Principles of Mining Part 1
Principles of Mining.
by Herbert C. Hoover.
PREFACE.
This volume is a condensation of a series of lectures delivered in part at Stanford and in part at Columbia Universities. It is intended neither for those wholly ignorant of mining, nor for those long experienced in the profession.
The bulk of the material presented is the common heritage of the profession, and if any one may think there is insufficient reference to previous writers, let him endeavor to find to whom the origin of our methods should be credited. The science has grown by small contributions of experience since, or before, those unnamed Egyptian engineers, whose works prove their knowledge of many fundamentals of mine engineering six thousand eight hundred years ago. If I have contributed one sentence to the acc.u.mulated knowledge of a thousand generations of engineers, or have thrown one new ray of light on the work, I shall have done my share.
I therefore must acknowledge my obligations to all those who have gone before, to all that has been written that I have read, to those engineers with whom I have been a.s.sociated for many years, and in particular to many friends for kindly reply to inquiry upon points herein discussed.
PRINCIPLES OF MINING.
CHAPTER I.
Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines.
DETERMINATION OF AVERAGE METAL CONTENT; SAMPLING, a.s.sAY PLANS, CALCULATIONS OF AVERAGES, PERCENTAGE OF ERRORS IN ESTIMATE FROM SAMPLING.
The following discussion is limited to _in situ_ deposits of copper, gold, lead, silver, tin, and zinc. The valuation of alluvial deposits, iron, coal, and other mines is each a special science to itself and cannot be adequately discussed in common with the type of deposits mentioned above.
The value of a metal mine of the order under discussion depends upon:--
_a_. The profit that may be won from ore exposed; _b_. The prospective profit to be derived from extension of the ore beyond exposures; _c_. The effect of a higher or lower price of metal (except in gold mines); _d_. The efficiency of the management during realization.
The first may be termed the positive value, and can be approximately determined by sampling or test-treatment runs. The second and the third may be termed the speculative values, and are largely a matter of judgment based on geological evidence and the industrial outlook.
The fourth is a question of development, equipment, and engineering method adapted to the prospects of the enterprise, together with capable executive control of these works.
It should be stated at the outset that it is utterly impossible to accurately value any mine, owing to the many speculative factors involved. The best that can be done is to state that the value lies between certain limits, and that various stages above the minimum given represent various degrees of risk. Further, it would be but stating truisms to those engaged in valuing mines to repeat that, because of the limited life of every mine, valuation of such investments cannot be based upon the principle of simple interest; nor that any investment is justified without a consideration of the management to ensue. Yet the ignorance of these essentials is so prevalent among the public that they warrant repet.i.tion on every available occasion.
To such an extent is the realization of profits indicated from the other factors dependent upon the subsequent management of the enterprise that the author considers a review of underground engineering and administration from an economic point of view an essential to any essay upon the subject. While the metallurgical treatment of ores is an essential factor in mine economics, it is considered that a detailed discussion of the myriad of processes under hypothetic conditions would lead too far afield. Therefore the discussion is largely limited to underground and administrative matters.
The valuation of mines arises not only from their change of ownership, but from the necessity in sound administration for a knowledge of some of the fundamentals of valuation, such as ore reserves and average values, that managerial and financial policy may be guided aright. Also with the growth of corporate ownership there is a demand from owners and stockholders for periodic information as to the intrinsic condition of their properties.
The growth of a body of speculators and investors in mining stocks and securities who desire professional guidance which cannot be based upon first-hand data is creating further demand on the engineer.
Opinions in these cases must be formed on casual visits or second-hand information, and a knowledge of men and things generally. Despite the feeling of some engineers that the latter employment is not properly based professionally, it is an expanding phase of engineers'
work, and must be taken seriously. Although it lacks satisfactory foundation for accurate judgment, yet the engineer can, and should, give his experience to it when the call comes, out of interest to the industry as a whole. Not only can he in a measure protect the lamb, by insistence on no investment without the provision of properly organized data and sound administration for his client, but he can do much to direct the industry from gambling into industrial lines.
An examination of the factors which arise on the valuation of mines involves a wide range of subjects. For purposes of this discussion they may be divided into the following heads:--
1. _Determination of Average Metal Contents of the Ore._ 2. _Determination of Quant.i.ties of Ore._ 3. _Prospective Value._ 4. _Recoverable Percentage of Gross Value._ 5. _Price of Metals._ 6. _Cost of Production._ 7. _Redemption or Amortization of Capital and Interest._ 8. _Valuation of Mines without Ore in Sight._ 9. _General Conduct of Examination and Reports._
DETERMINATION OF AVERAGE METAL CONTENTS OF THE ORE.
Three means of determination of the average metal content of standing ore are in use--Previous Yield, Test-treatment Runs, and Sampling.
