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The excavatability of the rock mass in a proposed open pit mine at Globe-Progress has been assessed. The rock mass was initially evaluated by determining variations in seismic velocity and by using the Revised Size-Strength Chart. These two assessments should be performed during the feasibility or early investigation stages of a project. A complete rock mass excavatability assessment using a suite of geological and geotechnical properties was then performed using three methods: RMR System; Modified Rippability Rating; and a productivity estimation method. These three methods should be applied during the investigation and design stages of a project. The preliminary assessments show that most of the open pit rock mass is expected to be rippable. The complete assessment differentiates weak, fair and good rock masses within the open pit. Weak rock mass exists along the Globe-Progress Shear zone, located along the northern and eastern pit walls and also in the western pit wall where the Chemist Shop Fault is located are both regions are expected to be diggable. Relatively weak rock mass also exists along the Globe-Progress Shear axial hinge. The Globe-Progress Shear limbs are generally fair to good rock where moderate to hard ripping should be expected.

Jan 1, 1996

By J. A. Espinosa-Guillen, J. A. Lopez-Molina, S. García, J. A. Valencia-Quintanar

"The design and implementation of grouting treatments in rock masses are procedures that require continuous adjustment of parameters and criteria to optimize the results. In this proposal we describe a set of tools that enhance decision-making for this type of jobs particularly in dam projects. The methodology is focused on hydrogeological zoning of the site and its constant update combining engineer’s experience with artificial intelligence techniques to integrate the site knowledge; as well as the evaluation of grouting results for different scrutiny scales, with special attention on the relationship between water absorption and grout consumption. INTRODUCTIONSeveral methodologies for design, implementation and evaluation for grouting rock masses have been developed for the solution of specific problems and tested in diverse geological conditions. Each of these methodologies is focused on results evaluation for different scrutiny scales (Table 1) and is employed to assist decision-making before or during the grouting process.Some methods define specifications for grouting each stage of the borehole, making theoretical, semi empirical or experience-based considerations to define basic parameters as maximum pressure, maximum volume, grouting time, flow rate, etc. Ultimately each approach aim to optimize the injection process, adjusting volumes or the grouting time required to obtain satisfactory results, reducing risk of creating new flow paths or unnecessary grout travels, and enhancing the mixture properties to achieve adequate penetrability and long-term behaviour. Some of these criteria have been widely used in dam projects, for example the concept of Grouting Based on Facts to define the maximum pressure and volume (Ewert, 1997), the GIN method (Lombardi & Deere, 1993; El Tani, 2012), or the North American standards based on Apparent Lugeon measures (Naudts, 1995; Bruce 2011); on the other hand, there are relatively new criteria that have shown good results for dam grouting as the Aperture Control Method (Bonin et al., 2012; Carter et al., 2012) or the Real Time Grouting Control Method (Stille et al., 2012)."

Jan 1, 2015

By Anne Charline Sauvage

Blast designers and blasters need to know the rock mass influence on blast to increase explosive effi-ciency and to optimize costs, but also to succeed in limiting blast emissions (vibration, overpressure, flyrock) This paper presents an applied approach which makes it possible to structure the information con-cerning the rock mass and the blasting.

Jan 1, 2013

By M. du Plessis, G. More O’Ferrall, A. Hartzenberg

"Lonmin Platinum has experienced several cases of large-scale hangingwall instabilities during the extraction of the Upper Group 2 Chromitite Layer (UG2) at a number of the Marikana operations along the Western Limb of the Bushveld Complex. These instabilities were all attributed to the presence and interaction of prominent geological features and highlighted that assumptions made in the design of the stable pillars and stable span were potentially overly simplistic in these areas. Investigations into the various case studies over the past ten years have resulted in the identification and classification of the rock mass characteristics of the geological structures causing the instabilities.In order to get a better understanding of these instabilities, it is important to understand the structural geology in general, and the sequence of events that led to the formation of the Bushveld Complex in particular. The tectonics involved in the formation of the various layers around the economic mineralized layers has been investigated, and the influence of these tectonic events on the stability of the UG2 stopes hypothesized.Following this investigation, the behaviour of the various layers in the hangingwall of the UG2 is better understood. This paper presents a description of the ground conditions being experienced in the underground stoping environment, the possible source of the associated structures and the resultant behavioural mechanism of these structures causing the rock mass instabilities."

