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By M. J. Howes, C. A. Nixon

INTRODUCTION A safe heat stress control strategy for an underground mine has three elements: Application of an environmental measure which reflects physiological strain with sufficient accuracy for the range of conditions encountered underground. Acceptance of a functional relationship between the environ- mental measure and human performance which is used to optimise the environmental conditions achievable with either ventilation or ventilation and refrigeration. A management control strategy based on the environmental measure which is designed to ensure that work in environments where excessive physiological strain may occur is prevented and corrective action is initiated. The environmental measure that reflects physiological strain is the link between the three elements and, since the turn of the century, the discussion of the merits of various indices has been prolific. One problem in selecting a suitable measure or index is the ease with which it can be physically obtained relative to accurately reflecting the physiological strain. For example, wet bulb temperature is simple to measure and, for a particular mining sys- tem, it may adequately represent physiological strain, however, it would not necessarily provide the same relatively safe measure in a different mining system. The acceptance of a measure which can be universally applied has been confounded by both development and predisposition. That is not to say that there is only one "correct" measure and all others are unsuitable. It is self evident that if the application of a particular index has resulted in adequate control, then that mea- sure is correct for that situation. However, an understanding of the limitations is necessary to ensure that adequate control is maintained as mining conditions change. Almost 100 years after the question of heat stress in mines started to be dealt with in a collective manner, an analysis of the available information is leading towards a general strategy to control this problem. In the paper, the developments in heat stress assessment are briefly examined and followed since the earliest published observations on the effect of heat in mines (Haldane, 1905), efforts to determine a relationship between an environmental measure and human performance are reviewed and summarised and the benefits of control strategies such as acclimatisation and shortened shifts are discussed as they relate to Mount Isa Mines. The results of testing the prototype air cooling power instrument are discussed and a heat stress control strategy outlined. HEAT STRESS AND AIR COOLING POWER The operation of the human engine is analogous to other engines where the conversion of chemical energy from the oxidation of fuel to useful mechanical energy is not 100% efficient. In a diesel engine it is about 33% and in a human engine less than 20% resulting in at least five times as much heat produced by the meta- bolic process as useful work done. Metabolic energy production is related to the rate at which oxygen is consumed and is about 340 W for each litre of oxygen per minute. Using measured oxygen consumption and an average body surface area of 2.0 m2, the approximate metabolic energy production associated with different mining tasks is (Morrison et al. 1968):- • Rest, 50 W/m2 • Light work, 75 to 125 W/m2 (machine, LHD or drill jumbo operators) • Medium work, 125 to 175 W/m2 (airleg drilling, light construction work) • Hard work, 175 to 275 W/m2 (barring down, building bulkheads and timbering) • Very hard work, over 275 W/m2 (shovelling rock) Heat balance is achieved when the rate of producing heat (the metabolic heat production rate) is equal to the rate at which the body can reject heat mainly through radiation, convection and evaporation. Heat exchange between the lungs and the air in- haled and exhaled is normally less than 5% of the total and there- fore usually ignored. Any heat not rejected to the surroundings will cause an increase in body core temperature. Since heat stress is related to the balance between the body and the surrounding thermal environment, the main parameters required to be known when determining acceptable conditions are those associated with the heat production and transfer mechanisms. These can be summarised as follows: Metabolic heat production rates (M - W) Skin surface area (A3) (and effects of clothing) Dry bulb temperature (t[ ]) Radiant temperature (t[ ]) Air velocity (V) Air pressure (P) Air vapour pressure (e [ ]) The rate of heat transfer to or from the environment depends on the equilibrium skin temperature t, and the sweat rate S,. These in turn depend on the response of the body to the imposed heat stress and the effect of thermoregulation (Stewart, 1981). Thermoregulation The body contains temperature sensitive structures which send impulses to the brain at a rate depending on the temperature. Both hot and cold signals can be differentiated and the thermoregulatory response ahivated according to which signal pre- dominates. If "cold" signals are dominant, body heat loss is re-

Jan 1, 1997

By Babcock. C. O.

