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The authors summarise the development and recent advances in the reconstruction and visualisation of three-dimensional objects from point data and describe applications to the reconstruction of orebody shapes from drill-hole and other data. In particular, Dijkstra's algorithm is proposed and implemented as a means of optimal reconstruction of complex orebody and topographical shapes from irregularly located sample data. The surfaces of the shapes are constructed from triangular tiles and the algorithms proposed by the authors are guaranteed to find the optimal set of tiles that "best" construct the surfaces on the basis of specified objective criteria. The algorithms are illustrated by applications to a complex silver/gold/zinc/lead deposit.

Jan 1, 2002

By Alessandro Navarra, Roberto Parra, Boyd Davis, Frank Mucciardi

A smelter scheduling algorithm has been developed, which allocates the oxygen production between the smelting furnace and the converter aisle, so as to maximize copper throughput. The algorithm is intended for daily operation planning, controlling the sequencing of the converter cycles, and the oxygen drawn by these cycles. In some cases, it may be worthwhile to decrease converter oxygen allocation in favour of the smelting furnaces. Thus, a better utilization of the oxygen plant can increase primary copper throughput by several percentage points. This principle is demonstrated through sample computations. The approach presented in this paper can be incorporated into smelter management software.

Jan 1, 2015

By G. ALBORNOZ, S. Utili, A. AGOSTI, C. VALDERRAMA, R. PELL, N. Morales

The steepness of the slopes of an open pit mine has a substantial influence on the financial return of the mine. The paper proposes a novel design methodology where overall steeper pitwalls are employed without compromising the safety of the mine. In current design practice, pitwall profiles are often planar in cross-section within each rock layer; i.e., the profile inclination across each layer tends to be constant. Here instead, a new geotechnical software, OptimalSlope, is employed to determine optimal pitwall profiles of depth varying inclination. OptimalSlope seeks the solution of a mathematical optimization problem where the overall steepness of the pitwall, from crest to toe, is maximized for an assigned lithology, geotechnical properties, and factor of safety (FoS). Bench geometries (bench height, face inclination, minimum berm width) are imposed in the optimization as constraints which bind the maximum local inclination of the sought optimal profile together with any other constraints such as geological discontinuities that may influence slope failure. The obtained optimal profiles are always steeper than their planar counterparts (i.e., the planar profiles exhibiting the same FoS) up to 8° depending on rock type and severity of constraints on local inclinations. The design of a copper mine is first carried out employing planar pitwalls, secondly adopting the optimal pitwall profiles determined by OptimalSlope. The adoption of optimal slope profiles leads to a 34% higher net present value and reductions of carbon footprint and energy consumption of 0.17 Mt CO2 eq and 82.5 million MJ respectively due to a 15% reduction of rockwaste volume.

Feb 9, 2022

By G. ALBORNOZ, S. Utili, A. AGOSTI, C. VALDERRAMA, R. PELL, N. Morales

The steepness of the slopes of an open pit mine has a substantial influence on the financial return of the mine. The paper proposes a novel design methodology where overall steeper pitwalls are employed without compromising the safety of the mine. In current design practice pitwall profiles are often planar in crosssection and the profile in between ramps especially tend to be planar and defined by a constant inter-ramp angle. Sometimes rock layers exhibiting different strengths require the inclination of the profile to vary with depth, but the inclination across each layer is usually constant. Here instead, a new geotechnical software, OptimalSlope, is employed to determine optimal pitwall profiles of depth varying inclination. OptimalSlope seeks the solution of a mathematical optimization problem where the overall steepness of the pitwall, from crest to toe, is maximized for an assigned lithology, geotechnical properties and Factor of Safety (FoS). Bench geometries (bench height, face inclination, minimum berm width) are imposed in the optimization as constraints which bind the maximum local inclination of the sought optimal profile together with any other constraints such as geological discontinuities that may influence slope failure. The obtained optimal profiles are always steeper than their planar counterparts (i.e. the planar profiles exhibiting the same FoS) up to 8 degrees depending on rock type and severity of constraints on local inclinations. The design of a copper mine is first carried out employing planar pitwalls, secondly adopting the optimal pitwall profiles determined by OptimalSlope. The adoption of optimal slope profiles leads to a 34% higher net present value and reductions of carbon footprint and energy consumption of 0.17 Mt CO2 eq and 82.5 million MJ respectively due to a 15% reduction of rockwaste volume.

Mar 2, 2022

By G. ALBORNOZ, S. Utili, A. AGOSTI, C. VALDERRAMA, R. PELL

The steepness of an openpit mine’s slopes has a substantial influence on the mine’s financial return. This paper proposes a novel design methodology where overall steeper pitwalls are employed without compromising the safety of the mine. In current design practice, pitwall profiles are often planar in cross section within each rock layer: that is, the profile inclination across each layer tends to be constant. Here, instead, a new geotechnical software, OptimalSlope, is used to determine optimal pitwall profiles of depth-varying inclination. OptimalSlope seeks the solution of a mathematical optimization problem where the overall steepness of the pitwall, from crest to toe, is maximized for an assigned lithology, geotechnical properties and factor of safety (FoS).

