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By J. B. Cheatham

An analysis of indexing is given for an idealized plastic rock. Indexing refers to chipping from a bit tooth to a previously formed crater. A method is indicated for computing the dependence of chip size and shape as well as force on the tooth for various tooth shapes as a function of crater configuration and distance to the previous crater. Pressure on the tooth is found to vary with depth of penetration after a critical depth has been reached. Damp sand model experiments indicate that simple solutions using linear and logarithmic spiral slip-line fields for Coulomb plastic materials give reasonable approximations to the failure patterns. Both idealized roller cone bits and fixed blade or drag bits are considered, and methods are presented for approximating the force on the bit and the chip volume when the rock is subjected to sufficiently high pressure to behave plastically. One of the primary objectives of drilling research investigations is to develop theoretical equations which can be used to predict the behavior of rock under drilling loading conditions. Since rocks usually fail in a brittle manner at atmospheric conditions, much current research is directed to studies of the brittle failure of rock under the action of drilling too1s. 1,2 The results of triaxial test on rocks indicate that both rock strength and ductility increase at high confining pressures.3 Recent results from single bit-tooth indentation experiments on dry rocks indicate that the transition from brittle to ductile failure under a bit tooth can occur at pressures sufficiently low to be of interest in oil well drilling.4 Single bit tooth experiments and analyses are not directly applicable to the drilling process since one of the important facets in drilling is the interaction between a bit-tooth and the previously formed crater. This interaction is referred to as indexing.' The purpose of the present paper is to indicate how plasticity theory can be applied to the analysis of indexing for plastic rock. Drag bit or fixed-blade drilling is considered and a discussion is given of the drilling action of an idealized roller cone bit. Results of simple experimental studies using a damp sand model are given as a method of visualizing the failure patterns in rocks under high confining pressures. These results are compared with plasticity theory using simple solutions based on linear and logarithmic spiral slip-lines. Discontinuous stress fields are proposed for drag bit drilling based upon the soil mechanics analysis of Shields. SINGLE BIT TOOTH RESULTS Single bit tooth indentation experiments using dry rocks under pressures from 0 to 5000 psi have indicated a correlation between the shape of a force-displacement curve and the nature of the rock failure beneath the tool.4 Continuous linear curves are in-

Jan 1, 1965

By J. Paone, S. Tandanand

This paper studies the behavior of rock at the initial state of crater formation resulting from stresses created under a drill bit. The purpose of this study is to determine which mechanical properties of rock are important in rock fragmentation by drilling. Although a definite relation between the drilling strength and relevant mechanical properties has not been established, maximum yield strength or hardness of rock is apparently a parameter of drillability of rock. The strengths of rock were considered from the Mohr-Coulomb criterion from which the surface of failure was constructed. The results from previous triaxial tests on Solenhofen limestone were adopted in establishing a limit of failure. Inelastic behavior of Solenhofen limestone was observed under a low velocity impact of a hemispherical bit and under static indentation with a similar bit. Permanent set at low applied loads in the indented area was measured with an interferometric technique. A quantitative determination of strengths of the rock was made under static indentation. The maximum yield strength estimated from the average stress over the contact area for plastic deformation was used as the crushing strength of rock under a drill bit. Much research has been done on energy requirements and mechanisms of energy dissipation to perfect rock fragmentation by a drilling process. But more needs to be done. More needs to be known about the mechanisms of energy dissipation or failure criteria of rocks in the drilling process in order to evaluate the efficiency of energy requirements in specific rock fragmentation. This paper examines some published studies on rock failure and energy dissipation and presents some findings in that phase of research concerned with rock fragmentation by drilling. This work is specifically concerned with rock behavior at an early stage of failure induced by a concentrated load. Consideration is limited to the primary phase of the crater formation under drill bit, i.e., before chipping takes place. Failure Phenomena of Rocks: Failure of rocks can be classified into two types, fracture and plastic flow. Both involve separation of material to form new surfaces with complete or partial loss of cohesion. Fracture is further classified as extension (or cleavage) fracture and shear fracture. Extension fracture involves separation in a plane without shear stress component, while shear fracture involves slippage along a plane as a result of combined stresses. Then, shear fracture inclines to the axes of the principal stresses. Plastic flow occurs under combined stresses, especially at high confining pressure and temperature, and denotes macroscopically irrecoverable deformation of rocks. Flow mechanisms have been classified as in-tergranular failure, intragranular gliding, and re-crystallization of mineral constituents.6 Failure phenomena in rocks are complicated because they include fractures and plastic flow as well as a friction process developed intrinsically as the internal stresses increase. All can occur in one rupture process, depending on the varying stress conditions. Both fracture and plastic flow are encountered in rock drilling. Rock failure under a drill bit as observed in drop tests simulating a single blow of a percussion drill, consists of two types, crushing and chipping. Crushing is considered as a separation of material particles by many fractures resulting from the application of high compressive stresses exceeding the strength of rock at the contact area. Chipping results from subsurface fractures extended to the face surface; this phase is preceded by crushing or surface deformation. The state of stress under the drill bit and the strength of rock create and control these two types of failure. The state of stress under the bit and in the vicinity of the contact area depend on the bit configuration and the magnitude of applied force. The strength of rock, characterized by its ability to resist penetration, depends on its composition and structure. However, the term "strength" quantitatively defined, is still ambiguous and may or may not correspond to the tensile, compressive and shear strength obtained from simple tests. Rock Failure Criterion: Rocks are weak in tension, their tensile strength being many times less than their compressive strength. This characteristic excludes