This report presents equations derived from experimental testing to convert borehole pressure cell data from vertical and horizontal cells to the biaxial ground stress changes. While hydraulic pressure cells in boreholes have been in extensive use since 1957, methods of data reduction have been slow to develop. The methods of Sellers (1970) and Bauer et al. (1985), respectively, indicate a linear relationship between cell pressure change and the rock stress change. Lu presented a theory for creep behavior (Babcock et al., 1982). In the present work, in laboratory testing, the logarithm of the cell pressure was related to the stress change in seven elastic materials for a range of Young's moduli of 3.45 to 85.5 GPa (0.5 to 12.4 x 106 psi). The gage response depends upon the setting pressure of the gage, the gage pressure at any time, the rock properties, and the cross-sensitivity of the gage to transverse loading. The setting pressure of the cell should be proportional to the Young's modulus of the rock, the absolute stress can be determined by overcoring in strong rock, and the in situ Poisson's ratio can be estimated in some cases from the cell responses.

Jan 1, 1986

By Graham Swan, Richard K. Brummer

The paper begins by describing an underhand cut-and-fill mining concept for a 50m thick, generally tabular though irregularly shaped orebody dipping at 30 degrees and occurring at a depth of between 2300 and 2700m in the Sudbury Basin. From this, the broad design requirements of a fill system are stated. Two and three-dimensional numerical models are then described which were built to evaluate the theoretical benefits of different types of fill reinforcement. Included in this evaluation are the effects of span, fill strength, fill tightness, as well as static and dynamic loading types. Results, supported by large-scale physical models, are presented to show the significance of reinforcement on stable, undermined fill performance. Finally the paper describes work which has been done to evaluate the suitability of so-called silicated cemented backfill. This system is, in principal, attractive for deep mining applications since transportation is in the "safe" hydraulic regime, while fill water run-off, segregation and shrinkage effects are potentially eliminated in the stopes. The results from various surface and underground trial pours are reported which substantiate the proposed use of this type of backfill at depth.

Jan 1, 2001

By Biswajit Samanta, Pranjal Pathak

A multimine mineral value chain (MVC) consists of multiple mines in the upstream supplying raw materials to multiple destinations in the downstream. The short-term mine production scheduling problem of a multimine MVC aims to determine the optimal extraction sequence and destination allocation of blocks from all the mines collaboratively to meet the quality and quantity requirements of all the processing plants in each period, subject to all relevant technical and operational constraints of the mining system. It is carried out at shorter scales of days/weeks/months under the purview of long-term production scheduling. An optimal short-term production schedule for MVC involving multiple mines that share the same infrastructure (processing units, stockpiles and waste dumps) requires coordination across the network of mines. Optimizing the short-term production schedules independently at each mine fails to capture the benefit of collaboratively generating schedules for all the mines, resulting in suboptimal schedules. Additionally, in short-term production scheduling, the operations are modeled in greater detail with additional decision variables and constraints to model the more complex multimine MVC situations. This makes the large-scale instances of the problem computationally intractable for standard mixed-integer programming (MIP) solvers. This work presents a customized genetic algorithm (GA)-based heuristic approach to obtain near-optimal solutions to the industrial-scale instances of the short-term production scheduling problem of multimine MVC within a reasonable computation time.

Oct 1, 2022

By Arthur P. Chase

The Tacubaya subway tunnels form a link in the Sistema de Transporte Colectivo (Mass Transit System) of the Federal District of Mexico. One tunnel 327 m long lies to the north of Tacubaya Station, the other 811 m long, to the south. The tunnels are designed to accommodate two subway trains, one inbound and one outbound, within the inside diameter of 8.5 m. The designers of the tunnel lining and tunnel driving equipment were faced with the problem of driving two subway tunnels 9.0 m outside diameter through water-bearing soil, directly beneath a high speed limited access highway, a main drainage sewer, structures including residences and office buildings, on an alignment curved for 67 per cent of tunnel length, and on grades as high as 7 per cent, within a limited budget, with minimum damage to property and disruption to the community. Planning The following decisions affecting tunnel design and construction were made at an early stage of planning: Shield. To enhance safety, a tunnel shield would be used for tunnel driving. Dewatering. The water-bearing soil could be effectively dewatered; consequently, tunnel driving could be performed in free air. Hand Mining. To minimize investment in equipment, hand mining would be used to excavate and support the face.

