Principles of Mining: Valuation, Organization and Administration
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Title: Principles of Mining: Valuation, Organization and Administration
Author: Herbert Hoover
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Language: English
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*** START OF THE PROJECT GUTENBERG EBOOK PRINCIPLES OF MINING: VALUATION, ORGANIZATION AND ADMINISTRATION ***
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PRINCIPLES OF MINING
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PRINCIPLES OF MINING
VALUATION, ORGANIZATION AND ADMINISTRATION
COPPER, GOLD, LEAD, SILVER, TIN AND ZINC
BY
HERBERT C. HOOVER
_Member American Institute of Mining Engineers, Mining and Metallurgical
Society of America, Société des Ingénieurs Civils de France, Fellow
Royal Geographical Society, etc._
First Edition
_FOURTH THOUSAND_
McGRAW-HILL BOOK COMPANY
239 WEST 39TH STREET, NEW YORK
BOUVERIE STREET, LONDON, E.C.
1909
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 accumulated 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 associated for many years,
and in particular to many friends for kindly reply to inquiry upon
points herein discussed.
CONTENTS.
CHAPTER 1.
Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines
Determination of average metal content; sampling, assay plans,
calculations of averages, percentage of errors in estimate from
sampling.
CHAPTER II.
Mine Valuation (_Continued_)
Calculation of quantities of ore, and classification of ore in sight.
CHAPTER III.
Mine Valuation (_Continued_)
Prospective value. Extension in depth; origin and structural character
of the deposit; secondary enrichment; development in neighboring
mines; depth of exhaustion.
CHAPTER IV.
Mine Valuation (_Continued_)
Recoverable percentage of the gross assay value; price of metals;
cost of production.
CHAPTER V.
Mine Valuation (_Continued_)
Redemption or amortization of capital and interest.
CHAPTER VI.
Mine Valuation (_Concluded_)
Valuation of mines with little or no ore in sight; valuations on
second-hand data; general conduct of examinations; reports.
CHAPTER VII.
Development of Mines
Entry to the mine; tunnels; vertical, inclined, and combined shafts;
location and number of shafts.
CHAPTER VIII.
Development of Mines (_Continued_)
Shape and size of shafts; speed of sinking; tunnels.
CHAPTER IX.
Development of Mines (_Concluded_)
Subsidiary development: stations; crosscuts; levels; interval between
levels; protection of levels; winzes and rises. Development in the
prospecting stage; drilling.
CHAPTER X.
Stoping
Methods of ore-breaking; underhand stopes; overhand stopes; combined
stope. Valuing ore in course of breaking.
CHAPTER XI.
Methods of Supporting Excavation
Timbering; filling with waste; filling with broken ore; pillars
of ore; artificial pillars; caving system.
CHAPTER XII.
Mechanical Equipment
Conditions bearing on mine equipment; winding appliances; haulage
equipment in shafts; lateral underground transport; transport in
stopes.
CHAPTER XIII.
Mechanical Equipment (_Continued_)
Drainage: controlling factors; volume and head of water; flexibility;
reliability; power conditions; mechanical efficiency; capital outlay.
Systems of drainage,--steam pumps, compressed-air pumps, electrical
pumps, rod-driven pumps, bailing; comparative value of various
systems.
CHAPTER XIV.
Mechanical Equipment (_Concluded_)
Machine drilling: power transmission; compressed air _vs._ electricity;
air drills; machine _vs._ hand drilling. Workshops. Improvement in
equipment.
CHAPTER XV.
Ratio of Output to the Mine
Determination of possible maximum; limiting factors; cost of equipment;
life of the mine; mechanical inefficiency of patchwork plant;
overproduction of base metal; security of investment.
CHAPTER XVI.
Administration
Labor efficiency; skill; intelligence; application coördination;
contract work; labor unions; real basis of wages.
CHAPTER XVII.
Administration (_Continued_)
Accounts and technical data and reports; working costs; division
of expenditure; inherent limitations in accuracy of working costs;
working cost sheets. General technical data; labor, supplies, power,
surveys, sampling, and assaying.
CHAPTER XVIII.
Administration (_Concluded_)
Administrative reports.
CHAPTER XIX.
The Amount of Risk in Mining Investments
Risk in valuation of mines; in mines as compared with other commercial
enterprises.
CHAPTER XX.
The Character, Training, and Obligations of the Mining Engineering
Profession
Index
PRINCIPLES OF MINING.
CHAPTER I.
Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines.
DETERMINATION OF AVERAGE METAL CONTENT; SAMPLING, ASSAY 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 repetition 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 Quantities 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 space becomes the essential basis of determination
of quantity 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 assaying.
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 quantity that constitutes 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 assay 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
assistants. 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 accumulated 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 massive 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 pass 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 assaying. If convenient to assay
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 assays or analyses 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.
ASSAY OF SAMPLES.--Two assays, or as the case may be, analyses,
are usually made of every sample and their average taken. In the
case of erratic differences a third determination is necessary.
ASSAY PLANS.--An assay plan is a plan of the workings, with the
location, assay 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 quantities and of the most fundamental importance in
estimating the probabilities of ore extension beyond the range of
the openings. The final assay plan should show the average value
of the several blocks of ore, and it is from these averages that
estimates of quantities must be made up.
CALCULATIONS OF AVERAGES.--The first step in arriving at average
values is to reduce erratic high assays 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 assay 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 assay.
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 assays have been
eliminated. There are cases of profitable mines where the values
were all in spots, and an assay plan would show 80% of the assays
_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 assays, 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 assay 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 assay 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 assaying twenty ounces per ton be added
to a dump of five tons averaging one ounce per ton, the result has
not an average assay of twenty-one ounces divided by the number of
dumps. Likewise one sample over a width of two feet, assaying twenty
ounces per ton, if averaged with another sample over a width of five
feet, assaying 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 assays. 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 quantity 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 assumed to penetrate.
We may also let:--
_C_ = The number of cubic feet per ton of ore.
_V_ = Assay value of the sample.
Then _WLD_/C_ = tonnage of the prismoid.*
_V WLD_/C_ = total metal contents.
[Footnote *: Strictly, the prismoidal formula should be used, but
it complicates the study unduly, and for practical purposes the
above may be taken as the volume.]
The average value of a number of samples is the total metal contents
of their respective prismoids, divided by the total tonnage of
these prismoids. If we let _W_, _W_1, _V_, _V_1 etc., represent
different samples, we have:--
_V(_WLD_/_C_) + _V_1 (_W_1 _L_1 _D_1/_C_) + _V_2 (_W_2 _L_2 _D_2/_C_)
---------------------------------------------------------------------
_WLD_/_C_ + _W_1 _L_1 _D_1/_C_ + _W_2 _L_2 _D_2/_C_
= average value.
This may be reduced to:--
(_VWLD_) + (_V_1 _W_1 _L_1 _D_1) + (_V_2 _W_2 _L_2 _D_2,), etc.
---------------------------------------------------------------
(_WLD_) + (_W_1 _L_1 _D_1) + (_W_2 _L_2 _D_2), etc.
As a matter of fact, samples actually represent the value of
the outer shell of the block of ore only, and the continuity of
the same values through the block is a geological assumption.
From the outer shell, all the values can be taken to penetrate
equal distances into the block, and therefore _D_, _D_1, _D_2
may be considered as equal and the equation becomes:--
(_VWL_) + (_V_1 _W_1 _L_1) + (_V_2 _W_2 _L_2), etc.
---------------------------------------------------
(_WL_) + (_W_1 _L_1) + (_W_2 _L_2), etc.
The length of the prismoid base _L_ for any given sample will be
a distance equal to one-half the sum of the distances to the two
adjacent samples. As a matter of practice, samples are usually taken
at regular intervals, and the lengths _L_, _L_1, _L_2 becoming thus
equal can in such case be eliminated, and the equation becomes:--
(_VW_) + (_V_1 _W_1) + (_V_2 _W_2), etc.
----------------------------------------
_W_ + _W_1 + _W_2 , etc.
The name "assay foot" or "foot value" has been given to the relation
_VW_, that is, the assay value multiplied by the width sampled.[*]
It is by this method that all samples must be averaged. The same
relation obviously can be evolved by using an inch instead of a
foot, and in narrow veins the assay inch is generally used.
[Footnote *: An error will be found in this method unless the two
end samples be halved, but in a long run of samples this may be
disregarded.]
Where the payable cross-section is divided into more than one sample,
the different samples in the section must be averaged by the above
formula, before being combined with the adjacent section. Where
the width sampled is narrower than the necessary stoping width,
and where the waste cannot be broken separately, the sample value
must be diluted to a stoping width. To dilute narrow samples to
a stoping width, a blank value over the extra width which it is
necessary to include must be averaged with the sample from the
ore on the above formula. Cases arise where, although a certain
width of waste must be broken with the ore, it subsequently can
be partially sorted out. Practically nothing but experience on
the deposit itself will determine how far this will restore the
value of the ore to the average of the payable seam. In any event,
no sorting can eliminate all such waste; and it is necessary to
calculate the value on the breaking width, and then deduct from
the gross tonnage to be broken a percentage from sorting. There
is always an allowance to be made in sorting for a loss of good
ore with the discards.
PERCENTAGE OF ERROR IN ESTIMATES FROM SAMPLING.--It must be remembered
that the whole theory of estimation by sampling is founded upon
certain assumptions as to evenness of continuity and transition
in value and volume. It is but a basis for an estimate, and an
estimate is not a statement of fact. It cannot therefore be too
forcibly repeated that an estimate is inherently but an approximation,
take what care one may in its founding. While it is possible to
refine mathematical calculation of averages to almost any nicety,
beyond certain essentials it adds nothing to accuracy and is often
misleading.
It is desirable to consider where errors are most likely to creep
in, assuming that all fundamental data are both accurately taken
and considered. Sampling of ore _in situ_ in general has a tendency
to give higher average value than the actual reduction of the ore
will show. On three West Australian gold mines, in records covering
a period of over two years, where sampling was most exhaustive as
a daily régime of the mines, the values indicated by sampling were
12% higher than the mill yield plus the contents of the residues.
On the Witwatersrand gold mines, the actual extractable value is
generally considered to be about 78 to 80% of the average shown
by sampling, while the mill extractions are on average about 90
to 92% of the head value coming to the mill. In other words, there
is a constant discrepancy of about 10 to 12% between the estimated
value as indicated by mine samples, and the actual value as shown
by yield plus the residues. At Broken Hill, on three lead mines,
the yield is about 12% less than sampling would indicate. This
constancy of error in one direction has not been so generally
acknowledged as would be desirable, and it must be allowed for
in calculating final results. The causes of the exaggeration seem
to be:--
_First_, inability to stope a mine to such fine limitations of
width, or exclusion of unpayable patches, as would appear practicable
when sampling, that is by the inclusion when mining of a certain
amount of barren rock. Even in deposits of about normal stoping
width, it is impossible to prevent the breaking of a certain amount
of waste, even if the ore occurrence is regularly confined by walls.
If the mine be of the impregnation type, such as those at Goldfield,
or Kalgoorlie, with values like plums in a pudding, and the stopes
themselves directed more by assays than by any physical differences
in the ore, the discrepancy becomes very much increased. In mines
where the range of values is narrower than the normal stoping width,
some wall rock must be broken. Although it is customary to allow for
this in calculating the average value from samples, the allowance
seldom seems enough. In mines where the ore is broken on to the
top of stopes filled with waste, there is some loss underground
through mixture with the filling.
_Second_, the metal content of ores, especially when in the form of
sulphides, is usually more friable than the matrix, and in actual
breaking of samples an undue proportion of friable material usually
creeps in. This is true more in lead, copper, and zinc, than in
gold ores. On several gold mines, however, tests on accumulated
samples for their sulphide percentage showed a distinctly greater
ratio than the tenor of the ore itself in the mill. As the gold is
usually associated with the sulphides, the samples showed higher
values than the mill.
In general, some considerable factor of safety must be allowed
after arriving at calculated average of samples,--how much it is
difficult to say, but, in any event, not less than 10%.
CHAPTER II.
Mine Valuation (_Continued_).
CALCULATION OF QUANTITIES OF ORE, AND CLASSIFICATION OF ORE IN SIGHT.
As mines are opened by levels, rises, etc., through the ore, an
extension of these workings has the effect of dividing it into
"blocks." The obvious procedure in determining tonnages is to calculate
the volume and value of each block separately. Under the law of
averages, the multiplicity of these blocks tends in proportion
to their number to compensate the percentage of error which might
arise in the sampling or estimating of any particular one. The
shapes of these blocks, on longitudinal section, are often not
regular geometrical figures. As a matter of practice, however, they
can be subdivided into such figures that the total will approximate
the whole with sufficient closeness for calculations of their areas.
The average width of the ore in any particular block is the arithmetical
mean of the width of the sample sections in it,[*] if the samples be
an equal distance apart. If they are not equidistant, the average
width is the sum of the areas between samples, divided by the total
length sampled. The cubic foot contents of a particular block is
obviously the width multiplied by the area of its longitudinal
section.
[Footnote *: This is not strictly true unless the sum of the widths
of the two end-sections be divided by two and the result incorporated
in calculating the means. In a long series that error is of little
importance.]
The ratio of cubic feet to tons depends on the specific gravity
of the ore, its porosity, and moisture. The variability of ores
throughout the mine in all these particulars renders any method
of calculation simply an approximation in the end. The factors
which must remain unknown necessarily lead the engineer to the
provision of a margin of safety, which makes mathematical refinement
and algebraic formulæ ridiculous.
There are in general three methods of determination of the specific
volume of ores:--
_First_, by finding the true specific gravity of a sufficient number
of representative specimens; this, however, would not account for
the larger voids in the ore-body and in any event, to be anything
like accurate, would be as expensive as sampling and is therefore
of little more than academic interest.
_Second_, by determining the weight of quantities broken from measured
spaces. This also would require several tests from different portions
of the mine, and, in examinations, is usually inconvenient and
difficult. Yet it is necessary in cases of unusual materials, such
as leached gossans, and it is desirable to have it done sooner
or later in going mines, as a check.
_Third_, by an approximation based upon a calculation from the
specific gravities of the predominant minerals in the ore. Ores
are a mixture of many minerals; the proportions vary through the
same ore-body. Despite this, a few partial analyses, which are
usually available from assays of samples and metallurgical tests,
and a general inspection as to the compactness of the ore, give a
fairly reliable basis for approximation, especially if a reasonable
discount be allowed for safety. In such discount must be reflected
regard for the porosity of the ore, and the margin of safety necessary
may vary from 10 to 25%. If the ore is of unusual character, as
in leached deposits, as said before, resort must be had to the
second method.
The following table of the weights per cubic foot and the number
of cubic feet per ton of some of the principal ore-forming minerals
and gangue rocks will be useful for approximating the weight of
a cubic foot of ore by the third method. Weights are in pounds
avoirdupois, and two thousand pounds are reckoned to the ton.
============================================
| | Number of
| Weight per | Cubic Feet
| Cubic Foot | per Ton of
| | 2000 lb.
------------------|------------|------------
Antimony | 417.50 | 4.79
Sulphide | 285.00 | 7.01
Arsenical Pyrites | 371.87 | 5.37
Barium Sulphate | 278.12 | 7.19
Calcium: | |
Fluorite | 198.75 | 10.06
Gypsum | 145.62 | 13.73
Calcite | 169.37 | 11.80
Copper | 552.50 | 3.62
Calcopyrite | 262.50 | 7.61
Bornite | 321.87 | 6.21
Malachite | 247.50 | 8.04
Azurite | 237.50 | 8.42
Chrysocolla | 132.50 | 15.09
Iron (Cast) | 450.00 | 4.44
Magnetite | 315.62 | 6.33
Hematite | 306.25 | 6.53
Limonite | 237.50 | 8.42
Pyrite | 312.50 | 6.40
Carbonate | 240.62 | 8.31
Lead | 710.62 | 2.81
Galena | 468.75 | 4.27
Carbonate | 406.87 | 4.81
Manganese Oxide | 268.75 | 6.18
Rhodonite | 221.25 | 9.04
Magnesite | 187.50 | 10.66
Dolomite | 178.12 | 11.23
Quartz | 165.62 | 12.07
Quicksilver | 849.75 | 2.35
Cinnabar | 531.25 | 3.76
Sulphur | 127.12 | 15.74
Tin | 459.00 | 4.35
Oxide | 418.75 | 4.77
Zinc | 437.50 | 4.57
Blende | 253.12 | 7.90
Carbonate | 273.12 | 7.32
Silicate | 215.62 | 9.28
Andesite | 165.62 | 12.07
Granite | 162.62 | 12.30
Diabase | 181.25 | 11.03
Diorite | 171.87 | 11.63
Slates | 165.62 | 12.07
Sandstones | 162.50 | 12.30
Rhyolite | 156.25 | 12.80
============================================
The specific gravity of any particular mineral has a considerable
range, and a medium has been taken. The possible error is
inconsequential for the purpose of these calculations.
For example, a representative gold ore may contain in the main
96% quartz, and 4% iron pyrite, and the weight of the ore may be
deduced as follows:--
Quartz, 96% x 12.07 = 11.58
Iron Pyrite, 4% x 6.40 = .25
-----
11.83 cubic feet per ton.
Most engineers, to compensate porosity, would allow twelve to thirteen
cubic feet per ton.
CLASSIFICATION OF ORE IN SIGHT.
The risk in estimates of the average value of standing ore is dependent
largely upon how far values disclosed by sampling are assumed to
penetrate beyond the tested face, and this depends upon the geological
character of the deposit. From theoretical grounds and experience,
it is known that such values will have some extension, and the
assumption of any given distance is a calculation of risk. The
multiplication of development openings results in an increase of
sampling points available and lessens the hazards. The frequency
of such openings varies in different portions of every mine, and
thus there are inequalities of risk. It is therefore customary in
giving estimates of standing ore to classify the ore according
to the degree of risk assumed, either by stating the number of
sides exposed or by other phrases. Much discussion and ink have
been devoted to trying to define what risk may be taken in such
matters, that is in reality how far values may be assumed to penetrate
into the unbroken ore. Still more has been consumed in attempts
to coin terms and make classifications which will indicate what
ratio of hazard has been taken in stating quantities and values.
