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By Gregory A. Hahn

Explorationists and engineers rarely speak the same language. Explorationists are not cognizant of the information that engineers require to make the appropriate choices and decisions. Engineers can- not "translate"geo1ogic parlance and data into information relevant to proper decision making. This often creates a physical and intellectual "rift" between engineers and geologists that inhibits a smooth transition to development. A transition team leader who is grounded in both disciplines can best facilitate integration and communications between the explorationists, who understand the intrinsic attributes of a given deposit, and the engineers, who have to design for extraction and beneficiation of an orebody.

Jan 1, 2001

By M. G. Hester, G. S. Adisoma

To address the problem of grade estimation in a general three-dimensional shape and the uncertainty associated with the estimate, the technique of jackknifing/ block-kriging shortcut is proposed. A new estimator called jackknife kriging is introduced first. Through the jackknife variance, a confidence limit for the reserve-grade estimate can be calculated. Unlike the kriging variance, which is more a measure of data configuration and which is independent of data values, the jackknife variance reflects the true variability of the data. This approach provides a simple way to set a confidence level for global estimation of resources.

Jan 1, 1997

By T. Bartnitzki, N. Fietz

"INTRODUCTION For a long time now automation has been state of the art in production engineering and chemical engineering. The advantages of automation are, for instance, higher reliabilities of production processes, higher product qualities as well as capacities and improved safety conditions for the personnel. In contrast, many operations in mining are still conducted manually by machine operators instead of autonomous control units. One example for this is the excavation of underground hard coal which is still executed with aid of human perception. The Institute for Mining and Metallurgical Machinery (IMR) has been working on possibilities for sensor-based automation of mining machinery for many years now. Thereto the focus is set on the implementation of common material analysis techniques into ruggedized conditions as a basis for automation. Laser-induced breakdown spectroscopy (LIBS) for instance is an atom emission technique which enables the determination of the elemental composition of a sample. After introducing LIBS this paper will give an overview on dust formation during the cutting process. With the illustration of a few examples the challenges in determining dust concentrations specifically such of cutting processes are explained in further detail. The final chapter will outlay the possibilities and challenges in utilizing cutting-induced dust for the automation of shearer loaders. LASER-INDUCED BREAKDOWN SPECTROSCOPY LIBS Fundamentals LIBS (laser-induced breakdown spectroscopy) is a contact-free method for analyzing materials in any state of aggregate. It pertains the atom emission techniques and is based on the generation of plasma, inducing avalanche ionization on the surface of a solid material or any spot in a gas or aqueous solution. With sufficient background information on the expected elements and an additional calibration, this method can determine all present elements not only qualitatively but also quantitatively. However, this method cannot be utilized for determining the molecular composition of materials – if this feature is required a complementary method such as Raman analysis needs to be added. (1, 2)"

Jan 1, 2015

By J. A. Herbst

Successful transitions from micro- to macro-engineering are the keys to effective technology transfer between research and development organizations and industrial end users. At the same time, it has proven to be one of the most difficult tasks that the minerals industry has had to manage. Typically, developers of fundamental information concerning how mineral processing subsystems work have been academics and government scientists. These are the individuals giving the most important input to micro-engineering models that can benefit industrial operations. Publication is the usual route for "attempting" to transfer this technology to the end users. Unfortunately, with such publications, very little direct communication occurs concerning real industry needs or the future steps required to make the particular micro-engineering model useful. In the past, the industry has relied on in-house R&D groups and plant metallurgists to "translate" publications, to provide useful macro-engineering tools for plant applications. To some extent, engineering companies have also been asked to serve this function. However, these firms have been rather ineffective in this area since their conservative nature has caused them to look rather suspiciously at new technology. This approach to technology transfer has worked, albeit clumsily, for the last several decades. This communication system is now on the verge of total collapse due to conditions of the minerals industry. Mining companies can no longer afford the significant overhead expenses of specialized technical staffs. Universities are finding it extremely difficult to interest US students in mineral engineering programs, and funding for such programs is weak. Faculty members involved in micro-engineering research today tend to focus on pure (non-application-oriented) research.