Jan 1, 1997

By P. Diehl

The increasing public interest in a useful framework for an assessment and classification of mineral resources (1) is documented by the recently published international classification scheme of the United Nations (1979) and the revision of the classification system of USBM/USGS (2) (1980). Moreover, various classification systems are currently discussed by the mining industry. In spite of major improvements in respect of the concepts, definitions, and taxonomy of ore classification, it has been recognized that the recent practice to classify mineral resources does not create truly reproductible results, i.e. an assessment to the various categories which is free from personal bias or corporate interests. Following are geostatistical methods proposed for a standardization and quantification of various terms in ore classification. After critical review of present practices, we will establish a precise link between the classical terms such as "measured", "indicated", and "inferred" reserves and the geostatistical concept of estimation errors. Moreover, we will demonstrate, how the basic criteria of economic feasibility, geologic assurance and recovery can be taken into account by geostatistics. A specific algorithm will be proposed to block out and to classify reserves according to the degree of geologic assurance. . We will also show computerized methods which perform complete classification procedures, and will also exemplify them with typical case studies.

Jan 1, 1982

By Chris A. Fleming, Daan Seymore

The Golden Jubilee Mine in South Africa is the first mine in the Western World to introduce resin-in­pulp technology for the recovery of gold from a cyanide-leached slurry. Located in the Eastern Transvaal region of the country, the plant processes approximately 375 metric tons• of ore per day, of which over 90 per cent is mined in an open pit adjacent to the metaflurgical plant, while the remaining 5 to 10 per cent is trucl<ed in from two small high-grade deposits, located about 10 kilometers from the plant. The gold grade in the open pit is about 1 git, while the values m the two high-grade deposits range between 5 and 15 git. At the current treatment rate, the proven reserves m the three locations will last about another 10 years. Early testwork indicated that the ore was not well suited to conventional filtration processing or to heap leaching because of its high cfay content, and that carbon-m-pulp (CIP) would probably prove to be the most viable metallurgical route. Tcstwork to establish the feasibility of CIP for this application was carried out at Mintek in 1985. This worl<, which was based on batch-leaching and carbon-loading tests, indicated that CIP was technically feasible, but that both the rate of gold loading and the gold-loading capacity of the carbon were inferior to those obtained with Witwatersrand ores. The poor adsorption characteristics of the carbon were attributed to the abnormally high concentration of natural organic compounds (humates and fulvates) in the ore. Batch tests were therefore also carried out with strong-base resins, since resins are known (1] to be far less susceptible to organic fouling than is activated carbon. The results were very promising, and pointed to fast kinetics and a high loading capacity. (Fig. 1 ). Notwithstanding these findings, it was decided to recover gold with activated carbon at Golden Jubilee Mine because the CIP process was, by then, well established in South Africa and elsewhere in the world, whereas resin-in-pulp (RIP) was unproven technology. The r>lant was commissioned in September 1986 and, for 18 months, operated in a carbon-in-leach (CIL) configuration, i.e. with a total of . six leach tanks, the last four of which contained activated carbon. As could have been predicted from the laboratory results, the performance of the CIL plant was generally poor, low gold loadings on the carbon (less than 1500 git) and high losses of soluble gold (0.2 to 0.3 p.p.m.) bemg characteristic of the operation. Consequently, it

Jan 1, 1990

By Michael L. Nave

Belt Conveyors are an important method for transportation of bulk materials in the mining industry. The control of the application of the starting torque from the belt drive system to the belt fabric affects the performance, life cost, and reliability of the conveyor. This paper examines applications of each starting method within the coal mining industry.

Jan 1, 1993

The concept of optical basicity is now being widely applied to rationalize and predict the chemical properties of slags. It employs signals from a probe ion to indicate the "state" or relative "freeness" of the oxygen ions in the slag, and hence provides a fundamental measure of slag basicity. Values of the bulk optical basicity of a slag can either be measured spectroscopically in samples of transparent solid glassy slag, or calculated very simply and accurately from the chemical composition of the slag. The way in which these values vary in different systems are illustrated as isoptical basicity lines on ternary diagrams, and the patterns obtained are discussed. The difficulties associated with assigning optical basicities to the oxides of transition elements are also reviewed briefly. It has been demonstrated that these bulk values can be used as the basis of a flux control model for steelmaking to achieve end-point chemistries much more reliably. Furthermore, several correlations have been established which allow the prediction of the slag-metal distribution of various solute elements. This approach has been used to predict the phosphorus distribution at the end of steelmaking, and also to custom design fluxes for the ladle and tundish to aid in the control of residual elements in the steel such as suphur, hydrogen and nitrogen.