The old terms "ore in sight" and "profit in sight" have been of
late years subject to much malediction on the part of engineers
because these expressions have been so badly abused by the charlatans
of mining in attempts to cover the flights of their imaginations. A
large part of Volume X of the "Institution of Mining and Metallurgy"
has been devoted to heaping infamy on these terms, yet not only
have they preserved their places in professional nomenclature,
but nothing has been found to supersede them.
Some general term is required in daily practice to cover the whole
field of visible ore, and if the phrase "ore in sight" be defined,
it will be easier to teach the laymen its proper use than to abolish
it. In fact, the substitutes are becoming abused as much as the
originals ever were. All convincing expressions will be misused
by somebody.
The legitimate direction of reform has been to divide the general
term of "ore in sight" into classes, and give them names which will
indicate the variable amount of risk of continuity in different parts
of the mine. As the frequency of sample points, and consequently the
risk of continuity, will depend upon the detail with which the mine
is cut into blocks by the development openings, and upon the number
of sides of such blocks which are accessible, most classifications
of the degree of risk of continuity have been defined in terms of
the number of sides exposed in the blocks. Many phrases have been
coined to express such classifications; those most currently used
are the following:--
Positive Ore \ Ore exposed on four sides in blocks of a size
Ore Developed / variously prescribed.
Ore Blocked Out Ore exposed on three sides within reasonable
distance of each other.
Probable Ore \
Ore Developing / Ore exposed on two sides.
Possible Ore \ The whole or a part of the ore below the
Ore Expectant / lowest level or beyond the range of vision.
No two of these parallel expressions mean quite the same thing;
each more or less overlies into another class, and in fact none
of them is based upon a logical footing for such a classification.
For example, values can be assumed to penetrate some distance from
every sampled face, even if it be only ten feet, so that ore exposed
on one side will show some "positive" or "developed" ore which, on
the lines laid down above, might be "probable" or even "possible"
ore. Likewise, ore may be "fully developed" or "blocked out" so far
as it is necessary for stoping purposes with modern wide intervals
between levels, and still be in blocks too large to warrant an
assumption of continuity of values to their centers (Fig. 1). As
to the third class of "possible" ore, it conveys an impression
of tangibility to a nebulous hazard, and should never be used in
connection with positive tonnages. This part of the mine's value
comes under extension of the deposit a long distance beyond openings,
which is a speculation and cannot be defined in absolute tons without
exhaustive explanation of the risks attached, in which case any
phrase intended to shorten description is likely to be misleading.
[Illustration: Fig. 1.--Longitudinal section of a mine, showing
classification of the exposed ore. Scale, 400 feet = 1 inch.]
Therefore empirical expressions in terms of development openings
cannot be made to cover a geologic factor such as the distribution
of metals through a rock mass. The only logical basis of ore
classification for estimation purposes is one which is founded
on the chances of the values penetrating from the surface of the
exposures for each particular mine. Ore that may be calculated
upon to a certainty is that which, taking into consideration the
character of the deposit, can be said to be so sufficiently surrounded
by sampled faces that the distance into the mass to which values
are assumed to extend is reduced to a minimum risk. Ore so far
removed from the sampled face as to leave some doubt, yet affording
great reason for expectation of continuity, is "probable" ore.
The third class of ore mentioned, which is that depending upon
extension of the deposit and in which, as said above, there is great
risk, should be treated separately as the speculative value of the
mine. Some expressions are desirable for these classifications, and
the writer's own preference is for the following, with a definition
based upon the controlling factor itself.
They are:--
Proved Ore Ore where there is practically no risk of
failure of continuity.
Probable Ore Ore where there is some risk, yet warrantable
justification for assumption of continuity.
Prospective Ore Ore which cannot be included in the above
classes, nor definitely known or stated in
any terms of tonnage.
What extent of openings, and therefore of sample faces, is required
for the ore to be called "proved" varies naturally with the type
of deposit,--in fact with each mine. In a general way, a fair rule
in gold quartz veins below influence of secondary alteration is
that no point in the block shall be over fifty feet from the points
sampled. In limestone or andesite replacements, as by gold or lead
or copper, the radius must be less. In defined lead and copper
lodes, or in large lenticular bodies such as the Tennessee copper
mines, the radius may often be considerably greater,--say one hundred
feet. In gold deposits of such extraordinary regularity of values
as the Witwatersrand bankets, it can well be two hundred or two
hundred and fifty feet.
"Probable ore" should be ore which entails continuity of values
through a greater distance than the above, and such distance must
depend upon the collateral evidence from the character of the deposit,
the position of openings, etc.
Ore beyond the range of the "probable" zone is dependent upon the
extension of the deposit beyond the realm of development and will
be discussed separately.
Although the expression "ore in sight" may be deprecated, owing to
its abuse, some general term to cover both "positive" and "probable"
ore is desirable; and where a general term is required, it is the
intention herein to hold to the phrase "ore in sight" under the
limitations specified.
CHAPTER III.
Mine Valuation (_Continued_).
PROSPECTIVE VALUE.[*] EXTENSION IN DEPTH; ORIGIN AND STRUCTURAL
CHARACTER OF THE DEPOSIT; SECONDARY ENRICHMENT; DEVELOPMENT IN
NEIGHBORING MINES; DEPTH OF EXHAUSTION.
[Footnote *: The term "extension in depth" is preferred by many
to the phrase "prospective value." The former is not entirely
satisfactory, as it has a more specific than general application.
It is, however, a current miner's phrase, and is more expressive.
In this discussion "extension in depth" is used synonymously, and
it may be taken to include not alone the downward prolongation of
the ore below workings, but also the occasional cases of lateral
extension beyond the range of development work. The commonest instance
is continuance below the bottom level. In any event, to the majority
of cases of different extension the same reasoning applies.]
It is a knotty problem to value the extension of a deposit beyond
a short distance from the last opening. A short distance beyond
it is "proved ore," and for a further short distance is "probable
ore." Mines are very seldom priced at a sum so moderate as that
represented by the profit to be won from the ore in sight, and what
value should be assigned to this unknown portion of the deposit
admits of no certainty. No engineer can approach the prospective
value of a mine with optimism, yet the mining industry would be
non-existent to-day were it approached with pessimism. Any value
assessed must be a matter of judgment, and this judgment based on
geological evidence. Geology is not a mathematical science, and
to attach a money equivalence to forecasts based on such evidence
is the most difficult task set for the mining engineer. It is here
that his view of geology must differ from that of his financially
more irresponsible brother in the science. The geologist, contributing
to human knowledge in general, finds his most valuable field in the
examination of mines largely exhausted. The engineer's most valuable
work arises from his ability to anticipate in the youth of the mine
the symptoms of its old age. The work of our geologic friends is,
however, the very foundation on which we lay our forecasts.
Geologists have, as the result of long observation, propounded for
us certain hypotheses which, while still hypotheses, have proved
to account so widely for our underground experience that no engineer
can afford to lose sight of them. Although there is a lack of safety
in fixed theories as to ore deposition, and although such conclusions
cannot be translated into feet and metal value, they are nevertheless
useful weights on the scale where probabilities are to be weighed.
A method in vogue with many engineers is, where the bottom level
is good, to assume the value of the extension in depth as a sum
proportioned to the profit in sight, and thus evade the use of
geological evidence. The addition of various percentages to the
profit in sight has been used by engineers, and proposed in technical
publications, as varying from 25 to 50%. That is, they roughly
assess the extension in depth to be worth one-fifth to one-third
of the whole value of an equipped mine. While experience may have
sometimes demonstrated this to be a practical method, it certainly
has little foundation in either science or logic, and the writer's
experience is that such estimates are untrue in practice. The quantity
of ore which may be in sight is largely the result of managerial
policy. A small mill on a large mine, under rapid development,
will result in extensive ore-reserves, while a large mill eating
away rapidly on the same mine under the same scale of development
would leave small reserves. On the above scheme of valuation the
extension in depth would be worth very different sums, even when the
deepest level might be at the same horizon in both cases. Moreover,
no mine starts at the surface with a large amount of ore in sight.
Yet as a general rule this is the period when its extension is most
valuable, for when the deposit is exhausted to 2000 feet, it is
not likely to have such extension in depth as when opened one hundred
feet, no matter what the ore-reserves may be. Further, such bases
of valuation fail to take into account the widely varying geologic
character of different mines, and they disregard any collateral
evidence either of continuity from neighboring development, or from
experience in the district. Logically, the prospective value can
be simply a factor of how _far_ the ore in the individual mine
may be expected to extend, and not a factor of the remnant of ore
that may still be unworked above the lowest level.
An estimation of the chances of this extension should be based
solely on the local factors which bear on such extension, and these
are almost wholly dependent upon the character of the deposit.
These various geological factors from a mining engineer's point
of view are:--
1. The origin and structural character of the ore-deposit.
2. The position of openings in relation to secondary alteration.
3. The size of the deposit.
4. The depth to which the mine has already been exhausted.
5. The general experience of the district for continuity and
the development of adjoining mines.
THE ORIGIN AND STRUCTURAL CHARACTER OF THE DEPOSIT.--In a general
way, the ore-deposits of the order under discussion originate primarily
through the deposition of metals from gases or solutions circulating
along avenues in the earth's crust.[*] The original source of metals
is a matter of great disagreement, and does not much concern the
miner. To him, however, the origin and character of the avenue
of circulation, the enclosing rock, the influence of the rocks
on the solution, and of the solutions on the rocks, have a great
bearing on the probable continuity of the volume and value of the
ore.
[Footnote *: The class of magmatic segregations is omitted, as
not being of sufficiently frequent occurrence in payable mines to
warrant troubling with it here.]
All ore-deposits vary in value and, in the miner's view, only those
portions above the pay limit are ore-bodies, or ore-shoots. The
localization of values into such pay areas in an ore-deposit are
apparently influenced by:
1. The distribution of the open spaces created by structural
movement, fissuring, or folding as at Bendigo.
2. The intersection of other fractures which, by mingling of
solutions from different sources, provided precipitating
conditions, as shown by enrichments at cross-veins.
3. The influence of the enclosing rocks by:--
(a) Their solubility, and therefore susceptibility to replacement.
(b) Their influence as a precipitating agent on solutions.
(c) Their influence as a source of metal itself.
(d) Their texture, in its influence on the character of
the fracture. In homogeneous rocks the tendency
is to open clean-cut fissures; in friable
rocks, zones of brecciation; in slates or schistose
rocks, linked lenticular open spaces;--these
influences exhibiting themselves in miner's terms
respectively in "well-defined fissure veins,"
"lodes," and "lenses."
(e) The physical character of the rock mass and the
dynamic forces brought to bear upon it. This
is a difficult study into the physics of stress in
cases of fracturing, but its local application has
not been without results of an important order.
4. Secondary alteration near the surface, more fully discussed
later.
It is evident enough that the whole structure of the deposit is
a necessary study, and even a digest of the subject is not to be
compressed into a few paragraphs.
From the point of view of continuity of values, ore-deposits may
be roughly divided into three classes. They are:--
1. Deposits of the infiltration type in porous beds, such as
Lake Superior copper conglomerates and African gold bankets.
2. Deposits of the fissure vein type, such as California quartz veins.
3. Replacement or impregnation deposits on the lines of fissuring
or otherwise.
In a general way, the uniformity of conditions of deposition in
the first class has resulted in the most satisfactory continuity of
ore and of its metal contents. In the second, depending much upon
the profundity of the earth movements involved, there is laterally
and vertically a reasonable basis for expectation of continuity
but through much less distance than in the first class.
The third class of deposits exhibits widely different phenomena
as to continuity and no generalization is of any value. In gold
deposits of this type in West Australia, Colorado, and Nevada,
continuity far beyond a sampled face must be received with the
greatest skepticism. Much the same may be said of most copper
replacements in limestone. On the other hand the most phenomenal
regularity of values have been shown in certain Utah and Arizona
copper mines, the result of secondary infiltration in porphyritic
gangues. The Mississippi Valley lead and zinc deposits, while irregular
in detail, show remarkable continuity by way of reoccurrence over
wide areas. The estimation of the prospective value of mines where
continuity of production is dependent on reoccurrence of ore-bodies
somewhat proportional to the area, such as these Mississippi deposits
or to some extent as in Cobalt silver veins, is an interesting
study, but one that offers little field for generalization.
THE POSITION OF THE OPENINGS IN RELATION TO SECONDARY ALTERATION.--The
profound alteration of the upper section of ore-deposits by oxidation
due to the action of descending surface waters, and their associated
chemical agencies, has been generally recognized for a great many
years. Only recently, however, has it been appreciated that this
secondary alteration extends into the sulphide zone as well. The
bearing of the secondary alteration, both in the oxidized and upper
sulphide zones, is of the most sweeping economic character. In
considering extension of values in depth, it demands the most rigorous
investigation. Not only does the metallurgical character of the ores
change with oxidation, but the complex reactions due to descending
surface waters cause leaching and a migration of metals from one
horizon to another lower down, and also in many cases a redistribution
of their sequence in the upper zones of the deposit.
The effect of these agencies has been so great in many cases as
to entirely alter the character of the mine and extension in depth
has necessitated a complete reëquipment. For instance, the Mt.
Morgan gold mine, Queensland, has now become a copper mine; the
copper mines at Butte were formerly silver mines; Leadville has
become largely a zinc producer instead of lead.
From this alteration aspect ore-deposits may be considered to have
four horizons:--
1. The zone near the outcrop, where the dominating feature
is oxidation and leaching of the soluble minerals.
2. A lower horizon, still in the zone of oxidation, where the
predominant feature is the deposition of metals as native,
oxides, and carbonates.
3. The upper horizon of the sulphide zone, where the special
feature is the enrichment due to secondary deposition
as sulphides.
4. The region below these zones of secondary alteration, where
the deposit is in its primary state.
These zones are seldom sharply defined, nor are they always all
in evidence. How far they are in evidence will depend, among other
things, upon the amount and rapidity of erosion, the structure and
mineralogical character of the deposit, and upon the enclosing
rock.
If erosion is extremely rapid, as in cold, wet climates, and rough
topography, or as in the case of glaciation of the Lake copper
deposits, denudation follows close on the heels of alteration,
and the surface is so rapidly removed that we may have the primary
ore practically at the surface. Flat, arid regions present the
other extreme, for denudation is much slower, and conditions are
most perfect for deep penetration of oxidizing agencies, and the
consequent alteration and concentration of the metals.
The migration of metals from the top of the oxidized zone leaves
but a barren cap for erosion. The consequent effect of denudation
that lags behind alteration is to raise slowly the concentrated
metals toward the surface, and thus subject them to renewed attack
and repeated migration. In this manner we can account for the enormous
concentration of values in the lower oxidized and upper sulphide
zones overlying very lean sulphides in depth.
Some minerals are more freely soluble and more readily precipitated
than others. From this cause there is in complex metal deposits a
rearrangement of horizontal sequence, in addition to enrichment at
certain horizons and impoverishment at others. The whole subject
is one of too great complexity for adequate consideration in this
discussion. No engineer is properly equipped to give judgment on
extension in depth without a thorough grasp of the great principles
laid down by Van Hise, Emmons, Lindgren, Weed, and others. We may,
however, briefly examine some of the theoretical effects of such
alteration.
Zinc, iron, and lead sulphides are a common primary combination.
These metals are rendered soluble from their usual primary forms
by oxidizing agencies, in the order given. They reprecipitate as
sulphides in the reverse sequence. The result is the leaching of
zinc and iron readily in the oxidized zone, thus differentially
enriching the lead which lags behind, and a further extension of
the lead horizon is provided by the early precipitation of such
lead as does migrate. Therefore, the lead often predominates in
the second and the upper portion of the third zone, with the zinc
and iron below. Although the action of all surface waters is toward
oxidation and carbonation of these metals, the carbonate development
of oxidized zones is more marked when the enclosing rocks are
calcareous.
In copper-iron deposits, the comparatively easy decomposition and
solubility and precipitation of the copper and some iron salts
generally result in more extensive impoverishment of these metals
near the surface, and more predominant enrichment at a lower horizon
than is the case with any other metals. The barren "iron hat" at the
first zone, the carbonates and oxides at the second, the enrichment
with secondary copper sulphides at the top of the third, and the
occurrence of secondary copper-iron sulphides below, are often
most clearly defined. In the easy recognition of the secondary
copper sulphides, chalcocite, bornite, etc., the engineer finds a
finger-post on the road to extension in depth; and the directions
upon this post are not to be disregarded. The number of copper
deposits enriched from unpayability in the first zone to a profitable
character in the next two, and unpayability again in the fourth,
is legion.
Silver occurs most abundantly in combination with either lead,
copper, iron, or gold. As it resists oxidation and solution more
strenuously than copper and iron, its tendency when in combination
with them is to lag behind in migration. There is thus a differential
enrichment of silver in the upper two zones, due to the reduction
in specific gravity of the ore by the removal of associated metals.
Silver does migrate somewhat, however, and as it precipitates more
readily than copper, lead, zinc, or iron, its tendency when in
combination with them is towards enrichment above the horizons of
enrichment of these metals. When it is in combination with lead
and zinc, its very ready precipitation from solution by the galena
leaves it in combination more predominantly with the lead. The
secondary enrichment of silver deposits at the top of the sulphide
zone is sometimes a most pronounced feature, and it seems to be
the explanation of the origin of many "bonanzas."
In gold deposits, the greater resistance to solubility of this
metal than most of the others, renders the phenomena of migration to
depth less marked. Further than this, migration is often interfered
with by the more impervious quartz matrix of many gold deposits.
Where gold is associated with large quantities of base metals,
however, the leaching of the latter in the oxidized zone leaves the
ore differentially richer, and as gold is also slightly soluble,
in such cases the migration of the base metals does carry some of
the gold. In the instance especially of impregnation or replacement
deposits, where the matrix is easily permeable, the upper sulphide
zone is distinctly richer than lower down, and this enrichment is
accompanied by a considerable increase in sulphides and tellurides.