By I. V. Lunkin, E. B. Muhamedzhanov, A. B. Begalinov, B. R. Rakishev

Almost all the ore deposits of ferrous, non-ferrous and rare metals of Kazakstan, are exploiting by the open-cast method, are the complex-structural, multi-component ones. Their rational working requires precise organization of extracting works. In this connection it is necessary to set up the best intercommunications between drilling-blasting, excavating-loading and transport works. This requires the stable functioning of the quarry for dispatch of ore raw material of required quality with minimum of corresponding expenses. For this purpose, proceeding from the quarry’s ore output and the assumed parameters of the exploitation system, the first problem about rational arrangement of excavating-loading equipment in extracting faces is solved. By solving the problem the model with dynamic, adapting properties had been used. It was solved numerically by the method of statistical tests. By setting up the necessary link between type-sizes of excavating-loading and transport equipment, the minimum prime cost of loading and transportation of 1 ton of mining mass from the face to the receiving station was adopted as the criterion of optimality. Depending on the type of excavating-loading equipment, the efficiency function may be different. By using wheel loaders, their displacement between the faces is possible, therefore, the efficiency function of the problem may include expenses for their displacement. By using excavators like power shovel, the problem’s restrictions must exclude its displacement between the faces. The efficiency function consists of minimum expenses for loading, proceeding from set of volumes of extraction from the faces, satisfying required quality. The volumes of extraction from the faces, satisfying required quality of ore in output stream, are determined by the method of statistical tests. Sample range is given, proceeding from the restrictions for maximum productivity of the excavating-loading equipment. Volumes of extraction, not satisfying required quality, are cut off. The efficiency function meaning is then determined and minimized. Keywords: Excavating-loading equipment, its placing in extracting faces, optimal load-carrying capacity, specific expenses for loading and transportation of mining mass.

Jan 1, 2003

By Walter C. Labys

INTRODUCTION Interest in multicommodity stabilization schemes has increased recently for several reasons, a most important one being the experienced wide swings in primary commodity prices. These prices rose sharply between mid - 1972 and end - 1974 giving commodity exporting countries an opportunity to gain sizeable increases in export earnings. But since then, prices have tumbled and these countries are searching for a means to stabilize if not to increase their earnings. While this problem is particularly serious for developing countries, the developed countries are concerned about the impending upward price swing, which would increase inflation before recovery from the world recession is assured. As a direct consequence of the emergency meeting of the U.N. General Assembly devoted to commodity problems in April of 1974, interest has been renewed in the Keynesian (4) plan for an international multicommodity buffer stock program. In particular, UNCTAD (8) is designing an integrated commodity scheme to be discussed within that body. In terms of approaches that have appeared in designing such a program, none exist which relate to the interpretation of the independence and interdependence of prices of the commodities of interest. Typical criteria for selecting commodities for the scheme have included their importance in world trade, their particular origin from developing countries, and their feasibility for storage. But the financial management of a multicommodity buffer stock requires a consideration of commodity prices, yields, and risks as does as any portfolio of assets. The approach which we take in this study is that of application

Jan 1, 1977

By N. T. Beukes, W. Banda

Recovery of Co from slag is a recent advancement in the extractive metallurgy of nonferrous metals. In this study a DC arc technology at laboratory scale has been applied to investigate the selective recovery of Co from slag, under three different flux types with an emphasis on influencing the activity of FeOx, SiO2 and CoO in the slag. It is known that reduction of slag by carbon is only up to a certain level after which, the recovery will depend on the chemistry of the slag, hence the need to modify the slag chemistry. Two power settings were employed to induce higher temperatures and aggressive agitation. The results were interpreted by comparing how much Co and Fe was in the slag and alloy. TiO2 reduced the amount of Fe in the product alloy compared to when CaO and CaF2 were used. The change in power did not seem to have had a major effect on the recovery although the amount of material lost to flue dust was more at a higher power rate.

Jan 1, 2003

By D von Horn

Mineral sand orebodies are typically mined for their TiO2 content. Increasingly over the past 30 years, the major mineral focus has shifted from natural rutile to ilmenite and an acceptance that the latter generally needs some form of upgrading for economic conversion into TiO2 pigment. This upgrading obviously has a cost, and in conjunction with diminishing mineable feed grades, results in higher cost TiO2 units for chloride route Pigment Plant feedstocks. The net cost of feedstock can be significantly influenced by the recovery and sale of accessory minerals and by-products from the processing chain to the extent that some producers have the potential to achieve a zero net cost. Whilst slagging plants typically reduce net cost from rutile, zircon and pig iron revenues, operations supporting Becher type synthetic rutile operations have been limited to revenues from rutile and zircon only. A range of alumino silicate minerals show industrial potential, as does activated carbon, iron oxide and gypsum, by-products of the synthetic rutile process. Tiwest is a good example of a company maximising revenue from the accessory minerals as well as from by-products of the synthetic rutile process.

