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By Gen-Hua Shi

The deformation of a discontinuous rock is a sum of individual translations, rotations, and strains of the component blocks. These produce opening and slip between blocks along the discontinuities. Rather than attempting to analyze such deformations with a mathematical model representing the geometric and stress/strain properties of all points, for the back-calculation of observed displacements we have produced a novel approach to solve the inverse problem. Using a field of displacement measurements and a map of the system of discontinuities, the method, determines the intrablock and interblock motions by a least squares formulation. In this brief paper we address only two- dimensional formulations. However, computer codes have also been developed for three dimensional problems.

Jan 1, 1984

By Y. H. Hatzor

"This is an extended abstract for a keynote lecture delivered by the author during the 2015 ISRM congress in Montreal on the application of the numerical discontinuous deformation analysis (DDA) method in rock mechanics practice. Due to the large scope of the topic this lecture will focus on studies performed by the rock mechanics group at Ben-Gurion University, alone or in collaboration which other research groups, and is not intended to provide a comprehensive review of everything that has been done on the subject worldwide during the past two decades. A forthcoming textbook (Hatzor et al., in preparation) will attempt to provide such comprehensive coverage.DDA has been developed by Dr. Gen-hua Shi while he was doing his PhD studies under the supervision of Professor R. E. Goodman at U. C. Berkeley (Shi, 1988). Dr. Shi has invented a new numerical discrete element method which provides a solution for dynamic deformation of block systems, hence its applicability to rock mechanics practice. The method is similar in essence to the finite element method in its implicit formulation of the time integration scheme and where in every time step the minimum potential energy of the entire system is sought, but here every element is a finite block with six degrees of freedom. The blocks are assumed to be stiff (simply deformable) so that most of the energy is consumed by slip along pre-existing discontinuities, the frictional resistance of which is assumed to obey the Coulomb-Mohr failure criterion for rock joints. The greatest advantage of DDA over alternative numerical discrete element methods is its robust area (volume) integration which ensures great accuracy even when the blocks are of irregular shapes, including non-convex blocks which may contain holes. The greatest disadvantage is the necessity to solve in every time step very large matrices of unknowns, imposing great CPU demand when the block system involves a large number of blocks. Another disadvantage is the sensitivity of the solution to the choice of the penalty parameter which is implemented in DDA in the form of stiff springs that are attached to contacts once detected automatically.The inherently dynamic formulation of the DDA method lends itself to solution of dynamic problems in rock mechanics. Dynamic analysis with DDA can be performed in different ways corresponding to different rock mechanics problems and loading conditions. Three main classes of loading conditions which are relevant to rock mechanics applications are discussed here: 1) dynamic loading of a single bock which rests on a stationary foundation, 2) response of a block to dynamic loading of the foundations, 3) wave propagation through a block system.The most common approach is to introduce the dynamic force to a specific block in an otherwise fixed block system and check the resulting deformation, typically the time dependent displacement or rotation of the loaded block. This approach is particularly useful for dynamic rock slope stability studies when a stability of a specific rock block against earthquake vibrations is in question. The first 2D-DDA benchmark test of this approach was performed by Hatzor and Feintuch (2001) who introduced harmonic acceleration functions into a block which rests on an inclined plane. The analytical solution proposed for this problem by Hatzor and Feintuch (2001) was later generalized by Kamai and Hatzor (2008). The first 3D-DDA benchmarking for this approach was presented by Bakun-Mazor et al. (2012) who studied single and double face sliding of blocks which rest on stationary foundations and subjected to harmonic input acceleration functions."