Jan 1, 1967

By Charles T. Holland, David A. Olsen

Considerable work has resulted in the development of a formula by which the strength of coal pillars for an L to T ratio of up to 12 may be estimated. One of the factors involved in this formula is the coefficient of friction between the coal pillar and the adjacent rock with which it is in contact. This paper presents the results of studies on sandstone, limestone, shale and coal and the coefficient of friction between coal and the other three under wet and dry conditions. With the coefficients of friction thus determined and the use of results obtained earlier by Meikle and Holland, it seems probable that coal pillar strength may be more closely estimated. Several investigators1-3 have found that the com-pressive strength of cubical coal specimens can be correlated by an equation such as

Jan 1, 1969

By B. Paul, C. C. Fu

Experiments indicate that the fatigue limit of various drill steels becomes vanishingly small in the presence of water and other corrosive liquids. Therefore one must generally expect fatigue failures of drill steels in a great many field operations. However, it is theoretically possible to so choose the hammer impact speed of a percussion drill in order to maximize the total length of hole drilled before failure occurs. In this paper the existence of an optimum speed is demonstrated and it is shown to be comparable to presently used piston speeds. The influence on drilling speed and hole length of a number of other pertinent design features, such as bit geometry, hammer geometry and steel properties is also established. Although machinery should be designed to obtain optimum performance, it is not always clear just what performance characteristic is to be optimized. For example in a rock drill it would be desirable to optimize all of the following characteristics: drilling speed, bit life, steel life, total length of hole drilled before failure, and efficiency of energy conversion. The word failure could signify excessive bit wear, bit fracture, steel fracture, or some other type of component failure. It is not possible in general to optimize all performance criteria simultaneously. For example, one could achieve fantastically large drilling rates at the expense of bit or steel life, energy requirements and physical size of system. It therefore becomes necessary to compromise requirements in order to achieve a well-balanced albeit non-optimum design. It is, however, extremely useful to explore the interrelationships between the different performance characteristics. Such a procedure would help to establish theoretical limits of performance within the framework of existing knowledge and also serve as a practical design procedure for special applications where a particular performance characteristic is of greatest concern to the user (e.g., steel breakage might be especially undesirable in certain locations). It is the purpose of this paper to examine the problem of how one may drill the deepest possible hole before breakage of the drill steel occurs. Of course the problem is almost trivial if a well defined fatigue limit (endurance limit) exists for the drill steel. In such cases one merely keeps the piston impact speed sufficiently low to insure that the stresses in the steel never exceed the fatigue limit, thereby achieving an infinite life. If, however, no definite fatigue limit exists, as seems to be the case in the presence of even mildly corrosive agents such as water (see later discussion), then a finite life is inescapable and one can at best hope to maximize the useful life of the system. Indeed it will be shown that the system life is related to drilling speed in the manner shown schematically in Fig. 1-a. Even if a definite fatigue

Jan 1, 1965

By F. A. Loving

This paper describes experiments which represent an effort to measure preciscly the pressure-time history in detonating condensed commercial explosives. The performance of explosives in mining has been a favorite subject for experimentalists and theorists for many decades. Much useful empirical information has been developed; but it has not yet been possible to predict, or even to account for, the behavior of explosives in mining on the basis of fundamental physical principals. A basic piece of information that would appear necessary for any rigorous analysis is the pressure-time history in the detonating condensed explosive. The experiments described here represent an effort to measure this relationship precisely in commercial explosives. THE EXPERIMENTAL METHOD The experimental method, first described by Cowan and Jacksonl has been extensively evaluated by Cowan and Balchan for relatively simple explosives. The experimental procedure involves the detonation of a layer of explosive between metal plates whose external surfaces are polished to a mirror finish (Fig. 1). Precise measurements of the deflection of