The predominant characteristic of alteration in gold deposits is,
however, enrichment in the oxidized zone with the maximum values
near the surface. The reasons for this appear to be that gold in its
resistance to oxidation and wholesale migration gives opportunities
to a sort of combined mechanical and chemical enrichment.
In dry climates, especially, the gentleness of erosion allows of
more thorough decomposition of the outcroppings, and a mechanical
separation of the gold from the detritus. It remains on or near
the deposit, ready to be carried below, mechanically or otherwise.
In wet climates this is less pronounced, for erosion bears away
the croppings before such an extensive decomposition and freeing
of the gold particles. The West Australian gold fields present an
especially prominent example of this type of superficial enrichment.
During the last fifteen years nearly eight hundred companies have
been formed for working mines in this region. Although from four
hundred of these high-grade ore has been produced, some thirty-three
only have ever paid dividends. The great majority have been unpayable
below oxidation,--a distance of one or two hundred feet. The writer's
unvarying experience with gold is that it is richer in the oxidized
zone than at any point below. While cases do occur of gold deposits
richer in the upper sulphide zone than below, even the upper sulphides
are usually poorer than the oxidized region. In quartz veins
preëminently, evidence of enrichment in the third zone is likely
to be practically absent.
Tin ores present an anomaly among the base metals under discussion,
in that the primary form of this metal in most workable deposits
is an oxide. Tin in this form is most difficult of solution from
ground agencies, as witness the great alluvial deposits, often of
considerable geologic age. In consequence the phenomena of migration
and enrichment are almost wholly absent, except such as are due
to mechanical penetration of tin from surface decomposition of
the matrix akin to that described in gold deposits.
In general, three or four essential facts from secondary alteration
must be kept in view when prognosticating extensions.
Oxidation usually alters treatment problems, and oxidized ore
of the same grade as sulphides can often be treated more cheaply.
This is not universal. Low-grade ores of lead, copper, and zinc
may be treatable by concentration when in the form of sulphides,
and may be valueless when oxidized, even though of the same grade.
Copper ores generally show violent enrichment at the base of the
oxidized, and at the top of the sulphide zone.
Lead-zinc ores show lead enrichment and zinc impoverishment in
the oxidized zone but have usually less pronounced enrichment
below water level than copper. The rearrangement of the metals
by the deeper migration of the zinc, also renders them
metallurgically of less value with depth.
Silver deposits are often differentially enriched in the oxidized
zone, and at times tend to concentrate in the upper sulphide zone.
Gold deposits usually decrease in value from the surface through
the whole of the three alteration zones.
SIZE OF DEPOSITS.--The proverb of a relation between extension
in depth and size of ore-bodies expresses one of the oldest of
miners' beliefs. It has some basis in experience, especially in
fissure veins, but has little foundation in theory and is applicable
over but limited areas and under limited conditions.
From a structural view, the depth of fissuring is likely to be more
or less in proportion to its length and breadth and therefore the
volume of vein filling with depth is likely to be proportional to
length and width of the fissure. As to the distribution of values,
if we eliminate the influence of changing wall rocks, or other
precipitating agencies which often cause the values to arrange
themselves in "floors," and of secondary alteration, there may be
some reason to assume distribution of values of an extent equal
vertically to that displayed horizontally. There is, as said, more
reason in experience for this assumption than in theory. A study
of the shape of a great many ore-shoots in mines of fissure type
indicates that when the ore-shoots or ore-bodies are approaching
vertical exhaustion they do not end abruptly, but gradually shorten
and decrease in value, their bottom boundaries being more often
wedge-shaped than even lenticular. If this could be taken as the usual
occurrence, it would be possible (eliminating the evident exceptions
mentioned above) to state roughly that the minimum extension of an
ore-body or ore-shoot in depth below any given horizon would be
a distance represented by a radius equal to one-half its length. By
length is not meant necessarily the length of a horizontal section,
but of one at right angles to the downward axis.
On these grounds, which have been reënforced by much experience among
miners, the probabilities of extension are somewhat in proportion
to the length and width of each ore-body. For instance, in the A
mine, with an ore-shoot 1000 feet long and 10 feet wide, on its
bottom level, the minimum extension under this hypothesis would
be a wedge-shaped ore-body with its deepest point 500 feet below
the lowest level, or a minimum of say 200,000 tons. Similarly,
the B mine with five ore-bodies, each 300 hundred feet long and
10 feet wide, exposed on its lowest level, would have a minimum of
five wedges 100 feet deep at their deepest points, or say 50,000
tons. This is not proposed as a formula giving the total amount of
extension in depth, but as a sort of yardstick which has experience
behind it. This experience applies in a much less degree to deposits
originating from impregnation along lines of fissuring and not at
all to replacements.
DEVELOPMENT IN NEIGHBORING MINES.--Mines of a district are usually
found under the same geological conditions, and show somewhat the same
habits as to extension in depth or laterally, and especially similar
conduct of ore-bodies and ore-shoots. As a practical criterion, one
of the most intimate guides is the actual development in adjoining
mines. For instance, in Kalgoorlie, the Great Boulder mine is (March,
1908) working the extension of Ivanhoe lodes at points 500 feet
below the lowest level in the Ivanhoe; likewise, the Block 10 lead
mine at Broken Hill is working the Central ore-body on the Central
boundary some 350 feet below the Central workings. Such facts as
these must have a bearing on assessing the downward extension.
DEPTH OF EXHAUSTION.--All mines become completely exhausted at
some point in depth. Therefore the actual distance to which ore
can be expected to extend below the lowest level grows less with
every deeper working horizon. The really superficial character of
ore-deposits, even outside of the region of secondary enrichment
is becoming every year better recognized. The prospector's idea
that "she gets richer deeper down," may have some basis near the
surface in some metals, but it is not an idea which prevails in
the minds of engineers who have to work in depth. The writer, with
some others, prepared a list of several hundred dividend-paying
metal mines of all sorts, extending over North and South America,
Australasia, England, and Africa. Notes were made as far as possible
of the depths at which values gave out, and also at which dividends
ceased. Although by no means a complete census, the list indicated
that not 6% of mines (outside banket) that have yielded profits,
ever made them from ore won below 2000 feet. Of mines that paid
dividends, 80% did not show profitable value below 1500 feet, and
a sad majority died above 500. Failures at short depths may be
blamed upon secondary enrichment, but the majority that reached
below this influence also gave out. The geological reason for such
general unseemly conduct is not so evident.
CONCLUSION.--As a practical problem, the assessment of prospective
value is usually a case of "cut and try." The portion of the capital
to be invested, which depends upon extension, will require so many
tons of ore of the same value as that indicated by the standing
ore, in order to justify the price. To produce this tonnage at
the continued average size of the ore-bodies will require their
extension in depth so many feet--or the discovery of new ore-bodies
of a certain size. The five geological weights mentioned above
may then be put into the scale and a basis of judgment reached.
CHAPTER IV.
Mine Valuation (_Continued_).
RECOVERABLE PERCENTAGE OF THE GROSS ASSAY VALUE; PRICE OF METALS;
COST OF PRODUCTION.
The method of treatment for the ore must be known before a mine
can be valued, because a knowledge of the recoverable percentage
is as important as that of the gross value of the ore itself. The
recoverable percentage is usually a factor of working costs. Practically
every ore can be treated and all the metal contents recovered, but
the real problem is to know the method and percentage of recovery
which will yield the most remunerative result, if any. This limit to
profitable recovery regulates the amount of metal which should be
lost, and the amount of metal which consequently must be deducted
from the gross value before the real net value of the ore can be
calculated. Here, as everywhere else in mining, a compromise has to
be made with nature, and we take what we can get--profitably. For
instance, a copper ore may be smelted and a 99% recovery obtained.
Under certain conditions this might be done at a loss, while the
same ore might be concentrated before smelting and yield a profit
with a 70% recovery. An additional 20% might be obtained by roasting
and leaching the residues from concentration, but this would probably
result in an expenditure far greater than the value of the 20%
recovered. If the ore is not already under treatment on the mine,
or exactly similar ore is not under treatment elsewhere, with known
results, the method must be determined experimentally, either by
the examining engineer or by a special metallurgist.
Where partially treated products, such as concentrates, are to be
sold, not only will there be further losses, but deductions will
be made by the smelter for deleterious metals and other charges.
All of these factors must be found out,--and a few sample smelting
returns from a similar ore are useful.
To cover the whole field of metallurgy and discuss what might apply,
and how it might apply, under a hundred supposititious conditions
would be too great a digression from the subject in hand. It is
enough to call attention here to the fact that the residues from
every treatment carry some metal, and that this loss has to be
deducted from the gross value of the ore in any calculations of
net values.
PRICE OF METALS.
Unfortunately for the mining engineer, not only has he to weigh
the amount of risk inherent in calculations involved in the mine
itself, but also that due to fluctuations in the value of metals.
If the ore is shipped to custom works, he has to contemplate also
variations in freights and smelting charges. Gold from the mine
valuer's point of view has no fluctuations. It alone among the
earth's products gives no concern as to the market price. The price
to be taken for all other metals has to be decided before the mine
can be valued. This introduces a further speculation and, as in
all calculations of probabilities, amounts to an estimate of the
amount of risk. In a free market the law of supply and demand governs
the value of metals as it does that of all other commodities. So
far, except for tariff walls and smelting rings, there is a free
market in the metals under discussion.
The demand for metals varies with the unequal fluctuations of the
industrial tides. The sea of commercial activity is subject to
heavy storms, and the mine valuer is compelled to serve as weather
prophet on this ocean of trouble. High prices, which are the result
of industrial booms, bring about overproduction, and the collapse of
these begets a shrinkage of demand, wherein consequently the tide
of price turns back. In mining for metals each pound is produced
actually at a different cost. In case of an oversupply of base metals
the price will fall until it has reached a point where a portion of
the production is no longer profitable, and the equilibrium is
established through decline in output. However, in the backward
swing, due to lingering overproduction, prices usually fall lower
than the cost of producing even a much-diminished supply. There is
at this point what we may call the "basic" price, that at which
production is insufficient and the price rises again. The basic
price which is due to this undue backward swing is no more the
real price of the metal to be contemplated over so long a term
of years than is the highest price. At how much above the basic
price of depressed times the product can be safely expected to
find a market is the real question. Few mines can be bought or
valued at this basic price. An indication of what this is can be
gained from a study of fluctuations over a long term of years.
It is common to hear the average price over an extended period
considered the "normal" price, but this basis for value is one which
must be used with discretion, for it is not the whole question when
mining. The "normal" price is the average price over a long term.
The lives of mines, and especially ore in sight, may not necessarily
enjoy the period of this "normal" price. The engineer must balance
his judgments by the immediate outlook of the industrial weather.
When lead was falling steadily in December, 1907, no engineer would
accept the price of that date, although it was then below "normal";
his product might go to market even lower yet.
It is desirable to ascertain what the basic and normal prices are,
for between them lies safety. Since 1884 there have been three cycles
of commercial expansion and contraction. If the average prices
are taken for these three cycles separately (1885-95), 1895-1902,
1902-08) it will be seen that there has been a steady advance in
prices. For the succeeding cycles lead on the London Exchange,[*]
the freest of the world's markets was £12 12_s._ 4_d._, £13 3_s._
7_d._, and £17 7_s._ 0_d._ respectively; zinc, £17 14_s._ 10_d._,
£19 3_s._ 8_d._, and £23 3_s._ 0_d._; and standard copper, £48 16_s._
0_d._, £59 10_s._ 0_d._, and £65 7_s._ 0_d._ It seems, therefore,
that a higher standard of prices can be assumed as the basic and
normal than would be indicated if the general average of, say,
twenty years were taken. During this period, the world's gold output
has nearly quadrupled, and, whether the quantitative theory of
gold be accepted or not, it cannot be denied that there has been
a steady increase in the price of commodities. In all base-metal
mining it is well to remember that the production of these metals
is liable to great stimulus at times from the discovery of new
deposits or new processes of recovery from hitherto unprofitable
ores. It is therefore for this reason hazardous in the extreme
to prophesy what prices will be far in the future, even when the
industrial weather is clear. But some basis must be arrived at,
and from the available outlook it would seem that the following
metal prices are justifiable for some time to come, provided the
present tariff schedules are maintained in the United States:
[Footnote *: All London prices are based on the long ton of 2,240
lbs. Much confusion exists in the copper trade as to the classification
of the metal. New York prices are quoted in electrolytic and "Lake";
London's in "Standard." "Standard" has now become practically an
arbitrary term peculiar to London, for the great bulk of copper
dealt in is "electrolytic" valued considerably over "Standard."]
==========================================================================
| Lead | Spelter | Copper | Tin | Silver
|------------|----------|----------|----------|---------------
|London| N.Y.|Lon.| N.Y.|Lon.| N.Y.|Lon.| N.Y.| Lon. | N.Y.
| Ton |Pound|Ton |Pound|Ton |Pound|Ton |Pound|Per oz.|Per oz.
------------|------|-----|----|-----|----|-----|----|-----|-------|-------
Basic Price | £11. |$.035|£17 |$.040|£52 |$.115|£100|$.220| 22_d._|$.44
Normal Price| 13.5| .043| 21 | .050| 65 | .140| 130| .290| 26 | .52
==========================================================================
In these figures the writer has not followed strict averages, but
has taken the general outlook combined with the previous records.
The likelihood of higher prices for lead is more encouraging than
for any other metal, as no new deposits of importance have come
forward for years, and the old mines are reaching considerable
depths. Nor does the frenzied prospecting of the world's surface
during the past ten years appear to forecast any very disturbing
developments. The zinc future is not so bright, for metallurgy
has done wonders in providing methods of saving the zinc formerly
discarded from lead ores, and enormous supplies will come forward
when required. The tin outlook is encouraging, for the supply from
a mining point of view seems unlikely to more than keep pace with
the world's needs. In copper the demand is growing prodigiously,
but the supplies of copper ores and the number of copper mines
that are ready to produce whenever normal prices recur was never
so great as to-day. One very hopeful fact can be deduced for the
comfort of the base metal mining industry as a whole. If the growth
of demand continues through the next thirty years in the ratio of
the past three decades, the annual demand for copper will be over
3,000,000 tons, of lead over 1,800,000 tons, of spelter 2,800,000
tons, of tin 250,000 tons. Where such stupendous amounts of these
metals are to come from at the present range of prices, and even
with reduced costs of production, is far beyond any apparent source
of supply. The outlook for silver prices is in the long run not
bright. As the major portion of the silver produced is a bye product
from base metals, any increase in the latter will increase the
silver production despite very much lower prices for the precious
metal. In the meantime the gradual conversion of all nations to
the gold standard seems a matter of certainty. Further, silver
may yet be abandoned as a subsidiary coinage inasmuch as it has
now but a token value in gold standard countries if denuded of
sentiment.
COST OF PRODUCTION.
It is hardly necessary to argue the relative importance of the
determination of the cost of production and the determination of
the recoverable contents of the ore. Obviously, the aim of mine
valuation is to know the profits to be won, and the profit is the
value of the metal won, less the cost of production.
The cost of production embraces development, mining, treatment,
management. Further than this, it is often contended that, as the
capital expended in purchase and equipment must be redeemed within
the life of the mine, this item should also be included in production
costs. It is true that mills, smelters, shafts, and all the
paraphernalia of a mine are of virtually negligible value when it
is exhausted; and that all mines are exhausted sometime and every
ton taken out contributes to that exhaustion; and that every ton of
ore must bear its contribution to the return of the investment,
as well as profit upon it. Therefore it may well be said that the
redemption of the capital and its interest should be considered
in costs per ton. The difficulty in dealing with the subject from
the point of view of production cost arises from the fact that,
except possibly in the case of banket gold and some conglomerate
copper mines, the life of a metal mine is unknown beyond the time
required to exhaust the ore reserves. The visible life at the time
of purchase or equipment may be only three or four years, yet the
average equipment has a longer life than this, and the anticipation
for every mine is also for longer duration than the bare ore in sight.
For clarity of conclusions in mine valuation the most advisable
course is to determine the profit in sight irrespective of capital
redemption in the first instance. The questions of capital redemption,
purchase price, or equipment cost can then be weighed against the
margin of profit. One phase of redemption will be further discussed
under "Amortization of Capital" and "Ratio of Output to the Mine."
The cost of production depends upon many things, such as the cost of
labor, supplies, the size of the ore-body, the treatment necessary,
the volume of output, etc.; and to discuss them all would lead
into a wilderness of supposititious cases. If the mine is a going
concern, from which reliable data can be obtained, the problem is
much simplified. If it is virgin, the experience of other mines
in the same region is the next resource; where no such data can be
had, the engineer must fall back upon the experience with mines
still farther afield. Use is sometimes made of the "comparison ton"
in calculating costs upon mines where data of actual experience
are not available. As costs will depend in the main upon items
mentioned above, if the known costs of a going mine elsewhere be
taken as a basis, and subtractions and additions made for more
unfavorable or favorable effect of the differences in the above
items, a fairly close result can be approximated.
Mine examinations are very often inspired by the belief that extended
operations or new metallurgical applications to the mine will expand
the profits. In such cases the paramount questions are the reduction
of costs by better plant, larger outputs, new processes, or alteration
of metallurgical basis and better methods. If every item of previous
expenditure be gone over and considered, together with the equipment,
and method by which it was obtained, the possible savings can be
fairly well deduced, and justification for any particular line
of action determined. One view of this subject will be further
discussed under "Ratio of Output to the Mine." The conditions which
govern the working costs are on every mine so special to itself,
that no amount of advice is very useful. Volumes of advice have
been published on the subject, but in the main their burden is
not to underestimate.