Jan 1, 2015

By Ludger Suarez-Burgoa

At the Porce III Underground Powerhouse Complex in Colombia, the observational method (Peck, 1969), was used to provide information to an underground wedge and a 2D Finite Element Method numerical models, both used to estimate the mechanical behavior of the hoisting rock mass. The observation process consisted in collecting fault events in the field and in interpreting Multiple Point Borehole Extensometers and Surface Convergence Displacement Points readings. The calibrated models were employed to predict the behavior of the pillars formed between the machine and transformer caverns. The observational method is an important activity during excavation of large openings and provides arguments to understand the rock mass mechanical behavior.

Jan 1, 2008

By Levent Ozdemir, Charles Merguerian

Between 1996 and 1999, a high-performance Robbins TBM [235-282] excavated a 5 mile long, 23´2? wide, and ~700´ deep tunnel through the subsurface of southwestern Queens. Low penetration rates (~6´/hr [actual] vs. ~9´/hr [anticipated])resulted from changed rock mass conditions mostly attributable to high-grade metamorphism of the rocks. Over a three-year period, as-built circumferential geologic mapping (scale 1?=10´) and digital imagery of the tunnel, fracture and fault analysis, structural, lithologic, and petrographic studies have shown that the rocks of the Queens Tunnel consist of orthogneiss of mesocratic, leucocratic, and mafic composition. These metaigneous rocks developed coarse-grained fabrics during Grenvillian (~1.0 Ga) granulite facies metamorphism, and retained their nearly anhydrous, poorly foliated character during subsequent high-grade Ordoviciande formation. Lacking a penetrative foliation, the coarse granoblastic rock texture and extraordinary garnet content (up to 50% in some zones) together proved animpediment to efficient chip production and resulted in bimodal production of blocks and excessive fines. TBM excavation of the Queens Tunnel was also hindered by geological conditions that included unexpected lithology and rock fabric orientation, a zone of crosscutting hypabyssal rhyodacite dikes, and unanticipated extent of brittle faults. The dikes and brittle faults produced blocky ground conditions and a collapsing face condition that produced cutter damage and decreased utilization. Such fundamental textural, mineralogic, and lithologic control over hard-rock TBM penetration can be predicted by careful pre-bid geological analysis. To determine the causes of lower than anticipated TBM performance, a detailed investigation was carried out that included analysis of operational data from the TBM data logger and an extensive laboratory test program on cores retrieved from tunnel walls. Integrated laboratory testing included punch, point load, tensile strength, Cerchar abrasivity, and linear cutting tests, independent petrographic analysis and machine performance analysis. These allied investigations have provided quantification that the rock mass exhibited an unusually high degree of toughness and rock directional properties and established geological causes for decreased TBM penetration rates.

Jan 1, 2003

By T. D. Rourke, Fred H. Kulhawy, O&apos

From mid-1976 to early 1978, a 5.64 m diameter tunnel, 2491 m long, was excavated by a modified Robbins full-face TBM under shallow cover in highly stressed sedimentary rock in Rochester, NY. In-situ stress measurements were made, and tunnel behavior was monitored with MPBXs, inclinometers, tape extensometers, and instrumented steel ribs. Detailed geologic mapping was also done. In this paper, the as-monitored tunnel behavior is described, and the TBM performance is evaluated from field records. Recommendations are also made for future tunneling in similar geologic environments.

Jan 1, 1981

By Emmanuel Henry

The Kiruna Mine, operated by Luossavaara-Kiirunavaara AB (LKAB), is a large-scale sublevel caving operation located in Arctic Sweden. Iron ore is extracted at a rate of 60 000 tpd from a four-kilometre long, 80-100 m thick and 60-degree dipping orebody. Actual production depth is 800 m under the top of the footwall and about 550 m under the average regional ground level. Because no support is left between the footwall and the hanging wall and despite the relatively low mining depth, extraction results in the formation of a huge stress shield modifying the original stress field and concentrating it just beneath the mining level. Effects of stress concentration on the rock mass are monitored through field observations and a seismic system. Severe stress-induced deterioration of openings is visible to a certain radial distance from the mining level: pillar crushing and fault slips are more and more common and extended. The seismic system, installed in collaboration with CANMET, confirms the field observations and completes them in the rock mass: fault slips and major seismic events are recorded. The system proves its effectiveness to outline the extension of the dynamic response of the rock mass, which actually seems much larger than field observations let think.