Jan 1, 1967

By Verne E. Hooker, Robert M. Becker

The evaluation of in-situ rock stresses from measurements of the change in diameter of a borehole that is stress-relieved by overcoring has become a common practice. Generally the stress evaluation has been based on isotropic relations whereas rock in varying degrees is aniso tropic. A plane elasticity solution fora circular hole along one axis of an orthotropic medium has been adapted to evaluation of in situ stress. The necessary elastic parameters for this evaluation may conveniently be obtained from static tests on the overcore in conjunction with a consistent orthotropic thick-wall cylinder solution. The method and equations for the laboratory and field evaluations are summarized and illustrated. The determination of in-situ rock stresses from boreholc deformation measurements has gained widespread acceptance. Hastl measured the change in diameter of a borehole that was stress-relieved by drilling a larger concentric core; this overcoring method has produced a major portion of the field data for recent stress evaluations in rock. These evaluations are based on the elastic properties of the rock, which are conveniently determined by testing the overcore.6-8 The stress evaluation and the overcore testing procedures generally assume isotropic relations whereas rock is anisotropic in varying degrees. Recently, an anisotropic plane stress solution was adapted for evaluation of in-situ stress9 and a related plane strain solution was developed for the testing of stress-relief core. 10 The present paper unifies the stress evaluation and overcore testing procedures for a general class of anisotropic rock. Equations are presented for calculating the state of stress in a plane normal to the borehole, and a consistent thick-wall cylinder solution is given for determining the necessary elastic properties. In addition, a complete example of stress evaluation from laboratory and field data is presented, and the order of error in computing the state of stress from isotropic relations is illustrated. Several limitations of the results should be emphasized. All results assume small linearly elastic deformations of a homogeneous medium. Rock characterized by orthotropic, transversely isotropic, and isotropic elasticity is considered; however, the anisotropic results assume a special relation among certain elastic constants in addition to geometric orientation with respect to a plane of elastic symmetry. For some stress determinations in rock, these may be severe limitations. On the other hand, the anisotropic evaluation procedure involves little additional effort and is much more flexible than the corresponding isotropic evaluation procedure. The collection of field data is identical. The laboratory determination of elastic parameters is no more difficult and time-consuming for the anisotropic than for the isotropic model. Only the calculations require some additional effort for the anisotropic evaluation, and this additional effort is eliminated by use of a small computer. The flexibility of the anisotropic procedure is greater because more than two independent elastic constants are available in fitting rock data. For the special relationship assumed among orthotropic constants, five independent elastic constants are available for the determination of in-situ secondary principal stresses as compared with two independent elastic constants for the isotropic model. Much of the material presented is either directly from the literature or adapted from the literature through superposition or the usual transformations. Consequently, only enough detail for clarity of presentation is included. RELATIONS FROM ANISOTROPIC ELASTICITY Materials that have three mutually orthogonal planes of elastic symmetry are called orthotropic. By directing the axes of the coordinates perpendicular to these planes, Hooke's law for an orthotropic solid 11 is

Jan 1, 1970

By Robert H. Merrill, David W. Wisecarver, Raymond M. Stateham

The US. Bureau of Mines, in cooperation with US. Borax and Chemical Corp. and Kennecott Copper Corp., has investigated the use of the microseismic method to evaluate the stability of large, open-pit slope walls. The method is based on the phenomenon that stressed rock normally emits subaudible rock noises, and the number of rock noises per unit time (noise rate) and the magnitude of the rock noises (amplitude) increase as the stresses in the rock approach the failure stress of the rock. Therefore, the detection and recording of those rock noises serve as a semiquantitative method of predicting the incipient failure of rock. This report briefly describes the three different types of micro-seismic apparatus, the procedures, and the results of microseismic investigations in the slope walls of the Boron mine near Boron, CaL, and the Kimbley, Liberty, and Tripp-Veteran open-pit mines near Ely, Nev. Microseismic monitoring within a frequency band of SO to 5000 Hz indicates noise rates in stable, inactive mining areas are between 0 and 10 noises per hour; the rates in stable, active mining areas are between 10 and 50 noises per hour; and the rate in unstable areas is as high as 2500 noises per hour. High microseismic noise rates in the Liberty pit correlate with the time of nearby earthquakes, indicating that the earthquakes affected the slope wall. The results provide evidence that the microseismic technique is applicable to large pit walls, and that the wide-band, wide-range microseismic equipment appears to be suitable for open-pit investigations. The microseismic method is based on the phenomenon that stressed rock normally emits subaudible rock noises, and the number of rock noises per unit time (noise rate) and the magnitude of the rock noises (amplitude) increase as the stresses in the rock approach the failure stress of the rock. Therefore, the detection and recording of those rock noises serve as a semiquantitative method of predicting the incipient failure of rock. The method has been used for many years to detect incipient failure in roofs or pillars in underground mines. In 1963 the U.S. Bureau of Mines (USBM) started an investigation of the microseismic method in large, open-pit slope walls. The purpose of this investigation was to evaluate the method in open-pit slopes where the rock may be fractured and broken and where the size of the rock mass under investigation is much larger than normally encountered underground. In addition, both the stresses in the rock and the strength of rock near pits are lower than usually found underground. Consequently, there was some doubt concerning the feasibility of the method for open pits, and the economics of such an investigation may have been prohibitive especially if large walls had to be monitored with closely spaced geophones. The successful application of the microseismic method to underground operations has improved safety at little, or no sacrifice, to production or extraction ratios. The anticipated reward in open-pit mining would be the improvement of safety with a minimum sacrifice to mining operations. There is also a possibility that the method could be used to optimize the unloading (stripping) of potential failure areas by the removal of intact rock from the slope wall rather than the cleanup of a slide from the bottom of the pit. This report contains a brief description of three types of microseismic apparatus used in four different pit walls, each of which is different in height, slope, rock types, or has different planes of weaknesses, such as faults, fractures, or joints. Because the geologic features of the pit walls are varied and complex, for brevity, this report dwells mostly on the microseismic apparatus, techniques, the rock noise rates, and the slope movements measured at the various sites. PROGRESS AND DEVELOPMENT The microseismic method was developed over 20 years ago; and the method and examples of investigations in underground mines are summarized by Obert and Duvall. 1 In more recent years, the method has been applied in several underground mines, and an in-situ test under controlled stress conditions is described by Morgan and Merrill. 2 Experience has shown that, on occasions, the microseismic noise rate and amplitude reach a peak value and then start to decrease before a failure occurs in an underground mine; on other occasions, the noise rate steadily increases to a maximum at failure. The method has been applied to slopes by Goodman and Blake,3 and by Paulsen. 4 Goodman and Blake found that the noises corresponded with failures in the slope

