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By A. L. Holley

The application of scientific methods to the investigation of natural laws and to the conduct of the useful arts which are founded upon them, is year by year mitigating the asperity and enlarging the outcome of human endeavor. More notably, perhaps, are these the facts in that system of productive and constructive arts of which engineering is the general name. In metallurgical engineering especially, within the period of our own recollection, how rapid has been the rate and how wide the scope of progress: the scientific discovery and mining of metalliferous veins; the economical separation and reduction of ores of every grade; the production and regulation of high temperatures; the varied improvements in the manufacture of iron, in saved heat and work, in uniformity and range of products; and, most important of all, the creation and the utilization, to be counted by the million tons a year, of the cheap constructive steels. Wonderful as this range and degree of development may appear to the public eye, the close and thoughtful observer must, nevertheless, conclude that neither the profession nor the craft of engineering may congratulate themselves too complaisantly, but that they should rather acknowledge to each other the embarrassing incompleteness of the union between engineering science and art. There is a small school of philosophers whom we may designate as original investigators, men who come close to nature, who search into first principles, and who follow that scientific and therefore fruitful method by which the relations of matter and force are discovered, classified, and brought within the reach of practice. These wonderful men do not indeed create the laws of nature, as they sometimes almost seem to, but they go up into the trembling mountain and the thick darkness and bring down the tables upon which they are written.

By Tuomas Hirsi

The world’s first large scale modular solvent extraction plants have been delivered by Outotec. The first of these is now in operation and has proven that the VSF®X technology can deliver the excellent performance of the Outotec VSF® solvent extraction process. Modular delivery allows site work to be minimized and the manufacturing done in a controlled environment, allowing for serial production manufacturing benefits. Container based delivery was found to be a highly efficient way of utilizing the standardized transportation methods on a global scale. Site work with modular units was found to be efficient and highly predictable. In this paper, we present the first successful Outotec VSF®X deliveries and discuss the benefits of the modular delivery and design compared to the standard solvent extraction installation’s delivery. The process performance of the VSF®X is also discussed with experiences from the first industrial reference presented.

By Robert H. Richards

OF the several professions-the chemist, the civil engineer, the mining engineer, the mechanical engineer-the courses of instruction, as arranged at the scientific schools, differ considerably as to the amount of practical information which the student is able to gain. The analytical chemist has facility for a very thorough review of the processes which he will be called upon to perform. The student in civil engineering by his field practical learns the use of his tools and the art of taking field-notes. The mechanical engineering student is in the vicinity of machine-shops, which he can visit, and at which . he can work. The student in mining engineering has no such advantages. The mines are at a distance, and the railroad fare to get to them is oftentimes an insuperable difficulty. The aim of these laboratories is essentially to give to the student in mining and metallurgy a chance to study on a small scale the practical parts of his profession. We cannot, in a small laboratory, build a mine to timber, to work, and to survey; we cannot make artificial quicksands and other impediments to mining. In short, we cannot study exploration; but we can study the mechanical preparation and the subsequent smelting of ores. Before presenting the plan of these laboratories it may be interesting to indicate the progress of the idea from its beginning. During the summer of 1870 President Runkle visited the mines of Colorado, and while there, conceived the idea of making an expedition with the mining students to some of the Western mining regions. He talked over the scheme with many railroad and mining men, and everywhere received encouragement. In the summer of 1871 the Institute party visited the mines of Colorado, and spent six weeks in taking notes of them. President Runkle here conceived the idea of building up a mining and metallurgical laboratory ; and by the aid of Booth & Co. of San Francisco, a stamp-mill was obtained, with the Washoe silver-working apparatus. During the year

By J. Phillip Mackey

The Peter Hayes Symposium on Pyrometallurgy, held as part of Extraction 2018, is an acknowledgement of his contributions to the basic science and principles underpinning modern pyrometallurgical processing. After completing his PhD at Strathclyde University, Scotland, in 1974, Peter took up a teaching position at The University of Queensland, Brisbane, Queensland, Australia in 1976. Peter Hayes’ research at the University since then has been focussed on: • The mechanisms and kinetics of heterogeneous solid/solid, gas/solid and liquid/ solid reactions, and • Experimental measurement of phase equilibria in complex high temperature metallurgical systems. This paper provides a brief biography of Dr. Peter Hayes and gives a full listing of Peter Hayes’ publications.