Jan 1, 1990

By Gerald H. Luttrell, Seyed Hassan Amini, Aaron Noble

Single-unit separations in mineral processing are typically not able to meet the strict purity requirements for consumer markets. As a result, multistage separation circuits are often employed. Because these circuits represent a large and inflexible capital investment, process engineers are careful to ensure that the circuit is optimally designed to meet the desired objectives. The set of interdependent decisions that constitute the circuit design may involve the selection of different unit operations, different equipment specifications, different operational parameters, and different unit interconnections. To assist circuit designers in assessing these options, researchers have attempted to establish standard design methodologies that involve various techniques and tools.

By F. L. Jackson

When using perlite as an insulation, it is important to determine the requirements for different applications as this influences the processing of the perlite. In cryogenic applications, perlite properties of low density and fine particle size are desirable, while Loose fill insulation applications require similar properties and water repellency. However, in perlite insulating concrete applications, a coarser particle, of higher density, is required to provide improved compression strength. The essential properties of perlite including, particle size, density and surface treatment are discussed in relation to the various insulation applications. Also typical mineral processing and manufacturing techniques are reviewed

Jan 1, 1983

By Pierre Mousset-Jones, Felipe Calizaya

This paper summarizes the current research trends in the ventilation design for the construction of very long tunnels, and presents the results of leakage flow measurements in three auxiliary ventilation systems. The study includes an estimation of an important design parameter, namely, the leakage path resistance, and a discussion of its effects on the overall efficiency of a ventilation system. A sample problem is used to illustrate the calculations.

Jan 1, 1997

By John A. Herbst, William T. Pate, A. Edward Oblad

Dynamic optimization is a cost-effective means to increase production or improve product quality in a plant. Several model-based approaches to dynamic optimization of mineral processing operations have been developed and implemented in plants. This paper reviews the phenomenological models that are the basis for dynamic optimization and the alternative methods of mathematical optimization. These methods range from theoretically complex and costly to implement to intuitively comprehensible and readily implemented.