Jan 1, 1970

By William G. Pariseau, H. Douglas Dahl

Recent subsidence legislation indicates that mining engineers would be welt advised to be able to predict and control surface damage caused by mine subsidence. To date, such an ability is practically nonexistent. Model analysis is suggested as one of the alternative paths available which might yield fruitful results. Similitude requirements developed for a self-loaded body in static or quasi-static equilibrium indicate that complete similitude without centrifuging is an impracticability. However, a pilot experimental study which used a simplifying assumption to correctly model mine subsidence has produced results in qualitative agreement with field observations. The purpose of this paper is to present a discussion of the various approaches that can be taken in the study of mine subsidence phenomena. Particular attention is focused upon the rational selection and use of laboratory models. Broadly interpreted, mine subsidence is the deformation of the rock mass enclosing a mine. Depending upon a number of factors, the movement of the subsiding rock mass may disrupt gas and water lines or other buried utilities, damage surface structures such as buildings and bridges, dislocate streams, roads, and rail lines, aggravate acid mine drainage and fire problems, and generally mar the landscape. It is clearly a problem that no mine manager can safely ignore. It is also a problem that will grow with the general population increase. In the following discussion, a summary review of past and present approaches to subsidence studies is given. The possibilities of duplicating subsidence phenomena in laboratory models are examined, and an analysis of a particular type of model is presented. Some preliminary results obtained from a model of the particular type analyzed are then discussed. REVIEW OF PREVIOUS WORK Historically, subsidence investigations have been empirical studies in the field and laboratory or theoretical analyses of mathematically idealized media. Empirical and theoretical work in the United States has generally lagged behind investigations abroad. In the United States, field studies are mostly pre-World War 11. These are summarized in the Mining Engineer's Handbook. ' Field studies in Europe are more recent and more extensive. Those made in Great Britain are summarized in the Subsidence Engineers Handbook2 and represent observations made at 157 different collieries. Such studies by themselves are of limited usefulness as are all empirical studies. One can never be certain that conditions at one mine will be similar enough to those at another to warrant the drawing of like conclusions. European subsidence formulas rely heavily upon the "angle of draw" and "critical area" concepts. The angle of draw is defined as the angle between a vertical line through the face, and another line extending from the face to the surface at the point where movement is zero. The critical area is defined in relation to the least extraction necessary to produce maximum subsidence. Fig. 1 illustrates the angle of draw and critical area concepts. First and second "limits of influence" are also shown. The angle of draw and associated critical area concept are obviously not well defined, being dependent upon the accuracy of the surface survey. In Great Britain, the angle of draw has increased through the years from about 26 to 35°. In the United States, zero and negative angles of draw have been reported. In the authors' opinion, these purely geometrical concepts represent an oversimplification of subsidence phenomena and their use, in the United States at least, should be discouraged. Empirical observations of laboratory models containing layers of earth, sand, clay, and plaster were made by Fayol (cited by Peele) as early as 1885. An outgrowth of his work was the "dome theory," a verbal description of what is assumed to occur in subsiding rock masses. The dome theory has since fallen into disrepute. Theoretical analyses worthy of the name treat a subsiding rock mass as a deformable body. In these analyses, the actual rock mass is replaced by an idealized material that deforms according to a simple stress-strain relationship. The stress equations of equilibrium expressing the Newtonian laws of mechanical action and the geometry of strain furnish additional equations that must be satisfied. A loading criterion-generally understood, and in some cases stated explicitly-completes the theory.

Jan 1, 1969

By R. Agarwal, S. Boshkov, M. T. Wane

The majority of the work done in the field of rock mechanics uses as a basis for analysis the classical linear theory of elasticity. Most workers in rock mechanics realize that removing the assumptions of homogeneity and isotropicity will bring the analysis of stress-strain relationships for geologic materials closer to reality. However, the algebra involved in reducing these restrictions is usually heavy. It is the purpose of this paper to relax the condition of isotropicity to that of orthotropicity and examine the sensitivity of this change for some simple geometries. In addition some necessary relationships between stress and strain for orthotropic materials will be developed. The recent years have seen an increasing interest in the field of rock mechanics. This is amply demonstrated by the number of articles appearing in the technical literature. The majority of these articles use as a basis for analysis the classical linear theory of elasticity. In addition, the assumptions that the material under consideration is elastically homogeneous and isotropic reduce the number of constants necessary to write an analytical relationship between stress and strain to two, e.g., Young's modulus and Poisson's ratio. Most workers in the area of rock mechanics realize that removing the conditions of homogeneity and isotropicity will bring the analysis of stress-strain relationship for geologic materials closer to reality. However, the algebra involved in analysis without imposing these restrictions is usually heavy. It is the purpose of this paper to relax the condition of isotropicity to that of orthotropicity and examine the sensitivity of this change on stress concentration for some simple geometries. In addition, it is shown that the expression for maximum stress concentration for some simple geometries considered can be further simplified if further assumptions are made. The maximum stress concentration, under these additional simplifying assumptions, is shown graphical1y. In the linear theory of elasticity, generalized Hooke's law assumes the following form