Jan 1, 1992

By Andy W. Stephens, William H. Langer

In Australia and America, encroachment by conflicting land uses, zoning restrictions, and the "not in my backyard" syndrome make it increasingly difficult to access high-quality aggregate resources located near the market areas. Attempts by government agencies in America to protect aggregate resources for future development have met with varying degrees of success. The State of Queensland, Australia, designates aggregate resource areas as Key Resource Areas, which protect the resource and the routes to transport the resource, provide a separation area from incompatible land uses, and indicate the likelihood that the area is free from conflicting social or environmental issues.

Jan 1, 2005

By Mayank Srivastava, Satya Harpalani

Production of methane is an inevitable consequence of mining coal. Although the number of mines practicing recovery of methane prior to, or during, coal mining is increasing, ventilation air methane (VAM) is still a significant source of methane addition in to atmosphere. Recent studies have shown that there are ways to recover the VAM energy, while simultaneously reducing the methane emission in to atmosphere. This paper discusses a case study, currently underway, to develop a technique to quantify the VAM emission from a mine. It also presents the different VAM utilization techniques and the suitability of one for the mine being studied. Finally, the paper summarizes the research issues that require further investigation.

Jan 1, 2005

By Anthony J. Ranalli, Florentino B. Maestas, Katherine Walton-Day, Richard W. Healy

Water movement and water chemistry were monitored in the unsaturated zone at two sites in fluvial tailings deposits along the Arkansas River near Leadville, Colorado. One of the sites was remediated by the incorporation of lime and biosolids into the soil. Preliminary results, based on data collected during the 11 months following remediation, indicate that differences between the two sites can largely be attributed to heterogeneity of the deposits. Remediation has increased the alkalinity in the upper soil zone, but as of yet, there is no indication that soils at depths greater than 30 cm have been affected.

Jan 1, 2000

By Roy E. Williams, Muriel S. Robinette

Ground-water contamination from uranium operations could be avoided with proper site analysis techniques. Contamination from tailings disposal sites is carried downgradient within permeable hydrostratigraphic units which can be located and delineated with a combination of drill holes and borehole geophysical logs. Engineering safeguards can be designed into a disposal site by determining if permeable hydrostratigraphic units exist which will dominate the flow system and provide seepage paths for contaminates. It is more cost-effective to accurately assess seepage potential with geophysical logs before contamination becomes a problem than to be faced with a major clean-up effort after contamination has occurred. If a uranium waste impoundment already has a ground-water contamination problem, then borehole geophysical logs may be used to delineate the contaminated zones which need to be cleaned up. It is less expensive to withdraw the contaminated plume from only within the affected zones rather than attempt to dewater the entire area. Consequently, the geophysical logs are invaluable in assessing which zones should be pumped and where packers should be set for construction of piezometers to allow monitoring of water-quality changes. A surface geophysical technique is being tested and developed for monitoring of seepage frum uranium tailings impoundments. Geoelectric soundings and profiles from direct current resistivity surveys can locate anomalous areas for the placement of drill holes to better assess seepage. This reconnaissance technique should eliminate random hit-or-miss drilling at sites where monitoring is required. Tests and experiments are being done on developing the capabilities of this technique to incorporate complex resistivity data to assess cultural impedence noise which complicates simple resistivity data.

Jan 1, 1980

By E. Koufetzis

Rock mass classification systems are core elements of tunneling and empirical mine design worldwide. The Bauxite division of S&B Industrial Minerals S.A. decided to implement a rock mass classification system in order to provide mining engineers and supervisors of the underground mines, with guidelines of stability performance and with a complementary tool for the selection of the appropriate tunnel support. The back analysis system employed is based on visual observation of especially selected underground mine sites, representative of all rock types. This fact combined with the failure or success of the already existing support system, constitute the fundamental part of the work undertaken. The paper is divided into three main parts. In the first part the classification methods of Q, RMR89 and GSI are presented and the advantages and disadvantages of each method in connection with underground mining are indicated. RMR89 and GSI are conclusively selected for use, the main criteria for the selection being, the simplicity in use and the competency of the support system suggested for each rock mass category. The second part points out the methodology for measurements, the practical difficulties encountered during this process and the guiding principles followed, in order to avoid these problems. In the third part, the final conclusion of this project is demonstrated and the different rock mass categories are presented with their relative support recommendations, as they were applied and tested in all phases of the bauxite mines? exploitation. The generated methodology is being implemented by the site mining engineers, for validation and potential improvement.

