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By S. D. Thompson

Since 1965 several researchers have independently developed computer models for designing gathering belt and surge bin capacities in underground coal mine belt systems. Table 1 summarizes the models applicable to U.S. mining systems. Most of the models, employ the Monte Carlo simulation technique. Basically, the belt loading at each loading point is randomly produced from probability distributions. In some cases, a combination of deterministic calculations and probability distributions are used to simulate the loading. Once the loading is simulated, it is systematically moved through the belt system in a deterministic fashion based on belt speeds, belt lengths, and storage bin discharge rates. The coal flowing from each loading point is tracked as it moves through the belt system. When the loading from tm different sources combines on a belt or in a surge bin, checks are made to determine if capacities have been exceeded. If capacities have been exceeded the amount of spillage is calculated. At the end of the simulated time period, the cumulative spill- age is used to evaluate the belt and surge bin capacities. Naturally, a considerable amount of spillage indicates the capacities are unacceptable. Acceptable capacities are generally indicated by minimal spillage. Numerous trial simulations are often necessary to find the acceptable capacities.

Jan 1, 1987

By A. Bieg, M. Samson, Z. Bell, A. Zinsser, J. Schuyler

As the world progresses toward the renewable energy transition, the demand for minerals increases exponentially. According to the International Energy Agency (IEA) 2021 Net Zero by 2050 Report, critical mineral production needs to grow six times to combat climate change. It’s estimated that four to seven percent of global greenhouse gas (GHG) emissions come from the mining sector’s Scope 1 and 2 (direct and indirect) emissions. Including Scope 3 (upstream, downstream, and embedded) emissions, the sector accounts for 28% of global GHG emissions. In a typical mining operation, diesel fuel is the biggest source of direct GHG emissions, and haulage is often the main source of diesel emissions. Large haul trucks have been the industry standard for over 50 years and offer flexibility, relatively low capital cost (especially with equipment lease options), and guaranteed technology with known maintenance. The challenge will be to justify their continued use when there are more economical options that lead to significant reductions in GHG emissions. The purpose of this study is to compare five haulage options in terms of GHG emissions, using the methodology defined by the Greenhouse Gas Protocol Scopes 1, 2, and 3 (Category 2). Additionally, this analysis compares operating and capital costs associated with the five haulage options (emerging and proven technologies): 1) Diesel-Electric Haul Trucks, 2) Battery-Electric Haul Trucks, 3) Fuel Cell Haul Trucks, 4) Railveyor, and 5) Conveyor. This analysis looks at the emissions and costs associated with operating the equipment (fuel and electricity), the embedded emissions and costs associated with the construction and installation of the equipment itself, and the associated infrastructure (roads, powerlines, and rail).

Feb 1, 2023

By Subhas G. Malghan

Feldspathic deposits occur widely throughout the United States, but North Carolina, California, Connecticut and South Carolina accounted for over 80% of the total domestic feldspar output for the year 1973.1 Pegmatites and granites constitute the major feldspar reserves of the United States,2 and in addition, feldspar is produced as a by-product by firms whose major products are spodumene and mica.3 Feldspar is concentrated by hand-cobbing and flotation; the latter forms the major method of separating and concentrating feldspar. Feldspar flotation is practiced in the United States, Mexico, Finland, Norway, West Germany, Japan and the USSR. According to the U. S. Bureau of Mines estimates, the production of feldspar in the United States and rest of the world were 704,000 tons and 2,514,000 tons respectively. Feldspar is principally used as a flux in making glass, pottery, porcelain, enamel,-tile and other ceramic products. In recent years, the domestic feldspar industry is faced with a number of problems. As a result of increased cost of energy and the introduction in 1972 of new legislative programs relating to air, water, and noise pollution, land-use restrictions, and mined-land rehabilitation, the production costs have increased. Apart from the increased cost of operation, an operational problem exists with the feldspar producers in North Carolina, especially those in the Spruce Pine area. This problem is concerned with the use of hydrofluoric acid in the feldspar flotation. Feldspar producers in Spruce Pine, North Carolina have been discharging process waste water into the North Toe River. The mill waste water contains active fluoride ions. Fluoride in excessive concentrations is undesirable in waters used for drinking. It is stated that water

