STATE OF ILLINOIS DEPARTMENT OF REGISTRATION AND EDUCATION IMPACT RESISTANCE OF ILLINOIS LIMESTONES AND DOLOMITES Richard D. Harvey ILLINOIS GEOLOGICAL SURVEY LIBRARY MAY 7 1963' ILLINOIS STATE GEOLOGICAL SURVEY John C. Frye, Chief URBANA CIRCULAR 345 1963 ,, ll^ 1 !, 1 ','; 1 .V;' 1 '':,!' L :'-.' l ;'-''-OGICAL SURVEY 3 3051 00004 5231 IMPACT RESISTANCE OF ILLINOIS LIMESTONES AND DOLOMITES Richard D. Harvey ABSTRACT The purpose of this study was to investigate the basic response of various textural types of relatively pure limestones and dolomites to a rapidly applied force (approximately 1 to 7 ft. /sec.) and to determine a quantitative measure of the im- pact resistance of such rocks. A simple instrument for determining the relative impact resistance of limestones and dolomites is described and the results of its use in testing 26 pure limestones of various textures and 10 dolomites are given. Analysis of test data indicates that the radius (r) of an indentation produced on a smooth carbonate rock surface is a function of the velocity (v) of impact of the indenter. The slope of the curve r2 versus v is constant for carbonate rocks and its reciprocal may be termed the impact modulus of the material being tested. The impact modulus of limestones and dolomites decreases with increasing porosity and decreases with increasing size of the crystals within the rock. Although there is considerable scat- ter of data points, both relationships appear to be linear. All of the limestones and dolomites tested deformed plastically immediately beneath the indenter by translation gliding. Fine-grained rocks reacted to impact primarily by the development of a distinct fractured zone around the point of indentation, whereas in coarse-grained limestones notable cleavage and j 1 1 2 }■ twinning of calcite took place in the area surrounding the indentation. INTRODUCTION The hardness of limestones and dolomites often varies considerably from one place to another, and it notably affects the commercial utilization of the stone. The term hardness as applied to solids is not always similarly defined, but it is agreed generally that it is a measure of the resistance to abrasion or deformation. 1 2 ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 A variety of tests have been developed to measure hardness that involve various rates of application of load. Mohs' scratch test is used commonly by mineralo- gists to determine relative hardness of minerals, but this test is not sensitive enough to be used effectively on carbonate rocks. The Brinnell, Rockwell, and Vickers tests (Tabor, 19 51), involving a slowly applied force that presses a spher- ical or pyramidal indenter into the sample, have been used effectively by metallur- gists. Brace (19 60), using the Vickers tester, showed that this test was applicable to the study of relatively isotropic and nonporous materials, including some lime- stones. The results of strength tests of solids as measured under slowly applied load (static) are considerably different from those derived from impact or a rapidly applied load. Under static conditions stresses are generally distributed through- out the material, although they often become concentrated in certain regions. Under impact or dynamic conditions, stress pulses which travel through the solid are generated; thus, only a small portion of the material is stressed at any instant (of time), and it behaves essentially independent of neighboring portions. Thus, many solid materials, particularly brittle ones, appear stronger and harder under impact than under static conditions. Limestones and dolomites undergo impact loading during crushing and dril- ling operations, when used as railroad ballast, in concrete highways, as road stone, and in other ways. In view of this, it was the general objective of this study to investigate the basic response of relatively pure Illinois limestones and dolomites to impact and to discover some of the phenomena that accompany impact of these rocks. As the limestones and dolomites of Illinois are similar to such rocks in other places, it is thought that the results of the study will be of general significance. A review of the literature on impact testing of materials reveals that sev- eral methods have been developed. Greaves (1909) measured the relative height of rebound of a diamond-tipped hammer falling freely on various metal surfaces (scleroscope hardness), and Gilbert (1954) determined the scleroscope hardness of single crystals of the Mohs' scale minerals. A "cloudburst" machine developed by Herbert (19 29) subjects the surface of a material to a rain of hard steel balls falling from a known height. Studies have been made of materials subjected to impact by high velocity projectiles (Whiffin, 1948; Maurer and Rinehart, 1960; and others). Obert et al. (1946) and the Page toughness test (A.S.T.M., 1961) determine impact toughness of rocks by dropping a hammer from continuously in- creasing heights until the specimen breaks. Impact tests in which a pendulum applies a load sufficient to break the material are described and discussed by Spath (1961). Singh and Hartman (1961) used an impact device consisting of a weighted chisel about one inch wide which was dropped from various heights on specimens of granite and limestone. Application of these and other tests to carbonate rocks is limited in one way or another, and it was thought that a simple impact apparatus utilizing a spherical indenter dropped vertically on a smooth rock surface would provide ad- ditional and useful information. The specific purposes of this investigation were to devise an apparatus and procedure for measuring impact resistance of limestones and dolomites that could be used to arrive at a numerical means of expressing this hardness, to evaluate the effect of impact on different textural types of relatively pure limestones and dolomites, and to determine the relation of impact hardness to other physical properties. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES ■ Acknowledgments Thanks are extended to J. E. Lamar, R. J. Helfinstine, and J. S. Machin of the Illinois State Geological Survey for their assistance and discussions dur- ing the course of this investigation, and to D. U. Deere and E. Y. Huang of the University of Illinois for their critical reading of the manuscript. IMPACT HARDNESS TESTER Description of Indenter The apparatus used in the present study consists of an indenter made of a 3/8 inch diameter steel rod, with a 5/32 inch diameter hardened steel sphere at- tached to its tip, that falls vertically upon the sample being tested. Figure 1 is a diagram of the apparatus drawn to scale. The height of fall of the indenter is indicated by an attached pointer, the tip of which moves in a groove in a meter stick fastened to the supporting frame. A spring loaded pawl, which is mounted on the indenter, is released when the indenter strikes the sample. The pawl en- gages a ratch at the highest point of indenter rebound, thereby preventing the in- denter from striking the sample a second time. The tip of the pointer prevents the rod from rotating during its fall and thus assures that the pawl is oriented properly. The indenter rod moves vertically through two laterally adjustable guides that are machined to allow the rod to touch them only on a very small area. The sample is clamped on an adjustable table to insure that the indented surface is perpendicular to the indenter. The entire apparatus is securely mounted on a sturdy laboratory bench. The kinetic energy of the indenter as it strikes the sample is equal to its potential energy at height h above the sample minus the frictional energy encoun- tered during the fall. The energy E of impact in ergs is, therefore, E = mgh-fh (1) where m is the mass of the indenter in grams, g is the gravitational acceleration (980 cm/sec 2 ), h is the height of fall in cm, and f is the force of friction encoun- tered during the fall. The second term on the right side of (1) is the total work done or energy expended against friction. The friction is given by f = y.N where \i is the coefficient of friction and N is the fraction of the mass of the indent- er that makes contact with the bearings and between the pointer and the sides of the groove in the meter stick during the fall. The static coefficient of friction in this case is approximately 0.2 and the kinetic coefficient would be even less (Fairman and Cutshall, 1946); however, N is not known. It is reasonable to as- sume that N would be less than 10 percent of the total weight of the indenter and would approach when the guides are in perfect alignment. Even with a value of 63.2 for N (10 percent of the weight of the indenter), 0.2 for |~l, and 10 cm fall for h, the frictional loss is 130 ergs. The potential energy with a 10 cm fall is 61.9 x 10 5 ergs, or approximately 48,000 times the friction loss under these assumed extreme conditions. Thus, friction during the fall may be neglected in this study. The velocity of a freely falling body which is initally at rest is given by v=gt (2) ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 Scale V/ f/W//ft*///fl///////tt Inches 6 8 10 12 Fig. 1 - Diagram of indenter shown in a rest position after indentation of sample. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES 5 where t is the time duration of fall. Since dh dT = V r t=t =/ gt dt = g_t^ J 2 t=o and the time of fall is thus t = (2h/g)*. From (2) the velocity in cm/sec is v = (2gh)* = 44.27(h)". (3) Testing Procedure The samples for impact hardness tests were blocks of limestone and dolo- mite, approximately 2 x 2 x 3/4 inch, sawed and ground so that their 2x2 inch surfaces were smooth and essentially parallel to each other and to the bedding of the stone. No notable differences were obtained in a test series of blocks of var- iable thickness cut from the same limestone sample. Some blocks thinner than 3/4 inch broke during impact tests and were deemed unsuitable. A slight polish was put on one of the 2x2 inch faces and the indentation tests made on this face. Although there was a slight amount of work hardening detected, the polish facili- tated accurate measurements of the indentations and did not materially