Jan 1, 1990

By B. A. Ferguson, P. W. MacMillan

INTRODUCTION Jack Spalding in Deep Mining, Chapter 3, states: "In deep mining, to start stoping an orebody without a definite plan of operations covering the whole extraction from beginning to end is to invite serious trouble. Any stoping without plan is bound to leave, toward the end, a number of pillars, remnants, or promontories, which, as they are reduced in size, are liable to fail and cause a general collapse. The object of stope planning is so to mine an orebody that at no stage in the operation is a remnant left. Definition: `When a block of ore is stoped in such a way that eventually a small piece is left entirely surrounded by stoping, that piece is termed an island remnant.&apos; The design of and adherence to a plan of stoping is of greater importance in preventing rock bursts than the type of ground control adopted." This, of course, is just an example of the old axiom that an ounce of prevention is worth a pound of cure. And in this context, mining does not have to be very deep before poor ground conditions, made worse by lack of good planning, force a mining company to resort to more expensive methods of ore recovery. At all times when rock pressures become excessive, stoping plans must be devised to avoid the creation of pillars or promontories. This is most readily recognized when mining deep narrow ore veins by open methods. It would be a little more general to say that stoping systems should seek to avoid or minimize localized concentrations of rock stress. Ore bodies, and particularly those at Falcon¬bridge, can reach large widths and leaving pillars for extraction at a later time cannot be avoided. However, good planning can reduce the effect of factors which create bad ground conditions. The necessary ingredients of planning are time and information: time to formulate and revise ideas; information, gained in exploration and early development, to provide the fullest knowledge of the ore body. In this way, plans become meaningful. It must always be kept in mind that the long-term results of good planning often require decisions not compatible with reaching earliest full production. PLANNING FOR DEEP MINING At Falconbridge Nickel Mines ore bodies presently being found and prepared for production lie at depths in excess of 610 m (2000 ft) below surface. Current un¬derground exploration is being directed towards favor¬able locations below 914.4 and 1219.2-m (3000 and 4000-ft) depths, at most mines. The Onaping Deep ore body has been traced to a depth of 1508.8 m (4950 ft) and at Falconbridge mine the ore body is under develop¬ment below the 5000 level. Planning for more efficient ground control has therefore become an important con¬sideration of future mining. HYDRAULIC BACK FILLING AND CUT-AND-FILL STOPING The advent of hydraulic back filling has led to the increasing use of flat-back cut-and-fill stoping methods during the last ten years, until it has probably become the commonest method of mining deep ore deposits in Canada. These methods account for almost all the pro¬duction from Falconbridge Mines at this time. The ad¬vantages claimed are: safety-a minimum of open ground; very little supplementary ground support (except rockbolted backs and walls); greater selectivity and flexibility in extraction (horizontal extension of the vein, high grade ore stringers going out into the walls); and high productivity and increased mechanization in larger ore widths. There is some difference of opinion as to whether hydraulic classified tailing back fill provides any great resistance to initial closure of the stope walls. The evi¬dence available suggests that it does not. Addition of portland cement to the back fill just prior to placement has produced a material having the properties of a weak concrete. It is confidently expected that this material will assist greatly in the efficient mining of pillars and generally in giving increased ground support to oppose closure. PRINCIPLES OF STOPE PLANNING BY LONGITUDINAL FLAT-BACK CUT-AND-FILL Again quoting from Spalding: "The practice of con¬trolling output by stopping and starting stopes is bad¬stopes once started should proceed without interruption, and control must therefore be obtained by altering the rate of stoping. It is therefore necessary that faces should normally advance at a medium rate which can be boosted, if required, to give temporarily a greater output. Modern high productivity stoping methods, however, generally aim to achieve and maintain the maximum output possible from a stope. Control of tonnage and grade, therefore, becomes a more complex problem requiring very careful scheduling and organiza¬tion. With the basic method of flat-back overhand stoping using hydraulic fill, it is not usually possible to mine in such a way as to avoid creating pillars." Consider an ore body as illustrated in Fig. 1. It is 274.3 m (900 ft) high by 228.6 m (750 ft) long on strike and averages 4.6 m (15 ft) in ore width. It rep¬resents approximately 907 000 t (1,000,000 st). The ore body could be mined by advancing one long single face through all the levels from bottom to top. A total face length of 228.6 m (750 ft) would accommo¬date five 45.7-m (150-ft) stopes. See Fig. la. Each of these stopes would produce approximately 1814 t/m (2000 stpm) and the ore body would require a period of ten years for complete extraction. A possible im¬provement to this scheme might be to stagger the indi¬vidual stope faces. See Fig. 1b. Problems of hanging wall failure can be reduced by this arrangement. From the point of view of reducing travelway maintenance, it is good practice to employ a stoping system of retreat. Stopes farthest from the shaft are mined first so that on completion, haulage drifts below can be aban

Jan 1, 1982

By A. Zorychta, T. Cyrul, Z. Kleczek

INTRODUCTION Underground mining causes disturbances of the primary state of stresses. Resulting from those disturbances a loss of stability of rocks that surround excavation may occur interrupting the production and creating life danger for the personnel. One of the manifestations of such an instability is a rock burst phenomenon which mainly occurs at great depths. From the mechanical mint of view the rock burst is a loss of stability /Filcek et a1.,1984; Pietuchow and Linkow, 1976/ due to : - quasi-static stress changes in the surrounding rocks; we will call it s seam burst , - dynamic stress changes in the surrounding rocks caused by rock shocks ; we will call it roof burst. Possibility of the rock burst occurrence Is uniquely determined by the state of stresses existing in the rock mass. In the following sections of the paper we will consider different aspects of this question. Moreover distributions of displacements and failure criteria for a coal seam at longwall mining will be defined. STATEMENT OF THE PROBLEM Determination of the vertical stresses and displacements resulting from longwail mining will be based on the Budryk’s idea of a stress wave /Salustowicz, 1955/. The idea originates from the analysis of a roof plate /beam/ resting on the deformable foundation /Sean/ and subjected to the cylindrical bending. Equation of the bending lice uniquely defines vertical stresses and displacements which are induced in the seam. The equation will account only the shear force effect. Elimination of the bending moment has been shown and discussed by Zorychta and Bcrecki /Zorychta, 1985; Borecki and