Jan 1, 1976

By G. Wang

With the depletion of easy-to-treat phosphate resources, low quality phosphate ores with high carbonates, particularly dolomite impurities have to be mined to meet the agricultural demand because of the continued growth of world population. The separation of dolomite from phosphate has been recognized as one of the most difficult subjects in mineral processing due to the similarities in their physical and chemical properties. Flotation is considered the most important approach for beneficiating both easy-to-treat and high impurity phosphate resources. There is no doubt that the development of reagents is the key for achieving satisfactory separation performance through flotation process. In order to separate dolomite from phosphate, Arr-Maz Custom Chemicals has made great efforts in developing flotation reagents for removal of carbonates from phosphate ores of different origins worldwide. This paper describes some flotation reagents and processes for the separation of dolomite or/and calcite impurities from phosphate in the ores from different locations.

Jan 1, 2010

By Shannon Seitz, Qingwen Shi, Junfeng Pan, Shuwen Wang, Brijes Mishra, Shaohong Liu

Delayed coal bursts in deep coal mines have caused significant fatalities and economic losses in recent years. Instead of occurring right around the advancing face, this particular type of coal burst is characterized by its occurrence at a certain distance behind the advancing face. To better understand the mechanism of a delayed coal burst, we used borehole camera, electromagnetic CT, and borehole deformation monitoring device to observe the fracturing and deformation process of an advancing entry’s surrounding coal in the field. Borehole camera detection showed a zonal disintegration phenomenon in the advancing entry’s surrounding coal. Electromagnetic CT detection showed that zonal disintegration developed within 14 days of excavation. Borehole deformation monitoring indicated a deformation rate difference between the intact zone and fractured zones. The deformation rate difference was observed to increase with time and cause increasing elastic energy accumulation in the intact zone. The cumulative elastic energy in the intact zone finally caused a delayed coal burst in the entry. Sensitivity analysis of the cumulative elastic energy was conducted based on a thick-walled model deduced from field detection. The model shows that the smaller thickness of the intact zone brings higher elastic energy in the intact zone. This investigation provides an improved understanding of delayed coal bursts in deep coal mines.

Oct 19, 2021

By A. L. Ling, A. K. Janzen

"Design of effective mine water treatment plants depends on the ability to reliably predict treatment outcomes, but systems with multiple chemical and physical treatment processes and recycle loops can be difficult to model. GoldPHREEQC is a modeling framework that integrates mass and flow routing capabilities of GoldSim software and water quality calculations provided by PHREEQC, and is well-suited to modeling parameters of interest in the mining industry, especially metals and sulfate. Physical processes such as membrane separation and greensand filtration are modeled by defining mass rejections for each parameter and flow routing based on vendor projections and bench- or pilot-scale equipment testing. GoldPHREEQC models chemical precipitation processes such as HDS metals removal and gypsum precipitation by (1) performing surface-aging and solubility calculations in PHREEQC and (2) using the GoldSim framework to direct supernatant and precipitate to subsequent process steps. Users can apply this modeling framework to predict effluent water quality, chemical requirements, sludge production, and required equipment capacity to support design, troubleshooting, and cost estimating. INTRODUCTION Design of effective mine water treatment plants depends on the ability to reliably predict treatment outcomes, but systems with multiple chemical and physical treatment processes and recycle loops can be difficult to model. GoldPHREEQC is a modeling framework that integrates mass and flow routing capabilities of GoldSim software (1) and water quality calculations provided by PHREEQC (2), and is well-suited to modeling treatment of parameters of interest in the mining industry, especially metals and sulfate. GoldPHREEQC can also be applied to other water treatment scenarios using inorganic reactions and processes. The GoldPHREEQC model framework moves water and mass between specified model nodes and calculates specified reaction and water quality outcomes. It can be organized to provide flow, load, and concentration information for each location, including effluent and byproduct streams, and outputs can be adapted to include power and chemical costs."

Jan 1, 2018

By P. J. Cook

Comminution is one of the fundamentals of mineral processing, requiring large expenditures to be made on capital equipment, installation, power and maintenance. The trend toward lower grades and higher operating costs, mean mining operations are becoming increasingly marginal. The challenge is to improve and more importantly, utilize crushing and milling technologies that provide for reduced capital and operating costs whilst providing increased unit efficiencies. The Svedala Barmac Autogenous Crushing Mill presents such an opportunity by providing many of the cost savings and production increases required by its ability to produce a finer mill feed size and realize reduced energy consumption. This paper briefly describes the operation of the Svedala Barmac Autogenous Crushing Mill and reviews its benefits towards improving the efficiency of crushing and milling operations.