Jan 1, 2008

By ev, Ze&apos Reches

The growth of networks of shear fractures is explored in a series of experiments with samples of wet clay. The samples are subjected to plane strain deformation in a rigid apparatus. The individual fractures observed on the upper surface of the clay samples grow longer by three mechanisms: in-plane propagation, off-plane propagation and coalescence. New, active fractures cut and displace older, less active ones. The lengths of individual fractures display lognormal distribution in most cases and power distribution in fewer. The calculated length parameters in the experiments, as well as in three field cases discussed here, suggest that the fundamental parameters in fracture analysis are the normalized cumulative length and the length of the shortest fracture measured.

Jan 1, 1986

By Margaret Armstrong, Chris Roth

One advantage of kriging is that it provides both an estimate of the block or point grade, and an indication of the local precision via the kriging variance. If one assumes that the estimation errors are normally distributed, then confidence intervals for the grades can be calculated. But in mining, grades are rarely normally distributed; in general, they are skew. This is particularly true for precious metals. In this paper we study confidence intervals for variables with non-normal distributions. Using a non linear geostatistical technique, the grades are transformed into their normally distributed equivalents. Confidence intervals are obtained for these normal variables, and back transformed to give the corresponding confidence intervals for the grades, for either points or blocks. This approach is applied to gold data from the Witwatersrand basin in South Africa.

Jan 1, 1996

By Don U. Deere, Edward J. Cording

INTRODUCTION Observations during construction form an integral part of the design and construction of major underground works. Observations as used herein include visual inspection, detailed geologic mapping, and correlation of geology with support conditions, as well as instrumentation to provide more precise information regarding rock movements and support load. This paper describes the application of an observational program to one of the more difficult design and construction problems underground -- the excavation and support of large chambers at shallow depth in rock of variable quality. Emphasis on underground construction for subways and utilities in urban areas is bringing this problem to increased prominence. It is our intent to focus on the design and construction problems associated with such excavations and to describe observational methods which can be employed to aid in their construction. Observational programs may serve two purposes. One is to monitor the rock and support conditions in order to provide early warning of potential construction problems. Such a program should be routinely used in critical locations on major underground excavations of the type described in this paper. The program should be closely coordinated with the inspection effort and construction control. The other purpose is to provide detailed information regarding the interaction of support conditions and rock displacements to aid in development of more efficient design and construction procedures on later projects. For this purpose, instrumentation might be concentrated in special test sections where specific and typical

Jan 1, 1997

By D. E. Munson, T. M. Torres, D. A. Blankenship

The Thermal/Structural Interactions (TSI) In Situ Tests are a series of large scale, well instrumented tests that have been constructed at the Waste Isolation Pilot Plant (WIPP) in southeastern New Mexico. As a precursor to the TSI tests, a ventilation drift (Room D) was mined, drilled and instrumented. This room provided the contractor an excellent area to practice controlled construction methods and was a proving ground for construction monitoring and documentation methods. All gages in this first room have been monitored since their initial installation, which has provided a small, but representative, data base. These data also were the first to be available from any TSI area for analysis. This paper discusses the construction activities in Room D and the data generated from the construction and drilling. Deformation of the room is compared briefly to numerical calculations that used a rather simple creep model as a reference. The constitutive model for salt, it appears, must be improved before it can predict the underground deformations.

Jan 1, 1986

By Mario Eduardo Rossi

The Universal Kriging (UK) and the Ordinary Kriging (OK) systems of equations are variations of the well-known system of Normal Equations. They differ only by the number of constraints present in the system. The dual version of these sytems enables one to interpret kriging as the fitting, of an interpolation surface, whose components are a series of variogram functions plus a polynomial trend model. This trend model should account for any systematic decrease or increase of the variable over the study area. It is shown that modeling the trend is useful only when the locations being estimated are beyond the range of influence of neighboring data (extrapolation cases). A case study based on a public-domain coal data set is presented. The variable described (seam thickness) shows an actual trend of increasing data values towards the NW corner of the region considered. UK and OK are used to estimate coal thickness at locations within sample data range (interpolation cases). The UK algorithm that includes a model for the trend does not improve the estimation when compared to the simpler OK algorithm with no trend model. Thus, in interpolation situations, the simpler OK algorithm is recommended.