Jan 1, 1965

By R. K. Agarwal

In this paper, a new technique developed to analyze two-dimensional nonhomogeneous models is described. A simple three-layered medium with a circular hole centrally located in the intermediate layer is considered. The layered sheet is loaded uniaxially perpendicular to the stratification. The Young's modulus of the intermediate layer is lower than that of the outer layers. The stress distribution around the circular hole in a stratified medium is significantly different when compared to the case of a continuous homogeneous medium. The distribution depends upon the ratio of the height of the intermediate layer and the hole diameter. A comparison of stress distribution and procedures for preparation and testing of the model are given. The potential of the technique is outlined. In the process of applying the techniques of stress analysis to problems of rock mechanics, the recent discernible trend has been to postulate highly idealized models of physical situations. As new techniques have been developed, more complicated models have been conceived to simulate mote accurately the physical environment to which the analysis results are eventually applied. In this investigation, a new technique is developed to analyze two-dimensional nonhomogeneous models. The technique is used to determine the stress concentration around a circular hole in a soft material overlain and underlain by a hard material. In mining practice, such situations arise commonly in coal deposits and frequently in bedded or vein-type metallic mineral deposits. DEFINITION OF THE PROBLEM A plate, consisting of three layers with a circular hole in the intermediate layer, is loaded uniaxially, Fig. 1. The variable in the experimental investigation is the height of the intermediate layer, H. The diameter of the hole, D, is kept constant. The stress concentration factors around the periphery of the hole, for various values of H/D, are evaluated using the technique of photoelasticity, Table I. TECHNIQUE OF EXPLORATION Photoelastic analyses of composite models have hitherto been limited to the study of lap and butt joints between glued metals and dissimilar materials.1-3 In mining, Haber and Oudenhoven used composite models to study the stress distribution around a circular hole in two-layered media and the behavior of elastic liners in shallow underground openings.4-5 They used the stress freezing technique devised by Dally et a1.6 The procedure used in this investigation is outlined below: Casting of Layer A: Flat sheets of plastic were cast in a silicon-coated mold using Araldite 502 with hardener 951 in the ratio of 100:8 by weight. After

Jan 1, 1969

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By Galen G. Waddell

Several years of rock-burst research conducted by the U.S. Bureau of Mines in cooperation with the mining companies of the Coeur d'Alene mining district, Idaho, in addition to progress made by others throughout the world, have led to a good understanding of the rock-burst problem. This paper describes conditions which have caused specific bursts, present capabilities of detecting stress buildup and bursts, control methods, and a suggested approach to analyzing any individual mine-burst problem. A rock burst is the sudden, violent release of stored strain energy in rock by some mechanism of rock failure, generally accompanied by expulsion of rock with consequent damage to the mine. A burst may be audible for only a few hundred feet, or on the surface it may sound like a sonic boom miles away. A Dictionary of Mining, Mineral, and Related Terms, U.S. Bureau of Mines (USBM)* 1968yand defines a burst as Bureau "That phenomenon which occurs when a volume of rock is strained beyond the elastic limit and the accompanying failure is of such a nature that accumulated energy

Jan 1, 1971

By Lawrence Adler

In-situ rock has well-recognized rupture and yielding responses. Attention is called to an intermediate response, granulation, which consists of an evenly distributed, small-scale crumbling accompanied by swelling. Granulation results in a negative slope for the inelastic portion of the stress-strain curve as successive interlocks are destroyed, and the load-carrying capacity of the material is reduced. Volumetric swelling with softening also takes place. The prerequisites for such a response are moderate confinement and a uniformly distributed defect pattern. Since rock masses, as well as rock as an intact material, have such patterns in their jointing and texture, respectively, granulation is characteristic of them. The presence of granulation can be demonstrated for a very wide scale, ranging from laboratory testing to regional geologic phenomena. The response of an engineered structure is considered in detail. Granulation appears to be dependent upon internal moments, the formation of which can be controlled by engineering design. The practical implications of such control can be significant in optimizing underground instability and in improving excavation techniques. Rock is usually considered to behave inelastically under high load, by fracturing as a brittle material, or by yielding as a ductile material, ignoring time dependency. These responses, which are characteristic of metallic behavior, appear idealized in Fig. 1, where linear-elasticity approximates the initial behavior. However, another major deformation mechanism peculiar to rock has long been recognized in geology, the granulation of an interlocked material. Granulation consists of a uniformly distributed fracturing and crumbling of the material, accompanied by swelling and softening. Predictably, the associated inelastic portion of the load-deformation curve has a negative slope,