PREVIOUS YIELD.--There are certain types of ore where the previous yield from known s.p.a.ce becomes the essential basis of determination of quant.i.ty and metal contents of ore standing and of the future probabilities. Where metals occur like plums in a pudding, sampling becomes difficult and unreliable, and where experience has proved a sort of regularity of recurrence of these plums, dependence must necessarily be placed on past records, for if their reliability is to be questioned, resort must be had to extensive test-treatment runs. The Lake Superior copper mines and the Missouri lead and zinc mines are of this type of deposit. On the other sorts of deposits the previous yield is often put forward as of important bearing on the value of the ore standing, but such yield, unless it can be _authentically_ connected with blocks of ore remaining, is not necessarily a criterion of their contents. Except in the cases mentioned, and as a check on other methods of determination, it has little place in final conclusions.
TEST PARCELS.--Treatment on a considerable scale of sufficiently regulated parcels, although theoretically the ideal method, is, however, not often within the realm of things practical. In examination on behalf of intending purchasers, the time, expense, or opportunity to fraud are usually prohibitive, even where the plant and facilities for such work exist. Even in cases where the engineer in management of producing mines is desirous of determining the value of standing ore, with the exception of deposits of the type mentioned above, it is ordinarily done by actual sampling, because separate mining and treatment of test lots is generally inconvenient and expensive.
As a result, the determination of the value of standing ore is, in the great majority of cases, done by sampling and a.s.saying.
SAMPLING.--The whole theory of sampling is based on the distribution of metals through the ore-body with more or less regularity, so that if small portions, that is samples, be taken from a sufficient number of points, their average will represent fairly closely the unit value of the ore. If the ore is of the extreme type of irregular metal distribution mentioned under "previous yield," then sampling has no place.
How frequently samples must be taken, the manner of taking them, and the quant.i.ty that const.i.tutes a fair sample, are matters that vary with each mine. So much depends upon the proper performance of this task that it is in fact the most critical feature of mine examination. Ten samples properly taken are more valuable than five hundred slovenly ones, like grab samples, for such a number of bad ones would of a surety lead to wholly wrong conclusions.
Given a good sampling and a proper a.s.say plan, the valuation of a mine is two-thirds accomplished. It should be an inflexible principle in examinations for purchase that every sample must be taken under the personal supervision of the examining engineer or his trusted a.s.sistants. Aside from throwing open the doors to fraud, the average workman will not carry out the work in a proper manner, unless under constant supervision, because of his lack of appreciation of the issues involved. Sampling is hard, uncongenial, manual labor.
It requires a deal of conscientiousness to take enough samples and to take them thoroughly. The engineer does not exist who, upon completion of this task, considers that he has got too many, and most wish that they had taken more.
The accuracy of sampling as a method of determining the value of standing ore is a factor of the number of samples taken. The average, for example, of separate samples from each square inch would be more accurate than those from each alternate square inch. However, the acc.u.mulated knowledge and experience as to the distribution of metals through ore has determined approximately the manner of taking such samples, and the least number which will still by the law of averages secure a degree of accuracy commensurate with the other factors of estimation.
As metals are distributed through ore-bodies of fissure origin with most regularity on lines parallel to the strike and dip, an equal portion of ore from every point along cross-sections at right angles to the strike will represent fairly well the average values for a certain distance along the strike either side of these cross-sections. In ma.s.sive deposits, sample sections are taken in all directions. The intervals at which sample sections must be cut is obviously dependent upon the general character of the deposit. If the values are well distributed, a longer interval may be employed than in one subject to marked fluctuations. As a general rule, five feet is the distance most accepted. This, in cases of regular distribution of values, may be stretched to ten feet, or in reverse may be diminished to two or three feet.
The width of ore which may be included for one sample is dependent not only upon the width of the deposit, but also upon its character.
Where the ore is wider than the necessary stoping width, the sample should be regulated so as to show the possible locus of values.
The metal contents may be, and often are, particularly in deposits of the impregnation or replacement type, greater along some streak in the ore-body, and this difference may be such as to make it desirable to stope only a portion of the total thickness. For deposits narrower than the necessary stoping width the full breadth of ore should be included in one sample, because usually the whole of the deposit will require to be broken.
In order that a payable section may not possibly be diluted with material unnecessary to mine, if the deposit is over four feet and under eight feet, the distance across the vein or lode is usually divided into two samples. If still wider, each is confined to a span of about four feet, not only for the reason given above, but because the more numerous the samples, the greater the accuracy.
Thus, in a deposit twenty feet wide it may be taken as a good guide that a test section across the ore-body should be divided into five parts.
As to the physical details of sample taking, every engineer has his own methods and safeguards against fraud and error. In a large organization of which the writer had for some years the direction, and where sampling of mines was constantly in progress on an extensive scale, not only in contemplation of purchase, but where it was also systematically conducted in operating mines for working data, he adopted the above general lines and required the following details.