Jan 1, 1999

By Nikhil Dhawan, Veeranjaneyulu Rayapudi, Singh Rahulkumar Sunil

The ever-increasing demand for steel and the subsequent depletion of high-grade ores requires the massive utilization of low-grade iron ores. In the present study, an iron ore slime sample containing 56.1% Fe was investigated using physical beneficiation, carbothermal reduction, and a microwave-assisted process; however, physical beneficiation and microwave exposure were found to be inefficient as they yielded lower iron recovery. Using coconut shell as an alternative reductant was found to be promising and does not lead to the formation of higher iron oxides, such as fayalite and wustite phases. The microwave-assisted carbothermal reduction was found at par with conventional reduction, saving time and heating. The optimum magnetic concentrate obtained in both carbothermal reduction routes (microwave and muffle furnace: Fe grade, Fe recovery, and yield of 64.3, 97, and 84%, and 67, 99, and 83%, respectively) are suitable for alternative iron-making or blast furnace units.

By Liming Yuan, Wei Tang, RICHARD THOMAS, DAVOOD BAHRAMI

The location and orientation of fire suppression nozzles is critical in suppressing mobile mine equipment fires. To effectively suppress such fires, optimization needs to be considered for the suppression nozzle locations and discharge angle. Detailed experiments were conducted to study the effectiveness of fire suppression agents with different nozzle configurations. A variety of fire suppression systems including dry chemical, wet chemical, dual agent (dry and wet chemical), carbon dioxide, and water mist were used. Six types of nozzle locations were studied, and their fire suppression effectiveness were compared. Results from this work highlight potential considerations when determining effective fire suppression designs.

Feb 1, 2025

By P. T. Bissert, L. Yan, M. D. Klein

"Since 2008, the U.S. Mine Safety and Health Administration (MSHA) has required the installation of refuge alternatives (RAs) in underground coal mines (MSHA, 2008). MSHA requires that RAs provide an environment with breathable air for entrapped miners for a 96-hour period. Heat buildup inside an occupied RA is a serious concern. Without a means to dissipate the heat and humidity generated by the occupants and the carbon dioxide scrubbing system, the temperature and humidity inside RAs could lead to severe discomfort or heat stress depending on the mine ambient temperature before and during occupation of the RA. In its 2006 report, the West Virginia Mine Safety Technology Task Force (2006) recommended an apparent temperature limit of 35 °C (95 °F) for RAs. In Title 30 Code of Federal Regulations Part 7.504, or 30 CFR 7.504, MSHA specifies a maximum apparent temperature of 35 °C (95 °F) inside an occupied RA (MSHA, 2016). The apparent temperature is calculated using both air temperature and relative humidity (Steadman, 1979).Calculations can be used to deter-mine if the air within an occupied RA will reach the apparent temperature limit. In these calculations, the mine temperature could be assumed to re-main constant. With this assumption, the effects of the mine strata thermal mass and thermal conductivity on the heat buildup in an RA are ignored. Re-search conducted by the U.S. National Institute for Occupational Safety and Health (NIOSH) shows that the mine air and strata temperatures surrounding an RA increase when subjected to the heat of an occupied RA (Yantek, 2014). Thus, calculations performed with the assumption that the mine temperature is constant would underpredict the resulting dry-bulb temperature and apparent temperature for a given RA occupancy. The mine air temperature has been used as the basis for RA temperature calculations. However, there has been no research to confirm that the mine air temperature is the appropriate basis."

Apr 1, 2017

By Long An, Chao Wu, Yuanhui Li, Xing Sun, Shuai Xu, Changyu Jin

Stage open stope mining (SOSM) maintains the stability of excavation openings by leaving a large number of rib pillars. Affected by the strong unloading due to stage mining and the low width-to-height (w/h) ratio of the pillars remaining, large-scale destabilization disasters of rib pillars or excavation openings easily occur when the distribution of ground stress or the size of rib pillars is unreasonable. In view of these problems, a physical SOSM model test was carried out based on an underground metal mine in the city of Chifeng in China, revealing the deformation and failure characteristics of the SOSM pillar group by overloading.