May 1, 2001

By Donald W. Gentry, John F. Abel

This paper presents some of the results of a rock mechanics instrumentation program designed for, and implemented at, longwall panel 4N at the York Canyon Mine near Raton, New Mexico. The objective of this particular instrumentation program was to determine the response of the rock mass to longwall mining of a thick coal seam utilizing shield-type supports. Measurements were made in the rock along the ground surface, above the coal seam, in the coal seam, and immediately below the coal seam. Longwall test panel 4N had a total developed length of 762 m (2500 ft) and a face width of 168 m (550 ft), Fig. 1. The seam mining height in the panel area was approximately 3 m (10 ft). The average depth of overburden above the panel is 107 m (350 ft) although it ranges from 73-134 m (240-440 ft). Roof support at the face was provided by 116 Hemscheidt 320 HSL shields. These shield-type supports weigh 11.4 metric tons each.

Jan 3, 1978

By Donald W. Gentry

This paper presents some of the results of a rock mechanics in¬strumentation program designed for, and implemented at, longwall panel 4N at the York Canyon Mine near Raton, New Mexico. The objective of this particular instrumentation program was to determine the response of the rock mass to longwall mining of a thick coal seam utilizing shield-type supports. Measurements were made in the rock along the ground surface, above the coal seam, in the coal seam and immediately below the coal seam. Longwall test panel 411 had a total developed length of 762 m (2500 ft) and a face width of 168 m (550 ft). The seam mining height in the panel area was approximately 3 m (10 ft). The average depth of overburden above the panel is 107 m (350 ft) al¬though it ranges from 73-134 m (240 - 440 ft). Roof support at the face was provided by Hemscheidt shields. These shield-type supports weigh 11.4 metric tons each.

Jan 1, 1977

By Donald W. Gentry, John F. Abel

This paper presents some of the results of a rock mechanics instrumentation program designed for, and implemented at. longwall panel 4N at the York Canyon Mine near Raton, New Mexico. The objective of this particular instrumentation program was to determine the response of the rock mass to longwall mining of a thick coal seam utilizing shield-type supports. Measurements were made in the rock along the ground surface, above the coal seam, in the coal seam, and immediately below the coal seam. Longwall test panel 4N had a total developed length of 762 m (2500 ft) and a face width of 168 m (550 ft), [Fig. 1]. The seam mining height in the panel area was approximately 3 m (10 ft). The average depth of overburden above the panel is 107 m (350 ft) although it ranges from 73-134 m (240-440 ft). Roof support at the face was provided by 116 Hemscheidt 320 HSL shields. These shield-type supports weigh 11.4 metric tons each.

Jan 1, 1979

By Michael L. Cramer, Kunsoo Kim

INTRODUCTION The Columbia River Basalt beneath the Hanford Site is one of several rock types being considered by the U.S. Department of Energy for the first commercial high-level nuclear waste repository. The Basalt Waste Isolation Project (BWIP) has been carrying out a comprehensive investigation to assess the feasibility of constructing a repository in basalt and to develop technology required for repository engineering and site characterization. Development of a nuclear waste repository requires a number of design considerations not usually necessary in the planning of conventional underground structures. Principal among these is the thermally induced stress field resulting from waste emplacement. This thermal stress, super- imposed on the preexisting in situ- and excavation- induced stress fields, needs to be evaluated in the design process due to the sensitivity of waste emplacement density to this factor. The nature of this thermally induced stress field is dependent on several factors, including the temperature distribution around the repository openings, the thermal properties of the rock mass, and the deformability of the rock mass. Re1iable performance of the repository structure is largely determined by the ability to under- stand the above rock mass characteristics and predict the underground opening response to waste emplacement based on this understanding. To gain an understanding of this rock mass behavior in a repository condition, the BWIP has conducted a large-scale heated block test in basalt at the Near-Surf ace Test Facility (NSTF) on the Hanford Site. This paper presents the results from the elevated temperature phase of the block test in which the thermal, mechanical, and thermo- mechanical response of the closely jointed basalt rock mass was evaluated as a function of stress and loading orientation at varying temperatures up to 200 oC. SITE GEOLOGY The NSTF test areas, including the block test site, are located in the entablature zone of the Pomona basalt f low. The Pomona flow entablature is structurally typical of most flows in the Columbia River Basalt Group in that it is characterized by long, undulating, polygonal columns up to 2.4 m in length. Columns vary from 15 to 30 cm in diameter, averaging about 20 cm. Over their length, columns can vary in dip by 150 to 200. The column structures are dissected by subhorizontal cross joints that are generally discontinuous and seldom cross columnar joint boundaries. Spacing of the cross joints also averages about 20 cm. A representative joint pattern taken from mapping of the tunnel wall near the block test site is shown in figure 1. Application of the Rock Mass Rating System (Bieniawski, l979) to the block test site yielded an overall value of 62. The corresponding value from application of the Q-system (Barton et al., 1974) is 8.7 (Cramer and Kim,1985). The NSTF is approximately 50 m below the surf ace. However, this depth is sti1l above the water table and conditions are generally dry. Interstitial water exists as the result of percolation of meteoric water from the surface.