By A. Mayton, A. Brien, W. Porter, O&apos

In 2004, management at Unimin's Gleason, TN operation began implementing ergonomic interventions specifically targeted to reduce risk of musculoskeletal injuries (MSIs). Together with corporate and site management, Unimin identified work site hazards and began to modify work practices/equipment. Some interventions were relatively simple and were implemented immediately. Others, like improvements to a mobile shredder, were more complex but were eventually resolved through a participatory approach with employees, management, manufacturers and NIOSH. This paper discusses ergonomic interventions that were successfully implemented using a bottom-up approach to reducing the risk of injury.

By Eckley B. Coxe

In making surveys in the anthracite coal regions of Pennsylvania, the ordinary engineer's chain (50 or 100 feet long) is generally used, both above and below ground. Sometimes, where it is difficult to chain, as, for instance, across a chasm, a wire is stretched from one station to the other, the distance is marked on the wire and its length is then measured with the ordinary chain. Having had occasion lately to make some surveys where it was necessary to determine with great accuracy the position of the land or property line, not

By G. Molinda, D. Dolinar

Each year, about 2,000 falls of supported roof occur in the more than 800 underground U.S. coal mines. Therefore to help improve the design of primary support systems, the National Institute for Occupational Safety and Health (NIOSH) conducted a nationwide study of roof falls in over 2,500 km of roadways at 37 coal mines. Information on the roof falls as well as other geotechnical, mining, geologic and roof bolting factors were collected and quantified Then a multi variate statistical analysis was conducted on the data with the roof fall rate being the outcome variable The results were used to derive preliminary design guidelines for predicting the roof bolt length, capacity, and pattern required to effectively reduce the roof fall rate. The equations are fairly limited by a relatively high statistical variance in the data. Also reported is a recent survey of U.S roof bolt manufacturers that shows a significant change in bolt types used over the last ten years.

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By Clara Godoy, Paulo Couceiro, Juan Navarro

The continuous automatization and digitalization of the different stages involved in any underground construction bring new possibilities to optimize the operation. One of the most important requirements for the development of these projects consist of a proper rock mass characterization for optimizing the stages of the drilling, blasting and support cycle. In the last few years the road to digitalization has gone through data science and big data, showing the importance of data gathered to describe the geological and geotechnical environment that surrounds the operations. Since rock characteristics have an important influence in the drilling response, the technological advances in the sensorization of drilling machinery such as the Measurement While Drilling system (MWD) allow to gather the necessary amount of information to be applied in data science processes to evaluate changes in the rock mass with higher resolution than conventional methods. In this paper, Machine Learning techniques have been used to combine data monitored from the drill rigwith scanner profiles of the excavated sections to develop an automatic geotechnical rock mass characterization model able to estimate potential zones of over- or under-break of the remaining rock mass in underground blasting. By comparison of scanner profiles of the excavated sections with the blasthole positions, an Excavated Mean Distance (EMD) between the contour blastholes and the excavated profile has been obtained, which may be considered as damage measure. Considering blasting factors as constant, the model combines the rotary, percussive, hydraulic flushing and the rate of advance of the drilling, and the confinement of the rock mass by depth, to detect zones with different rock properties. This provide an early information of the rock mass condition around the blastholes and the prediction of expected overbreak generated after blasting, being possible to design more efficient bastings, in which each borehole is filled with the right and necessary explosive charge. The analysis comprises data from 57 blasts (around 1700 contour blastholes) and more than 4000 excavated sections.

By John Henry Harden

IN 1874, with Mr. H. Y. Attrill, of Baltimore, Md., I made an examination of some property at Goderich with reference to sinking for and mining salt. With this end in view we visited all the wells in the neighborhood, but the information sought being of so unreliable a character I advised the putting down of a borehole on the property. This has since been done, the result of which has lately been published by Dr. T. Sterry Hunt in the Toronto Globe. From this there appears to have been passed through six beds of salt of an aggregate thickness of 125 feet. Rock-salt was known to exist, for, by the boring of existing wells, small crystals had been brought to the surface in the dirt, but no attempt had before been made to obtain a reliable sample or to prove the number and thickness of the beds. The question now remaining for discussion is, shall the present method of obtaining the salt be continued, or shall the beds be won by a shaft in a regular mining fashion, by which means the salt may be gotten in a condition almost ready for the market? The present mode of obtaining salt is by boreholes from 6 inches to 8 inches in diameter drilled to the beds, into which is inserted a pump. The "feeders" of fresh water intersected in drilling the well are allowed to descend on the outside of the pump-tube to the salt beds and there become saturated, when, on use of the pump, brine is obtained for evaporation. In the beginning brine can only be had in limited quantity, but by the daily application of the pump, and the gradual solution of the salt, a larger surface becomes exposed to the action of the fresh water, and a continuons supply of brine is obtained. It will then be understood that the supply of brine is dependent upon the feeders of fresh water intersected in boring the well, which, we are told, have never shown any sign of diminution, and this is the water that must be encountered in sinking a shaft. There are ten wells in operation at Goderich, the most important one to the present project being known as the Hawley Well, located at an elevation a few feet above Lake Huron at the mouth of the river Maitland, at, a much lower level and nearer to the proposed shaft than any other well in the district. At this well the feeders