Jul 1, 2023

By J. F. Brune

This is a shortened version of the paper ?The Methane-Air Explosion Hazard Within Coal Mine Gobs published in the 2013 volume of SME Transactions (Brune, 2013). This paper analyzes the explosion hazard resulting from the formation of methane-air mixtures in the mined-out gobs of underground longwall coal mines. Evidence from numerous mine explosions suggests that explosive methane zones can form within longwall gobs. Explosions and fires resulting from these methane accumulations have led to severe and fatal injuries to the miners, including the explosion of the Upper Big Branch mine in West Virginia, where 29 miners lost their lives. The paper also reviews current research on numerical modeling of gas flows in longwall gobs and outlines how targeted injection of nitrogen into gobs can effectively reduce the volume of such explosive methane zones. The paper concludes that comprehensive monitoring of gas compositions along the accessible fringes of the gobs along with inertization, improved ventilation schemes and further research are necessary to control this explosion hazard and make mining operations safe.

Feb 23, 2014

By Staff

Minerals contribute to U.S. gross domestic product (GDP) at several levels ? from mining and processing to the manufacturing of Anished products. In 2009, the estimated real GDP of the United States decreased by 2.4 percent compared with, and the estimated nominal GDP was about $14.2 trillion (Table 1). Trends in various sectors of the domestic economy are often reflected in mineral production and consumption rates. In 2009, the continued decline of the housing market was reflected in reductions in the production and consumption of cement, clays, construction sand and gravel, and crushed stone (those mineral commodities that are used almost exclusively in construction). Production of mineral commodities associated with the manufacture of goods for the housing market, such as ceramic tile, heating and air conditioning equipment, paint, plumbing and sanitaryware, roofing, wiring and wallboard also decreased. Declines in auto-mobile manufacturing resulted in reduced production

May 1, 2010

By Leonidio Stegmiller

Since the petroleum crisis in 1973, charcoal1 is being considered one of the most important fuel for the Brazilian consumers, mainly for pellet's producers. In replacing fuel by charcoal mixed up with ore, obviously one of the first thing to be investigated is its influence in the product's quality. Special attention has been given to the metallurgical characteristics. This paper infocus the effect of increasing dosings of charcoal to the pellet's porosity and how other physical and metallurgical characteristics will be affected accordingly. This work was carried out using two different finesses of charcoal and dosing varied from 0.5 to 2.0%.

Jan 1, 1982

By S. Lu, J. P. Barta, T. W. Meikle

Three nutrient amendments and a biological seed inoculant were evaluated for use in establishing vegetative cover on waste rock substrates. Randomized blocks were placed on three substrates. Treatments included two types of organic fertilizer, mineral fertilizer, Azospirillum bacterial inoculant, plus controls. The seed mix consisted of native grass species adapted to low nutrient conditions. Canopy cover has been monitored for three growing seasons. Results indicate : 1) two of three substrates support plant growth following amendment with organic fertilizers; 2) organic fertilizers increase cover substantially over mineral fertilizer; and 3)Azospirillum had no effect on canopy cover.

Jan 1, 1999

"Cast blasting is the primary means of overburden displacement in a surface coal mine. It serves two purposes; fragmenting the rock and throwing it directly to its spoil pile using explosive energy. Increased throw minimizes costs by reducing the amount of material that needs to be rehandled. Prior studies have shown that by only changing blasthole timing with the same blast design, fragmentation and throw alter. It is necessary in cast blasting to optimize both fragmentation and throw, since larger fragments will require more wasted energy to throw the same distance. In an operating mine in Georgia, an optimum interhole delay for fragmentation has been found by studying timings from 0 millisecond (ms) to 45 ms. Instantaneous timing between holes increased the throw by more than 31 m (100 ft), but fragmentation was poor. Shock and detonation wave collision is a potential reason for this increased throw.Explosives are utilized extensively by the mining industry in order to break rock, as either ore or overburden, for hauling, loading and crushing. An effective production blast strives to achieve optimum rock fragmentation in order to increase the efficiency and reduce the costs of those downstream operations, while simultaneously meeting environmental regulations. The goal of blasting with respect to fragmentation is, according to Hettinger (2015), “to decrease the average particle size of the fragmented rock without overly increasing fines or, in other words, improve fragmentation.”Additionally, the distance the rock is transported by the explosive energy from the blast, also known as throw, can increase efficiency by reducing the amount of material that is rehandled by mine equipment. The primary situation in which this is desirable is the cast blasting of overburden across the narrow pit of a surface coal mine. A key variable in a blast design pattern that can be manipulated to optimize both fragmentation and throw is delay timing between detonations. The invention and increased utilization of electronic detonators have allowed for precise delay timings to be used between rows, holes and even multiple primers within the same hole. These recent developments in the blasting community have also provided an opportunity to investigate whether or not the mechanism of shock or detonation wave collisions caused by short timing delays are responsible for any increased fragmentation or throw. This experiment attempts to demonstrate if an increase in throw can be achieved while maintaining optimum fragmentation."