Jan 1, 1986

By W. I. Duvall, L. D. Sadwin

Three explosives with different detonation characteristics were tested by studying their cratering ability in a granite-gneiss. The strain wave generating characteristics of these explosives were also studied in the same rock medium. Correlations between the relative performance of three explosives as evaluated by crater studies and other methods of evaluation are indicated. Numerous test methods have been employed to evaluate the output performance of explosives; for example, the underwater explosion method, the airblast method and the ballistic pendulum method.'*' For blasting applications, the study of explosion produced craters and explosion generated strain waves are the most meaningful. This laboratory has employed these techniques extensively for many years and has shown that the detonation properties of explosives and their ability to generate strain waves in rock are related and that the amplitude and shape of the strain wave is related to some of the crater parameters such as slab thickness and fly rock velocity.3'11 However, a good comparison between the relative performance of explosives as determined by the crater and strain wave methods had not been made. The purpose of this investigation was to determine if the relative performance of three explosives as determined by the crater method shows a correlation with the relative performance as determined by the strain wave method. If a good correlation exists between these two sets of relative performance, it should then be possible to relate the detonation properties of an explosive to its ability to break rock in a crater test. In most commercial blasting operations, the diameter of the blast hole remains constant even though the type of explosive may change. In general, it is the explosive volume rather than the weight which remains constant when two or more explosives of different density are compared. Therefore all tests in this investigation were conducted on a constant volume basis rather than on a constant weight basis. TEST SITE AND ROCK PROPERTIES The tests described in this paper were conducted at a granite quarry owned and operated by the Consolidated Quarries Div. of the Georgia Marble Co. at Lithonia, Ga. The tests were performed in an area where the exposed rock surface was nearly horizontal and where the general rock mass had few joints or faults. The rock has an apparent sp gr of 2.6 and a longitudinal propagation velocity of 18,000 fps. The characteristic impedance of Lithonia granite gneiss is 53(lb - sec/in3). EXPERIMENTAL PROCEDURE There are many parameters which must be considered in the study of explosion-produced craters. The role played by each variable in the explosive-rock-crater system can be determined by experimental techniques in which one parameter is varied while others are maintained constant. In this investigation, the crater geometry was studied as the depth was varied for each of three explosives. The explosive volume and rock-type were held constant for all crater tests. The experimental arrangement used in performing the crater tests is illustrated schematically in Fig. 1.