affect the relative results of the tests. The sample was clamped to the adjustable table and leveled; the indenter was raised by hand to the desired height and released. After striking the sample, the indenter rebounded and was caught by the pawl and ratch. The sample was then moved about 1 centimeter or more and the operation repeated to produce an- other dent. The amount of rebound of the indenter was highly dependent on the action of the pawl and ratch. The tip of the pawl underwent some wear after pro- longed use, and thus the friction encountered during rebound was not absolutely constant for each test. Therefore, the observed height of rebound did not truly reflect a characteristic property of the test sample. Measurements of Indentations The diameter of each indentation was measured by means of a vertical illumi- nation microscope to the nearest 0.01 mm. The depth of indentation was measured using a hard blue dental inlay casting wax to make a cast of the impression. The cast was sectioned with a razor blade so that the maximum depth of the indenta- tion could be measured with a microscope. Any plastic deformation of the wax mold due to sectioning with the razor was easily recognized. The depths of the indentations were determined to the nearest 0.01 mm. Reproducibility of Indentation Diameter Numbers of Indentations Required The reproducibility of the indentation diameter made in any single test block was evaluated in the following manner. Specimens of coarse-, medium-, 6 ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 and fine-grained limestones were indented 10 times each using an indenter fall of 6 centimeters. The average diameter of 3, 5, and all 10 indentations are shown in table 1, together with their respective standard deviations and limits for the mean (Bennett and Franklin, 1954, p. 28). Measurements of the diameter of 5 in- dentations spread over the surface of the sample were regarded as adequate for the test. Standard deviations based on 5 indentations computed for samples used in this study, other than coarse-grained ones, were equal to or less than 0.05 mm. Sample C2740 (table 1) gave the largest standard deviation of all the samples tested. Consistency of Indentation Results The variation in average indentation diameter of several test specimens cut from large single blocks of limestone was investigated for 13 such blocks, each representing a different type or stratum of limestone. Results of such tests are shown in table 2; textural and other characteristics of the samples mentioned are described subsequently. In general the results show a good consistency, and such variations as exist occur when limestones have a highly variable texture. IMPACT MODULUS Indentation tests were made on more than 36 different limestones and dolo- mites. Tests were made in which the height of fall varied from 1 to 10 cm for the limestones and 2 to 20 cm for the dolomites. The corresponding velocity of impact according to (3) is 44.3 to 140.0 and 62.6 to 197.9 cm/sec. Graphs of the square of the indentation radius (r) plotted against the impact velocity for several different types of limestones and a dolomite are shown in figure 2. Although there is some scatter of the points, they clearly indicate that r z is a linear function of the in- dentation velocity. This relation also was found true for impact craters in granite and sandstone produced by projectiles with velocities from 1000 to over 6000 feet per second (Maurer and Rinehart, 19 60). Extrapolation of the lines in figure 2 to zero velocity indicates they all pass through the origin, or nearly so, and thus an equation in the form, tm z = (|)v (4) where K is the reciprocal of the slope of the curve and v the velocity appears to predict satisfactorily the behavior of carbonate rocks using this impact tester. The units of K are l/(cm-sec.) when the height of fall and the radius of indentation are in cm. Of all the rocks tested, K ranges from 77 to 422 units (see table 5). Variations in K computed from specific values of r and v as v varies from 44.3 to 19 7.9 cm/sec. for several carbonate rocks are shown in figure 3. The average maximum difference in K for seventeen different carbonate rocks is 16 units. Some rocks show a maximum difference in K as small as 10 units which represents a maximum of 5 percent variation, and others such as K14 show a maximum dif- ference of 3 6 units, which represents a maximum of 14 percent variation in K. These percentage variations are not unusual for measurements of mechanical prop- erties of natural occurring rocks. Thus, for a rapid and relative determination of the impact resistance of carbonate rocks, the average diameter of at least 5 Impact Velocity (cm/sec) 50. K 3 ICO Impact velocity (cm /sec) Fig. 3 - Variation of K computed from results obtained using various impact veloc- ities for several limestones and a dolomite. See table 4 for description of samples. 