Jan 1, 1971

By R. J. Lutton

Empirical data from 91 rock excavations have been used to construct a family of slope curves on a chart relating excavation height and inclination. The highest and steepest slopes from each excavation are plotted and connected by a line. The 31 1ines appear to establish one or two geometrical slope fields through which the curves are projected. The curves apparently represent a lumped eflect of many factors too complex to be considered individually. Important factors such as geological structure or ground-water conditions can dominate the picture, but where these factors do not overshadow others, the slope chart should be useful for estimating or checking optimum inclination. The U.S. Army Corps of Engineers (USAE) has been engaged since 1962 with the U.S. Atomic Energy Commission in a joint research program to develop nuclear excavation technology. The Corps is responsible for collecting the requisite data on engineering and construction problems associated with nuclear excavation. The ultimate objective is to develop a capability to use nuclear explosives as a construction tool on public works projects such as harbors and canals. The present study on empirical inclination-height curves for conventionally excavated slopes is an outgrowth of an investigation' sponsored by the USAE Nuclear Cratering Group on applicability of data from existing excavations in establishing guides for engineering judgment in crater excavation. Data were generously contributed by over 50 mining companies among other organizations. Inasmuch as several companies preferred that their contribution be anonymous, all data are treated so here. Some Factors Affecting Stability Many factors affect or are suspected of affecting the stability of excavated slopes, e.g., adverse structural orientation, degree of structural ordering, ground water, climatic conditions, mechanics of excavation, and plan-profile configuration. Such factors are lumped together in developing a slope chart. Obviously geological structure and ground water can overshadow all other factors. Where such is the case, the simplification of slope charts may give an erroneous picture (not conservative enough). A further complication results from the fact that the concept of stability may vary according to the use of the excavations. For example, slope adjustments that would be regarded as failure in a powerhouse excavation, might be tolerable in a mining operation. Mine slopes are continually being modified by further excavation, and instability that would develop in a similar permanent excavation slope over a period of years might not have time to develop in a mine. Inclination vs. Height Charts Charts of inclination vs. height for particular formations or conditions have been used in the past as an aid for designing excavation slopes. Some of these have been based upon empirical analyses of collections of data and experience. MacDonald" and Lane have presented slope tables and charts for excavated and natural slopes in relatively weak sandstone and shale. Coates' has shown an inclination-height chart for slopes in incompetent rock. Most organizations have developed slope design criteria which relate bench widths, heights, and inclinations to use in various rocks. Slope data collected in present studies can be similarly used to develop inclination-height charts; however, a plot of all slopes on such a chart shows very little because of the wide spread of the data. Reasons for the dispersion of points are: (1) many slopes are not carried at optimum inclination, particularly in mines where maintaining roadways and following irregularities of ore bodies are more important than achieving steep inclinations; (2) many engineers and geologists with varied backgrounds and viewpoints have been involved in designing these slopes; and (3) each slope is characterized by a unique combination of factors affecting stability and in turn optimum inclination. Significant curves can sometimes be constructed where the points can be grouped into related clusters from the same excavation. The essence of this approach appears when only two slopes from each excavation are considered—the highest slope and the steepest slope, connected by a line segment (Fig. 1). This reduces considerably the usable data because in many cases only one of these two slopes is available. Nevertheless, the concession seems justified. Construction of Slope Curves Ninety-one pairs of points and connecting line segments were assembled in this study. The line segments were assumed to approximate a geometrical slope field (Fig. 2), and a family of curves has been visually projected through to represent the slope field. It should be

Jan 1, 1971

By W. I. Duvall, D. E. Stephenson

A theoretical solution is given for the energy that is radiated outward when either a cylindrical or spherical cavity located underground in a uniform stress field is suddenly created or enlarged. The method of derivation shows that the stress field in the solid rock surrounding the opening does work on the rock because of elastic displacements that result when the size of the cavity is increased. The amount of this work is sufficient to account for both the increase in the strain energy in the rock surrounding the opening and the seismic energy that radiates outward. Thus, the source of the radiant seismic energy is mainly the gravitational potential energy and not the strain energy stored in the rock. The amount of the radiant seismic energy is directly proportional to the volume of the rock removed from the opening or relieved of stress. Seismic energies from rockbursts are compared with earthquake energies. Also, the amount of gravitational potential energy released by underground explosions is calculated and found to be small compared to the seismic energy generated by the detonation of the explosive. A review of the early literature on rockbursts shows that a number of investigators calculated the amount of energy released by rockbursts. 1-5 However, none of these papers give the formula used to make these calculations or a reference to the derivation of any formulas. The general impression that one obtains from these early papers is that the main source of the seismic energy released by rock-burst is the strain energy stored in the rock before it is fractured. However, a few of the early papers appear to have considered the solid rock at a distance from the mine opening as a possible source of the seismic energy. Recently Black and starfield7 gave a theoretical solution for the strain energy in a stressed plate with and without a circular hole. Also, Press and Archambeau8 gave the theoretical solution for the seismic energy released when a spherical cavity is created in rock subjected to a three-dimensional stress field. Both of the above theoretical papers start with the condition of no opening and calculate the strain energy before and after the opening is suddenly formed. Neither of these papers appear to have calculated the work done by the applied stress field as the cavity is enlarged. The rockburst problem associated with deep mining is concerned with the failure of the solid rock surrounding an underground opening. Therefore, it seems appropriate to consider theoretically the problem of suddenly enlarging the size of an existing opening. The purpose of this paper is to present the theoretical solution for the energy that is available for release as seismic energy when an underground circular tunnel or spherical cavity is suddenly enlarged in diameter. To keep the mathematics as simple as possible, a uniform radial applied stress field is assumed and the rock is assumed to be isotropic, homogeneous and perfectly elastic.

