gatio n s in Salt s Cave, Mammoth Cave National Park, K e ntucky American Amiqllity 31 (6): 842 849. Studies on three l eve l s of Salts Cave revea led th a t th e cave was ex tensively mined f o r gypsum and m j r ab ili t e by p r e hi storic peop l e probably belonging to t he ea rly Woodl a nd culture groupi ng during th e las t millenium B C. Analyses of fecal remains yield ab und a nt evidence o f their foods a nd clues to thei r agricu l tural deve lopment w hi c h a p pa r en tly inclu ded c ulti va ti o n of sunflowe r squash a nd gou rds b u t n o t maize. The rep ort includes 1 2 radi oca r bon d a tes ranging from about 290 to 1190 B .c. ALL WATSON, PATTY JO (1966). Prehistor i c min ers of Salt s Cave Kentu c ky. Arc ha eology 19 (I): 237243. A popu l a r account of th e 1963 examinat ion of Salts Cave by the Illin ois State Mu se um and Cave Re sea rch Fou n datio n It p r ov i des a desc ripti o n of th e cave a nd a summary of the u se o f the cave by th e p r e hi storic mine r s of t h e l ast millenium B. C. Excellent photographs illu s tr a t e t h e article ALL Contributors: ALL, A. L. L a nge; JFQ, J F Quinlan 4 0
Description
Content: Solution of limestone under laminar flow between
parallel boundaries / Alan D. Howard and Barbara Y. Howard 
Annotated bibliography / James F. Quinlan.
Cave Notes(vols. 18) and
Caves and Karst: Research in Speleology(vols. 915)
were published by Cave Research Associates from 19591973. In
1975, the Tumbling Creek Cave Foundation compiled complete
sets of the journals in three volumes. The Foundation sells
hardbound copies of the material to support its
activities.