8 ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 indentations, produced by impact of the indenter dropped from a selected height, yields a characteristic value K to which the term impact modulus is applied. The indentations produced by a fall of 2 cm or less were too small to be observed readily in some samples. A fall of 10 cm caused ejection of some of the grains from around the indentation in many limestones and, hence, made measure- ments of the size of the indentation somewhat unsatisfactory. The standard dev- iation of K for sample K 14 (table 1) is 3. 1 units and for C2740 it is 24 units. The adoption of K as a quantitative measure of the impact hardness or resistance to im- pact of carbonate rocks enables comparison of results from rocks having a grossly different behavior and resistance to impact. INDENTER REBOUND AND ELASTIC RECOVERY OF ROCK SAMPLE When the indenter strikes a test block, it rebounds to varying heights de- pending mainly on its height of fall and the physical properties of the sample. The elasticity of individual calcite crystals at the site of an indentation enables the limestone to return partly to its position prior to impact. The depth of the resulting indentation, therefore, is less than the actual amount of penetration by the indenter. It is reasonable to assume that the maximum elastic rebound of the limestone would be in the center of the indentation and the minimum at the edge. The indenter point also undergoes some elastic deformation during impact. This is thought to be small as compared to that of the limestone because the elastic modulus (Young's modulus) of hardened steel is about 4 to 7 times that of limestone. Taking into account the foregoing, a relative value for the amount of re- covery of a limestone can be obtained as the difference between the maximum measured depth of an indentation, D m , and a depth, D c , calculated from the di- ameter of the indentation and the radius of the indenter as follows: D c = R - (R 2 - r 2 )2 where R is the radius of the indenter (1.985 mm) and r the radius of the indentation. The amount of elastic recovery of selected limestone samples in millimeters and in percent of the maximum indentation is shown in table 3. The elastic recov- ery shown is thought to be mainly that of the limestone, although a small part of the recovery may be due to flattening of the indenter point at the time of impact so that the indentation is larger than it would be otherwise. There is no apparent re- lation between the percentage of elastic recovery of the limestone and its impact modulus. APPLICATION OF IMPACT TEST TO LIMESTONES AND DOLOMITES Description of Samples The impact modulus of 26 limestones consisting essentially of calcite and 10 "pure" dolomites was determined according to the procedures previously de- scribed. Among the samples were limestones having a wide range of textual var- iations, including exceedingly fine-grained, lithographic types; medium-grained but finely crystalline oolites; and medium- and coarse-grained bioclastic lime- stones. X-ray and microscopic analyses of indented surfaces indicate many of the limestones are completely free of detectable quartz, dolomite, and other impurities. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES 9 Of the limestones reported in this study (see table 4) only samples NF512, NF511, NF527, 1009, and K19 have noteworthy amounts of impurities consisting of dolo- mite and/or quartz grains, but these grains are dispersed so thinly that they do not noticeably affect the impact modulus. No calcite was detected in any of the dolomites studied; however, samples 62-16-1, 62-16-2, and 61-7b contain a few widely scattered grains of quartz. Most of the fossil fragments in the limestones studied are parts of crinoids and bryozoans. The crinoid fragments are commonly single crystals; whereas, the bryozoan fragments are very fine-crystalline aggregates, usually fibrous, consist- ing of many individual crystalline particles whose orientation differs from its neigh- bors by a very low angle. The oolites are rounded grains composed of one or more rings of very fine polycrystalline calcite and usually possess a nucleus of one or more calcite crystals whose size is much larger than those in the outer rings. For descriptive purposes, the limestones are classified (table 4) accord- ingly: (1) type of major constituents (classification of Folk, 1959), (2) grain size grouped into fine, medium, and coarse categories according to the average clastic particle being < 0.063 mm as fine, 0.063 to 1.0 mm as medium, and > 1.0 mm as coarse (modified from Folk, 1959) . In the case of dolomites, it was useful to con- sider the medium range from 0.063 to 0.25 mm. Critical remarks based on micro- scopic analysis also are included in the table. Nature of Deformation Fracture Patterns Striking differences are evident in the behavior of limestones subjected to impact forces as applied in the test. All the dolomites behaved similarly and in much the same way as the fine-grained limestones. Impact on fine-grained lime- stones and dolomites developed indentations with sharp edges and narrow upheaved rims that stand approximately 0.005 mm above the surface of the rock, figure 4. Coarse-grained limestones, however, developed indentations whose edges are