Jan 1, 1965

By D. L. Sikarskie, B. Paul

A theory is presented for the static penetration of a single rigid wedge into brittle material. The material considered is one which exhibits both crushing and chipping phases in the penetration process. If the wedge angle and three parameters are specified, the theory predicts forces and associated penetrations during both the crushing and chipping phases. For certain ranges of the parameters agreement with the limited experimental data available is promising, except for the initial phase of the penetration process where refinements on the proposed theory are required. The theory also predicts that for certain values of the wedge angle and other known parameters, the chipping process does not occur and penetration is due entirely to crushing. When viewed in detail, the drilling of rock by percussive means involves, among other things, system dynamics, actuating forces, dynamic stress levels and the actual penetration mechanism of the bit into rock. If rock drills are to be significantly improved, a thorough understanding of the entire system would be highly desirable. In this paper, one aspect of the system, namely the mechanism of penetration of the bit, will be studied in detail. It has been found1 that for the velocities encountered in percussive drilling (of the order of 20 fps) a static analysis adequately describes the penetration process, at least for some rocks. Hence, we will only be concerned with describing analytically the static penetration of a single wedge shaped tool. It will further be assumed that the wedge is long enough to permit a two-dimensional analysis. Numerous authors have studied the static penetration of a wedge into rock. The following papers give some of this work and provide additional references to other work. Cheatham2,3 has assumed the rock to behave plastically and has obtained force-penetration equations for both Coulomb-Mohr and parabolic yield criteria. Evans and Murrell4 have studied the penetration of two types of coal and have found equations relating the penetration characteristic (P/dSc) to wedge angle for the various strength coals tested. race' attempted to find a correlation between hardness as determined by indenting the material and other mechanical properties and concluded that the results of such a test are generally inconclusive. His paper however contains a very extensive bibliography on the indenting of many different materials. Gnirk6 also has a fairly complete literature review on the static penetration of rock, of which he makes use in his indexing studies. A wide range of behavior is found in the wedge penetration of different rocks under different external conditions. For example, a rock that is essentially elastic-brittle at standard pressure may become elastic-plastic at a high confining pressure.7 It has also been observed4. " that some rocks will merely be crushed and indented by a wedge, whereas others will crack and form chips, furthermore the existence or non-existence of chips depends in great measure on the geometry of the indentor, type of rock and the depth of penetration. Hence, to attempt a theory which embraces all possible behavior is not practical at present. We, therefore, confine our attention to predicting the force-penetration characteristic and volume removal behavior for a type of rock which exhibits both crushing and chipping phases in the penetration process. Such behavior is characteristic of the harder rocks such as granites and represents a more difficult problem than the behavior of softer rocks such as coal and certain sandstones. In this preliminary study an attempt will be made to describe only the essential features of this complex penetration process. A qualitative description of these essential features is obtained with the aid of Fig. 1.1, where a wedge of vertex angle 28 is shown at some intermediate stage of the penetration process. As the wedge advances, the rock is fragmented (i.e. crushed) in some local region surrounding the wedge, the shape of this region being unknown. Simultaneous with the fragmentation in this local region, essentially elastic stresses are assumed to be building up in the surrounding rock. When a certain penetration level, di+1, is reached, the stresses along some surface are sufficient to cause failure and a chip is thus formed. The process now repeats, i.e., a crushing phase followed by the formation of a chip.

Jan 1, 1965

By J. J. Scott

This investigation utilizes three dimensional photo-elastic techniques to determine the stress distributions in the pillars and the roof of a room and pillar mine model. Castolite plastic was used for the construction of the model in which a stress pattern was developed by the stress freezing process. Analysis of the stress pattern was accomplished by observation of points in slices from the model with a polariscope and solving the data thus obtained by the shear-difference method. Slices through the centerline, edge of pillar and centerline of span were investigated. The results of this work provide information on the overall stress distribution in points of stress concentration in compression, shear and tension, show relative magnitude of stress throughout the model and indicate directions of the most important stress values. A generalized roof bolt pattern is developed for room and pillar mines based on the stress distribution. A digital computer was used in the reduction of data and proved to be extremely useful for investigation of this type. Underground excavations disturb the equilibrium of the earth's crust and a core of fracture, or altered stress distributions exists around the openings. This fact is well known by mining operators and investigators in the rock mechanics field. Analysis of the stress distribution in the areas around mine workings is a most difficult problem and one which has no simple and direct solution. Some of the approaches used by investigators in attempts to study stress distribution around mine openings involve mathematical analysis, photoelastic techniques, statistical analysis, model studies on brittle materials and observation of fracture patterns. Models involving imbedded strain gauges, gelatin models using imbedded strings to show internal movement, and many other unique laboratory techniques are employed. Work is also being done in mining operations where load cells, strain gauges, photostress material, convergence plugs, dynamic plugs, etc., are used to measure strain which can in turn be used to obtain stress. Some of these devices measure strain from which stress may be derived. All approaches to the solution of stress distribution are hampered by the fact that the earth is not a homogeneous, isotropic and elastic media. Geologic faults, fractures, bedding planes, vugs, variations in material composition, variations in grain size and structure, etc., make it extremely difficult to obtain results which can be universally applied to mining operations. The purpose of this investigation will be to demonstrate the use of three-dimensional photoelastic techniques to obtain the stress distribution in the pillars and roof of a room and pillar mining operation. This method utilizes full analysis of interior points, and thus it may be that small tensile or shear stresses found in the investigation will prove to be of greater significance than the more obvious points of stress concentration found by two-dimensional techniques. A digital computer was employed to simplify and to shorten the time necessary to obtain final results. Application of the computer to problems of this type may enable future investigators to attempt more elaborate analyses than have been previously considered feasible. THEORY Three Dimensional Stress Analysis-Shear Difference Solution:' Photoelastic studies are based on the fact that an optically isotropic transparent solid becomes optically anisotropic when subjected to forced deformation; the degree of optical anisotropy being proportional to the deformation of the material. There are two fundamental laws which govern photoelasticity: 1) Light is polarized in the directions of the principal stress axes, and is transmitted only on planes of principal stress. 2) The difference in principal stresses is proportional to the difference in the indices of refraction along the planes of principal stress. One method used in three-dimensional photoelastic work is to examine a slice of the object by normal incidence and oblique incidence. In normal incidence,