In considering the working costs of base-metal mines, much depends
upon the opportunity for treatment in customs works, smelters,
etc. Such treatment means a saving of a large portion of equipment
cost, and therefore of the capital to be invested and subsequently
recovered. The economics of home treatment must be weighed against
the sum which would need to be set aside for redemption of the
plant, and unless there is a very distinct advantage to be had by
the former, no risks should be taken. More engineers go wrong by
the erection of treatment works where other treatment facilities
are available, than do so by continued shipping. There are many
mines where the cost of equipment could never be returned, and
which would be valueless unless the ore could be shipped. Another
phase of foreign treatment arises from the necessity or advantage
of a mixture of ores,--the opportunity of such mixtures often gives
the public smelter an advantage in treatment with which treatment
on the mine could never compete.
Fluctuation in the price of base metals is a factor so much to be
taken into consideration, that it is desirable in estimating mine
values to reduce the working costs to a basis of a "per unit" of
finished metal. This method has the great advantage of indicating
so simply the involved risks of changing prices that whoso runs
may read. Where one metal predominates over the other to such an
extent as to form the "backbone" of the value of the mine, the
value of the subsidiary metals is often deducted from the cost of
the principal metal, in order to indicate more plainly the varying
value of the mine with the fluctuating prices of the predominant
metal. For example, it is usual to state that the cost of copper
production from a given ore will be so many cents per pound, or so
many pounds sterling per ton. Knowing the total metal extractable
from the ore in sight, the profits at given prices of metal can
be readily deduced. The point at which such calculation departs
from the "per-ton-of-ore" unto the per-unit-cost-of-metal basis,
usually lies at the point in ore dressing where it is ready for the
smelter. To take a simple case of a lead ore averaging 20%: this
is to be first concentrated and the lead reduced to a concentrate
averaging 70% and showing a recovery of 75% of the total metal
content. The cost per ton of development, mining, concentration,
management, is to this point say $4 per ton of original crude ore.
The smelter buys the concentrate for 95% of the value of the metal,
less the smelting charge of $15 per ton, or there is a working
cost of a similar sum by home equipment. In this case 4.66 tons of
ore are required to produce one ton of concentrates, and therefore
each ton of concentrates costs $18.64. This amount, added to the
smelting charge, gives a total of $33.64 for the creation of 70%
of one ton of finished lead, or equal to 2.40 cents per pound which
can be compared with the market price less 5%. If the ore were
to contain 20 ounces of silver per ton, of which 15 ounces were
recovered into the leady concentrates, and the smelter price for
the silver were 50 cents per ounce, then the $7.50 thus recovered
would be subtracted from $33.64, making the apparent cost of the
lead 1.86 cents per pound.
CHAPTER V.
Mine Valuation (_Continued_).
REDEMPTION OR AMORTIZATION OF CAPITAL AND INTEREST.
It is desirable to state in some detail the theory of amortization
before consideration of its application in mine valuation.
As every mine has a limited life, the capital invested in it must
be redeemed during the life of the mine. It is not sufficient that
there be a bare profit over working costs. In this particular,
mines differ wholly from many other types of investment, such as
railways. In the latter, if proper appropriation is made for
maintenance, the total income to the investor can be considered as
interest or profit; but in mines, a portion of the annual income
must be considered as a return of capital. Therefore, before the
yield on a mine investment can be determined, a portion of the
annual earnings must be set aside in such a manner that when the
mine is exhausted the original investment will have been restored.
If we consider the date due for the return of the capital as the time
when the mine is exhausted, we may consider the annual instalments
as payments before the due date, and they can be put out at compound
interest until the time for restoration arrives. If they be invested
in safe securities at the usual rate of about 4%, the addition of
this amount of compound interest will assist in the repayment of
the capital at the due date, so that the annual contributions to
a sinking fund need not themselves aggregate the total capital to
be restored, but may be smaller by the deficiency which will be
made up by their interest earnings. Such a system of redemption
of capital is called "Amortization."
Obviously it is not sufficient for the mine investor that his capital
shall have been restored, but there is required an excess earning
over and above the necessities of this annual funding of capital.
What rate of excess return the mine must yield is a matter of the
risks in the venture and the demands of the investor. Mining business
is one where 7% above provision for capital return is an absolute
minimum demanded by the risks inherent in mines, even where the
profit in sight gives warranty to the return of capital. Where
the profit in sight (which is the only real guarantee in mine
investment) is below the price of the investment, the annual return
should increase in proportion. There are thus two distinct directions
in which interest must be computed,--first, the internal influence
of interest in the amortization of the capital, and second, the
percentage return upon the whole investment after providing for
capital return.
There are many limitations to the introduction of such refinements
as interest calculations in mine valuation. It is a subject not
easy to discuss with finality, for not only is the term of years
unknown, but, of more importance, there are many factors of a highly
speculative order to be considered in valuing. It may be said that
a certain life is known in any case from the profit in sight, and
that in calculating this profit a deduction should be made from
the gross profit for loss of interest on it pending recovery. This
is true, but as mines are seldom dealt with on the basis of profit
in sight alone, and as the purchase price includes usually some
proportion for extension in depth, an unknown factor is introduced
which outweighs the known quantities. Therefore the application of
the culminative effect of interest accumulations is much dependent
upon the sort of mine under consideration. In most cases of uncertain
continuity in depth it introduces a mathematical refinement not
warranted by the speculative elements. For instance, in a mine
where the whole value is dependent upon extension of the deposit
beyond openings, and where an expected return of at least 50% per
annum is required to warrant the risk, such refinement would be
absurd. On the other hand, in a Witwatersrand gold mine, in gold
and tin gravels, or in massive copper mines such as Bingham and
Lake Superior, where at least some sort of life can be approximated,
it becomes a most vital element in valuation.
In general it may be said that the lower the total annual return
expected upon the capital invested, the greater does the amount
demanded for amortization become in proportion to this total income,
and therefore the greater need of its introduction in calculations.
Especially is this so where the cost of equipment is large
proportionately to the annual return. Further, it may be said that
such calculations are of decreasing use with increasing proportion of
speculative elements in the price of the mine. The risk of extension in
depth, of the price of metal, etc., may so outweigh the comparatively
minor factors here introduced as to render them useless of attention.
In the practical conduct of mines or mining companies, sinking
funds for amortization of capital are never established. In the
vast majority of mines of the class under discussion, the ultimate
duration of life is unknown, and therefore there is no basis upon
which to formulate such a definite financial policy even were it
desired. Were it possible to arrive at the annual sum to be set
aside, the stockholders of the mining type would prefer to do their
own reinvestment. The purpose of these calculations does not lie
in the application of amortization to administrative finance. It
is nevertheless one of the touchstones in the valuation of certain
mines or mining investments. That is, by a sort of inversion such
calculations can be made to serve as a means to expose the amount
of risk,--to furnish a yardstick for measuring the amount of risk
in the very speculations of extension in depth and price of metals
which attach to a mine. Given the annual income being received,
or expected, the problem can be formulated into the determination
of how many years it must be continued in order to amortize the
investment and pay a given rate of profit. A certain length of
life is evident from the ore in sight, which may be called the
life in sight. If the term of years required to redeem the capital
and pay an interest upon it is greater than the life in sight,
then this extended life must come from extension in depth, or ore
from other direction, or increased price of metals. If we then take
the volume and profit on the ore as disclosed we can calculate the
number of feet the deposit must extend in depth, or additional tonnage
that must be obtained of the same grade, or the different prices of
metal that must be secured, in order to satisfy the demanded term
of years. These demands in actual measure of ore or feet or higher
price can then be weighed against the geological and industrial
probabilities.
The following tables and examples may be of assistance in these
calculations.
Table 1. To apply this table, the amount of annual income or dividend
and the term of years it will last must be known or estimated factors.
It is then possible to determine the _present_ value of this annual
income after providing for amortization and interest on the investment
at various rates given, by multiplying the annual income by the
factor set out.
A simple illustration would be that of a mine earning a profit of
$200,000 annually, and having a total of 1,000,000 tons in sight,
yielding a profit of $2 a ton, or a total profit in sight of $2,000,000,
thus recoverable in ten years. On a basis of a 7% return on the
investment and amortization of capital (Table I), the factor is
6.52 x $200,000 = $1,304,000 as the present value of the gross
profits exposed. That is, this sum of $1,304,000, if paid for the
mine, would be repaid out of the profit in sight, together with
7% interest if the annual payments into sinking fund earn 4%.
TABLE I.
Present Value of an Annual Dividend Over -- Years at --% and Replacing
Capital by Reinvestment of an Annual Sum at 4%.
=======================================================
Years | 5% | 6% | 7% | 8% | 9% | 10%
-------|-------|-------|-------|-------|-------|-------
1 | .95 | .94 | .93 | .92 | .92 | .91
2 | 1.85 | 1.82 | 1.78 | 1.75 | 1.72 | 1.69
3 | 2.70 | 2.63 | 2.56 | 2.50 | 2.44 | 2.38
4 | 3.50 | 3.38 | 3.27 | 3.17 | 3.07 | 2.98
5 | 4.26 | 4.09 | 3.93 | 3.78 | 3.64 | 3.51
6 | 4.98 | 4.74 | 4.53 | 4.33 | 4.15 | 3.99
7 | 5.66 | 5.36 | 5.09 | 4.84 | 4.62 | 4.41
8 | 6.31 | 5.93 | 5.60 | 5.30 | 5.04 | 4.79
9 | 6.92 | 6.47 | 6.08 | 5.73 | 5.42 | 5.14
10 | 7.50 | 6.98 | 6.52 | 6.12 | 5.77 | 5.45
| | | | | |
11 | 8.05 | 7.45 | 6.94 | 6.49 | 6.09 | 5.74
12 | 8.58 | 7.90 | 7.32 | 6.82 | 6.39 | 6.00
13 | 9.08 | 8.32 | 7.68 | 7.13 | 6.66 | 6.24
14 | 9.55 | 8.72 | 8.02 | 7.42 | 6.91 | 6.46
15 | 10.00 | 9.09 | 8.34 | 7.79 | 7.14 | 6.67
16 | 10.43 | 9.45 | 8.63 | 7.95 | 7.36 | 6.86
17 | 10.85 | 9.78 | 8.91 | 8.18 | 7.56 | 7.03
18 | 11.24 | 10.10 | 9.17 | 8.40 | 7.75 | 7.19
19 | 11.61 | 10.40 | 9.42 | 8.61 | 7.93 | 7.34
20 | 11.96 | 10.68 | 9.65 | 8.80 | 8.09 | 7.49
| | | | | |
21 | 12.30 | 10.95 | 9.87 | 8.99 | 8.24 | 7.62
22 | 12.62 | 11.21 | 10.08 | 9.16 | 8.39 | 7.74
23 | 12.93 | 11.45 | 10.28 | 9.32 | 8.52 | 7.85
24 | 13.23 | 11.68 | 10.46 | 9.47 | 8.65 | 7.96
25 | 13.51 | 11.90 | 10.64 | 9.61 | 8.77 | 8.06
26 | 13.78 | 12.11 | 10.80 | 9.75 | 8.88 | 8.16
27 | 14.04 | 12.31 | 10.96 | 9.88 | 8.99 | 8.25
28 | 14.28 | 12.50 | 11.11 | 10.00 | 9.09 | 8.33
29 | 14.52 | 12.68 | 11.25 | 10.11 | 9.18 | 8.41
30 | 14.74 | 12.85 | 11.38 | 10.22 | 9.27 | 8.49
| | | | | |
31 | 14.96 | 13.01 | 11.51 | 10.32 | 9.36 | 8.56
32 | 15.16 | 13.17 | 11.63 | 10.42 | 9.44 | 8.62
33 | 15.36 | 13.31 | 11.75 | 10.51 | 9.51 | 8.69
34 | 15.55 | 13.46 | 11.86 | 10.60 | 9.59 | 8.75
35 | 15.73 | 13.59 | 11.96 | 10.67 | 9.65 | 8.80
36 | 15.90 | 13.72 | 12.06 | 10.76 | 9.72 | 8.86
37 | 16.07 | 13.84 | 12.16 | 10.84 | 9.78 | 8.91
38 | 16.22 | 13.96 | 12.25 | 10.91 | 9.84 | 8.96
39 | 16.38 | 14.07 | 12.34 | 10.98 | 9.89 | 9.00
40 | 16.52 | 14.18 | 12.42 | 11.05 | 9.95 | 9.05
=======================================================
Condensed from Inwood's Tables.
Table II is practically a compound discount table. That is, by
it can be determined the present value of a fixed sum payable at
the end of a given term of years, interest being discounted at
various given rates. Its use may be illustrated by continuing the
example preceding.
TABLE II.
Present Value of $1, or £1, payable in -- Years, Interest taken
at --%.
===================================
Years | 4% | 5% | 6% | 7%
------|------|------|------|-------
1 | .961 | .952 | .943 | .934
2 | .924 | .907 | .890 | .873
3 | .889 | .864 | .840 | .816
4 | .854 | .823 | .792 | .763
5 | .821 | .783 | .747 | .713
6 | .790 | .746 | .705 | .666
7 | .760 | .711 | .665 | .623
8 | .731 | .677 | .627 | .582
9 | .702 | .645 | .592 | .544
10 | .675 | .614 | .558 | .508
| | | |
11 | .649 | .585 | .527 | .475
12 | .625 | .557 | .497 | .444
13 | .600 | .530 | .469 | .415
14 | .577 | .505 | .442 | .388
15 | .555 | .481 | .417 | .362
16 | .534 | .458 | .394 | .339
17 | .513 | .436 | .371 | .316
18 | .494 | .415 | .350 | .296
19 | .475 | .396 | .330 | .276
20 | .456 | .377 | .311 | .258
| | | |
21 | .439 | .359 | .294 | .241
22 | .422 | .342 | .277 | .266
23 | .406 | .325 | .262 | .211
24 | .390 | .310 | .247 | .197
25 | .375 | .295 | .233 | .184
26 | .361 | .281 | .220 | .172
27 | .347 | .268 | .207 | .161
28 | .333 | .255 | .196 | .150
29 | .321 | .243 | .184 | .140
30 | .308 | .231 | .174 | .131
| | | |
31 | .296 | .220 | .164 | .123
32 | .285 | .210 | .155 | .115
33 | .274 | .200 | .146 | .107
34 | .263 | .190 | .138 | .100
35 | .253 | .181 | .130 | .094
36 | .244 | .172 | .123 | .087
37 | .234 | .164 | .116 | .082
38 | .225 | .156 | .109 | .076
39 | .216 | .149 | .103 | .071
40 | .208 | .142 | .097 | .067
===================================
Condensed from Inwood's Tables.
If such a mine is not equipped, and it is assumed that $200,000
are required to equip the mine, and that two years are required
for this equipment, the value of the ore in sight is still less,
because of the further loss of interest in delay and the cost of
equipment. In this case the present value of $1,304,000 in two
years, interest at 7%, the factor is .87 X 1,304,000 = $1,134,480.
From this comes off the cost of equipment, or $200,000, leaving
$934,480 as the present value of the profit in sight. A further
refinement could be added by calculating the interest chargeable
against the $200,000 equipment cost up to the time of production.
TABLE III.
===========================================================================
Annual | Number of years of life required to yield--% interest, and in
Rate of | addition to furnish annual instalments which, if reinvested at
Dividend.| 4% will return the original investment at the end of the period.
---------|-----------------------------------------------------------------
% | 5% | 6% | 7% | 8% | 9% | 10%
| | | | | |
6 | 41.0 | | | | |
7 | 28.0 | 41.0 | | | |
8 | 21.6 | 28.0 | 41.0 | | |
9 | 17.7 | 21.6 | 28.0 | 41.0 | |
10 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0 |
| | | | | |
11 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0
12 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0
13 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6
14 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7
15 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0
| | | | | |
16 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0
17 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5
18 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3
19 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4
20 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6
| | | | | |
21 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9
22 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3
23 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8
24 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4
25 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0
| | | | | |
26 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7
27 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4
28 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1
29 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9
30 | 3.8 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7
===========================================================================
Table III. This table is calculated by inversion of the factors
in Table I, and is the most useful of all such tables, as it is
a direct calculation of the number of years that a given rate of
income on the investment must continue in order to amortize the
capital (the annual sinking fund being placed at compound interest
at 4%) and to repay various rates of interest on the investment. The
application of this method in testing the value of dividend-paying
shares is very helpful, especially in weighing the risks involved in
the portion of the purchase or investment unsecured by the profit
in sight. Given the annual percentage income on the investment from
the dividends of the mine (or on a non-producing mine assuming a
given rate of production and profit from the factors exposed), by
reference to the table the number of years can be seen in which
this percentage must continue in order to amortize the investment
and pay various rates of interest on it. As said before, the ore
in sight at a given rate of exhaustion can be reduced to terms of
life in sight. This certain period deducted from the total term
of years required gives the life which must be provided by further
discovery of ore, and this can be reduced to tons or feet of extension
of given ore-bodies and a tangible position arrived at. The test
can be applied in this manner to the various prices which must
be realized from the base metal in sight to warrant the price.
Taking the last example and assuming that the mine is equipped,
and that the price is $2,000,000, the yearly return on the price is
10%. If it is desired besides amortizing or redeeming the capital to
secure a return of 7% on the investment, it will be seen by reference
to the table that there will be required a life of 21.6 years. As the
life visible in the ore in sight is ten years, then the extensions
in depth must produce ore for 11.6 years longer--1,160,000 tons. If
the ore-body is 1,000 feet long and 13 feet wide, it will furnish
of gold ore 1,000 tons per foot of depth; hence the ore-body must
extend 1,160 feet deeper to justify the price. Mines are seldom so
simple a proposition as this example. There are usually probabilities
of other ore; and in the case of base metal, then variability of price
and other elements must be counted. However, once the extension
in depth which is necessary is determined for various assumptions
of metal value, there is something tangible to consider and to
weigh with the five geological weights set out in Chapter III.
The example given can be expanded to indicate not only the importance
of interest and redemption in the long extension in depth required,
but a matter discussed from another point of view under "Ratio of
Output." If the plant on this mine were doubled and the earnings
increased to 20% ($400,000 per annum) (disregarding the reduction
in working expenses that must follow expansion of equipment), it
will be found that the life required to repay the purchase
money,--$2,000,000,--and 7% interest upon it, is about 6.8 years.