Jan 1, 2001

By Su Zhen

Based on the technical features of the Feng- huang-shan concentrator, the authors have designed a new scheme for optimal search and self-adaptive control in flotation process, in order to apply computer control to the concentrator. Hence, a plant test of optimal control in bulk flotation of copper and iron sulfides was successfully carried out. The control parameters are xanthate addition, pulp level, and amount of aeration, etc., in flotation cells. Two mathematical models of multiple parameters established by the authors were adapted and flotation efficiency was used as an objective function in the control.

Jan 1, 1984

By M. Vulkov

The paper is focused on the optimal selection of grinding medium for a drum mill. The decision-making is based on the fuzzy multiple attribute approach. One way to optimize the grinding process in a tumbling mill is associated with the development and testing a new shape of grinding body. Family of new grinding bodies ? spheroidal tetrahedrons (tetraballpebs) has been manufactured. Two types of spheroidal tetrahedrons and a classical ball (sphere) with one and the same weight are compared. A fuzzy entropy method to calculate the weight of the attributes is suggested. A grinding body which is the best approximation to the fuzzy formulated technological conditions is selected. Keywords: grinding, spheroidal tetrahedrons (tetraballpebs), balls, fuzzy sets

Sep 1, 2012

By G. H. Walrod, J. M. Mutmansky, Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths, from 150 m to 300 m (500 ft to 1000 ft), and six different diameters, from 4.27 m to 7.32 m (14 ft to 24 ft), were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1979

By Jan M. Mutmansky, Gordon H. Walrod, Y. J. Wang

The approach proposed in this paper is, as stated by the authors, an update of methods well discussed in the literature. The authors are to be congratulated for their excellent effort in quantifying a difficult problem with realistic cost data. Economic analysis of the components of a mine ventilation system is complicated by both the dynamic nature of the system and the uncertainty as to the time when system changes occur. We wish to address three specific areas of this paper which require further consideration: shaft designed air capacity, shaft location, and economic criteria used within the analysis

Jan 11, 1979

By Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths (from 500 feet to 1000 feet) and six different diameters (from 14 feet to 24 feet) were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1977

By Jan M. Mutmansky, Gordon H. Walrod, Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths, from 150 m to 300 m (500 ft to l000ft), and six different diameters, from 4.27 m to 7.32 m (14 ft to 24 ft), were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1980

By Nelson M. Solow

Raise boring of mine ventilation shafts in many cases offers a lower cost and higher speed method of construction in comparison to conventional shaft sinking. Where underground access is available for raise boring the potential savings indicate that raise boring should be considered as an alternative to other methods. Raise boring machines are currently in use which have the capability for reaming shafts up to twenty feet in diameter, depending on the strata and depth. These large capacity machines make it possible to consider raise bored shafts for moving large volumes of air. Although we will consider here only ventilation shafts, raise boring should also be considered for men and material shafts. When the mine planner has determined the volume of air required through a shaft at a particular location he is faced with the problem of selecting the shaft size. The principal factors in optimizing the shaft size are the construction costs for the shaft 'and the power cost to move the air through the shaft. The larger diameter the' shaft is the more it costs to construct, but for a given volume of air the power required (cost) becomes lower as the diameter increases. The construction cost is paid only once, when the shaft is constructed. The power costs, however, are paid throughout the life of the shaft. Methods of optimizing air shaft size found in the literature (References 1 and 2) amortize the construction cost and include it in the average annual cost of operating the airshaft. These methods derive a formula for the average annual cost vs. shaft size and de-rive the formula to compute the optimum size for a given air flow rate. It is, however, desirable to take into account tax considera-