By Persifor Frazer

I DESIRE to say that, owing to the number of papers which have been more or less crowded at this session of the Institute, and the fact that, as one of the Local Committee, I have the distinguished honor to feel somewhat like one of the hosts, I should not tax the patience of members at this late hour, but would have my paper read by title were it in any way possible to do this. But the task I have set myself this evening is to present to the eyes of the members of the Institute certain objects which have occupied more or less of my time during the last eighteen months or two years. The objects I allude to are some of the igneous rocks of this country, which, until quite recently, have been less understood than any others. It will be well known to some of the members that some of the cooled lavas of a previous age of our planet, when not directly coarsely crystalline and granular, were considered and spoken of as " natural glasses," or perfectly uncrystalline, vitreous, or hyaline masses of matter. Among the first results of the use of the microscope was the dispersion of this fallacy. Sir David Brewster, Mr. H. C. Sorby, and William Nichol (the discoverer of the celebrated calcite prism, which bears his name), had, with greater or less success, examined sections of various rocks and minerals, both by transmitted and reflected light, and also in the form of powder. But, until the genius of Vogelsang undertook the subject, these investigations had no permanent value, nor did they constitute an independent line of mineralogical and geological research. Since the close of his labors, by Vogelsang's premature and much-lamented death, the subject has been made one of renewed interest by his brother-in-law, Ferdinand Zirkel, as well as by Rosenbusch, Tschermak, and many others abroad, and at home by the commencement of a systematic study of the traps of Connecticut by Messrs. E. D. Dana and G. W. Hawes, of New Haven, and by the splendid set of described sections of the traps of the West which have been furnished by Zirkel to illustrate Clarence King's report. I had the honor of presenting a large number of thin sections of our traps at the Washington meeting, for the inspection of the members, with the aid of a table microscope belonging to the Smithsonian Institution. Here I propose to project these sections upon the

By B. W. Frazer

In the numbers of the Engineering and Mining Journal of June 27th and July llth, 1874, there appeared some very complete statistics of the working of some anthracite blast-furnaces belonging to a large establishment in this country, followed by calculations of the heat requirements of the furnaces, similar to those which have been made for European furnaces by Mr. I. Lowthian Bell, Prof. Gruner, Prof. Akerman and others. To the author of these valuable papers, Mr. John A. Church, of New York, the thanks of American iron metallurgists are due for this attempt (the first, to my knowledge at least), to attack systematically and scientifically the problem of economy of fuel in our anthracite blast-furnaces, by applying the formulas obtained from European practice and from the experiments of European metallurgists, to the determination of the amounts and the modes of distribution of the heat production and absorption in our furnaces. In order to facilitate a comparison of the results thus obtained for the anthracite furnaces in question with those obtained for the best types of European coke furnaces, I have reduced 60 the same standad of heat units (the product of the ton and the degree Centigrade), and placed side by side, the calculations of the heat requirements of one of the furnaces of the Clarence works, as given by Mr. Bell, of a furnace at Pouzin, on the banks of the Rhone, given by Prof. Gruner, and of the anthracite furnaces for 1869-73, as given by Mr. Church. Table I shows the different conditions of working of the three furnaces, of which Table II gives the respective heat requirements. I have made this latter table in such a manner as to give for each furnace its heat requirements, both according to the views of Mr. Bell and those of Prof. Gruner. Mr. Bell assumes that all the carbonic acid produced by the decomposition of the carbonate of lime of the charge, is reduced to carbonic oxide by contact with solid carbon ; also, that the carbon of t,he pig iron is a portion of that deposited in the ore in the upper part of the furnace, by the dissociation of carbonic oxide. Prof. Gruner, on the other hand, assumes that all the carbonic acid of the carbonates of the charge escapes unreduced, and that the carbon deposited in the upper part. of the furnace, by the dissociation of carbonic oxide, is again converted into carbonic oxide or