Jan 1, 1965

By F. W. Osterwald, C. R. Dunrud

A continuously recording seismic network was constructed in 1962 by the U.S. Geological Survey to locate epicenters and record incidence of bumps (bounces, rock bursts) that occur in the bituminous coal mines of the Book Cliffs coal field near Sunny-side, Utah. The coal is mined because of its value as coking coal, although these bumps may be a hazard to life and property. Daily records of tremors caused by bumps for 1 3/4 years indicate that a seasonal pattern, as well as a daily pattern, exists for the number of bumps that occur in a given period. Maxima occur in May and June and November and December. Marked increases at 5-day to 9-day intervals are superimposed on these seasonal maxima. The largest bumps commonly occur during seasonal maxima when the rate of occurrence suddenly decreases and the amplitude of the individual bumps increases. Knowledge of this pattern may lead to prediction of general locations and periods of increased hazard from bumps. Experience to date has shown that prediction of precise times and locations of hazardous bumps is not possible, and may never be; primarily because even a small bump can be a hazard to life and property. Some bumps or bump sequences are actually composites, consisting or two or more discrete bumps a few tenths of a second to a few seconds apart. Violent and spontaneous releases of coal and rock from faces, ribs and roofs of mines (termed bumps or bounces by miners) are a common hazard to life and property in the coal mines located in the Book Cliffs near Sunnyside, Utah (Fig. 1). These bumps

Jan 1, 1965

By L. N. Cosner, C. F. Austin, J. K. Pringle

Shock wave attenuation studies with three igneous rocks are reported: a spessartite elastic to low intensity stress waves, a diorite which is anelastic, and a porous scoria. The level of shock passing through a given thickness of rock has been determined by donor-receptor methods using high speed streak cameras. Test results include shock propagation velocities adjacent to the explosive, the dependence of test results upon test geometry, and the variation in shock wave attenuation in these three common igneous rock fabrics. The utilization of explosives in rock mediums involves a series of interrelated phenomena. These are the detonation process within the explosive, the transfer of energy from the explosion products to the surrounding rock medium in the form of sound or shock waves, and the transmission of the resulting waves through the rock medium to create damage in the rock mass. The subject of this paper is the investigation of the close-in phenomena that occur in the intensely shocked rock immediately adjacent to a detonating explosive charge. The specific aspects studied include propagation velocities, free surface velocities, pulse attenuations and the determination of the equations of state for the test rocks employed. In addition, a series of tests was conducted to indicate the dependence of the test results on the charge diameter utilized. The equations of state for rock materials have been investigated by a number of authors. Lombard, ',' Grine and Fowles,3,4 Zharkov, 5 Hughes and McQueen,6 Chabai,7,8 and Bass9 have published equation of state data on rock materials similar in structure or composition to those investigated in the study. Rinehart10 has prepared a voluminous tabulation of the available equation of state data from these publications and in addition has included data on many other rock and earth materials in his compilation. The reader is referred to the extensive tabulations and bibliography of Rinehart for classical studies involving the equations of state of metals and other solids and liquids. The problems of sympathetic detonation between drill holes in hard rock environments has received the attention of various authors as have the problems of explosive rock coupling close-in stress wave attenuation and explosive diameter effects. 11 to 18 In particular, the don or-receptor geometry of this report is very similar to the geometry of adjacent drill holes in rock. Most published pulse velocity and attenuation work in rock has been devoted to velocities at much lower amplitudes than those associated with close-in explosives phenomena and most attenuation studies involve transmission and attenuation across large spans of material. Excellent work in these areas has been published by the U. S. Bureau of Mines and by many individuals and groups engaged in geophysical research. SELECTION OF TEST MATERIALS A series of rock materials was desired for this test program that would be meaningful industrially, and that would also yield comparative results from a research viewpoint. Based on the availability of a series of related petro-fabrics, for which there is an abundance of physical and shock response data, three igneous rocks were selected as the test series. The applicability of shock wave studies in igneous rocks to industrial problems is readily demonstrated. Hardrock tunneling, quarrying and mining take place in igneous rocks throughout the world. From a research point of view, igneous rocks exhibit a wide variety of grain sizes and considerable diversity in composition, yet the common igneous rocks have a general similarity in their constituent mineral structures and in their grain-to-grain bonding mechanisms. The latter is based on the concept of rock formation through magma cooling and crystallization, though the degree of liquefaction in granitic plutonic masses is indeed a moot question. Three specific types of igneous rock were chosen for study. A coarse-grained granitic textured rock was desired that would serve as a representative of the widely abundant intrusive rocks of the world and

Jan 1, 1967

By Carl D. Broadbent

In 1956, Kennecott Copper Corp. instituted a slope mechanics program. Its objective was to obtain effi-ient and safe pit slopes. Since then, Kennecott has onducted a great deal of research into the area, most otably at the Kimbley Pit. This paper, which describes the transitional work at this period and draws from the pertinent experimental work done by others, paves the way for the next step of the program: refining the design process and applying it for profit. The goal of slope mechanics is to achieve efficient and safe pit slopes. In the case of ultimate mine slopes, the objective is to minimize the stripping ratio by steepening the slopes to their maximum stable limit. On the other hand, the inclination of working slopes is normally established by operating space requirements and the function of slope mechanics should be the continuous surveillance of slope conditions to assure long-term stability and provide timely warning of impending slides so that corrective measures may be incorporated in production planning. In 1956, Kennecott instituted a program to provide