As at this increased rate of production there is in the ore in
sight a life of five years, the extension in depth must be depended
upon for 1.8 years, or only 360,000 tons,--that is, 360 feet of
extension. Similarly, the present value of the ore in sight is
$268,000 greater if the mine be given double the equipment, for
thus the idle money locked in the ore is brought into the interest
market at an earlier date. Against this increased profit must be
weighed the increased cost of equipment. The value of low grade
mines, especially, is very much a factor of the volume of output
contemplated.
CHAPTER VI.
Mine Valuation (_Concluded_).
VALUATION OF MINES WITH LITTLE OR NO ORE IN SIGHT; VALUATIONS ON
SECOND-HAND DATA; GENERAL CONDUCT OF EXAMINATIONS; REPORTS.
A large number of examinations arise upon prospecting ventures
or partially developed mines where the value is almost wholly
prospective. The risks in such enterprises amount to the possible loss
of the whole investment, and the possible returns must consequently
be commensurate. Such business is therefore necessarily highly
speculative, but not unjustifiable, as the whole history of the
industry attests; but this makes the matter no easier for the mine
valuer. Many devices of financial procedure assist in the limitation
of the sum risked, and offer a middle course to the investor between
purchase of a wholly prospective value and the loss of a possible
opportunity to profit by it. The usual form is an option to buy the
property after a period which permits a certain amount of development
work by the purchaser before final decision as to purchase.
Aside from young mines such enterprises often arise from the possibility
of lateral extension of the ore-deposit outside the boundaries of
the property of original discovery (Fig. 3), in which cases there
is often no visible ore within the property under consideration
upon which to found opinion. In regions where vertical side lines
obtain, there is always the possibility of a "deep level" in inclined
deposits. Therefore the ground surrounding known deposits has a
certain speculative value, upon which engineers are often called to
pass judgment. Except in such unusual occurrences as South African
bankets, or Lake Superior coppers, prospecting for deep level of
extension is also a highly speculative phase of mining.
The whole basis of opinion in both classes of ventures must be
the few geological weights,--the geology of the property and the
district, the development of surrounding mines, etc. In any event,
there is a very great percentage of risk, and the profit to be gained
by success must be, proportionally to the expenditure involved,
very large. It is no case for calculating amortization and other
refinements. It is one where several hundreds or thousands of per
cent hoped for on the investment is the only justification.
OPINIONS AND VALUATIONS UPON SECOND-HAND DATA.
Some one may come forward and deprecate the bare suggestion of an
engineer's offering an opinion when he cannot have proper first-hand
data. But in these days we have to deal with conditions as well as
theories of professional ethics. The growing ownership of mines
by companies, that is by corporations composed of many individuals,
and with their stocks often dealt in on the public exchanges, has
resulted in holders whose interest is not large enough to warrant
their undertaking the cost of exhaustive examinations. The system
has produced an increasing class of mining speculators and investors
who are finding and supplying the enormous sums required to work
our mines,--sums beyond the reach of the old-class single-handed
mining men. Every year the mining investors of the new order are
coming more and more to the engineer for advice, and they should
be encouraged, because such counsel can be given within limits,
and these limits tend to place the industry upon a sounder footing
of ownership. As was said before, the lamb can be in a measure
protected. The engineer's interest is to protect him, so that the
industry which concerns his own life-work may be in honorable repute,
and that capital may be readily forthcoming for its expansion.
Moreover, by constant advice to the investor as to what constitutes
a properly presented and managed project, the arrangement of such
proper presentation and management will tend to become an _a priori_
function of the promoter.
Sometimes the engineer can make a short visit to the mine for data
purposes,--more often he cannot. In the former case, he can resolve
for himself an approximation upon all the factors bearing on value,
except the quality of the ore. For this, aside from inspection of
the ore itself, a look at the plans is usually enlightening. A
longitudinal section of the mine showing a continuous shortening of
the stopes with each succeeding level carries its own interpretation.
In the main, the current record of past production and estimates
of the management as to ore-reserves, etc., can be accepted in
ratio to the confidence that can be placed in the men who present
them. It then becomes a case of judgment of men and things, and
here no rule applies.
Advice must often be given upon data alone, without inspection
of the mine. Most mining data present internal evidence as to
credibility. The untrustworthy and inexperienced betray themselves
in their every written production. Assuming the reliability of data,
the methods already discussed for weighing the ultimate value of
the property can be applied. It would be possible to cite hundreds
of examples of valuation based upon second-hand data. Three will,
however, sufficiently illustrate. First, the R mine at Johannesburg.
With the regularity of this deposit, the development done, and
a study of the workings on the neighboring mines and in deeper
ground, it is a not unfair assumption that the reefs will maintain
size and value throughout the area. The management is sound, and
all the data are given in the best manner. The life of the mine
is estimated at six years, with some probabilities of further ore
from low-grade sections. The annual earnings available for dividends
are at the rate of about £450,000 per annum. The capital is £440,000
in £1 shares. By reference to the table on page 46 it will be seen
that the present value of £450,000 spread over six years to return
capital at the end of that period, and give 7% dividends in the
meantime, is 4.53 x £450,000 = £2,036,500 ÷ 440,000 = £4 12_s_.
7_d_. per share. So that this mine, on the assumption of continuity
of values, will pay about 7% and return the price. Seven per cent
is, however, not deemed an adequate return for the risks of labor
troubles, faults, dykes, or poor patches. On a 9% basis, the mine
is worth about £4 4_s_. per share.
Second, the G mine in Nevada. It has a capital of $10,000,000 in
$1 shares, standing in the market at 50 cents each. The reserves
are 250,000 tons, yielding a profit for yearly division of $7 per
ton. It has an annual capacity of about 100,000 tons, or $700,000
net profit, equal to 14% on the market value. In order to repay
the capital value of $5,000,000 and 8% per annum, it will need
a life of (Table III) 13 years, of which 2-1/2 are visible. The
size of the ore-bodies indicates a yield of about 1,100 tons per
foot of depth. At an exhaustion rate of 100,000 tons per annum,
the mine would need to extend to a depth of over a thousand feet
below the present bottom. There is always a possibility of finding
parallel bodies or larger volumes in depth, but it would be a sanguine
engineer indeed who would recommend the stock, even though it pays
an apparent 14%.
Third, the B mine, with a capital of $10,000,000 in 2,000,000 shares
of $5 each. The promoters state that the mine is in the slopes of
the Andes in Peru; that there are 6,000,000 tons of "ore blocked
out"; that two assays by the assayers of the Bank of England average
9% copper; that the copper can be produced at five cents per pound;
that there is thus a profit of $10,000,000 in sight. The evidences
are wholly incompetent. It is a gamble on statements of persons
who have not the remotest idea of sound mining.
GENERAL CONDUCT OF EXAMINATION.
Complete and exhaustive examination, entailing extensive sampling,
assaying, and metallurgical tests, is very expensive and requires
time. An unfavorable report usually means to the employer absolute
loss of the engineer's fee and expenses. It becomes then the initial
duty of the latter to determine at once, by the general conditions
surrounding the property, how far the expenditure for exhaustive
examination is warranted. There is usually named a money valuation
for the property, and thus a peg is afforded upon which to hang
conclusions. Very often collateral factors with a preliminary sampling,
or indeed no sampling at all, will determine the whole business.
In fact, it is becoming very common to send younger engineers to
report as to whether exhaustive examination by more expensive men
is justified.
In the course of such preliminary inspection, the ore-bodies may
prove to be too small to insure adequate yield on the price, even
assuming continuity in depth and represented value. They may be
so difficult to mine as to make costs prohibitive, or they may
show strong signs of "petering out." The ore may present visible
metallurgical difficulties which make it unprofitable in any event.
A gold ore may contain copper or arsenic, so as to debar cyanidation,
where this process is the only hope of sufficiently moderate costs.
A lead ore may be an amorphous compound with zinc, and successful
concentration or smelting without great penalties may be precluded.
A copper ore may carry a great excess of silica and be at the same
time unconcentratable, and there may be no base mineral supply
available for smelting mixture. The mine may be so small or so
isolated that the cost of equipment will never be justified. Some
of these conditions may be determined as unsurmountable, assuming
a given value for the ore, and may warrant the rejection of the
mine at the price set.
It is a disagreeable thing to have a disappointed promoter heap
vituperation on an engineer's head because he did not make an exhaustive
examination. Although it is generally desirable to do some sampling
to give assurance to both purchaser and vendor of conscientiousness,
a little courage of conviction, when this is rightly and adequately
grounded, usually brings its own reward.
Supposing, however, that conditions are right and that the mine is
worth the price, subject to confirmation of values, the determination
of these cannot be undertaken unless time and money are available
for the work. As was said, a sampling campaign is expensive, and
takes time, and no engineer has the moral right to undertake an
examination unless both facilities are afforded. Curtailment is
unjust, both to himself and to his employer.
How much time and outlay are required to properly sample a mine
is obviously a question of its size, and the character of its ore.
An engineer and one principal assistant can conduct two sampling
parties. In hard rock it may be impossible to take more than five
samples a day for each party. But, in average ore, ten samples for
each is reasonable work. As the number of samples is dependent
upon the footage of openings on the deposit, a rough approximation
can be made in advance, and a general idea obtained as to the time
required. This period must be insisted upon.
REPORTS.
Reports are to be read by the layman, and their first qualities
should be simplicity of terms and definiteness of conclusions.
Reports are usually too long, rather than too short. The essential
facts governing the value of a mine can be expressed on one sheet
of paper. It is always desirable, however, that the groundwork data
and the manner of their determination should be set out with such
detail that any other engineer could come to the same conclusion
if he accepted the facts as accurately determined. In regard to the
detailed form of reports, the writer's own preference is for a single
page summarizing the main factors, and an assay plan, reduced to a
longitudinal section where possible. Then there should be added,
for purposes of record and for submission to other engineers, a
set of appendices going into some details as to the history of
the mine, its geology, development, equipment, metallurgy, and
management. A list of samples should be given with their location,
and the tonnages and values of each separate block. A presentation
should be made of the probabilities of extension in depth, together
with recommendations for working the mine.
GENERAL SUMMARY.
The bed-rock value which attaches to a mine is the profit to be
won from proved ore and in which the price of metal is calculated
at some figure between "basic" and "normal." This we may call the
"_A_" value. Beyond this there is the speculative value of the
mine. If the value of the "probable" ore be represented by _X_,
the value of extension of the ore by _Y_, and a higher price for
metal than the price above assumed represented by _Z_, then if
the mine be efficiently managed the value of the mine is _A_ +
_X_ + _Y_ + _Z_. What actual amounts should be attached to _X,
Y, Z_ is a matter of judgment. There is no prescription for good
judgment. Good judgment rests upon a proper balancing of evidence.
The amount of risk in _X, Y, Z_ is purely a question of how much
these factors are required to represent in money,--in effect, how
much more ore must be found, or how many feet the ore must extend
in depth; or in convertible terms, what life in years the mine
must have, or how high the price of metal must be. In forming an
opinion whether these requirements will be realized, _X, Y, Z_
must be balanced in a scale whose measuring standards are the five
geological weights and the general industrial outlook. The wise
engineer will put before his clients the scale, the weights, and
the conclusion arrived at. The shrewd investor will require to
know these of his adviser.
CHAPTER VII.
Development of Mines.
ENTRY TO THE MINE; TUNNELS; VERTICAL, INCLINED, AND COMBINED SHAFTS;
LOCATION AND NUMBER OF SHAFTS.
Development is conducted for two purposes: first, to search for
ore; and second, to open avenues for its extraction. Although both
objects are always more or less in view, the first predominates
in the early life of mines, the prospecting stage, and the second
in its later life, the producing stage. It is proposed to discuss
development designed to embrace extended production purposes first,
because development during the prospecting stage is governed by
the same principles, but is tempered by the greater degree of
uncertainty as to the future of the mine, and is, therefore, of
a more temporary character.
ENTRY TO THE MINE.
There are four methods of entry: by tunnel, vertical shaft, inclined
shaft, or by a combination of the last two, that is, by a shaft
initially vertical then turned to an incline. Combined shafts are
largely a development of the past few years to meet "deep level"
conditions, and have been rendered possible only by skip-winding. The
angle in such shafts (Fig. 2) is now generally made on a parabolic
curve, and the speed of winding is then less diminished by the
bend.
The engineering problems which present themselves under "entry"
may be divided into those of:--
1. Method.
2. Location.
3. Shape and size.
The resolution of these questions depends upon the:--
a. Degree of dip of the deposit.
b. Output of ore to be provided for.
c. Depth at which the deposit is to be attacked.
d. Boundaries of the property.
e. Surface topography.
f. Cost.
g. Operating efficiency.
h. Prospects of the mine.
[Illustration: Fig. 2.--Showing arrangement of the bend in combined
shafts.]
From the point of view of entrance, the coöperation of a majority
of these factors permits the division of mines into certain broad
classes. The type of works demanded for moderate depths (say vertically
2,500 to 3,000 feet) is very different from that required for great
depths. To reach great depths, the size of shafts must greatly
expand, to provide for extended ventilation, pumping, and winding
necessities. Moreover inclined shafts of a degree of flatness possible
for moderate depths become too long to be used economically from
the surface. The vast majority of metal-mining shafts fall into
the first class, those of moderate depths. Yet, as time goes on
and ore-deposits are exhausted to lower planes, problems of depth
will become more common. One thing, however, cannot be too much
emphasized, especially on mines to be worked from the outcrop, and
that is, that no engineer is warranted, owing to the speculation
incidental to extension in depth, in initiating early in the mine's
career shafts of such size or equipment as would be available for
great depths. Moreover, the proper location of a shaft so as to
work economically extension of the ore-bodies is a matter of no
certainty, and therefore shafts of speculative mines are tentative
in any event.
Another line of division from an engineering view is brought about
by a combination of three of the factors mentioned. This is the
classification into "outcrop" and "deep-level" mines. The former
are those founded upon ore-deposits to be worked from or close
to the surface. The latter are mines based upon the extension in
depth of ore-bodies from outcrop mines. Such projects are not so
common in America, where the law in most districts gives the outcrop
owner the right to follow ore beyond his side-lines, as in countries
where the boundaries are vertical on all sides. They do, however,
arise not alone in the few American sections where the side-lines
are vertical boundaries, but in other parts owing to the pitch of
ore-bodies through the end lines (Fig. 3). More especially do such
problems arise in America in effect, where the ingress questions
have to be revised for mines worked out in the upper levels (Fig.
7).
[Illustration: Fig. 3.--Longitudinal section showing "deep level"
project arising from dip of ore-body through end-line.]
If from a standpoint of entrance questions, mines are first classified
into those whose works are contemplated for moderate depths, and those
in which work is contemplated for great depth, further clarity in
discussion can be gained by subdivision into the possible cases arising
out of the factors of location, dip, topography, and boundaries.
MINES OF MODERATE DEPTHS.
Case I. Deposits where topographic conditions permit the
alternatives of shaft or tunnel.
Case II. Vertical or horizontal deposits, the only practical
means of attaining which is by a vertical shaft.
Case III. Inclined deposits to be worked from near the surface.
There are in such instances the alternatives of either
a vertical or an inclined shaft.
Case IV. Inclined deposits which must be attacked in depth,
that is, deep-level projects. There are the alternatives
of a compound shaft or of a vertical shaft, and
in some cases of an incline from the surface.
MINES TO GREAT DEPTHS.
Case V. Vertical or horizontal deposits, the only way of reaching
which is by a vertical shaft.
Case VI. Inclined deposits. In such cases the alternatives are
a vertical or a compound shaft.
CASE I.--Although for logical arrangement tunnel entry has been
given first place, to save repetition it is proposed to consider
it later. With few exceptions, tunnels are a temporary expedient
in the mine, which must sooner or later be opened by a shaft.
CASE II. VERTICAL OR HORIZONTAL DEPOSITS.--These require no discussion
as to manner of entry. There is no justifiable alternative to a
vertical shaft (Fig. 4).
[Illustration: Fig. 4.--Cross-sections showing entry to vertical
or horizontal deposits. Case II.]
[Illustration: Fig. 5.--Cross-section showing alternative shafts
to inclined deposit to be worked from surface. Case III.]
CASE III. INCLINED DEPOSITS WHICH ARE INTENDED TO BE WORKED FROM
THE OUTCROP, OR FROM NEAR IT (Fig. 5).--The choice of inclined or
vertical shaft is dependent upon relative cost of construction,
subsequent operation, and the useful life of the shaft, and these
matters are largely governed by the degree of dip. Assuming a shaft
of the same size in either alternative, the comparative cost per
foot of sinking is dependent largely on the breaking facilities
of the rock under the different directions of attack. In this,
the angles of the bedding or joint planes to the direction of the
shaft outweigh other factors. The shaft which takes the greatest
advantage of such lines of breaking weakness will be the cheapest
per foot to sink. In South African experience, where inclined shafts
are sunk parallel to the bedding planes of hard quartzites, the cost
per foot appears to be in favor of the incline. On the other hand,
sinking shafts across tight schists seems to be more advantageous
than parallel to the bedding planes, and inclines following the
dip cost more per foot than vertical shafts.
An inclined shaft requires more footage to reach a given point
of depth, and therefore it would entail a greater total expense
than a vertical shaft, assuming they cost the same per foot. The
excess amount will be represented by the extra length, and this
will depend upon the flatness of the dip. With vertical shafts,
however, crosscuts to the deposit are necessary. In a comparative
view, therefore, the cost of the crosscuts must be included with
that of the vertical shaft, as they would be almost wholly saved
in an incline following near the ore.
The factor of useful life for the shaft enters in deciding as to
the advisability of vertical shafts on inclined deposits, from the
fact that at some depth one of two alternatives has to be chosen.