Jan 1, 1964

By S. H. Penn

Preliminary experimental evidence seems to preclude the use of unlubricated mechanical force drills on the moon. Measured values of the coefficients of friction and adhesion between metallic and nonmetal-lic solids have been shown to increase in an ultra-high vacuum environment. The paucity of real knowledge of the influence of a hard lunar vacuum upon interacting solid surfaces, relegates current proposals to sample the moon with a mechanical force drill, to the equivalent of wildcatting on earth. Within a few years, drilling will be attempted on the lunar surface with tools that have been designed with parameters that are normally considered for most conventional terrestrial drills. Lunar drills must be light in weight, portable, have reasonable penetration rates, low manpower requirements, etc. Although the initial equipment cost is expected to be high, this will probably not be a critical factor. Early lunar drilling will be limited to shallow holes with depths of 10 ft or less. The primary function of these holes will be to furnish samples of lunar surface materials but they may also be utilized for other purposes, such as geophysical experiments. Instruments may be installed in them capable of measuring thermal diffusivity, gamma radiation, etc. As sampling will be the primary objective of the earliest holes, sample contamination is a parameter that effectively excludes such otherwise promising techniques as explosive or plasma jet drilling. The most desirable method is probably some form of mechanical force drilling that has the capability of operating in the extreme lunar thermal environment (125° to 37S°K), high vacuum (10- l3 torr range), and low gravity.

Jan 1, 1968

By M. M. Singh, J. W. Brown

Three rocks of highly varied physical properties are selected for the first reported experimental study concerning microseismic activity of rock under tension to determine the effects of static fatigue, loading rate, repeated loading and rock anistropy compared to compression and bending loads. The microseismic method of detecting rock under deformation may be a great potential tool in surveillance and location in situ of dangerously stressed strata, as well as predicting rock failures. Noises emitted under load or the rate of energy (energy of noise pulses generated per unit time) are computed for varying conditions. The tests are conducted at constant load on a dead weight loading machine to eliminate all possible extraneous noises — an indispensable precaution — at various load levels. Experimental results are reported including the relation of total energy emitted to tensile strength of rock and the possibility of simulating a phenomenological model for microseismic activity. Plots of some of the experiments are included. INTRODUCTION Rock failure, whether on a large scale faulting in the earth's crust and rock bursts in mines, or on small scale ruptures of laboratory test specimens, generates transient vibrations in the rock mass. Mechanisms of intermittent deformation, such as twinning and cracking through and between mineral grains, also produce similar vibrations, but of very small amplitude. Such vibrations from both deformation and failure are referred to as microseismic activity, rock noise, or occasionally seismo-acoustical activity. An individual rock noise is sometimes