much less sharp and surrounded by a light colored upheaved zone in which com- plex deformation had occurred. The light colored zone consists of cleaved, twinned and buckled crystalline particles which were forced free of the rock in a few places as illustrated in the top of figure 5. By comparison the fine-grained limestones show only simple fracturing, and crystals adjacent to and surrounding the fractures and indentation have not suffered notable deformation. Medium-grained limestones composed of oolites and finely crystalline fossil fragments, such as bryozoans and brachiopods, behaved as fine-grained limestones, although a few oolite grains buckled and otherwise behaved as a unit during impact tests. Medium-grained limestones consisting of a few coarsely crystalline crinoid fragments with a fine- grained matrix show characteristics of both types of fracturing and deformation de- pending upon which type of material the indenter strikes. Two types of fractures that develop during impact are recognized, (1) radial fractures extending outward from the dent, and (2) fractures approximately 0.8 to 1.0 mm beneath and essentially parallel to the surface of the specimen. Both types are most clearly observed in fine-grained limestones as illustrated in figure 6; however, in coarse-grained specimens these fractures appear to be present but their patterns are more obscure and complex. In the coarse specimens, the interaction of both types of fractures gives rise to the buckling and the light colored zone described above. The parallel fractures split into numerous subparallel 10 ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 Fig. 4 - Photograph of an indentation in reflected light showing characteristic fracture pattern of fine-grained limestones. Light is shining from left to right and "d" is the diameter of the indentation. Fig. 5 - Photograph of an indentation in reflected light showing characteristic fracture pattern of coarse-grained limestones. The light is shining from left to right and "d" is the diameter of the indentation. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES ilPc' SECTION VIEW Diagram of plan and section view of an indentation in fine-grained (sub- lithographic) limestone. fractures which intersect the radial frac- tures, thereby isolating many particles. Radial fractures tend to follow grain boundaries, and thus their trace on the surface of the specimen is nearly a straight line in fine-grained and very ir- regular in coarse-grained limestones (compare figure 4 and 5). Radial frac- tures generally extend further in fine- grained than in coarse-grained rocks, which is probably related to the grain boundary phenomenon just mentioned. Inspection of fracture patterns, partic- ularly in fine-grained specimens, shows that the terminating arcs of the parallel itai Fractures fractures are bounded by radial fractures m Gliding as s hown in the plan view of figure 6. This indicates that the radial fractures preceded the formation of the parallel fractures. Crystal Deformation Many of the individual crystals in the limestones and dolomites were deformed at and near the point of impact. According to Handin et al. (1957), calcite crystals that have undergone transla- tion gliding (slip) on jlOllj crystallographic planes develop color centers which give the crystal a blue color after irradiation. It was found, as did Brace (19 60) and Pavlova and Shreiner (1961), that indented areas in which translation gliding took place could be recognized by this blue color after irradiation with unfiltered Cu radiation for a period of one hour at 35 kv-18 ma imput to the x-ray tube. By placing the indented specimen 3 to 5 cm from the x-ray source, good results were obtained. The calcite crystals of limestones yielded plastically by translation gliding within a segment of a spheroid immediately below the area of contact with the indenter and some distance into the specimen. By sawing through the middle of an indentation and irradiating the cross section of the indentation, the maximum depth to which the translation gliding took place could be measured (see section view in figure 6) . The depth to which translation gliding took place appeared to increase gradually from approximately . 1 to 1.0 mm with increasing impact velo- city from 44.27 to 139.98 cm/sec. Maximum depth of this gliding for several limestones varies from 0.72 to 0.93 mm with an impact velocity of 125.2 cm/sec. These depths do not appear to be related to the measured indentation diameters of the different limestones. Generally, the blue color extended a few hundreths of a millimeter below the parallel nearly horizontal fractures. Close examination of irradiated indentations revealed that color centers were absent along planes that had cleaved and that larger crystals tended to be a deeper blue than smaller ones. The blue color disappeared when the sample was heated to 200° C. Dolomite crystals located within the indentation also developed blue color centers as a result of the impact. Correlation between color centers and crystallographic mechanisms of deformation observed in dolomite