Jan 1, 1989

By F. Feichtinger, M. Riess, A. Lammer

Introduction This article discusses the unique range of properties of platinum and its applications as a high technology metal. World reserves of this strategic and precious metal are confined mostly to South Africa and, to a far lesser extent, the Soviet Union. An analysis is given of past trends in world platinum output. The timepath is computed for the world platinum output rate, covering a period of more than 350 years. This is based on the postulate that the industrial conversion of a virgin resource progresses according to a Sigmoid curve. This computation is performed by means of a nonlinear, three-stage optimization model employing a multiform Sigmoid function. Finally, the price dynamics are examined. Platinum is the most important of the group of the platinum metals to which it gives its name. Other platinum group metals are iridium, osmium, palladium, rhodium, and rhutenium. The metals occur in nature in close association and are chemically very similar to each other. Three members of the group - platinum, iridium, and osmium - are the heaviest metals known to man. Platinum's density is 11% heavier than gold and about twice the weight of the same volume of silver or lead. Properties Platinum is a typical grayish-white metal. Its special properties were known 1000 years ago to the American Indian craftsmen of what is now Ecuador and Colombia. From those distant beginnings, platinum is now firmly established as the most precious and distinctive metallic element known to mankind. It is shown in Table 1, platinum has a unique wide range of physical, chemical, and mechanical properties including high melting point, resistance to chemical attack, high catalytic activity, mechanical strength, and malleability. These properties make it indispensable for use in many industries. Application Platinum is first and foremost a high technology metal. During the last few decades, fertile scientific minds searched for and developed widespread cost-effective uses for this precious metal. Its unique properties render it irreplaceable in many key industrial processes. Important major fields of application include: • protection of man's natural environment (pollution control), • defense, • fuel production, • fertilizer manufacture, • glass and glass fiber manufacture, • pollution-free energy generation - replacement of nuclear and fuel operated power plants, • electronics, • dentistry, • medicine, and • jewelry. Besides these industrial markets, platinum is increasingly finding a place in investment portfolios around the world as investors switch from gold and silver holdings to this relatively scarce and strategic commodity. Platinum has a growing popularity among private investors. This is being accelerated by the predicted "big crash" of the US dollar and its associated weak currencies, which American financial analysts are expecting towards the end of the decade. Figure 1 shows the demand for platinum in various applications throughout the western world in 1986. The total demand amounted to 88.6 t (97.6 st) of which autocatalyst usage accounted for 32.8 t (36 st) or 37%, the biggest share. Catalytic converter technology is increasingly centered on rhodium-platinum three-way catalysts. These catalysts are able to deal with all three pollutants - carbon monoxide, hydrocarbons, and nitrogen oxides - in a single catalytic unit. The introduction of these three-way converters will result in a further steep rise in the platinum demand for autocatalysts. Among all the metals used in the antipollution devices for automobiles, platinum remains

Jan 2, 1988

By Lynn B. Hales, Randy A. Ynchausti

Introduction There continues to be a large economic opportunity associated with improving process performance through advanced process control systems within the minerals industry. The basis for this opportunity lies in the inherently low efficiencies of many of the unit operations found in mineral processing plants as well as the continual variation that is present in the ores being processed. The ageless target of such control systems is improved recoveries and concentrate grades, higher processing rates and lower unit costs. Many plants are enjoying the benefits of modem, well functioning process control systems but few if any have achieved plant-wide optimization in an economical sense. As new process modeling and control technologies, such as neural networks, continue to evolve and develop, the potential for plant- wide optimization is becoming a closer reality. Neural network technology appears to have a significant potential in the general field of process control and control of mineral processing operations. Neural networks are an emerging technology that have been evolving out of the study of biological systems since the early 1940's. The first software simulation of neural computing networks was reported in 1956 by Nathanial Rochester of IBM Research during the first conference on artificial intelligence which was sponsored by the Rockefeller Foundation. Neural Networks Neural networks can be considered to be a class of computer program that perform their problem solving functions based on a rudimentary model of the human brain and how it solves problems. Traditional computer programs and even computers themselves solve problems or process data sequentially and in a deterministic manner. The human brain, on the other hand, processes data and solves problems in a massively parallel fashion. We think of computers normally in terms of having a single processing unit, sometimes a co-processor to assist in certain activities such as mathematical functions or communications, bytes of memory, processing speed and program/data storage size.