Jan 1, 1967

By Tuncel M. Yegulalp, Malcolm T. Wane

In general, many problems relating to the exploitation of mineral deposits are probabilistic in nature. This derives from the fact that the geologic universe is inherently random. Probability theory and statistics have been found useful for forecasting the behavior of natural events that occur in the geologic universe. The objective of this paper is to illustrate the application of the theory of extremes to this fore-casting problem. For example, it is customary for design purposes to determine the rupture strength of geologic materials. The theory of extremes is exceedingly useful in describing that portion of the frequency distribution of rupture strength which contains the least strengths. Parameters describing the distribution of the least strengths are more important to the designer of mining excavations than parameters describing the total distribution. The basic principles of the theory of extremes will be detailed and illustrated. Any person required to work in the laboratory of nature is aware that uncertainty is a salient feature of all mining enterprises. A mining engineer required to plan the most efficient, practicable, profitable, and safe mine finds himself face to face with numerous ill-understood and often unquantifiable states of nature. Basic information necessary for adequate planning is often lacking or derived from incomplete tests on samples or experience of doubtful validity. The planning procedure usually takes the form of determining a feasible layout with the intent of determining an optimal layout when and if the necessary details and information become available. The crux of the entire procedure is the choosing of numbers to put into the operational and structural models which encompass the plan. Many times these numbers must be assigned qualitatively from past experiences and are called the "most probable ones." At other times, load records, performance records and material tests provide a basis for extrapolation. In any event, the numbers are chosen from a distribution or set of all numbers. Since each number in the distribution represents a possible state, the choice of any particular value is based upon a decision rule. To illustrate, consider the design of an underground structure or the design of a rock slope. The initial step is the formulation of the various possible structural actions which result from the geometry of the layout. For a given structural model various intensities of behavior are possible depending upon the load, deformation, and material characteristic spec-trums, respectively. Of particular interest to mining people is the failure behavior or condition, i.e., when there is a complete collapse of structural resistance by either structural instability or fracture. A necessary feature of the analysis is the "rupture strength" of the material. Information on the rupture strength is derived from testing either in situ or in the laboratory and the usual outcome is a variation in the test results. The methodology used to overcome this variation is to construct a frequency distribution of rupture strengths, and then determine a measure of central tendency and variability. The main idea involved is that the central tendency number will be used in the failure calculations and the measure of dispersion will be used to estimate the probability of failure. In particular if the distribution of rupture strength is normal, the mean rupture strength is the central tendency number and the standard deviation of the rupture strength is the measure of variability. Suppose the mean value of rupture strength is 1000 psi and the standard deviation is 200 psi. Insertion of 1000 psi into the failure calculation produces results that are unsafe, hence a common decision rule is to reduce the mean value by a "factor of ignorance" so that the failure calculation will produce a "safe result." If two is chosen as a factor of ignorance, this means the value inserted in the calculation is 500 psi or 2.5 times the standard deviation. The next step is to determine the percentage chance that failure will occur from a design created on this basis. Tables on the normal distribution function show that this percentage chance is 0.621% or approximately 7 times out of 1000. In practice, however, the situation is more complicated than represented by the foregoing illustration. The laboratory or field testing program usually constitutes a pathetically small sample of the geologic universe of interest and not enough testing is carried out to determine the exact form of the distribution of the test results. The normal, Cauchy and Student's T distributions are strikingly similar, and it becomes a matter of mathematical convenience to assume the normal law for phenomena which follow other laws.