crystals has ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 not been investigated to date; however, dolomite is known to slip on j 0001 j only (Higgs and Handin, 1959), and thus it is thought that the color centers are formed as a result of dislocations or vacancies produced along \ 0001 > during impact. Deformation lamellae were observed on surfaces of many crystals in the rock surrounding the zone of translation gliding in limestones. Twin lamellae pro- duced by impact were not observed on dolomite crystals. According to Higgs and Handin (1959, p. 275), dolomite crystals do not twin at room temperature. Exami- nation of thin sections of indented limestone surfaces using a polarizing microscope equipped with a universal stage revealed that the lamellae in calcite crystals re- sulted from lamellar twinning on {0112 > and cleavage on jlOllj . A small num- ber of crystals had lamellae parallel to j 022l| in this zone. The latter lamellae, according to Turner et al. (1954, p. 909), are a result of translation gliding rather than twinning. No detailed measurements of the orientation of the J0112 j twin- ning were made, but it was observed that such lamellae were preferentially oriented in such a way that a line drawn from the center of the indentation would intersect the lamellae at angles near 90 degrees. Figure 7 is a photomicrograph of part of an indentation and surrounding area in reflected light. It is a rare example that shows twin lamellae only in crystals located some distance from the indentation. This in- dicates that either the crystals adjacent to the dent just happened to be improperly oriented so that neither twinning nor cleavage could take place, or that the primary and secondary elastic waves generated by the impact interacted in a way to reen- force each other to produce deformation in a curved zone, as in figure 7. In addition, Fig. 7 - Photomicrograph of part of an indentation as seen from above in reflected light showing twin lamellae J0112J- on crystals (a) some distance from the indentation. Note that crystals adjacent to the indentation are un- twinned . IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES 13 this zone is located in the position where the parallel fractures generally inter- sect the surface. RELATION OF IMPACT MODULUS TO POROSITY AND CRYSTAL SIZE Data relating the strength of carbonate rocks to other physical proper- ties are limited. From static tests on five nonporous limestones, Brace (1961) concluded that Vicker's hardness is related to the strength and maximum grain size of the rock. Finogenov (1958) using a similar test showed that the hardness of ar- gillaceous carbonate rocks increased with increasing carbonate content and de- creased with increasing porosity. Absolute porosity measurements reflect the macro- and microscopic im- perfections of limestones, dolomites, and other solid materials. The fact that these imperfections, as well as crystal imperfections such as dislocations, va- cancies, and interstitial ions, etc., largely determine the mechanical properties of solids is well known (Mott, 1952; Evans and Pomeroy, 1958; and others); but many problems that relate the interactions of these imperfections with specific polycrystalline solids remain. The impact modulus of the carbonate rocks described above was deter- mined with the results listed in table 5. The modulus ranged from 77 to 275 for limestones and 149 to 422 for the dolomites. The effective porosity of each in- dented block was determined from water absorption and bulk volume displacement measurements, and the results are shown in table 5. Effective porosity ranges from 0.01 to 17.3 percent. The absolute porosities are undoubtedly slightly higher than these apparent values; nevertheless, relations between impact modu- lus and porosity should be evident from the data. A plot of K versus effective porosity for limestones and dolomites (fig. 8) shows a linear decrease in K as the porosity increases for both rock types. The data for the limestones has been divided into two groups to show the relation be- tween K and porosity for specimens with similar median crystal size (see below). The slope of the curves joining points of similar crystal size appears to increase slightly as the crystal size decreases. Crystal particle size distribution of the limestones was determined from thin section analysis by the point count method (Friedman, 1958). The apparent maximum dimension of 100 or more individual crystalline particles located on a grid covering approximately 6 sq. cm. of rock was grouped into 11 size ranges. Cumulative frequency curves were constructed from the data and the quartile dis- tribution sizes obtained are listed in table 5. Q , M , and Q correspond, re- spectively, to that crystalline particle size for which /5 percent, 50 percent, and 25 percent of the particles are larger than the value given in the table. When the logarithm of M (median) is plotted against K for limestones which have an effective porosity of less than 4 percent, figure 9, a linear trend of increasing K with decreasing M is evident, although there is considerable scatter to the points. The Q, and Q values of the samples when similarly plotted give much the same trend but the scatter of points is slightly greater. As a result of the small differences in the median crystal size of the dolomites, a plot of K versus M for these rocks does not show a significant trend. Effective porosity (%) • Impact modulus versus effective porosity for pure limestones and dolomites. Median crystal size, Md (mm) . 