The vertical shaft, when it reaches a point below the deposit where
the crosscuts are too long (_C_, Fig. 5), either becomes useless,
or must be turned on an incline at the intersection with the ore
(_B_). The first alternative means ultimately a complete loss of
the shaft for working purposes. The latter has the disadvantage
that the bend interferes slightly with haulage.
The following table will indicate an hypothetical extreme case,--not
infrequently met. In it a vertical shaft 1,500 feet in depth is taken
as cutting the deposit at the depth of 750 feet, the most favored
position so far as aggregate length of crosscuts is concerned. The
cost of crosscutting is taken at $20 per foot and that of sinking
the vertical shaft at $75 per foot. The incline is assumed for two
cases at $75 and $100 per foot respectively. The stoping height
upon the ore between levels is counted at 125 feet.
Dip of | Depth of | Length of |No. of Crosscuts| Total Length
Deposit from | Vertical | Incline | Required from | of Crosscuts,
Horizontal | Shaft | Required | V Shaft | Feet
-------------|-------------|-------------|----------------|---------------
80° | 1,500 | 1,522 | 11 | 859
70° | 1,500 | 1,595 | 12 | 1,911
60° | 1,500 | 1,732 | 13 | 3,247
50° | 1,500 | 1,058 | 15 | 5,389
40° | 1,500 | 2,334 | 18 | 8,038
30° | 1,500 | 3,000 | 23 | 16,237
==========================================================================
Cost of |Cost Vertical| Total Cost | Cost of Incline|Cost of Incline
Crosscuts $20| Shaft $75 | of Vertical | $75 per Foot | $100 per Foot
per Foot | per Foot |and Crosscuts| |
-------------|-------------|-------------|----------------|---------------
$17,180 | $112,500 | $129,680 | $114,150 | $152,200
38,220 | 112,500 | 150,720 | 118,625 | 159,500
64,940 | 112,500 | 177,440 | 129,900 | 172,230
107,780 | 112,500 | 220,280 | 114,850 | 195,800
178,760 | 112,500 | 291,260 | 175,050 | 233,400
324,740 | 112,500 | 437,240 | 225,000 | 300,000
From the above examples it will be seen that the cost of crosscuts
put at ordinary level intervals rapidly outruns the extra expense
of increased length of inclines. If, however, the conditions are
such that crosscuts from a vertical shaft are not necessary at so
frequent intervals, then in proportion to the decrease the advantages
sway to the vertical shaft. Most situations wherein the crosscuts
can be avoided arise in mines worked out in the upper levels and
fall under Case IV, that of deep-level projects.
There can be no doubt that vertical shafts are cheaper to operate
than inclines: the length of haul from a given depth is less; much
higher rope speed is possible, and thus the haulage hours are less
for the same output; the wear and tear on ropes, tracks, or guides
is not so great, and pumping is more economical where the Cornish
order of pump is used. On the other hand, with a vertical shaft
must be included the cost of operating crosscuts. On mines where
the volume of ore does not warrant mechanical haulage, the cost of
tramming through the extra distance involved is an expense which
outweighs any extra operating outlay in the inclined shaft itself.
Even with mechanical haulage in crosscuts, it is doubtful if there
is anything in favor of the vertical shaft on this score.
[Illustration: Fig. 6.--Cross-section showing auxiliary vertical
outlet.]
In deposits of very flat dips, under 30°, the case arises where the
length of incline is so great that the saving on haulage through
direct lift warrants a vertical shaft as an auxiliary outlet in
addition to the incline (Fig. 6). In such a combination the crosscut
question is eliminated. The mine is worked above and below the
intersection by incline, and the vertical shaft becomes simply a
more economical exit and an alternative to secure increased output.
The North Star mine at Grass Valley is an illustration in point. Such
a positive instance borders again on Case IV, deep-level projects.
In conclusion, it is the writer's belief that where mines are to
be worked from near the surface, coincidentally with sinking, and
where, therefore, crosscuts from a vertical shaft would need to be
installed frequently, inclines are warranted in all dips under 75°
and over 30°. Beyond 75° the best alternative is often undeterminable.
In the range under 30° and over 15°, although inclines are primarily
necessary for actual delivery of ore from levels, they can often
be justifiably supplemented by a vertical shaft as a relief to a
long haul. In dips of less than 15°, as in those over 75°, the
advantages again trend strongly in favor of the vertical shaft. There
arise, however, in mountainous countries, topographic conditions
such as the dip of deposits into the mountain, which preclude any
alternative on an incline at any angled dip.
CASE IV. INCLINED DEPOSITS WHICH MUST BE ATTACKED IN DEPTH (Fig.
7).--There are two principal conditions in which such properties
exist: first, mines being operated, or having been previously worked,
whose method of entry must be revised; second, those whose ore-bodies
to be attacked do not outcrop within the property.
The first situation may occur in mines of inadequate shaft capacity
or wrong location; in mines abandoned and resurrected; in mines
where a vertical shaft has reached its limit of useful extensions,
having passed the place of economical crosscutting; or in mines in
flat deposits with inclines whose haul has become too long to be
economical. Three alternatives present themselves in such cases: a
new incline from the surface (_A B F_, Fig. 7), or a vertical shaft
combined with incline extension (_C D F_), or a simple vertical
shaft (_H G_). A comparison can be first made between the simple
incline and the combined shaft. The construction of an incline from
the surface to the ore-body will be more costly than a combined
shaft, for until the horizon of the ore is reached (at _D_) no
crosscuts are required in the vertical section, while the incline
must be of greater length to reach the same horizon. The case arises,
however, where inclines can be sunk through old stopes, and thus
more cheaply constructed than vertical shafts through solid rock;
and also the case of mountainous topographic conditions mentioned
above.
[Illustration: Fig. 7.--Cross-section of inclined deposit which
must be attacked in depth.]
From an operating point of view, the bend in combined shafts (at
_D_) gives rise to a good deal of wear and tear on ropes and gear.
The possible speed of winding through a combined shaft is, however,
greater than a simple incline, for although haulage speed through
the incline section (_D F_) and around the bend of the combined
shaft is about the same as throughout a simple incline (_A F_), the
speed can be accelerated in the vertical portion (_D C_) above that
feasible did the incline extend to the surface. There is therefore an
advantage in this regard in the combined shaft. The net advantages
of the combined over the inclined shaft depend on the comparative
length of the two alternative routes from the intersection (_D_)
to the surface. Certainly it is not advisable to sink a combined
shaft to cut a deposit at 300 feet in depth if a simple incline
can be had to the surface. On the other hand, a combined shaft
cutting the deposit at 1,000 feet will be more advisable than a
simple incline 2,000 feet long to reach the same point. The matter
is one for direct calculation in each special case. In general, there
are few instances of really deep-level projects where a complete
incline from the surface is warranted.
In most situations of this sort, and in all of the second type
(where the outcrop is outside the property), actual choice usually
lies between combined shafts (_C D F_) and entire vertical shafts (_H
G_). The difference between a combined shaft and a direct vertical
shaft can be reduced to a comparison of the combined shaft below
the point of intersection (_D_) with that portion of a vertical
shaft which would cover the same horizon. The question then becomes
identical with that of inclined _versus_ verticals, as stated in Case
III, with the offsetting disadvantage of the bend in the combined
shaft. If it is desired to reach production at the earliest date,
the lower section of a simple vertical shaft must have crosscuts
to reach the ore lying above the horizon of its intersection (_E_).
If production does not press, the ore above the intersection (_EB_)
can be worked by rises from the horizon of intersection (_E_).
In the use of rises, however, there follow the difficulties of
ventilation and lowering the ore down to the shaft, which brings
expenses to much the same thing as operating through crosscuts.
The advantages of combined over simple vertical shafts are earlier
production, saving of either rises or crosscuts, and the ultimate
utility of the shaft to any depth. The disadvantages are the cost
of the extra length of the inclined section, slower winding, and
greater wear and tear within the inclined section and especially
around the bend. All these factors are of variable import, depending
upon the dip. On very steep dips,--over 70°,--the net result is in
favor of the simple vertical shaft. On other dips it is in favor
of the combined shaft.
CASES V AND VI. MINES TO BE WORKED TO GREAT DEPTHS,--OVER 3,000
FEET.--In Case V, with vertical or horizontal deposits, there is
obviously no desirable alternative to vertical shafts.
In Case VI, with inclined deposits, there are the alternatives
of a combined or of a simple vertical shaft. A vertical shaft in
locations (_H_, Fig. 7) such as would not necessitate extension in
depth by an incline, would, as in Case IV, compel either crosscuts
to the ore or inclines up from the horizon of intersection (_E_).
Apart from delay in coming to production and the consequent loss of
interest on capital, the ventilation problems with this arrangement
would be appalling. Moreover, the combined shaft, entering the deposit
near its shallowest point, offers the possibility of a separate
haulage system on the inclined and on the vertical sections, and
such separate haulage is usually advisable at great depths. In
such instances, the output to be handled is large, for no mine of
small output is likely to be contemplated at such depth. Several
moderate-sized inclines from the horizon of intersection have been
suggested (_EF_, _DG_, _CH_, Fig. 8) to feed a large primary shaft
(_AB_), which thus becomes the trunk road. This program would cheapen
lateral haulage underground, as mechanical traction can be used
in the main level, (_EC_), and horizontal haulage costs can be
reduced on the lower levels. Moreover, separate winding engines
on the two sections increase the capacity, for the effect is that
of two trains instead of one running on a single track.
SHAFT LOCATION.--Although the prime purpose in locating a shaft
is obviously to gain access to the largest volume of ore within
the shortest haulage distance, other conditions also enter, such
as the character of the surface and the rock to be intersected,
the time involved before reaching production, and capital cost.
As shafts must bear two relations to a deposit,--one as to the
dip and the other as to the strike,--they may be considered from
these aspects. Vertical shafts must be on the hanging-wall side
of the outcrop if the deposit dips at all. In any event, the shaft
should be far enough away to be out of the reach of creeps. An
inclined shaft may be sunk either on the vein, in which case a
pillar of ore must be left to support the shaft; or, instead, it
may be sunk a short distance in the footwall, and where necessary
the excavation above can be supported by filling. Following the
ore has the advantage of prospecting in sinking, and in many cases
the softness of the ground in the region of the vein warrants this
procedure. It has, however, the disadvantage that a pillar of ore
is locked up until the shaft is ready for abandonment. Moreover, as
veins or lodes are seldom of even dip, an inclined shaft, to have
value as a prospecting opening, or to take advantage of breaking
possibilities in the lode, will usually be crooked, and an incline
irregular in detail adds greatly to the cost of winding and maintenance.
These twin disadvantages usually warrant a straight incline in the
footwall. Inclines are not necessarily of the same dip throughout,
but for reasonably economical haulage change of angle must take
place gradually.
[Illustration: Fig. 8.--Longitudinal section showing shaft arrangement
proposed for very deep inclined deposits.]
In the case of deep-level projects on inclined deposits, demanding
combined or vertical shafts, the first desideratum is to locate
the vertical section as far from the outcrop as possible, and thus
secure the most ore above the horizon of intersection. This, however,
as stated before, would involve the cost of crosscuts or rises and
would cause delay in production, together with the accumulation
of capital charges. How important the increment of interest on
capital may become during the period of opening the mine may be
demonstrated by a concrete case. For instance, the capital of a
company or the cost of the property is, say, $1,000,000, and where
opening the mine for production requires four years, the aggregate
sum of accumulated compound interest at 5% (and most operators
want more from a mining investment) would be $216,000. Under such
circumstances, if a year or two can be saved in getting to production
by entering the property at a higher horizon, the difference in
accumulated interest will more than repay the infinitesimal extra
cost of winding through a combined shaft of somewhat increased
length in the inclined section.
The unknown character of the ore in depth is always a sound reason
for reaching it as quickly and as cheaply as possible. In result,
such shafts are usually best located when the vertical section
enters the upper portion of the deposit.
The objective in location with regard to the strike of the ore-bodies
is obviously to have an equal length of lateral ore-haul in every
direction from the shaft. It is easier to specify than to achieve
this, for in all speculative deposits ore-shoots are found to pursue
curious vagaries as they go down. Ore-bodies do not reoccur with
the same locus as in the upper levels, and generally the chances
to go wrong are more numerous than those to go right.
NUMBER OF SHAFTS.--The problem of whether the mine is to be opened
by one or by two shafts of course influences location. In metal
mines under Cases II and III (outcrop properties) the ore output
requirements are seldom beyond the capacity of one shaft. Ventilation
and escape-ways are usually easily managed through the old stopes.
Under such circumstances, the conditions warranting a second shaft
are the length of underground haul and isolation of ore-bodies or
veins. Lateral haulage underground is necessarily disintegrated by
the various levels, and usually has to be done by hand. By shortening
this distance of tramming and by consolidation of the material
from all levels at the surface, where mechanical haulage can be
installed, a second shaft is often justified. There is therefore
an economic limitation to the radius of a single shaft, regardless
of the ability of the shaft to handle the total output.
Other questions also often arise which are of equal importance
to haulage costs. Separate ore-shoots or ore-bodies or parallel
deposits necessitate, if worked from one shaft, constant levels
through unpayable ground and extra haul as well, or ore-bodies may
dip away from the original shaft along the strike of the deposit
and a long haulage through dead levels must follow. For instance,
levels and crosscuts cost roughly one-quarter as much per foot as
shafts. Therefore four levels in barren ground, to reach a parallel
vein or isolated ore-body 1,000 feet away, would pay for a shaft
1,000 feet deep. At a depth of 1,000 feet, at least six levels
might be necessary. The tramming of ore by hand through such a
distance would cost about double the amount to hoist it through
a shaft and transport it mechanically to the dressing plant at
surface. The aggregate cost and operation of barren levels therefore
soon pays for a second shaft. If two or more shafts are in question,
they must obviously be set so as to best divide the work.
Under Cases IV, V, and VI,--that is, deep-level projects,--ventilation
and escape become most important considerations. Even where the
volume of ore is within the capacity of a single shaft, another
usually becomes a necessity for these reasons. Their location is
affected not only by the locus of the ore, but, as said, by the time
required to reach it. Where two shafts are to be sunk to inclined
deposits, it is usual to set one so as to intersect the deposit at
a lower point than the other. Production can be started from the
shallower, before the second is entirely ready. The ore above the
horizon of intersection of the deeper shaft is thus accessible from
the shallower shaft, and the difficulty of long rises or crosscuts
from that deepest shaft does not arise.
CHAPTER VIII.
Development of Mines (_Continued_).
SHAPE AND SIZE OF SHAFTS; SPEED OF SINKING; TUNNELS.
SHAPE OF SHAFTS.--Shafts may be round or rectangular.[*] Round
vertical shafts are largely applied to coal-mines, and some engineers
have advocated their usefulness to the mining of the metals under
discussion. Their great advantages lie in their structural strength,
in the large amount of free space for ventilation, and in the fact
that if walled with stone, brick, concrete, or steel, they can be
made water-tight so as to prevent inflow from water-bearing strata,
even when under great pressure. The round walled shafts have a longer
life than timbered shafts. All these advantages pertain much more to
mining coal or iron than metals, for unsound, wet ground is often
the accompaniment of coal-measures, and seldom troubles metal-mines.
Ventilation requirements are also much greater in coal-mines. From
a metal-miner's standpoint, round shafts are comparatively much
more expensive than the rectangular timbered type.[**] For a larger
area must be excavated for the same useful space, and if support
is needed, satisfactory walling, which of necessity must be brick,
stone, concrete, or steel, cannot be cheaply accomplished under
the conditions prevailing in most metal regions. Although such
shafts would have a longer life, the duration of timbered shafts
is sufficient for most metal mines. It follows that, as timber
is the cheapest and all things considered the most advantageous
means of shaft support for the comparatively temporary character
of metal mines, to get the strains applied to the timbers in the
best manner, and to use the minimum amount of it consistent with
security, and to lose the least working space, the shaft must be
constructed on rectangular lines.
[Footnote *: Octagonal shafts were sunk in Mexico in former times.
At each face of the octagon was a whim run by mules, and hauling
leather buckets.]
[Footnote **: The economic situation is rapidly arising in a number
of localities that steel beams can be usefully used instead of
timber. The same arguments apply to this type of support that apply
to timber.]
The variations in timbered shaft design arise from the possible
arrangement of compartments. Many combinations can be imagined,
of which Figures 9, 10, 11, 12, 13, and 14 are examples.
[Illustration: FIG. 9. FIG. 10. FIG. 11. FIG. 12. FIG. 13. FIG.
14.]
The arrangement of compartments shown in Figures 9, 10, 11, and
13 gives the greatest strength. It permits timbering to the best
advantage, and avoids the danger underground involved in crossing
one compartment to reach another. It is therefore generally adopted.
Any other arrangement would obviously be impossible in inclined
or combined shafts.
SIZE OF SHAFTS.--In considering the size of shafts to be installed,
many factors are involved. They are in the main:--
_a_. Amount of ore to be handled.
_b_. Winding plant.
_c_. Vehicle of transport.
_d_. Depth.
_e_. Number of men to be worked underground.
_f_. Amount of water.
_g_. Ventilation.
_h_. Character of the ground.
_i_. Capital outlay.
_j_. Operating expense.
It is not to be assumed that these factors have been stated in
the order of relative importance. More or less emphasis will be
attached to particular factors by different engineers, and under
different circumstances. It is not possible to suggest any arbitrary
standard for calculating their relative weight, and they are so
interdependent as to preclude separate discussion. The usual result
is a compromise between the demands of all.
Certain factors, however, dictate a minimum position, which may
be considered as a datum from which to start consideration.
_First_, a winding engine, in order to work with any economy, must
be balanced, that is, a descending empty skip or cage must assist
in pulling up a loaded one. Therefore, except in mines of very
small output, at least two compartments must be made for hoisting
purposes. Water has to be pumped from most mines, escape-ways are
necessary, together with room for wires and air-pipes, so that at
least one more compartment must be provided for these objects.
We have thus three compartments as a sound minimum for any shaft
where more than trivial output is required.