Jan 1, 1969

By R. T. Keyes, R. B. Clay, L. L. Udy, V. O. Cook, M. A. Cook

Based on compressibility and stress wave velocity in rock, initial explosive loading conditions, the thermochemistry of the explosive and reasonable description of the pressure-distance relations behind the shock front, the distribution of energy between the products of detonation and the burden are estimated as a function of time for various loading conditions. These include 'powder factor', loading density A (fraction of borehole occupied by explosive), and the explosive itself. Factors responsible for rock fragmentation are discussed in terms of: 1) 'release wave fracturing', 2) 'shear wave fracturing', and 3) 'release of loading fracturing' or 'rock bursting'. Release wave fracturing appears to occur only in the immediate vicinity of free faces, and shear wave fracturing only adjacent to the borehole under normal blasting conditions. Rock bursting is thus considered to be the most important means of rock fracturing in blasting. Means for maximizing it are considered. The most important factors to consider include maximum available energy A, explosive density p1, loading density A and 'powder factor'. Maximum efficiency is attained in general by maximizing the A . p1 product. This is achieved by using high density explosives at a loading density of unity (A = 1.0). Ways for achieving this condition are discussed. The bulk-handled aluminized slurry blasting agents have the desired properties for achieving optimum conditions for high blasting efficiency based on the theory outlined herein. Factors considered most important in the blasting of rock are: 1) The maximum available energy A, determined by the heat of explosion Q and the mechanical efficiency ?, a factor intimately associated with the mode of application (A = Q at highest gas concentrations). 2) The 'borehole pressure', pb, or the maximum pressure developed in the borehole after passage of the detonation wave and before the burden has had time to move or become compressed appreciably. (Owing to the short duration of the detonation wave at any particular point in the borehole, the fact that the explosive may not always fill the borehole completely and the further fact that the burden may not actually see the detonation pressure, the borehole pressure is considered more significant than the detonation pressure p2 as a performance factor in borehole blasting.) The borehole pressure is determined by the explosion or adiabatic pressure, p3 , and the loading density, A, or the fraction of the borehole filled by explosive. 3) The physical conditions important in the application of the explosive are: a) The 'powder factor,' (We/Wr), or the ratio of the wt of the explosive to that of the rock being blasted expressed as lb per ton or more generally in lb/cu yd. b) The bulk density, p1 ?. c) The 'burden' or 'line of least resistance,' the spacing between boreholes, the geometry of the borehole pattern and sequence of firing. d) The physical and chemical properties of the rock, most significant of which are possible heterogeneties, such as faulting, prefracture, and greater than micro-scale chemical heterogeneities. (This factor is not considered here but deserves a great deal of careful consideration.) All of these factors need to be carefully considered in the most economical engineering of a blast. Here is considered firstly an outline of the present status of dynamic rock mechanics, particularly as it pertains to blasting. The factors pertaining to the most efficient application of blasting agents are also considered, followed by a discussion of methods of application to achieve optimum explosives performance. ROCK MECHANICS Dynamic rock mechanics is currently a rapidly developing science contributing greatly to a better understanding and consequently the more effective application of explosives in blasting of rock.1-22 Basic to the development of the science of dynamic rock mechanics were the advances of Goransen23 and the Los Alamos and NOL groups24-28 concerning rock and stress wave phenomena and the transmission and reflection characteristics of stress waves at interfaces between different media. Basing considerations on this new knowledge as well as new experimental methods of study (ultra-high speed streak and framing cameras and electronic timers) the theory of fracture and failure of solids under impulsive loading by stress waves developed rapidly.14,16,27-29 Also the

Jan 1, 1967

By L. D. Clark, S. S. Saluja

A physical law, governing the rupture of rock by confined explosive charge correspondent to current expressions for determining weight of charge to rupture rock burden, W, was developed in the form Q = cVw3 by two early investigators performing unique experiments with ice. The coefficient C, is found by trial blast. Recent physical tests conducted with rock, synthetic materials and ice to establish the validity of the theory on which it and other related formulae are based indicated: (a) that failure under hydrodynamic impact pressure is by tension rather than shear as was assumed; (b) that the fundamental law of mechanics, enabling the determination of Q = cvw3, modified to the form P = R x Sa x Wb is valid when low velocity explosives are used; (c) that rock breakage under the action of low velocity explosives is entirely due to explosion gas pressure, as was believed; (d) that under the action of high velocity explosive it is due to the joint effects of scabbing and gas pressure; and that further possible modification could make the above equation also applicable to these joint mechanisms. shape could be easily frozen and because large loads would not be required. They found: (a) that the not unfamiliar shearing equation for metals was applicable to ice where P = load in lb; S = periphery of pressure surface, in.; W = burden, in.; K = modulus of rupture by shear in lb per in.2; and (b) that "the form of cavity produced by the application of gradual pressure is similar to that obtained by blasting in rock under similar conditions of free face and pressure surface!" This similarity in crater shapes leads to the conclusion that rock would rupture by shear, as did ice, and its behavior under the force of a blast could be governed by such a relationship as P = S x W x K. Three important interrelated empirical expressions were derived and rock, charging and spacing coefficients C,, C, and e were established and substantiated by trial blasts. In checking the accuracy of the main assumptions, duplication of the ice tests, substituting rock, suggested that K is not constant and that P = K x W x S, though valid for ice, does not necessarily hold for homogeneous limestone.' Conclusions from this later work raised questions making continued investigation desirable because such conclusions do not destroy the practical value of the empirical equations or theory. Further study for the establishment of the relationship between load, burden and periphery of the pressure surface and possible application of these to the mechanism of rock blasting was undertaken by the authors of this paper. MECHANICAL TESTING - EXPERIMENTAL PROCEDURE Certain inconsistencies in the results of the aforementioned tests repeated on three types of limestone suggested these inconsistencies be attributed to rock inhomogeneity. It was also suspected that the loading speed, which could not be held uniform, may have contributed. The earlier work with both rock and ice

Jan 1, 1964