Jan 1, 2015

By C. Yanqui

"Discontinuum Mechanics is based on two foundations: the idealization of the internal structure of substances, and the principle of the arithmetic mean value. For a linear discontinuum, the methods of Crystallography are used to describe their structure, in which nodes stands for the position of the homologous points such as molecules, grains, or any other motif. The principle of the mean value states that the value of any discrete function at a node is equal to the arithmetic average of the values of this function at the neighboring nodes. This principle leads to an elliptical linear differential equation of the second order, with coefficients given by the statistical second moments of the Cartesian components of the metric vector. As long as those coefficients are components of a symmetric second-order tensor, there are three mutually perpendicular directions, in which the variances reach their extreme values and the covariances are zero, showing that the mean value principle transforms the discontinuum into a statistically equivalent orthotropic continuum.The application of Discontinuum Mechanics to linear rock masses is simple and direct. It is sufficient to define the motif as the plane of geological discontinuity, and the metric vector as the normal vector to this plane, whose magnitude is the spacing between two consecutive planes belonging to the same set of discontinuities. Furthermore, heterogeneities of rock masses can be also included in this description by substituting the plane of discontinuity by a zone of weakness. In this way, the magnitude of the normal vector results from the product of the spacing and the RQD or the RMR. In going further in this theory, at least three conclusions show up. First, in the evaluation of rock masses, it is necessary to determine the orientation, spacing, and RMR for each set of discontinuities. Second, the conventional method of finding the principal families from the contours of equal concentration of poles on the stereographic projection excluding the spacing does not have any physical meaning. Third, any problem of rock mechanics can be solved in a rigorous and reliable way by integrating the differential equation of the mean value."

Jan 1, 2015

By Lawrence Devon Smith

"The concept of risk is well established in the mining industry. It is acknowledged when estimates of reserves are expressed as proven or probable, when mining and metallurgical recoveries are applied to the ore, and when contingencies are added to costs. However, it is difficult to provide a quantitative assessment of risk. The significant sources of risk in a mineral project and how these are addressed in project evaluations are discussed.The discount rate is examined as a fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed, and a methodology for the analysis of risk levels is proposed that assesses the constituent components of the discount rate: real interest, mineral project risks, and country risk.IntroductionThis paper examines the components of the discounted cash flow discount rate and proposes a method of estimating project-specific discount rates. The motivation for this work comes from experience of project evaluations in which owners and purchasers had agreed on virtually every aspect of the evaluation except how much the project was worth. Agreement was reached on reserves, grade, recovery, capital costs, operating costs, taxes, and, by combining these components, even on the final cash flow values. The only difference in opinion concerned the discount rate to be used in the calculation of the net present value. Depending on the life of the project, such differences of opinion can cause a variation of more than 50% in the value placed on a project! This is illustrated in Figure I."

Jan 1, 1995

By L. D. Smith

Paper presented at the conference: Risk assessment in the extractive industries, held in Exeter, UK, 23-24 March 1994, and first published London: IMM, 1994, preprint volume. 22pp., 15 refs. The concept of risk is well established in the mining industry but it is difficult to provide a quantitative assessment of risk. A discussion is presented of the significant sources of risk in a mineral project and how they are addressed. The discount rate is examined as a fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed and a methodology for the analysis of risk levels is proposed which assesses the constituent components of the discount rate (real interest, mineral project risks and country risk)

Dec 1, 1994

By Lawrence Devon Smith

"The concept of risk is well established in the mining industry. It is acknowledged when estimates of reserves are expressed as proven or probable, when mining and metallurgical recoveries are applied to the ore, and when contingencies are added to costs. However, it is difficult to provide a quantitative assessment of risk. The significant sources of risk in a mineral project and how these are addressed in project evaluations are discussed. The discount rate is examined as a fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed, and a methodology for the analysis of risk levels is proposed that assesses the constituent components of the discount rate: real interest, mineral project risks, and country risk.IntroductionThis paper examines the components of the discounted cash flow discount rate and proposes a method of estimating project-specific discount rates. The motivation for this work comes from experience of project evaluations in which owners and purchasers had agreed on virtually every aspect of the evaluation except how much the project was worth. Agreement was reached on reserves, grad~, recovery, capital costs, operating costs, taxes, and, by combining these components, even on the fmal cash flow values. The only difference in opinion concerned the discount rate to be used in the calculation of the net present value. Depending on the life of the project, such differences of opinion can cause a variation of more than 50% in the value placed on a project! This is illustrated in Figure 1."