Jan 1, 1986

By Gregory B. Baecher, Walter Steiner, Herbert H. Einstein

1. INTRODUCTION Empirical methods have always been important in tunneling in contrast to many other branches of engineering. Beginning in the late 19th century, when engineering entered the phase of formal modeling, this dichotomy could be seen to emerge even in the work of individuals. Culmann (1), Ritter (2) Kommerell (3) and others simultaneously were developing analytical approaches to bridge and building design and empirical approaches to tunnel design. The dichotomy remains. Empirical or simple analytical methods are used at most in the preliminary design of bridges and buildings, while they are used in all phases of tunnel design and construction. In fact, the past decade has seen a resurgence of interest in empirical methods, and with it discussion and controversy. This discussion has centered on the suitability of various methods. In some applications identical results are obtained with differing methods and in some cases radically different ones. On certain occasions the discussion has focused more on the methodological rather than empirical by taking issue with the appropriateness of particular parameters or the structure of some methods. This paper attempts to establish a basis for judging the suitability of empirical methods in tunnel design, and their applicability to particular cases. The paper makes no claim of exhaustiveness, and instead emphasizes basic requirements for application. Various methods are reviewed against this background. A detailed comparison of empirical methods and a description of their concept and background is now being prepared (4). Specifically the paper first defines empirical methods, and their purpose (Section 2), describes their structure (Section 3), and focuses on the basic requirements each must satisfy (Section 4). Then

Jan 1, 1979

By P. Huttagosol

The use of computer models to design ultimate pit limits during feasibility study and long range mine planning is becoming a significant practice in open pit mining. One of the problems in determining optimal ultimate pit limits using true optimization techniques has been they require a great deal of computer memory and execution time. In this paper, the maximum closure of a graph, which is a true optimizing model developed by Lerchs and Grossmann, is modified for solving ultimate pit limit problems. By using some properties of the original L&G graph algorithm, the tree configuration can be reduced to only connections between positive ore nodes. The modified algorithm is shown to require less memory and processing time while still yielding an optimal solution.

Jan 1, 1989

By Hayward B. Oblad, Gary F. Meenan

Two optoelectronic detectors were developed by CONSOL R&D for fine coal processing applications. One sensing device is used to estimate the amount of fine coal in the solids fraction of the froth flotation tailings slurry. The other probe, based on similar technology, is capable of measuring sol ids concentrations as high as 10 weight percent in fine coal slurry streams. These patented optoelectronic sensors are installed in several CONSOL coal preparation plants and are an integral part of the fine-coal control systems.

Jan 1, 1993

By Nader Shahcheraghi, Verya Nasri, Mehdi Bakhshi, Ali Haghighat

An accidental fire load is one of the major loads considered in design of segmental linings in transit tunnel. Typically, a two-dimensional coupled thermo-mechanical finite element analysis (FEA) is conducted. The conventional approach involves using standard fire curves (temperature-time curves) which can lead to a significant overestimation of fire load and tunnel lining thickness in metro tunnels. The focus of this paper is on the cutting-edge approach, using 3D computational fluid dynamics (CFD) analysis of real train fires in metro tunnels and coupled thermo-mechanical finite element analysis (FEA) to accurately and cost-effectively design fiber-reinforced concrete (FRC) segmental tunnel linings for large-scale metro projects.

Jun 23, 2024

By Howard M. Wells

Investment in minerals development usually entails big financial outlays. which will remain at risk for a long time before the venture can begin to generate a return cash flow. Before &apos;committing himself to such a venture the investor would be wise to carefully examine the possible consequences of his exposure to risk. In this context risk is defined in multiple terms, which relate the magnitude of possible loss with the probability that such loss may occur--normally the probability will decrease as the amount of possible loss increases. The analysis of risk is an essential component of the decision making process, especially so in the case of low grade high tonnage mining ventures where a very real possibility exists that future unfavorable circumstances may lead to losses that could cripple or ruin even the richest corporation. Wells (1979) postulates a rationale for making the investment decision under uncertainty based on the comparison of two independent risk criteria: 1) the risk inherent in the venture represented by the negative portion of the cumulative distribution of the net present value (NPV), as derived by a stochastic evaluation procedure, 2) the limits of risk the decision maker is willing to accept, taking account of the financial capacity-of the &apos;firm to absorb various levels of future cash shortfall should the venture prove disappointing. The chance the investor would be prepared to accept can be expected to decrease as the amount of the possible shortfall increases. The limits of acceptable risk are-defined by a curve called the "LL-curve" which can be directly compared with the cumu¬lative NPV curve. A positive investment decision is implied if the limits of acceptable risk are not exceeded.

Jan 1, 1982