9 - Impact modulus versus median crystal size for limestones with effective porosity less than 4 percent. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES 15 CONCLUSIONS A simple and rapid test has been devised to determine the ability of carbonate rocks to resist deformation by impact. The equation where r is the average radius of at least 5 indentations produced by impact of a spherical indenter of velocity v and K is a constant characteristic of the material, quantitatively describes the behavior of carbonate rocks subjected to impact. This equation was evaluated only for cases in which v ranged from approximately 40 to 200 cm/sec. , thus the boundary conditions for the equation have not been defined. It is proposed that the term impact modulus be applied to K. The units of K are l/(cm-sec), provided that the radius and distance of fall of the indenter are meas- ured in cm. The impact modulus ranges from 149 to 422 for 10 pure dolomites and 77 to 275 for 26 pure limestones. Impact penetration of carbonate rocks by a spherical indenter produces well-defined zones of plastic and brittle deformation. An indentation is formed by translation gliding on the j 1011 | in calcite and J0001 [ ? in dolomite crystals and by compaction of crystals in the case of porous rocks. A zone in which cleav- age on 1 1011 | and lamellar twinning on 4 112 \ takes place on individual cal- cite crystals surrounds the indentation. This zone has a diameter roughly equal to twice the diameter of the indentation and includes an upheaved area adjacent to the dent, which varies in height and width depending on the texture of the rocks. Lamellae parallel to j 0221 > also were observed microscopically in calcite crys- tals in this zone near the rim. Impact on coarse-grained limestones produces a considerably wider and higher upheaved area than on fine-grained stones. Cleavage and twinning of crys- tals, and buckling up of crystalline fragments by fracturing along grain boundaries are predominately observed on coarse-grained limestones. If the impact velocity is sufficient, small particles of stone from the outer margins of the deformed zone may be exploded free from the surface of the specimen. Fine-grained limestones and dolomites, on the other hand, show little crystal deformation adjacent to the indentation. Two types of fractures are evident and most clearly observed in fine- grained limestones. One set of fractures radiates from the indentation rim; the other set is located approximately 1 mm beneath and nearly parallel to the surface of the sample immediately beneath the indentation, but it turns to intersect the surface some distance from the dent. These limiting characteristics of coarse- and fine-grained rocks also are developed in medium-grained limestones but to a more limited extent. The resistance to impact of relatively pure limestones and dolomites is, for the most part, controlled by the porosity and size of the crystals composing the rock. TABLE 1 - NUMBER OF INDENTATIONS AND THE LIMITS OF THE MEAN DIAMETER Number Mean Range for Standard Limits of of dents diameter (in mm) 10 dents (in mm) deviation (in mm) the mean* (in mm) Coarse-grained limestone (C2740) 3 1.720 0.140 0.35 5 1.830 0.179 0.22 10 1.808 1.62-2.02 0.172 0.12 Medium-grained limestone (K7) 3 1.537 0.025 0.06 5 1.536 0.025 0.03 10 1.541 1.51-1.56 0.023 0.02 Fine-grained li mestone (K14) 3 1.313 0.014 0.03 5 1.310 0.010 0.01 10 1.308 1.305-1.330 0.006 0.004 ett and Franklii Average diamete r - mm Sample Block Average Standard number 2 3 4 deviation K5 1 47 1.44 1 .59 1.50 1.500 0.065 K7 1 59 1.57 ] .54 1.566 0.025 K14 1 43 1.30 1 .35 1.360 0.065 K18 1 74 1.74 1 .85 1.79 1.780 0.078 1000 1 68 1.68 ] .67 1.677 0.008 1001 1 35 1.35 1 .34 1.347 0.007 1008 1 76 1.65 1 .72 1.710 0.056 1009 1 28 1.29 ] .30 1.290 0.010 1010 1 48 1.40 1 .45 1.443 0.041 NF512 1 28 1.34 1 .31 1.310 0.036 NF526 1 35 1.35 1 .32 1.340 0.017 1007** 1 30 1.25 1 .26 1.270 0.026 NF557** 1 32 1.28 1 .29 1.29 1.295 0.016 * Average diame er for 5 indentatio ns produc ed by a fall of 6 cm ** Samples 1007 and NP557 are both siliceous, dolomitic limestones and < included to show that the average indentation diameter of impure a rocks may have variations similar to pure limestones. TABLE 3 - ELASTIC RECOVERY OF LIMESTONES* K14 K18 1000 1006 1010 NF516 NF554 0.09 0.10 0.06 0.13 0.15 0.10 0.08 0.13 0.08 0.09 0.08 0.07 0.12 0.05 0.04 0.07 0.11 0.06 Initial height of fall - DESCRIPTION OF SAMPLES (Folk, 1959) LIMESTONES NF512 NF526 : and feldspar gr; K5a Thebes K6 Marblehead K7 Marblehead 1000 Anna 1001 Anna 1006 Ullin 1009 Cave in Rock 1010 Cave in Rock NF511 Elizabethtowr NF519 Jonesboro NF527 Jonesboro 