A fresh face of ore is first broken and then a trench cut about five inches wide and two inches deep. This trench is cut with a hammer and moil, or, where compressed air is available and the rock hard, a small air-drill of the hammer type is used. The spoil from the trench forms the sample, and it is broken down upon a large canvas cloth. Afterwards it is crushed so that all pieces will pa.s.s a half-inch screen, mixed and quartered, thus reducing the weight to half. Whether it is again crushed and quartered depends upon what the conditions are as to a.s.saying. If convenient to a.s.say office, as on a going mine, the whole of the crushing and quartering work can be done at that office, where there are usually suitable mechanical appliances. If the samples must be taken a long distance, the bulk for transport can be reduced by finer breaking and repeated quartering, until there remain only a few ounces.
PRECAUTIONS AGAINST FRAUD.--Much has been written about the precautions to be taken against fraud in cases of valuations for purchase. The best safeguards are an alert eye and a strong right arm. However, certain small details help. A large leather bag, arranged to lock after the order of a mail sack, into which samples can be put underground and which is never unfastened except by responsible men, not only aids security but relieves the mind. A few samples of country rock form a good check, and notes as to the probable value of the ore, from inspection when sampling, are useful. A great help in examination is to have the a.s.says or a.n.a.lyses done coincidentally with the sampling. A doubt can then always be settled by resampling at once, and much knowledge can be gained which may relieve so exhaustive a program as might be necessary were results not known until after leaving the mine.
a.s.sAY OF SAMPLES.--Two a.s.says, or as the case may be, a.n.a.lyses, are usually made of every sample and their average taken. In the case of erratic differences a third determination is necessary.
a.s.sAY PLANS.--An a.s.say plan is a plan of the workings, with the location, a.s.say value, and width of the sample entered upon it. In a mine with a narrow vein or ore-body, a longitudinal section is sufficient base for such entries, but with a greater width than one sample span it is desirable to make preliminary plans of separate levels, winzes, etc., and to average the value of the whole payable widths on such plans before entry upon a longitudinal section. Such a longitudinal section will, through the indicated distribution of values, show the shape of the ore-body--a step necessary in estimating quant.i.ties and of the most fundamental importance in estimating the probabilities of ore extension beyond the range of the openings. The final a.s.say plan should show the average value of the several blocks of ore, and it is from these averages that estimates of quant.i.ties must be made up.
CALCULATIONS OF AVERAGES.--The first step in arriving at average values is to reduce erratic high a.s.says to the general tenor of other adjacent samples. This point has been disputed at some length, more often by promoters than by engineers, but the custom is very generally and rightly adopted. Erratically high samples may indicate presence of undue metal in the a.s.say attributable to unconscious salting, for if the value be confined to a few large particles they may find their way through all the quartering into the a.s.say.
Or the sample may actually indicate rich spots of ore; but in any event experience teaches that no dependence can be put upon regular recurrence of such abnormally rich spots. As will be discussed under percentage of error in sampling, samples usually indicate higher than the true value, even where erratic a.s.says have been eliminated. There are cases of profitable mines where the values were all in spots, and an a.s.say plan would show 80% of the a.s.says _nil_, yet these pockets were so rich as to give value to the whole.
Pocket mines, as stated before, are beyond valuation by sampling, and aside from the previous yield recourse must be had to actual treatment runs on every block of ore separately.
After reduction of erratic a.s.says, a preliminary study of the runs of value or shapes of the ore-bodies is necessary before any calculation of averages. A preliminary delineation of the boundaries of the payable areas on the a.s.say plan will indicate the sections of the mine which are unpayable, and from which therefore samples can be rightly excluded in arriving at an average of the payable ore (Fig. 1). In a general way, only the ore which must be mined need be included in averaging.
The calculation of the average a.s.say value of standing ore from samples is one which seems to require some statement of elementals.
Although it may seem primitive, it can do no harm to recall that if a dump of two tons of ore a.s.saying twenty ounces per ton be added to a dump of five tons averaging one ounce per ton, the result has not an average a.s.say of twenty-one ounces divided by the number of dumps. Likewise one sample over a width of two feet, a.s.saying twenty ounces per ton, if averaged with another sample over a width of five feet, a.s.saying one ounce, is no more twenty-one ounces divided by two samples than in the case of the two dumps. If common sense were not sufficient demonstration of this, it can be shown algebraically.
Were samples equidistant from each other, and were they of equal width, the average value would be the simple arithmetical mean of the a.s.says. But this is seldom the case. The number of instances, not only in practice but also in technical literature, where the fundamental distinction between an arithmetical and a geometrical mean is lost sight of is amazing.
To arrive at the average value of samples, it is necessary, in effect, to reduce them to the actual quant.i.ty of the metal and volume of ore represented by each. The method of calculation therefore is one which gives every sample an importance depending upon the metal content of the volume of ore it represents.
The volume of ore appertaining to any given sample can be considered as a prismoid, the dimensions of which may be stated as follows:--
_W_ = Width in feet of ore sampled.
_L_ = Length in feet of ore represented by the sample.
_D_ = Depth into the block to which values are a.s.sumed to penetrate.