Jan 6, 2017

By Ebrahim Tarshizi, Livernois Ryan, Emily Sarver, Zoe Scopa, Robert Setterlind, Leah Frost

"The mines of the future present a host of challenges, which may appear exciting or daunting, depending on one’s perspective. Whether some sectors of the public recognize it or not, the demand for raw resources is not going away any time soon. In fact, it is rising, as the global population grows, urbanizes and attempts to steadily increase quality of life. Yet, at the same time that much of the highly developed world is calling for greener goods, reduced consumption and cleaner production, in other areas there are cries for clean water and sanitation, consistent energy supply, access to health care and education, personal security and support for basic human rights. The balancing act for sustainable development of our global society is, indeed, precarious and the mining community is a key player. Fortunately, many industry members have accepted this role and the responsibility to provide leadership and a solid foundation for progress. Looking ahead, we need new generations of leaders, including many mine engineers who are ready to tackle all sorts of complex problems.There are tremendous needs just for technological innovations. Increasingly tough deposits will require that the industry continues to expand scale toward “mega pits” and “super caves;” fully develop unconventional recovery techniques like in situ leaching and gasification or deep-sea extraction and seriously consider off-earth endeavors. Such work will take entirely autonomous equipment, novel separations, processing and recycling methods, and systems that can withstand extreme physical conditions, just to name a few. It will also take a level of systems integration never-before seen in the mining industry, complete with big data issues, sophisticated predecitve analytics and modeling efforts and cyber-security challenges.Moreover, increasingly complex environmental problems will require creative solutions. Addressing issues like pollution control across multiple media, emerging contaminants, optimal management of wastes, selective mining and shared use of resources between mine operations and surrounding communities and ecosystems are among the top priorities. Really, a complete paradigm shift must occur, such that the focus is on overall improvement of environmental conditions, rather than minimization of impacts. A similar shift will be required in the social realm. How can miners be safer and healthier on-site and off? How can the industry contribute to communities such that they are better off, now and longterm, for having a mine next door? How can artisanal mining practices be transformed to also contribute to sustainable development? How can the industry’s work be a factor in increasing economic and political stability? How can the public understanding of raw resources and the need for mining enterprises be improved?Given the coming challenges, there is no doubt that the mine engineers of the future will need highly diverse skillsets — meshing traditional and contemporary competencies to a degree not previously considered in mining, or most others fields. To be sure, the scope and scale of mining projects make them wholly different than most other engineering work, aside from perhaps the largest civil and urban development projects. While on-the-job experience will continue to be essential, formal education programs (i.e., at post-secondary institutions) must lay critical groundwork."