1600 Bedford, Indi 1008 NF516 NF554 CM1962 (depth of 2000 fe< New Harmony, Indi; (depth of 5464 fes Salem Mediur 1 Bios P arite Complex particles, fine and Kimmswick Mediun l Biomicrite Many crystals are cleaved and twinned, partly recrystallized Kimmswick Mediur i Biomicrite Bryozoan and Crinoid fragments, partly recrystallized Burlington Mediun i Biomicrite Crinoid fragments Burlington Mediur i Biomicrite Bryozoan fragments Fredonia Mediun i Oosparite Complex particles Fredonia Mediur i Bio-oospari e Complex particles Harrodsburg Mediun i Biosparite Bryozoan fragments Fredonia Mediun l Oo-biomicri e Crinoid fragments Fredonia Mediun Oosparite Complex particles Fredonia Mediun i Biomicrite Brachiopod fragments Grand Tower Mediun l Biomicrite Crinoid fragments Harrodsburg Mediun i Biomicrite Recrystallized with sutured Salem Mediun Bio-oospari e Superficial oolite, forami- Kimmswick Coarse Biomicrite Notably recrystallized Harrodsburg Coarse Biosparite Crinoid fragments with over- growths Harrodsburg Coarse Biosparite Bryozoan fragments Harrodsburg Coarse Biosparite Crinoid fragments with over- Bryozoan fragments Notably recrystall 61-7b Bourbonna LS Waukesha 61-8b Kankakee Racine 62-16-1 Joliet Joliet 62-16-2 Joliet Kankakee 62-20 Grafton Joliet 62-17 Thornton Racine 62-17c Thornton Racine 62-171 Thornton Racine 62-21 Elizabeth Galena ' Grain s chems ize classifica e. For dolomi is 0.063 to ion aft for li es the 250 mm er Folk (1959 mestones <0.0t grain size rei (modified -afte ine Replacement Even, granoblastic, subhe- dral grain boundaries, mottled gray and brown ine Replacement Even, granoblastic,* subhe- dral grain boundaries ine Replacement Even, granoblastic, subhe- dral grain boundaries ine Replacement Even, granoblastic, subhe- dra'l grain boundaries ine Replacement Even, granoblastic, subhe- dral grain boundaries ine Biogenic Uneven, subhedral grain boundaries edium Replacement Even, granoblastic, anhedral and sutured grain boundari edium Biogenic Even, granoblastic, subhe- dral grain boundaries edium Biogenic Crinoidal ghosts, uneven, subhedral grain boundaries oarse Replacement Even, granoblastic, euhedral >. 16) which is based on the average size of alio- mm, fine; 0.063 to 1.0 mm, medium; and >0. 025 mm, :s to the median crystal size in which the medium Folk, 1959, p. 19). ILLINOIS STATE GEOLOGICAL SURVEY CIRCULAR 345 TABLE 5 - PHYSICAL PROPERTIES OF SAMPLES Impact modulus K* Cry stal size Effective Sample 1 Grain** quar tiles (mm) porosity number (cm-sec) Qi M d Q 3 (percent) LIMESTONES 1009 275 Medium .002 .009 31 0.5 1006 263 Medium .001 .002 015 0.3 NE512 262 Fine .003 .008 02 0.4 1001 259 Medium .002 .003 009 2.5 K14 257 Fine .002 .003 004 1.3 NF526 254 Fine .003 .005 013 0.05 NF519 236 Medium .005 .014 05 0.01 NF511 233 Medium .002 .008 02 0.1 NF554 226 Coarse .003 .005 02 0.6 1010 223 Medium .001 .002 05 2.7 K5 217 Medium .015 .03 18 0.2 NF527 211 Medium .003 .02 12 2.6 K6 199 Medium .010 .02 62 2.1 K7 190 Medium .013 .02 09 2.8 K5a 187 Medium .015 .09 38 0.6 K5b 184 Coarse .134 .76 1 23 1.5 1000 164 Medium .001 .003 010 8.1 CM1962 164 Coarse .025 .31 1 23 1.3 1008 160 Coarse .003 .009 20 4.6 K19 155 Coarse .011 .02 03 8.4 K3 148 Medium .002 .006 04 6.6 C2740 143 Coarse .27 .62 1 11 0.9 K18 136 Coarse .007 .50 90 4.7 1002 136 Coarse .005 .02 76 6.7 NF516 135 Coarse .02 .35 54 1.2 1600 77 Medium DOLOMITES .015 .026 35 17.3 62-17 422 Medium .063 .109 190 0.4 62-171 422 Medium .067 .144 62 0.7 62-16-1 394 Fine .029 .051 088 1.5 61-6a 363 Fine .036 .051 077 1.3 62-17c 360 Medium .069 .154 268 2.6 61-8b 347 Fine .030 .044 063 4.2 62-16-2 347 Medium .025 .036 054 5.6 61-7b 279 Medium .024 .051 088 5.1 62-20 278 Medium .026 .036 051 7.9 62-21 149 Coarse .21 .33 47 13.0 1 = v/r/<#(equation 4) where r is the radius of indentation (cm), and v impact velocity (cm/sec) . All K values listed are computed from results obtained in which v = 108.5 cm/sec (height of fall of indenter equal to 6 cm). lame as footnote to grain size in table 4. IMPACT RESISTANCE OF LIMESTONES AND DOLOMITES REFERENCES American Society for Testing and Materials, 1961, Standard method of test for toughness of rock, ASTM Designation D3-18, in 1961 Book of Standards, Part 4: ASTM, Philadelphia, p. 613-614. Brace, W. F., 1960, Behavior of rock salt, limestone, and anhydrite during in- dentation: Jour. Geophys. Research, v. 65, no. 6, p. 1773-1788. Brace, W. F., 1961, Dependence of fracture strength of rocks on grain size, in Fourth symposium on rock mechanics: Penn. State Univ. Mineral Indus- tries Experiment Sta. Bull. 76, p. 99-103. Bennett, C. A., and Franklin, N. L., 1954, Statistical analysis in chemistry and the chemical industry: New York, John Wiley & Sons, Inc. , 724 p. Evans, I., and Pomeroy, C. D., 1958, The strength of cubes of coal in uniaxial compression, in W. H. 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[London] Proc, v. 194A, no. 1038, p. 300-322. Illinois State Geological Survey Circular 345 20 p., 9 figs., 5 tables, 1963 Printed by Authority of State of Illinois, Ch. 127, IRS, Par. 58.25. CIRCULAR 345 ILLINOIS STATE GEOLOGICAL SURVEY URBANA