Jan 1, 2003

By H. K. Taylor, B. Denby, L. D. Smith

Contributions by H.K. Taylor and G.A. Davis discuss the three papers published in Transactions IMM A, vols. 103 and 104, with responses by Smith and Dowd

Dec 1, 1995

By Donald R. Lessard

I. INTRODUCTION There is no question that the choice of an appropriate discount rate is a critical element in virtually all business decisions in extractive industries. The standard textbook approach relies on a single overall cost of capital for an entire firm, itself a weighted average of the firm's cost of debt and equity. But a single rate is appropriate only if the commercial risks and financing structures are similar for all projects under consideration. In extractive industries, appropriate discount rates are likely to vary greatly from project to project. Risks of projects differ markedly by mineral, by country in which the project is located, by stage in production, and by position in the project's life. Further, for a variety of institutional reasons, financing structures vary greatly in relation to these same variables and thus the discount rate appropriate to the entire investment and, in particular, to the sponsor's equity investment will vary even more markedly. Failure to select discount rates which reflect these differences can result in extremely distorted decisions. Our interest in this subject results from our ongoing research on alternative ownership and financing structures for large scale extractive ventures in less developed countries where risks to the various participants--the sponsors, the financiers, and the host government--vary dramatically with the different options. Given the magnitude of these differences, a single discount rate for all options is clearly inappropriate. However, there appear to be few guidelines for practicing managers to follow in setting appropriate rates. In this paper, we take a first step in this direction.

Jan 1, 1977

By Christopher R. Lattanzi

"Discounted cash flow analysis provides a means of relating the magnitude of expected future cash profits to the magnitude of the initial cash investment required to purchase an asset or to develop it for commercial production. The objectives of discounted cash flow analysis are to determine:.. The net present value of a stream of expected future cash revenues and expenditures... The rate of return which the expected future cash flows will yield on a given level of initial cash investment.In the case of mineral properties, discounted cash flow analysis is generally accepted as the preferred method of valuation, whenever sufficient data are available to permit its reasoned application. Sufficient data are required to support estimation of all of the individual elements of cash revenue and cash expenditure which will be associated with the development and operation of the property, up to the end of its estimated life. It is the accuracy of these input estimates which determines the validity of the resulting determinations of profitability and rate of return on invested capital.In undertaking any discounted cash flow analysis, it is important to recognize certain fundamental attributes of the mining industty:.. The basis of any mineral development is the existence of an ore reserve... Costs are determined by the number of tonnes mined and processed, while revenues are determined by the number of pounds or ounces of metal produced. The two are related by the recovered grade of the ore... Profit is typically more sensitive to changes in revenue than it is to changes in cost... Commodity price is a principal determinant of revenue, but it is also the factor with which is associated the greatest level of financial risk.In the end, of all of the factors which must be considered in the discounted cash flow valuation of a mineral property, the most significant are the reliability of the reserve estimate, particularly with respect to recovered grade, the price at which the product is to be sold, and the risk of not maintaining the projected level of price."

Jan 1, 2003

By Lawrence Devon Smith

"This paper examines the impact of the various assumptions that go into an economic evaluation, and shows how these can be combined to show an exciting result that may not really exist. An example of an embellished case (the kind that one frequently sees when projects are being promoted) is developed and the cumulative impact is analysed to show the actual project underneath. The paper also points out some areas to watch for overly optimistic assumptions such as prices, inflation, and debt. The concept of a ""bare bones"" base case is proposed (constant metal prices, constant dollars, no inflation, no debt, no interest, on a project basis, after tax) as a common reference point.As well, the discount rate is examined as a fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed, and a methodology for the analysis of risk levels is proposed that assesses the constituent components of the discount rate: real interest, mineral project risks, and country risk.INTRODUCTIONOften, the first time that all of the technical and economic data for a mineral project comes together in one place is when the economic evaluation is developed. This typically happens when work on the project has progressed to a sufficient level of detail that the effort to produce a year-by-year cash flow is justified, usually at the pre-feasibility or feasibility study stage. The data involved will include:• production; tonnes waste and ore mined, ore grade, mining recovery, metallurgical recovery, metal sold• revenue; metal price, smelting & refining charges, marketing costs• operating Costs; mining, milling, administration, fees, royalties• capital Costs; exploration, development, construction, indirect costs (engineering, management), contingencies, start-up, inventories, working capital, replacement and sustaining capital, closure costs• taxes and royalties• exclusions; depreciation (this is not a cash item), sunk costs (only costs going forward)."