Jan 1, 1992

By Don Fisher, Jean Juilland

Introduction A section of the Federal Land Policy and Management Act of 1976 specifies the procedure for areas the US Bureau of Land Management manages that have wilderness qualities. In part, FLPMA specifies that within 15 years of its approval, the Secretary of the Interior shall review roadless areas of 20 km2 (5,000 acres) or more and roadless islands of public lands identified during the inventory as having wilderness characteristics described in the Wilderness Act of 1964. Further, the Secretary shall report to the President his recommendation as to the suitability of each area or island for preservation as wilderness. However, before any recommendations for, wilderness designation, mineral surveys shall be conducted by the US Geological Survey and the US Bureau of Mines to determine if any mineral values are present. And finally, a Presidential recommendation for wilderness designation becomes effective only if so provided by an Act of Congress. BLM Inventory Procedures To fulfill these legal requirements, BLM is inventorying the land it manages for wilderness qualities. Since the law sets special provisions for Alaska, BLM included in its inventory only the public lands it manages in the conterminous US. In 1980, after public input, BLM picked 967 areas to be considered as Wilderness Study Areas. All of the selected WSAs are in 11 western states and the areas total about 97,128 km2 (24 million acres). From these 967 areas, through its multiple-use planning system, BLM is making initial recommendations of areas to be considered suitable for preservation as wilderness. Those WSAs that BLM initially considers suitable for wilderness preservation will have mineral surveys conducted by the USGS and the USBM, to determine mineral values. Based on these mineral surveys and other resources information including wilderness qualities, the Interior Secretary will report to the President his recommendations on the WSAs suitable for wilderness preservation. To make the initial recommendation of suitability, BLM managers will need information about geology, energy, and mineral (GEM) resources as well as information about other resources. BLM has begun a GEM assessment program to provide its managers with that information. This program is designed to provide information for a WSA suitability decision process that aims to supply minimum necessary GEM information. In essence, the program will provide preliminary assessment of the mineral potential for each WSA. Assessing the WSAs To accomplish this, a two-phase program was designed. In phase one, only existing data are collected and used. In phase two, new data are generated and added to existing data. Phase two begins only if BLM geologists, mining engineers, or managers consider the information provided in phase one as inadequate. This avoids unnecessary work and expenses and allows the program to proceed without undue delay. Figure 1 shows the two-phase process, including BLM's GEM in-

Jan 10, 1983

By Howard L. Hartman

Introduction The federal government's declining role in funding research has created a critical dollar gap for university departments of mining engineering. Industry, too, is affected by the drought. Research is lagging. Hardpressed universities are going to the private sector for funding. Mining companies should not shower universities with philanthropy, but a research partnership should be contracted on a pay-as-you-go basis. A model exists at The University of Alabama (albeit not in mining) that could be adopted by the mining industry. An equal partnership arrangement between a university and an industry for conducting research is proposed. The concept is not that a corporation sponsors and a university performs the research. Nor does it call for educational contributions or giveaways from industry. Rather, the corporation and the educational institution enter into a cooperative research endeavor, a full and equal partnership. Both parties contribute and both share the benefits. A key to the relationship is that it has a single objective: it must generate profits or reduce costs for the company. Working Model Recent literature is replete with examples of proposals for joint research endeavors, involving both contracts and grants, between industry and universities (Bronwell, 1971; Bugliarello, 1978; Branscomb, 1981; Sanford and Holland, 1982). They are all good proposals and offer something to both parties. They are, however, not widely supported. Few have received a favorable nod from the US mining industry. Though it may be logical, for example, to remake the American Mining Congress (or some new consortium) in the mold of umbrella-type industry organizations to fund cooperative research with mining institutions, such proposals have never flown. What model, then, will work? First, look for a model that has worked in industry in general. Second, seek to apply it to mining specifically. There is a model project that satisfies the first of those criteria. It is a project complicated by a third party, in addition to a corporation and a university. In January 1983, the "Factory of the Future Project" was initiated between The University of Alabama (UA) and General Motors Corp. (GM). The United Auto Workers (UAW) is a third party to the agreement. The factory was GM's Rochester Products Division manufacturing plant in Tuscaloosa, AL, also home of UA's main campus (Fig. 1). Saving a Plant The agreement came about at the initiative of GM and the UAW. Faced with having to close the plant because of excessive production costs, company and union officials proposed to the university that an applied research facility be established at the plant. The university would operate the laboratory, dedicated to $470,000 a year cost reductions for the company. The school would lease the 5.1 km2 (55,000 sq ft) space for $470,000 a year for three years. Any savings effected by the university's research effort would be credited toward to the rent. GM said the small factory, which made replacement carburetors