_Second_, there is a certain minimum size of shaft excavation below
which there is very little economy in actual rock-breaking.[*]
In too confined a space, holes cannot be placed to advantage for
the blast, men cannot get round expeditiously, and spoil cannot be
handled readily. The writer's own experience leads him to believe
that, in so far as rock-breaking is concerned, to sink a shaft
fourteen to sixteen feet long by six to seven feet wide outside
the timbers, is as cheap as to drive any smaller size within the
realm of consideration, and is more rapid. This size of excavation
permits of three compartments, each about four to five feet inside
the timbers.
[Footnote *: Notes on the cost of shafts in various regions which
have been personally collected show a remarkable decrease in the
cost per cubic foot of material excavated with increased size of
shaft. Variations in skill, in economic conditions, and in method
of accounting make data regarding different shafts of doubtful
value, but the following are of interest:--
In Australia, eight shafts between 10 and 11 feet long by 4 to
5 feet wide cost an average of $1.20 per cubic foot of material
excavated. Six shafts 13 to 14 feet long by 4 to 5 feet wide cost
an average of $0.95 per cubic foot; seven shafts 14 to 16 feet
long and 5 to 7 feet wide cost an average of $0.82 per cubic foot.
In South Africa, eleven shafts 18 to 19 feet long by 7 to 8 feet
wide cost an average of $0.82 per cubic foot; five shafts 21 to
25 feet long by 8 feet wide, cost $0.74; and seven shafts 28 feet
by 8 feet cost $0.60 per cubic foot.]
The cost of timber, it is true, is a factor of the size of shaft,
but the labor of timbering does not increase in the same ratio.
In any event, the cost of timber is only about 15% of the actual
shaft cost, even in localities of extremely high prices.
_Third_, three reasons are rapidly making the self-dumping skip
the almost universal shaft-vehicle, instead of the old cage for
cars. First, there is a great economy in labor for loading into
and discharging from a shaft; second, there is more rapid despatch
and discharge and therefore a larger number of possible trips;
third, shaft-haulage is then independent of delays in arrival of
cars at stations, while tramming can be done at any time and
shaft-haulage can be concentrated into certain hours. Cages to
carry mine cars and handle the same load as a skip must either
be big enough to take two cars, which compels a much larger shaft
than is necessary with skips, or they must be double-decked, which
renders loading arrangements underground costly to install and
expensive to work. For all these reasons, cages can be justified only
on metal mines of such small tonnage that time is no consideration
and where the saving of men is not to be effected. In compartments
of the minimum size mentioned above (four to five feet either way)
a skip with a capacity of from two to five tons can be installed,
although from two to three tons is the present rule. Lighter loads
than this involve more trips, and thus less hourly capacity, and,
on the other hand, heavier loads require more costly engines. This
matter is further discussed under "Haulage Appliances."
We have therefore as the economic minimum a shaft of three compartments
(Fig. 9), each four to five feet square. When the maximum tonnage
is wanted from such a shaft at the least operating cost, it should
be equipped with loading bins and skips.
The output capacity of shafts of this size and equipment will depend
in a major degree upon the engine employed, and in a less degree
upon the hauling depth. The reason why depth is a subsidiary factor
is that the rapidity with which a load can be drawn is not wholly a
factor of depth. The time consumed in hoisting is partially expended
in loading, in acceleration and retardation of the engine, and in
discharge of the load. These factors are constant for any depth,
and extra distance is therefore accomplished at full speed of the
engine.
Vertical shafts will, other things being equal, have greater capacity
than inclines, as winding will be much faster and length of haul less
for same depth. Since engines have, however, a great tractive ability
on inclines, by an increase in the size of skip it is usually possible
partially to equalize matters. Therefore the size of inclines for
the same output need not differ materially from vertical shafts.
The maximum capacity of a shaft whose equipment is of the character
and size given above, will, as stated, decrease somewhat with extension
in depth of the haulage horizon. At 500 feet, such a shaft if vertical
could produce 70 to 80 tons per hour comfortably with an engine
whose winding speed was 700 feet per minute. As men and material
other than ore have to be handled in and out of the mine, and
shaft-sinking has to be attended to, the winding engine cannot
be employed all the time on ore. Twelve hours of actual daily
ore-winding are all that can be expected without auxiliary help.
This represents a capacity from such a depth of 800 to 1,000 tons
per day. A similar shaft, under ordinary working conditions, with
an engine speed of 2,000 feet per minute, should from, say, 3,000
feet have a capacity of about 400 to 600 tons daily.
It is desirable to inquire at what stages the size of shaft should
logically be enlarged in order to attain greater capacity. A
considerable measure of increase can be obtained by relieving the
main hoisting engine of all or part of its collateral duties. Where
the pumping machinery is not elaborate, it is often possible to
get a small single winding compartment into the gangway without
materially increasing the size of the shaft if the haulage compartments
be made somewhat narrower (Fig. 10). Such a compartment would be
operated by an auxiliary engine for sinking, handling tools and
material, and assisting in handling men. If this arrangement can
be effected, the productive time of the main engine can be expanded
to about twenty hours with an addition of about two-thirds to the
output.
Where the exigencies of pump and gangway require more than two
and one-half feet of shaft length, the next stage of expansion
becomes four full-sized compartments (Fig. 11). By thus enlarging the
auxiliary winding space, some assistance may be given to ore-haulage
in case of necessity. The mine whose output demands such haulage
provisions can usually stand another foot of width to the shaft,
so that the dimensions come to about 21 feet to 22 feet by 7 feet
to 8 feet outside the timbers. Such a shaft, with three- to four-ton
skips and an appropriate engine, will handle up to 250 tons per
hour from a depth of 1,000 feet.
The next logical step in advance is the shaft of five compartments
with four full-sized haulage ways (Fig. 13), each of greater size
than in the above instance. In this case, the auxiliary engine
becomes a balanced one, and can be employed part of the time upon
ore-haulage. Such a shaft will be about 26 feet to 28 feet long
by 8 feet wide outside the timbers, when provision is made for
one gangway. The capacity of such shafts can be up to 4,000 tons a
day, depending on the depth and engine. When very large quantities
of water are to be dealt with and rod-driven pumps to be used,
two pumping compartments are sometimes necessary, but other forms
of pumps do not require more than one compartment,--an additional
reason for their use.
For depths greater than 3,000 feet, other factors come into play.
Ventilation questions become of more import. The mechanical problems
on engines and ropes become involved, and their sum-effect is to
demand much increased size and a greater number of compartments.
The shafts at Johannesburg intended as outlets for workings 5,000
feet deep are as much as 46 feet by 9 feet outside timbers.
It is not purposed to go into details as to sinking methods or
timbering. While important matters, they would unduly prolong this
discussion. Besides, a multitude of treatises exist on these subjects
and cover all the minutiæ of such work.
SPEED OF SINKING.--Mines may be divided into two cases,--those
being developed only, and those being operated as well as developed.
In the former, the entrance into production is usually dependent
upon the speed at which the shaft is sunk. Until the mine is earning
profits, there is a loss of interest on the capital involved, which,
in ninety-nine instances out of a hundred, warrants any reasonable
extra expenditure to induce more rapid progress. In the case of
mines in operation, the volume of ore available to treatment or
valuation is generally dependent to a great degree upon the rapidity
of the extension of workings in depth. It will be demonstrated
later that, both from a financial and a technical standpoint, the
maximum development is the right one and that unremitting extension
in depth is not only justifiable but necessary.
Speed under special conditions or over short periods has a more
romantic than practical interest, outside of its value as a stimulant
to emulation. The thing that counts is the speed which can be maintained
over the year. Rapidity of sinking depends mainly on:--
_a_. Whether the shaft is or is not in use for operating the
mine.
_b_. The breaking character of the rock.
_c_. The amount of water.
The delays incident to general carrying of ore and men are such that
the use of the main haulage engine for shaft-sinking is practically
impossible, except on mines with small tonnage output. Even with a
separate winch or auxiliary winding-engine, delays are unavoidable
in a working shaft, especially as it usually has more water to contend
with than one not in use for operating the mine. The writer's own
impression is that an average of 40 feet per month is the maximum
possibility for year in and out sinking under such conditions. In
fact, few going mines manage more than 400 feet a year. In cases
of clean shaft-sinking, where every energy is bent to speed, 150
feet per month have been averaged for many months. Special cases
have occurred where as much as 213 feet have been achieved in a
single month. With ordinary conditions, 1,200 feet in a year is
very good work. Rock awkward to break, and water especially, lowers
the rate of progress very materially. Further reference to speed
will be found in the chapter on "Drilling Methods."
TUNNEL ENTRY.--The alternative of entry to a mine by tunnel is
usually not a question of topography altogether, but, like everything
else in mining science, has to be tempered to meet the capital
available and the expenditure warranted by the value showing.
In the initial prospecting of a mine, tunnels are occasionally
overdone by prospectors. Often more would be proved by a few inclines.
As the pioneer has to rely upon his right arm for hoisting and
drainage, the tunnel offers great temptations, even when it is
long and gains but little depth. At a more advanced stage of
development, the saving of capital outlay on hoisting and pumping
equipment, at a time when capital is costly to secure, is often
sufficient justification for a tunnel entry. But at the stage where
the future working of ore below a tunnel-level must be contemplated,
other factors enter. For ore below tunnel-level a shaft becomes
necessary, and in cases where a tunnel enters a few hundred feet
below the outcrop the shaft should very often extend to the surface,
because internal shafts, winding from tunnel-level, require large
excavations to make room for the transfer of ore and for winding
gear. The latter must be operated by transmitted power, either
that of steam, water, electricity, or air. Where power has to be
generated on the mine, the saving by the use of direct steam, generated
at the winding gear, is very considerable. Moreover, the cost of
haulage through a shaft for the extra distance from tunnel-level
to the surface is often less than the cost of transferring the
ore and removing it through the tunnel. The load once on the
winding-engine, the consumption of power is small for the extra
distance, and the saving of labor is of consequence. On the other
hand, where drainage problems arise, they usually outweigh all
other considerations, for whatever the horizon entered by tunnel,
the distance from that level to the surface means a saving of
water-pumpage against so much head. The accumulation of such constant
expense justifies a proportioned capital outlay. In other words,
the saving of this extra pumping will annually redeem the cost of
a certain amount of tunnel, even though it be used for drainage
only.
In order to emphasize the rapidity with which such a saving of
constant expense will justify capital outlay, one may tabulate the
result of calculations showing the length of tunnel warranted with
various hypothetical factors of quantity of water and height of lift
eliminated from pumping. In these computations, power is taken at
the low rate of $60 per horsepower-year, the cost of tunneling at
an average figure of $20 per foot, and the time on the basis of
a ten-year life for the mine.
Feet of Tunnel Paid for in 10 Years with Under-mentioned Conditions.
=============================================================
Feet of | 100,000 | 200,000 | 300,000 | 500,000 |1,000,000
Water Lift | Gallons | Gallons | Gallons | Gallons | Gallons
Avoided |per Diem |per Diem |per Diem |per Diem |per Diem
-----------|---------|---------|---------|---------|---------
100 | 600 | 1,200 | 1,800 | 3,000 | 6,000
200 | 1,200 | 2,400 | 3,600 | 6,000 | 12,000
300 | 1,800 | 3,600 | 5,400 | 9,000 | 18,000
500 | 3,000 | 6,000 | 9,000 | 15,000 | 30,000
1,000 | 6,000 | 12,000 | 18,000 | 30,000 | 60,000
=============================================================
The size of tunnels where ore-extraction is involved depends upon
the daily tonnage output required, and the length of haul. The
smallest size that can be economically driven and managed is about
6-1/2 feet by 6 feet inside the timbers. Such a tunnel, with single
track for a length of 1,000 feet, with one turn-out, permits handling
up to 500 tons a day with men and animals. If the distance be longer
or the tonnage greater, a double track is required, which necessitates
a tunnel at least 8 feet wide by 6-1/2 feet to 7 feet high, inside
the timbers.
There are tunnel projects of a much more impressive order than those
designed to operate upper levels of mines; that is, long crosscut
tunnels designed to drain and operate mines at very considerable
depths, such as the Sutro tunnel at Virginia City. The advantage
of these tunnels is very great, especially for drainage, and they
must be constructed of large size and equipped with appliances
for mechanical haulage.
CHAPTER IX.
Development of Mines (_Concluded_).
SUBSIDIARY DEVELOPMENT;--STATIONS; CROSSCUTS; LEVELS; INTERVAL
BETWEEN LEVELS; PROTECTION OF LEVELS; WINZES AND RISES. DEVELOPMENT
IN THE PROSPECTING STAGE; DRILLING.
SUBSIDIARY DEVELOPMENT.
Stations, crosscuts, levels, winzes, and rises follow after the
initial entry. They are all expensive, and the least number that
will answer is the main desideratum.
STATIONS.--As stations are the outlets of the levels to the shaft,
their size and construction is a factor of the volume and character
of the work at the levels which they are to serve. If no timber
is to be handled, and little ore, and this on cages, the stations
need be no larger than a good sized crosscut. Where timber is to
be let down, they must be ten to fifteen feet higher than the floor
of the crosscut. Where loading into skips is to be provided for,
bins must be cut underneath and sufficient room be provided to
shift the mine cars comfortably. Such bins are built of from 50 to
500 tons' capacity in order to contain some reserve for hoisting
purposes, and in many cases separate bins must be provided on opposite
sides of the shaft for ore and waste. It is a strong argument in
favor of skips, that with this means of haulage storage capacity
at the stations is possible, and the hoisting may then go on
independently of trucking and, as said before, there are no idle
men at the stations.
[Illustration: Fig. 15.--Cross-section of station arrangement for
skip-haulage in vertical shaft.]
[Illustration: Fig. 16.--Cross-section of station arrangement for
skip-haulage in vertical shaft.]
It is always desirable to concentrate the haulage to the least
number of levels, for many reasons. Among them is that, where haulage
is confined to few levels, storage-bins are not required at every
station. Figures 15, 16, 17, and 18 illustrate various arrangements
of loading bins.
CROSSCUTS.--Crosscuts are for two purposes, for roadway connection
of levels to the shaft or to other levels, and for prospecting
purposes. The number of crosscuts for roadways can sometimes be
decreased by making the connections with the shaft at every second
or even every third level, thus not only saving in the construction
cost of crosscuts and stations, but also in the expenses of scattered
tramming. The matter becomes especially worth considering where
the quantity of ore that can thus be accumulated warrants mule
or mechanical haulage. This subject will be referred to later on.
[Illustration: Fig. 17.--Arrangement of loading chutes in vertical
shaft.]
On the second purpose of crosscuts,--that of prospecting,--one
observation merits emphasis. This is, that the tendency of ore-fissures
to be formed in parallels warrants more systematic crosscutting
into the country rock than is done in many mines.
[Illustration: Fig. 18.--Cross-section of station arrangement for
skip-haulage in inclined shaft.]
LEVELS.
The word "level" is another example of miners' adaptations in
nomenclature. Its use in the sense of tunnels driven in the direction
of the strike of the deposit has better, but less used, synonyms in
the words "drifts" or "drives." The term "level" is used by miners
in two senses, in that it is sometimes applied to all openings on one
horizon, crosscuts included. Levels are for three purposes,--for a
stoping base; for prospecting the deposit; and for roadways. As a
prospecting and a stoping base it is desirable that the level should
be driven on the deposit; as a roadway, that it should constitute
the shortest distance between two points and be in the soundest
ground. On narrow, erratic deposits the levels usually must serve
all three purposes at once; but in wider and more regular deposits
levels are often driven separately for roadways from the level
which forms the stoping base and prospecting datum.
There was a time when mines were worked by driving the level on ore
and enlarging it top and bottom as far as the ground would stand,
then driving the next level 15 to 20 feet below, and repeating the
operation. This interval gradually expanded, but for some reason
100 feet was for years assumed to be the proper distance between
levels. Scattered over every mining camp on earth are thousands
of mines opened on this empirical figure, without consideration
of the reasons for it or for any other distance.
The governing factors in determining the vertical interval between
levels are the following:--
_a_. The regularity of the deposit.
_b_. The effect of the method of excavation of winzes and rises.
_c_. The dip and the method of stoping.
REGULARITY OF THE DEPOSIT.--From a prospecting point of view the
more levels the better, and the interval therefore must be determined
somewhat by the character of the deposit. In erratic deposits there
is less risk of missing ore with frequent levels, but it does not
follow that every level need be a through roadway to the shaft or
even a stoping base. In such deposits, intermediate levels for
prospecting alone are better than complete levels, each a roadway.
Nor is it essential, even where frequent levels are required for
a stoping base, that each should be a main haulage outlet to the
shaft. In some mines every third level is used as a main roadway,
the ore being poured from the intermediate ones down to the haulage
line. Thus tramming and shaft work, as stated before, can be
concentrated.
EFFECT OF METHOD OF EXCAVATING WINZES AND RISES.--With hand drilling
and hoisting, winzes beyond a limited depth become very costly to
pull spoil out of, and rises too high become difficult to ventilate,
so that there is in such cases a limit to the interval desirable
between levels, but these difficulties largely disappear where
air-winches and air-drills are used.
THE DIP AND METHOD OF STOPING.--The method of stoping is largely
dependent upon the dip, and indirectly thus affects level intervals.
In dips under that at which material will "flow" in the stopes--about
45° to 50°--the interval is greatly dependent on the method of
stope-transport. Where ore is to be shoveled from stopes to the
roadway, the levels must be comparatively close together. Where
deposits are very flat, under 20°, and walls fairly sound, it is
often possible to use a sort of long wall system of stoping and to
lay tracks in the stopes with self-acting inclines to the levels.
In such instances, the interval can be expanded to 250 or even 400
feet. In dips between 20° and 45°, tracks are not often possible,
and either shoveling or "bumping troughs"[*] are the only help
to transport. With shoveling, intervals of 100 feet[**] are most
common, and with troughs the distance can be expanded up to 150
or 175 feet.
[Footnote *: Page 136.]