By T. B. Brooks

THE iron ores of the Marquette region are mostly extracted in open excavations; hence the process is more properly quarrying. Several attempts at underground work have been made, which have not, on the whole, been successful. The Edwards mine has been almost entirely wrought by candle-light. The slate ore pit, NO. 1, of the New England mine, is now worked in the same way, as is also the Pioneer furnace pit of the Jackson mine. The Champion mine was opened systematically for underground work, with two levels, 60 feet apart, and three shafts at distances apart along the bed of 200 feet; but this idea has been practically abandoned, the greater part of the ore in that mine being now taken out in open pits. Several other mines have occasionally worked underground stopes, but only temporarily; if such stopes could not be opened out to daylight, they have usually been abandoned. In brief, it may be said that no considerable amount of ore has as yet (1870) .been extracted underground in the region, and of that so mined very little has been taken out at a profit; and I may add that it seems to be the belief of the most experienced mining men that this state of things will hold for some time to come for reasons which will appear. Nearly the same remarks may be applied to the mines of the Iron Mountain region, Missouri, the ores of which are very similar in character to those of Marquette. Some of the New York and New Jersey magnetic deposits are wrought open, but this is the exception, underground mining there being the rule. The following brief sketch of the geological structure of the Marquette deposits will indicate some advantages of the method of mining employed. The iron-bearing (Huronian) series of rocks, are stratified beds, the principal ore formation being overlaid by a quartzite, and underlaid by a diorite, or greenstone. This ore formation is made up, first, of pure ore; second, of "mixed ore" (i. e., banded

By V. K. Banakar, R. P. Rajani, A. R. Chodankar

The Afanasiy-Nikitin Seamounts (ANS) in Eastern Equatorial Indian Ocean (Figure 1) are shown to be the exposed part of the presently buried 85°E Ridge system under the Bengal Fan sediment and were emplacement around 75-80 m.y. ago (Krishna, 2003). The first recovery of ferromanganese crusts from the ANS was made during 1994, and the samples (Figure 2) provided important clues on the evolution of this seamount (Banakar et al., 1997).

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By C. Kathryn Sole

The close proximity of cobalt and nickel on the Periodic Table and their frequent occurrence together in nature means that their separation in primary hydrometallurgical flowsheets is not only often necessary, but requires the use of innovative chemistry to achieve high selectivity. Today, increasingly stringent demands for the high-purity cobalt and nickel salts required for battery applications in consumer electronics, electric vehicles, and solar applications are again challenging the state of the art. The evolution of cobalt–nickel separations is traced from the basic precipitation technologies employed in 1960s, through commissioning of the first cobalt solvent-extraction plant in South Africa in 1974, to the commercialisation of organophosphinic-acid extractants (which provided a step-change improvement in selectivity) and their eventual widespread use in the 1980s and ’90s. This was followed later by their sulphur analogue, which enabled different possibilities for laterite processing in the new millennium. Separations in chloride media, which take advantage of the different speciation chemistries, and nickel extraction by oximes in ammoniacal systems are also discussed. More recently, chelating and solvent-impregnated resins have added further dimensions to the possibilities for flowsheet design and enabled higher purity products to be attained from both primary and secondary sources. Selected case studies and flowsheets are described.

By Christopher Mark

Australia and the United States both have large, modern underground coal mining industries. Many companies have invested in both countries, and there is growing awareness that technological developments in one country can rapidly affect the other. Yet the ability of technology to pass between the countries depends on comparability of ground conditions. Many Australian observers believe that their ground conditions are significantly poorer than typical U.S. conditions, but some U.S. professionals are not convinced. The author recently visited 10 Australian longwall mines and two room-and-pillar mines. Each mine visit included determination of the Coal Mine Roof Rating, roof support installed, pillar design, and an in-depth discussion of ground control experience. The Australian conditions observed are compared with an extensive data base from U.S. mines. The paper also offers observations on geotechnical data collection, monitoring, and the roles of the mine inspectorate and research community.