Jan 6, 2017

By Tamara Nestorovic, Luan T. Nguyen

"With the aim to mitigate excavation risks and reduce the costs caused by tunnel boring machine (TBM) stoppage when tunneling under uncertain soil conditions, prediction ahead of the tunnel face has become an increasing interest in the tunneling community. Our research topic is concerned with developing effective concepts for nondestructive identification of geological anomalies ahead of the tunnel face by waveform inversion of reflected tunnel seismic waves. The authors demonstrate that this new technique is promising in providing tunnel engineers with an accurate image of the geological situation that the TBM is going to encounter thanks to the waveforms’ rich information about the geological structure that affects propagation, reflection/refraction and mode conversion behavior of the elastic waves. By setting up a 2-dimensional numerical model for simulation of tunnel seismic wave propagation influenced by a dip layer change ahead of the tunnel face, the authors show that the waveform misfit to be minimized by the inversion process is highly multimodal and therefore propose a hybrid stochastic optimization method that can quickly and robustly converge to the global minimum. DEVELOPMENTS IN TUNNEL ADVANCE EXPLORATION Conventional site investigation by drilling boreholes helps to draw a general image of geological structures along the borehole axes but that image is likely to misrepresent the detailed geological structure due to limited sampled locations. Due to high costs and restricted boring space which deep tunneling and tunneling under urban areas encounter, many industrial and academic research groups have had great interest in developing nondestructive ahead of the tunnel face prediction systems. That means only excitation sources and receiving sensors, which are usually placed on the ground surface or on the side walls or on the cutter head of the TBM, are used for acquisition of the measurement data. The recorded signals in the form of seismic or electromagnetic/ electrical waves, which travel through the geological structure or are reflected back from it, hold the signature of the geological structure of concern, such as geological layer changes, fault zones, erratic rocks, boulders, construction remnants, etc., and therefore can be used to reconstruct the spatial and material properties of those hidden geological structures. Most common nondestructive ahead-of-tunnel investigation systems to date are based on interpretation of reflected elastic/ acoustic waves (seismic waves) and analysis of electromagnetic/ electrical resistivity signals (Mooney et al. 2012). However, due to insufficient penetration depth and spread of signals generated by radar and geoelectric sources, the use of seismic waves for ahead of the tunnel face prediction (tunnel reconnaissance) is more preferable (Kneib et al. 2000; Bohlen et al. 2007)."

Jan 1, 2016

By Russell Barr

Operational excellence is generally known as a management system integrated across critical functions that is geared towards continually improving operational performance. Functional areas such as health, environment and safety, quality and human resources are the focus of many corporate-wide operational excellence programs. Operational excellence also focuses on improving areas such as customer orientation, employee empowerment as well as process, and systems optimization. It is widely viewed as critical to sustaining business performance improvement. Although it is difficult to find a universally accepted definition, or even common foundation in many respects, operational excellence remains a popular term in the business world. Many organizations have developed their own version of organization excellence, influenced by such individual factors, other similar institutions or even third-party service providers. A mining organization is no different from other organizations in that adopting and implementing effective operational excellence programs can dramatically improve business execution and performance across regional or global interests. This paper brings together various perspectives of operational excellence and reconciles them for a useful composite for the mining industry. While most agree that operational excellence should include normal functions in a manufacturing operation such as production, maintenance and engineering and processes such as quality, environmental and continuous improvement, many other factors for operational excellence seem to vary from perspective to perspective. Thus, programs that manufacturers engage in may seem the same, but may, in fact, be different in key areas. This may affect organizational performance in tangible ways. Management must buy into the company?s definition of operational excellence and be dedicated to achieving it. A review of many of the existing definitions of operational excellence, explicit or embedded as part of a program, seems to yield the following common factors: ? It should help organizations better execute their processes and services. ? It should be geared towards improving quality ? It requires that the various operations should be aligned with the overall enterprise strategy. ? It should be geared towards continuous improvement. A composite of operational excellence definitions suggest that it is: ? Geared towards helping the organization achieve sustained profitability; ? tied to strategic alignment and business objectives; ? tied to solid investment strategies; ? integrated as part of the culture, process, time plan and performance; ? a relevant performance measurement system; ? extended to include all aspects of the supply chain (including external suppliers); ? integrated with health, safety and environmental (HSE) aspects. And, while the pursuit of operational excellence intuitively suggests that businesses should improve, it is very difficult to achieve given the difficult challenges facing companies today. Mining businesses face numerous pressures to perform in a global marketplace such as demand, energy cost, variable cost and pricing fluctuations as well as infrastructure challenges to further confound the environment. Companies generally must look to the following:

Jan 1, 2009

By Matthew Deutsch

A common casualty of modern openpit mine optimization is the assurance that the resulting design is actually achievable. Optimized mine plans that consider value and a bare minimum of precedence constraints do not, in general, translate into practical, operational mine designs that can be used in the field. Ultimate pits may come to a sharp point at the bottom. Schedules may require taking small parcels of material from many disparate areas of the pit in a single period, and grade control polygons may be ragged, narrow and not minable with realistic equipment. In this paper, these three fundamental openpit mine optimization problems are addressed by encoding them as maximum satisfiability problems. Maximum satisfiability provides a useful framework for problems that are nonlinear and may guarantee the optimality that metaheuristics cannot.