Jan 9, 1984

By Chris Groccia, Damodara R. Chinnasane

Vale is in the process of resuming mining in the lower 810 ore body (810 OB) below 4130L at Copper Cliff Mine – South Side. Production in the lower 810 OB had continued until it was temporarily ceased in 2017 to allow for the execution of activities associated with Copper Cliff Mine Phase 1 project. While mining the stopes in both the lower and mid part of the 810 OB, a seismic response was experienced that resulted in rockbursts and challenging mining conditions. The majority of the rockbursts experienced in the past were associated with stopes mined in a bottom-up mining sequence under a diminishing pillar situation between 3350L and 3540L. The current mining plan is comprised of both top-down and bottom-up mining fronts using a center-out chevron sequence of long hole open stopes to manage induced stresses. Numerical modeling assessments have been carried out to forecast the response of the rock mass due to the planned mining. Seismicity and stress induced damage surrounding excavations are anticipated, and areas requiring extra attention have been identified. A tactical approach is being used to prepare the area for production, including replacement of ground support elements that are damaged or have insufficient residual capacity, and installation of dynamic support in areas anticipated to experience bulking and/or dynamic loading that would exceed the current support system’s capacity. A series of monitoring programs are being put in place to confirm current conditions, and to monitor the response of the rock mass to proactively implement ground control tactics should the need arise. This paper provides a summary of the approach used to forecast, monitor, and manage the behavior of the 810 OB rock mass response to continued mining at depth.

Apr 26, 2022

By William J. Douglas

Defining Productivity Productivity is a principal concern to all organizations - industrial, commercial, government, and academic. As a ratio of output to input, productivity measures the efficiency of an industrial process, much as thermodynamic efficiency measures the useful work obtained from the available energy consumed. However, there is one important difference. Whereas thermodynamic efficiency is a dimensionless a ratio of energies, productivity output and input are usually measured in different physical units. Nevertheless, the resulting ratio is a normalized expression for unit of output per unit of input to the process. In the early days of coal, mining was essentially a hand loading operation. There was little expenditure of alternative forms of energy within the process. Loading required expenditures of human energy on the order of 1.2 MJ/t (1,000 Btu per st). And if we accept the conventional value "you load 16 tons," the output to input ratio is 14.5 t (16 st) per manshift. In energy terms, it is on the order of 116 MJ/t (100,000 Btu per st) produced per labor Btu expended. However, the latter measure of efficiency was not meaningful in economic terms, while the 14.5 t (16 st) per manshift was significant. Since labor was the principal component of cost, it represented a direct relationship to the cost of production: [ ] Furthermore, when workers were paid directly on the basis of tons produced, the labor cost per ton was specified directly by this rate. With the introduction of mechanized loading, significant increases in productivity occurred, when measured on the basis of tons per manshift. Electric power consumed about 11.6-116 MJ/t (10,000-100,000 Btu per st). This makes the 29-GJ/t (25 million Btu per st) coal output/input ratio between 100 and 1,000. That is one or two orders of magnitude lower than hand loading. However, electric energy was quite inexpensive compared to labor, which made the mechanization economically efficient. The accepted productivity measure continued to be tons per manshift. This measure includes some of the effects of mechanization: namely, the additional manpower needed to maintain the machines and support the equipment that uses electrical energy. However, it does not consider the capital and operating costs that relate to mechanized equipment. As a result, the concept of tons per machine-shift has emerged as an accepted measure of shift productivity. The only appropriate measure that encorporates the productivity of men and machines is an economic one. The output is the tonnage per shift and the impact is the cost per shift. [ ] This is simply the inverse of the cost per ton. In addition, much flexibility is available in allo¬cating costs to the three categories. This adds a level of intangibility to the measure. The amount of information needed to obtain all of the required costs is appreciable compared to the simple matter of counting tons and workers. Furthermore, financial information relating to production costs is closely held by mining companies, so historical statistics on economic productivity are not publicly available. To extend the concept further, consider the value of the tonnage produced, to obtain a dimensionless ($/$) measure of economic productivity.

Jan 11, 1983