By G. C. Wallick, W. R. Foster, J. G. Savins

The theory of the differentiation method for the Couette flow experiment is reviewed. Particular attention is given to the requirements on data analyses in the case of the class of non-Newtonian materials described as viscoplastics, i.e., materials characterized by a yield point or yield stress. Here changes in boundary conditions arise when the shearing stress attains a critical value with the result that the form of the basic integral equation for Couette flow is determined by the flow conditions existing during the measurement. INTRODUCTION In the preceding papers in this series,l,2 the salient features of the differentiation method of rheological analysis in Poiseuille-type flow were discussed. It was shown that a dual differentiation-integration method analysis of the Poiseuille flow of idealized generalized Newtonian and visco-plastic models could be used to develop a spectrum of highly sensitive response patterns in terms of certain characteristic derivative functions. These functions were shown to optimize the selection of the most appropriate functional relationship between f(p) and p from the Poiseuille flow experiment. The present paper reviews the theory of the differentiation method as applied to the equally important Couette flow experiment. We will also discuss the range of variables over which the basic integral equation for Couette flow is applicable when the non-Newtonian material is of the viscoplastic type, i.e., characterized by a yield point or yield stress. THEORY Having described the application of the differentiation method to Poiseuille-type flow in the preceding papers, we now proceed to the case where the test liquid is confined to the annular space between coaxial cylinders of length L, one of which is in motion, i.e., Couette flow, formulating the basic integral equation after the method of Mooney.3 The observed kinematical and dynamical quantities are the angular velocity O and the torque T. Here, the one nonvanishing component of the shear-rate tensor is

By J. S. Rinehart, W. C. Maurer

The mechanics of impact crater formation in rock, particularly sandstone, has been sutdied, the velocity range being approximately that normally associated with oilwell gun perforators. The bullets were small steel spheres having diameters of 3/16, 9/32 and 7/16 in; impact velocities ranged from 300 to 7,000 ft/sec. The craters have two distinct parts — a cylindrical hole (or burrow) with a diameter the same as that of the impacting sphere, and a wide-angle cup comprising most of the volume of the crater. The burrow is fornred as material in front of the projectile is crushed and pushed aside, forming a cylindrical hole surrounded by a high-density zone. The clip forms as fractures are initiated in front of the projectile and propagate along logarithmic spirals, approximaling maximum shear trajectories, to the free surface of the rock. A most significant observation (made for the first time) was that, below the base of the cup in one type of sandstone, there are a group of similar fractures, not extending to the surface, which are spaced uniformly a few millimeters apart. Each fracture follows roughly the contour of the base of the cup and appears to require a certain threshold impulse to initiate it. These fractures comprise a relatively high fraction of the total, newly exposed surface area. The volume of the material removed by crushing varies as the first power of the impact velocity and the volume removed by fracturing, as the second power of the impact velocity. Penetration varies linearly with the impact velocity and is inversely proportional to the specific acoustic resistance of the target material, the proportionality constant being dependent upon the shape of the projectile. INTRODUCTION Yield of oil from a producing well is frequently enhanced by firing bullets and shaped charges through the well casing into the oil-bearing rock, forming craters and fractures from which oil can flow more readily. The purpose of this investigation has been to develop a better understanding of the mechanics of impact crater formation in rock, particularly sandstone, the velocity range being approximately that normally associated with oilwell gun perforators. FORCES OPERATIVE DURING IMPACT When a projectile moving at considerable velocity strikes a- massive target such as oil-bearing sandstone, intense and complex transient stress situations develop within both the projectile and the rock or sandstone against which it is striking. Usually the struck rock fails, the missile or projectile penetrating into the rock to some depth where it comes to rest or is forcibly ejected from its burrow by expansion of a plug of target material compressed in front of it. When the impact velocity is very high, the projectile itself may fail, breaking apart or becoming distorted; this situation is not considered here, the discussion being limited to nondeforming projectiles. Many experimental studies'.' have been carried out to determine the nature of the mechanics of crater formation and the salient features of the forces coming into play, some of the earliest studies being the French Army experiments performed at Metz between 1835 and 1845.' The stratagem in most instances has been to make a post-mortem examination of the crater, measuring volume and depth of penetration and deducing force relationships from these observations rather than performing the more difficult (usually almost impossible) feat of measuring stresses during penetration. In many materials, the force acting during penetration of the projectile is found to be the sum of two components—(1) a constant force, independent of the velocity, representing some inherent strength of the target material; and (2) a component, proportional to the square of the velocity, representing inertial forces. For such materials, the average force per unit area acting on the projectile at any instant while it is in motion and being decelerated may be written F/A = a + bv2 . . . (1) where v is the velocity of the projectile at that instant, A is the cross-sectional area of the penetrating projectile taken normal to its trajectory, and a and b are constants which are dependent upon the target material and the shape of the projectile. It follows that the total penetration s is given by .........(2) where v, is the velocity of the projectile when it just strikes the target. Values of a and b for spherical projectiles impacting in a loose sand-gravel mixture and compacted earth were obtained in the Metz experiments. For sand-gravel, a and b are 620 psi and 0.0115 (psi) (ft/sec)', respectively; and for compacted earthworks, a and b are 432 psi and 0.0008 (psi) (ft/sec)'. Figs 1 and 2