Jan 1, 1977

By S Utili, A Agosti

The Overall Slope Angle (OSA) of pitwalls plays a crucial role in the financial return of an open pit mine. In current practice, pitwall profiles are designed to be planar in cross-section within each rock layer, ie the profile inclination across each layer tends to be constant. A new slope design software, OptimalSlope, has been recently proposed to determine the geotechnically optimal profile shapes for the pitwalls of mines. OptimalSlope seeks the solution of a mathematical optimisation problem where the overall steepness of the pitwall to be designed is maximised for an assigned stratigraphy, rock properties (unit weight and strength) and Factor of Safety. The geometry of the benches is provided as input to OptimalSlope. The results obtained so far on three mine case studies in isotropic rock masses (Utili et al, 2022; Agosti et al, 2021a, 2021b) show that optimal profiles are up to 5° steeper than their planar counterparts – ie the planar profiles exhibiting the same FoS – leading to realising significant saving on waste rock and as a consequence Net Present Value increments and carbon footprint reductions. OptimalSlope algorithms have been modified to deal with anisotropic rock masses characterised by direction dependent shear strength. In the paper, the case of rock masses in banded iron formations (BIF) is tackled. A data set of anisotropic rock shear strengths typical of Western Australia is considered. The Snowden modified nonlinear model was employed to characterise the anisotropy of the rock mass shear strength. From the OptimalSlope simulations performed emerges that optimal pitwall profiles can increase significantly the Overall Slope Angle in comparison with planar profiles featured by the same Factor of Safety. LEM stability analyses of all the profiles were also performed by Rocscience Slide 2 to independently verify the FoSs of the optimal profiles obtained.

Nov 29, 2022

By J. Winterton

Cripple Creek and Victor Gold Mining Co. is developing a full-scale pad injection program as part of the overall operational plan for the Valley Leach Facility. As part of the development process the mechanics of the injection methodology are evaluated in the context of physical injection measurements, outcome from geophysical monitoring, and gold leaching theory. The results indicate that hydraulic fracturing analogies advanced heretofore do not accurately describe injection phenomena in unconsolidated and noncohesive material typical of leach pads. A new interpretation is presented and extended to define operational strategies for maximizing gold production.

Feb 27, 2013

By Haijian Shi, Drew Pizzo

This article focuses on the appropriate application of subsurface investigation methods for transmission structures, which are typically designed to resist lateral rather than vertical loads. Currently, the three methods used most often for the subsurface investigation of transmission structures in the field are the Standard Penetration Test (SPT), the Cone Penetration Test (CPT), and the Flat Dilatometer Test (DMT). Each of these methods has advantages and disadvantages, and each is more applicable to some scenarios than to others. To gain a better understanding of these test methods and the implications of using them for various kinds of applications, a comparison study was conducted in the field in Maryland, for three boring locations. Each boring location was explored using each of the three tests as stated. The results of the tests and lessons learned are presented and compared, and these comparisons show that the three test methods agree on the majority of the findings. The results from each test method were also used to derive key parameters such as the soil friction angle for given foundation designs considered in order to establish a clear basis for comparison. Recommendations for performing transmission structure subsurface investigations are made in order to optimize the use of each method and thereby optimizing subsequent foundation designs. INTRODUCTION For overhead transmission structures, the most important structural requirement for determining the foundation design differs from the requirement for other structures such as buildings and bridges in accord with the conditions the transmission structures will need to withstand. In addition to the ability to bear a given vertical load consistent with its use, the foundation must bear lateral loads arising from wind and other weather conditions. The foundation types used most often for overhead transmission monopole structures include concrete drilled pier, vibratory caisson, and direct embedment. In order to determine an appropriate and even an optimum foundation design for any given set of conditions, an appropriate subsurface investigation method or approach is needed. Currently, the standard penetration test (SPT), the cone penetration test (CPT), and the flat dilatometer test (DMT) are the three most commonly used subsurface investigation methods.

Jan 1, 2018

By C. Guria

A modeling, simulation and optimization study of a complex industrial fluorspar beneficiation plant (Kadipani, Gujarat, India) with fourteen/ten flotation banks is carried out to find an optimum/near-optimum circuit for the given quality of feed ore. The phenomenological flotation model developed by Mehrotra and Kapur (1974) is used for circuit optimization. Two different optimization problems are formulated and solved. The first optimization problem involves a single objective function, which uses available plant data to estimate the feed-characterizing parameters, i.e., the flotation rate constants, by minimizing the weighted sum-of-square errors between the computed and plant values. The second optimization problem involves two objective functions to obtain several simplified circuits. The number of non-linking streams and the overall recovery of the concentrate, i.e., the acid-grade product, are maximized simultaneously in this problem. The single-objective variant (SGA-II-mJG) of the binary-coded elitist non-dominated sorting genetic algorithm with the jumping gene adaptation, NSGA-II-mJG, is used for the first problem, while NAGA-II-mJG (Guria et al., 2005 a) is used for the second problem. Simplified circuits with a few split streams are proposed on the basis of the present optimization study, which enhance the recovery of the acid-grade product without affecting its quality, for a given total volume of the flotation cell-bank. Even though the optimal solutions have certain drawbacks, they suggest a meaningful direction in using an iterative fitting of parameters to such optimal circuits, followed by re-optimization. Key words: Froth flotation, Mineral processing, Industrial fluorspar beneficiation, Feed identification, Circuit/network optimization, Global optimal, Jumping gene, Genetic algorithm, Multi-objective optimization

Jan 1, 2009