Jan 1, 2003

By L. D. Smith

"This paper examines the impact of the various assumptions that go into an economic evaluation, and shows how these can be combined to show an exciting result that may not really exist. An example of an embellished case (the kind that one frequently sees when projects are being promoted) is developed and the cumulative impact is analyzed to show the actual project underneath. The paper also points out some areas to watch for overly optimistic assumptions such as prices, inflation, and debt. The concept of a “bare bones” base case is proposed (constant metal prices, constant dollars, no inflation, no debt, no interest, on a project basis, after tax) as a common reference point.As well, the discount rate is examined as one of the fundamental means of reflecting risk in discounted cash flow evaluations. Current industry practice is discussed, and a methodology for the analysis of risk levels is proposed that assesses the constituent components of the discount rate: real interest, mineral project risks, and country risk."

Jan 1, 2002

By Sorentino C

Mineral valuation may appear to be a special field of financial valuation when in fact it is a subset of general investment decision theory. The only significant difference in mineral valuation is that in the case of valuing an on-going mineral asset, ie a mine, often there is no initial capital outlay involved. One is required to determine what the mineral asset as it stands is worth. But this is the same problem as determining the maximum one could pay today and not incur a loss over the life of the asset. In other words one needs to determine the Net Present Value (NPV) of the asset. The two most widely used discounted cash flow methods, NPV and Internal Rate of Return (IRR) came of age with the rapid adoption of the personal computer and spreadsheet programs. The two methods are directly related as the IRR is a special case of NPV. NPV measures the absolute increase in real wealth that can be expected from a certain investment, which makes it particularly suitable for mineral asset valuation, but ignores the efficiency of the investment. In contrast, IRR gives the expected efficiency of the investment but ignores the increase in wealth aspect. IRR has two serious theoretical weaknesses; multiple IRR's and a very rigid assumption about the rate of return of reinvested proceeds, plus if no initial equity expenditure is involved there is no IRR. The choice of the ""hurdle"" rate can also be a problem and in certain circumstances one can obtain different rankings of mutually exclusive projects using IRR and NPV. Although NPV and IRR supposedly measure financial risk, in fact they only address a very narrow area of risk, namely the time value of money given the real discount rate. They side step the issue of what the real discount rate should be and varying degrees of risk. The classical way to establish the real discount rate is to use the weighted average cost of capital.

Jan 1, 1994

INTRODUCTION The after-tax rate of return that properly discounts future cash flows is usually referred to as the "discounted cash flow-rate of return" (DCF-ROR). The method is also referred to as the internal rate of return, true rate of return, and investor's rate of return in some literature. According to Stermole (1974, p. 188) industry polls indicate that the DCF- ROR method is the number one economic evaluation decision method used by more than 90% of the industrial companies that use for- mal economic evaluation procedures. Other economic evaluation methods that have been used in the past, such as payback period, accounting ROR, etc., have largely given way to DCF-ROR analysis because they fail to account properly for the time value of money. DCF-ROR is generally defined as that rate of return that makes the present worth of future generated cash flow over the life of the project (including after tax salvage value) equal to the present worth of all after-tax investments. The "present worthing" of future cash flow involves discounting future cash flow to a present value according to the mathematics of compound interest at some interest rate. The determination of the interest rate that equates the present worth of future after-tax earnings with the present worth of all after-tax investments necessary to create such earnings is properly called the discounted cash flow rate of return analysis. Although present worth calculations are usually used for determining the DCF-ROR, the same results can be obtained by comparing income and costs of any equivalent point in time, i.e., future worth, etc.

Jan 1, 1980

By O. L. Papendorf

For purposes of simplification, a case is presented for an engineer to discount cash flows in real rather than in current terms when giving evidence in a court of law. The difference between the two methods is highlighted, and a recommendation is made in the case where differential rates apply.

Jan 1, 1981

SINCE I have told you of the distillation of waters and the extraction of oils from things-all ingenious and useful processes-I wish to continue to speak of the arts. I am reminded that I first wish to write down for you the discourse that I made to you on another occasion a few days ago concerning the operation of a mint, so that if you have lost it from your memory (and this would not be surprising since you have had no practice in it) you may repossess it if you should need to practice it or even to talk about it, and if you find yourself in this activity it may not be new to you. I told you, as I believe you will remember and so again I repeat, that a very great and constant diligence is required by one who wishes to operate a mint well, or to have it operated, because it has many parts which it is necessary for anyone who enters this work to understand very well; indeed, if he wishes that all the work of his helpers be done well, he will have to do it himself. And if it were possible, he should have a hundred hands and a hundred eyes together, and at the same time should be in different places, because some loss often occurs in what is handled because of the carelessness of the workers or because of their little real trustworthiness. It is understood that such things require great hard labors and many kinds of knowledge. The material handled in this work is most often either gold or silver all ready to be spent, and these things are very attractive to those who handle them. In addition to being made into pieces of money likely to disappear, it is very easy to lose, and whatever part is lacking for any reason whatever [132v] brings detriment and loss to the patron since it is a thing of value. Therefore, in short, anyone who wishes to exercise this art well, without being fraudulent therein, must watch the weights with all care because the essence of this art is naught but the division of a quantity of weight into many exactly defined pieces and the alloying of gold by carats and of silver by leghe, exactly established in accordance with what the prince grants you as remedy.* If through negligence you exceed in perfection