Jan 1, 1970

By E. P. Pfleider, W. G. Pariseau

This paper reports the theoretical and experimental results of an analysis of ore pass drawdown as a problem in soil plasticity. The method of analysis developed appears to be a promising technique of investigating the mechanics of fragmented materials. A reconstructed plasticity theory brings experiment and theory into reasonable agreement, and hence may provide the foundation needed for rational ore pass design. The gravity-induced movement of broken rock through ore passes is an economical method of transporting fragmented materials through large vertical distances in underground mines, provided the ore pass is well designed. Unfortunately, the design procedures now followed do not very often result in ore passes that function properly. On the one hand, the huge accumulation of empirical data pertaining to the movement of materials in gravel bunkers, storage bins, deep grain silos and other structures that have features in common with ore passes remains uncorrelated. On the other hand, there is a dearth of experimental data substantiating theoretical models of material behavior. Consequently, reliable generalizations encompassing the broad spectrum of problems involved have not been forthcoming. AS an initial step towards improving the situation, a detailed case study of two-dimensional ore pass drawdown was made. The mechanics of the process were analyzed theoretically as a problem in soil plasticity and tested experimentally through observations of a laboratory ore pass model. THEORY Taylor1 defines a soil as a "mass commonly considered to consist of a network or skeleton of solid particles, enclosing voids of varying size." Broken rock in an ore pass is such a material. In plasticity theory this material is replaced by an idealized substance that deforms elastically up to some state of stress at which slip or yield occurs,2 For com-pressive states of stress, the Mohr-Coulomb criterion is a satisfactory yield condition. After the yield point is reached, the ideal soil deforms in accordance with the concept of plastic potential.4 Under plane strain conditions the governing equations separate into a system of stress equations and a system of velocity equations.' Only stress variables appear in the stress system. The velocity system, however, contains a stress variable. The two systems are, therefore, coupled. Both systems are hyperbolic, and each has two real, distinct families of characteristic curves that coincide according to the classical theory of ideal soil plasticity. The

Jan 1, 1969

By M. J. Coolbaugh

Mining potash at depths of 3000 ft or more beneath thick water-bearing sediments in Saskatchewan presented a unique challenge to the North American mining industry. Potash is known to flow under pressure, but the knowledge of its flow characteristics at great depths was inadequate for safe design of mine workings and for assured protection from water above the salt formations. At the 3000-ft. depth of the Canadian mines, the potash is stressed beyond its elastic limit, and therefore mining design must deal primarily with its behavior as a plastic material. Recognizing that careful study would be required in order to assure safety and stability of mine workings in deep potash, IMC initiated an extensive rock mechanics investigation of structural properties of potash and salt under high-stress conditions. This presentation consists of a brief review of the development of some methods of testing potash in the laboratory and in the field; some of the rock mechanics concepts and principles derived; and their application to potash mine design. The mining of potash more than 3000 ft beneath the water-bearing sediments in Saskatchewan presented the unique challenge of designing stable mine workings and assuring protection from overhead water in a material that was believed to flow plastically, but whose behavior as a plastic material was not sufficiently known. Under the stress conditions ordinarily encountered in mining, most rocks behave as elastic materials; that is, they compress slightly under pressure, and rebound when the pressure is released. Salt and potash, however, are different. Even under the relatively low pressures encountered at shallow depths, these materials become slightly plastic and yield to stress by flowing.* The plastic properties become more pronounced at greater depth and pressure, and the question arises as to whether or not the plastic flow will be rapid enough and exert enough pressure to destroy underground structures or interrupt the mining process. It was found, however, that not only was there an insufficiency of information about the behavior of potash and salt, but conventional methods of testing these materials, such as determining the modulus of elasticity, Poisson's ratio, and uniaxial compressive strength, were inapplicable because of the high stress conditions prevailing at the 3000-ft depth. Potash under high pressure, for example, has practically no modulus of elasticity, its stress-strain relationship varies with time, and its compressive strength depends upon the degree of confinement. Elasticity and Stress/Strain Relationship: Fig. 1 shows a standard stress/strain chart for potash as made by the Department of Mines in Canada. Typically, when stress is applied to a hard-rock specimen, the specimen contracts, then expands to its original shape when the stress is withdrawn. This chart illustrates, however, that potash under stress yields to the stress by flowing, and does not expand when the stress is withdrawn. When the applied stress was held constant for 30 min, beginning at points A and C, the strain continued to increase and the potash flowed to points B and D, respectively. Points B, D, F, and H show that the potash did not return to its original shape when the stress was released. Thus it can be observed that potash has practically no elasticity and that the amount of strain depends upon the length of time that the stress is applied. Compressive Strength: The conventional method of determining the compressive strength of hard material is to find the maximum pressure that long slender specimens of the material can withstand without failing. As illustrated in Fig. 2,* line B, a standard 2-in. cube of potash subjected to a conventional type of uniaxial compressive test will exhibit a strength of about 5000 psi. However, the compressive strength exhibited can be made to change by changing the conditions under which the test is made. For example, if teflon plates lubricated with graphite are inserted between the press and the specimen, thus minimizing end constraint, the compressive strength is only about 2500 psi, shown in line A. If a specimen is cut in half, changing the width-to-height ratio to 2 : 1 instead of 1:1, and then tested without lubri-

Jan 1, 1968