Jan 1, 1942

AVING started to tell you of working potter's clay for making crucibles and shells, the wish came to me to tell you of the practice of this art also. Although it may seem at first glance to be outside the order and purpose of my writing, he who considers well will see that it is not unrelated to it but proper, since it is wholly dependent on the agency and power of fire if it is to be brought to its perfection. Moreover, the potter's glazes and colors are all substances of various metals or impure minerals and therefore belong to fire. Since it is my intention to treat of fire, minerals, and metals for you, I surely should not have omitted this, particularly because it is a necessary art which enriches and is greatly praised both for its ingenuity and its beauty. The art of the potter has two sources as its principal basis. One comes from the art of design, the other from various alchemical secrets and elemental mixtures. In regard to these, I find that, in my opinion, all this art depends in the last analysis on four things: on good judgment in general, and on the art of design so as to be able to make the vessels beautiful and of good shape, as well as to ornament them with painting; after baking them well the first and second times, the next thing is to know how to make and apply the glaze well and to paint them with varied and appropriate colors. The fourth is to see that you have good, fine clay without small stones or lumps-indeed this is to be considered as the first thing. Now this that I have called clay is what many call cretaceous earth and some call argil. It is found and dug up when the masters wish to make use of it and is put in a container to be moistened. When it is moistened, it is beaten on a bench with an iron rod and very well prepared. Mixing it carefully, every small stone, lump, or other hardness that it contains is removed and cleaned away. Then a shaft [145V] of iron is fitted as the journal in a large wheel. On the other end of the journal a small wheel is made which forms an instrument for working that is called a lathe. Having put some clay on this, it is made to rotate by pushing with one foot, and, by rotating it, vessels are worked into a pleasing shape and size. Then they are taken off and put on a board to dry. After drying artificially or naturally they are painted red,

Jan 1, 1942

By John Stubbs

Sub-Surface Shaft excavation Mine development Headframes Surface Production facilities Product storage and loading Tailings area Infrastructure Discovery Lodge Utilities Operations complex Port Marine loading Rail unloading and storage

May 1, 2013

While SME is hosting its Annual Meeting at the Phoenix Convention Center, Feb. 28 to March 3, one of the finest collections of mining history will be on display just 15 blocks away at the Arizona Mining and Mineral Museum. Inside the museum, visitors will be treated to a treasure trove of minerals, gems, me¬teorites, rocks, fossils, mining artifacts, historical exhibits and interactive displays on modern mining. The museum is located at 1502 West Washington. For SME Annual Meeting attendees, this is a free, eight-minute Dash bus ride 15 blocks west of the Phoenix Convention Center.

Jan 1, 2010

By B. W. Dyer

IN 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KC1) and carnallite (KMgC12.6H20). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. LOCATION AND GEOLOGY OF DEPOSITS The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado Rivera distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 2o E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 2o E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: [Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel]

Jan 1, 1945

By Sherwin F. Kelly

THAT gold ores occur in Georgia is a fact apparently not widely known outside of that state, yet in the last hundred years nearly $18,000,000 worth of gold has been mined there. The discovery of gold-hearing quartz was made in 1823 on the "Forty Acre Lot" (which now belongs to the Columbia Mining Co.), in McDuffie County, and about seven years later the first stamp mill on record was erected near there. In recent years Georgia's gold production has dwindled to an insignificant figure. However, with the increase in gold price, interest in this district has been revived, so an electrical geophysical survey was undertaken to aid in discovering new quartz veins, on a part of the Forty Acre Lot, the adjoining Hamilton mine, and the nearby Woodall property.

Jan 1, 1934