[Footnote **: Intervals given are measured on the dip.]
In dips of over 40° to 50°, depending on the smoothness of the foot
wall, the distance can again be increased, as stope-transport is
greatly simplified, since the stope materials fall out by gravity.
In timbered stopes, in dips over about 45°, intervals of 150 to
200 feet are possible. In filled stopes intervals of over 150 feet
present difficulties in the maintenance of ore-passes, for the wear
and tear of longer use often breaks the timbers. In shrinkage-stopes,
where no passes are to be maintained and few winzes put through, the
interval is sometimes raised to 250 feet. The subject is further
discussed under "Stoping."
Another factor bearing on level intervals is the needed insurance
of sufficient points of stoping attack to keep up a certain output.
This must particularly influence the manager whose mine has but
little ore in reserve.
[Illustration: Fig. 19.]
PROTECTION OF LEVELS.--Until recent years, timbering and occasional
walling was the only method for the support of the roof, and for
forming a platform for a stoping base. Where the rock requires no
support sublevels can be used as a stoping base, and timbering
for such purpose avoided altogether (Figs. 38, 39, 42). In such
cases the main roadway can then be driven on straight lines, either
in the walls or in the ore, and used entirely for haulage. The
subheading for a stoping base is driven far enough above or below
the roadway (depending on whether overhand or underhand stoping
is to be used) to leave a supporting pillar which is penetrated
by short passes for ore. In overhand stopes, the ore is broken
directly on the floor of an upper sublevel; and in underhand stopes,
broken directly from the bottom of the sublevel. The method entails
leaving a pillar of ore which can be recovered only with difficulty
in mines where stope-support is necessary. The question of its
adoption is then largely one of the comparative cost of timbering,
the extra cost of the sublevel, and the net value of the ore left.
In bad swelling veins, or badly crushing walls, where constant
repair to timbers would be necessary, the use of a sublevel is a
most useful alternative. It is especially useful with stopes to
be left open or worked by shrinkage-stoping methods.
If the haulage level, however, is to be the stoping base, some
protection to the roadway must be provided. There are three systems
in use,--by wood stulls or sets (Figs. 19, 30, 43), by dry-walling
with timber caps (Fig. 35), and in some localities by steel sets.
Stulls are put up in various ways, and, as their use entails the
least difficulty in taking the ore out from beneath the level,
they are much favored, but are applicable only in comparatively
narrow deposits.
WINZES AND RISES.
These two kinds of openings for connecting two horizons in a mine
differ only in their manner of construction. A winze is sunk underhand,
while a rise is put up overhand. When the connection between levels
is completed, a miner standing at the bottom usually refers to
the opening as a rise, and when he goes to the top he calls it
a winze. This confusion in terms makes it advisable to refer to
all such completed openings as winzes, regardless of how they are
constructed.
In actual work, even disregarding water, it costs on the average
about 30% less to raise than to sink such openings, for obviously
the spoil runs out or is assisted by gravity in one case, and in
the other has to be shoveled and hauled up. Moreover, it is easier
to follow the ore in a rise than in a winze. It usually happens,
however, that in order to gain time both things are done, and for
prospecting purposes sinking is necessary.
The number of winzes required depends upon the method of stoping
adopted, and is mentioned under "Stoping." After stoping, the number
necessary to be maintained open depends upon the necessities of
ventilation, of escape, and of passageways for material to be used
below. Where stopes are to be filled with waste, more winzes must
be kept open than when other methods are used, and these winzes
must be in sufficient alignment to permit the continuous flow of
material down past the various levels. In order that the winzes
should deliver timber and filling to the most advantageous points,
they should, in dipping ore-bodies, be as far as possible on the
hanging wall side.
DEVELOPMENT IN THE EARLY PROSPECTING STAGE.
The prime objects in the prospecting stage are to expose the ore
and to learn regarding the ore-bodies something of their size, their
value, metallurgical character, location, dip, strike, etc.,--so much
at least as may be necessary to determine the works most suitable
for their extraction or values warranting purchase. In outcrop mines
there is one rule, and that is "follow the ore." Small temporary
inclines following the deposit, even though they are eventually
useless; are nine times out of ten justified.
In prospecting deep-level projects, it is usually necessary to
layout work which can be subsequently used in operating the mine,
because the depth involves works of such considerable scale, even
for prospecting, that the initial outlay does not warrant any
anticipation of revision. Such works have to be located and designed
after a study of the general geology as disclosed in adjoining mines.
Practically the only method of supplementing such information is
by the use of churn- and diamond-drills.
DRILLING.--Churn-drills are applicable only to comparatively shallow
deposits of large volume. They have an advantage over the diamond
drill in exposing a larger section and in their application to
loose material; but inability to determine the exact horizon of
the spoil does not lend them to narrow deposits, and in any event
results are likely to be misleading from the finely ground state of
the spoil. They are, however, of very great value for preliminary
prospecting to shallow horizons.
Two facts in diamond-drilling have to be borne in mind: the indication
of values is liable to be misleading, and the deflection of the drill
is likely to carry it far away from its anticipated destination.
A diamond-drill secures a small section which is sufficiently large
to reveal the geology, but the values disclosed in metal mines must
be accepted with reservations. The core amounts to but a little
sample out of possibly large amounts of ore, which is always of
variable character, and the core is most unlikely to represent
the average of the deposit. Two diamond-drill holes on the Oroya
Brownhill mine both passed through the ore-body. One apparently
disclosed unpayable values, the other seemingly showed ore forty
feet in width assaying $80 per ton. Neither was right. On the other
hand, the predetermination of the location of the ore-body justified
expenditure. A recent experiment at Johannesburg of placing a copper
wedge in the hole at a point above the ore-body and deflecting
the drill on reintroducing it, was successful in giving a second
section of the ore at small expense.
The deflection of diamond-drill holes from the starting angle is
almost universal. It often amounts to a considerable wandering
from the intended course. The amount of such deflection varies
with no seeming rule, but it is probable that it is especially
affected by the angle at which stratification or lamination planes
are inclined to the direction of the hole. A hole has been known
to wander in a depth of 1,500 feet more than 500 feet from the
point intended. Various instruments have been devised for surveying
deep holes, and they should be brought into use before works are
laid out on the basis of diamond-drill results, although none of
the inventions are entirely satisfactory.
CHAPTER X.
Stoping.
METHODS OF ORE-BREAKING; UNDERHAND STOPES; OVERHAND STOPES; COMBINED
STOPE. VALUING ORE IN COURSE OF BREAKING.
There is a great deal of confusion in the application of the word
"stoping." It is used not only specifically to mean the actual
ore-breaking, but also in a general sense to indicate all the operations
of ore-breaking, support of excavations, and transportation between
levels. It is used further as a noun to designate the hole left
when the ore is taken out. Worse still, it is impossible to adhere
to miners' terms without employing it in every sense, trusting
to luck and the context to make the meaning clear.
The conditions which govern the method of stoping are in the main:--
_a_. The dip.
_b_. The width of the deposit.
_c_. The character of the walls.
_d_. The cost of materials.
_e_. The character of the ore.
Every mine, and sometimes every stope in a mine, is a problem special
to itself. Any general consideration must therefore be simply an
inquiry into the broad principles which govern the adaptability of
special methods. A logical arrangement of discussion is difficult,
if not wholly impossible, because the factors are partially
interdependent and of varying importance.
For discussion the subject may be divided into:
1. Methods of ore-breaking.
2. Methods of supporting excavation.
3. Methods of transport in stopes.
METHODS OF ORE-BREAKING.
The manner of actual ore-breaking is to drill and blast off slices
from the block of ground under attack. As rock obviously breaks
easiest when two sides are free, that is, when corners can be broken
off, the detail of management for blasts is therefore to set the holes
so as to preserve a corner for the next cut; and as a consequence
the face of the stope shapes into a series of benches (Fig.
22),--inverted benches in the case of overhand stopes (Figs. 20,
21). The size of these benches will in a large measure depend on
the depth of the holes. In wide stopes with machine-drills they
vary from 7 to 10 feet; in narrow stopes with hand-holes, from
two to three feet.
[Illustration: Fig. 20.]
The position of the men in relation to the working face gives rise
to the usual primary classification of the methods of stoping.
They are:--
1. Underhand stopes,
2. Overhand stopes,
3. Combined stopes.
These terms originated from the direction of the drill-holes, but
this is no longer a logical basis of distinction, for underhand
holes in overhand stopes,--as in rill-stoping,--are used entirely
in some mines (Fig. 21).
[Illustration: Fig. 21.]
UNDERHAND STOPES.--Underhand stopes are those in which the ore
is broken downward from the levels. Inasmuch as this method has
the advantage of allowing the miner to strike his blows downward
and to stand upon the ore when at work, it was almost universal
before the invention of powder; and was applied more generally
before the invention of machine-drills than since. It is never
rightly introduced unless the stope is worked back from winzes
through which the ore broken can be let down to the level below,
as shown in Figures 22 and 23.
[Illustration: Fig. 22.]
This system can be advantageously applied only in the rare cases
in which the walls require little or no support, and where very
little or no waste requiring separation is broken with the ore
in the stopes. To support the walls in bad ground in underhand
stopes would be far more costly than with overhand stopes, for
square-set timbering would be most difficult to introduce, and
to support the walls with waste and stulls would be even more
troublesome. Any waste broken must needs be thrown up to the level
above or be stored upon specially built stages--again a costly
proceeding.
A further drawback lies in the fact that the broken ore follows
down the face of the stope, and must be shoveled off each bench.
It thus all arrives at a single point,--the winze,--and must be
drawn from a single ore-pass into the level. This usually results
not only in more shoveling but in a congestion at the passes not
present in overhand stoping, for with that method several chutes
are available for discharging ore into the levels. Where the walls
require no support and no selection is desired in the stopes, the
advantage of the men standing on the solid ore to work, and of
having all down holes and therefore drilled wet, gives this method
a distinct place. In using this system, in order to protect the
men, a pillar is often left under the level by driving a sublevel,
the pillar being easily recoverable later. The method of sublevels
is of advantage largely in avoiding the timbering of levels.
[Illustration: Fig. 23.--Longitudinal section of an underhand stope.]
OVERHAND STOPES.--By far the greatest bulk of ore is broken overhand,
that is broken upward from one level to the next above. There are
two general forms which such stopes are given,--"horizontal" and
"rill."
[Illustration: Fig. 24.--Horizontal-cut overhand stope--longitudinal
section.]
The horizontal "flat-back" or "long-wall" stope, as it is variously
called, shown in Figure 24, is operated by breaking the ore in slices
parallel with the levels. In rill-stoping the ore is cut back from
the winzes in such a way that a pyramid-shaped room is created,
with its apex in the winze and its base at the level (Figs. 25 and
26). Horizontal or flat-backed stopes can be applied to almost any
dip, while "rill-stoping" finds its most advantageous application
where the dip is such that the ore will "run," or where it can be
made to "run" with a little help. The particular application of
the two systems is dependent not only on the dip but on the method
of supporting the excavation and the ore. With rill-stoping, it is
possible to cut the breaking benches back horizontally from the
winzes (Fig. 25), or to stagger the cuts in such a manner as to
take the slices in a descending angle (Figs. 21 and 26).
[Illustration: Fig. 25.--Rill-cut overhand stope--longitudinal section.]
In the "rill" method of incline cuts, all the drill-holes are "down"
holes (Fig. 21), and can be drilled wet, while in horizontal cuts
or flat-backed stopes, at least part of the holes must be "uppers"
(Fig. 20). Aside from the easier and cheaper drilling and setting
up of machines with this kind of "cut," there is no drill dust,--a
great desideratum in these days of miners' phthisis. A further
advantage in the "rill" cut arises in cases where horizontal jointing
planes run through the ore of a sort from which unduly large masses
break away in "flat-back" stopes. By the descending cut of the
"rill" method these calamities can be in a measure avoided. In
cases of dips over 40º the greatest advantage in "rill" stoping
arises from the possibility of pouring filling or timber into the
stope from above with less handling, because the ore and material
will run down the sides of the pyramid (Figs. 32 and 34). Thus
not only is there less shoveling required, but fewer ore-passes
and a less number of preliminary winzes are necessary, and a wider
level interval is possible. This matter will be gone into more
fully later.
[Illustration: Fig. 26.--Rill-cut overhand stope-longitudinal section.]
COMBINED STOPES.--A combined stope is made by the coincident working
of the underhand and "rill" method (Fig. 27). This order of stope
has the same limitations in general as the underhand kind. For
flat veins with strong walls, it has a great superiority in that
the stope is carried back more or less parallel with the winzes,
and thus broken ore after blasting lies in a line on the gradient
of the stope. It is, therefore, conveniently placed for mechanical
stope haulage. A further advantage is gained in that winzes may
be placed long distances apart, and that men are not required,
either when at work or passing to and from it, to be ever far from
the face, and they are thus in the safest ground, so that timber
and filling protection which may be otherwise necessary is not
required. This method is largely used in South Africa.
[Illustration: Fig. 27.--Longitudinal section of a combined stope.]
MINIMUM WIDTH OF STOPES.--The minimum stoping width which can be
consistently broken with hand-holes is about 30 inches, and this
only where there is considerable dip to the ore. This space is
so narrow that it is of doubtful advantage in any case, and 40
inches is more common in narrow mines, especially where worked
with white men. Where machine-drills are used about 4 feet is the
minimum width feasible.
RESUING.--In very narrow veins where a certain amount of wall-rock
must be broken to give working space, it pays under some circumstances
to advance the stope into the wall-rock ahead of the ore, thus
stripping the ore and enabling it to be broken separately. This
permits of cleaner selection of the ore; but it is a problem to
be worked out in each case, as to whether rough sorting of some
waste in the stopes, or further sorting at surface with inevitable
treatment of some waste rock, is more economical than separate
stoping cuts and inevitably wider stopes.
VALUING ORE IN COURSE OF BREAKING.--There are many ores whose payability
can be determined by inspection, but there are many of which it cannot.
Continuous assaying is in the latter cases absolutely necessary
to avoid the treatment of valueless material. In such instances,
sampling after each stoping-cut is essential, the unprofitable ore
being broken down and used as waste. Where values fade into the
walls, as in impregnation deposits, the width of stopes depends
upon the limit of payability. In these cases, drill-holes are put
into the walls and the drillings assayed. If the ore is found
profitable, the holes are blasted out. The gauge of what is profitable
in such situations is not dependent simply upon the average total
working costs of the mine, for ore in that position can be said to
cost nothing for development work and administration; moreover,
it is usually more cheaply broken than the average breaking cost,
men and machines being already on the spot.
CHAPTER XI.
Methods of Supporting Excavation.
TIMBERING; FILLING WITH WASTE; FILLING WITH BROKEN ORE; PILLARS
OF ORE; ARTIFICIAL PILLARS; CAVING SYSTEM.
Most stopes require support to be given to the walls and often to
the ore itself. Where they do require support there are five principal
methods of accomplishing it. The application of any particular method
depends upon the dip, width of ore-body, character of the ore and
walls, and cost of materials. The various systems are by:--
1. Timbering.
2. Filling with waste.
3. Filling with broken ore subsequently withdrawn.
4. Pillars of ore.
5. Artificial pillars built of timbers and waste.
6. Caving.
TIMBERING.--At one time timbering was the almost universal means of
support in such excavations, but gradually various methods for the
economical application of waste and ore itself have come forward,
until timbering is fast becoming a secondary device. Aside from
economy in working without it, the dangers of creeps, or crushing,
and of fires are sufficient incentives to do away with wood as
far as possible.
There are three principal systems of timber support to excavations,--by
stulls, square-sets, and cribs.
Stulls are serviceable only where the deposit is so narrow that
the opening can be bridged by single timbers between wall and wall
(Figs. 28 and 43). This system can be applied to any dip and is most
useful in narrow deposits where the walls are not too heavy. Stulls
in inclined deposits are usually set at a slightly higher angle than
that perpendicular to the walls, in order that the vertical pressure
of the hanging wall will serve to tighten them in position. The
"stull" system can, in inclined deposits, be further strengthened by
building waste pillars against them, in which case the arrangement
merges into the system of artificial pillars.
[Illustration: Fig. 28.--Longitudinal section of stull-supported
stope.]
[Illustration: Fig. 29.--Longitudinal section showing square-set
timbering.]
[Illustration: Fig. 30.--Square-set timbering on inclined ore-body.
Showing ultimate strain on timbers.]
Square-sets (Figs. 29 and 30), that is, trusses built in the opening
as the ore is removed, are applicable to almost any dip or width
of ore, but generally are applied only in deposits too wide, or to
rock too heavy, for stulls. Such trusses are usually constructed on
vertical and horizontal lines, and while during actual ore-breaking
the strains are partially vertical, ultimately, however, when the
weight of the walls begins to be felt, these strains, except in
vertical deposits, come at an angle to lines of strength in the
trusses, and therefore timber constructions of this type present
little ultimate resistance (Fig. 30). Square-set timbers are sometimes
set to present the maximum resistance to the direction of strain,
but the difficulties of placing them in position and variations in
the direction of strain on various parts of the stope do not often
commend the method. As a general rule square-sets on horizontal
lines answer well enough for the period of actual ore-breaking. The
crushing or creeps is usually some time later; and if the crushing
may damage the whole mine, their use is fraught with danger.
Reënforcement by building in waste is often resorted to. When done
fully, it is difficult to see the utility of the enclosed timber,
for entire waste-filling would in most cases be cheaper and equally
efficient.
[Illustration: Fig. 31.--"Cribs."]
There is always, with wood constructions, as said before, the very
pertinent danger of subsequent crushing and of subsidence in after
years, and the great risk of fires. Both these disasters have cost
Comstock and Broken Hill mines, directly or indirectly, millions of
dollars, and the outlay on timber and repairs one way or another
would have paid for the filling system ten times over. There are
cases where, by virtue of the cheapness of timber, "square-setting"
is the most economical method. Again, there are instances where the
ore lies in such a manner--particularly in limestone replacements--as
to preclude other means of support. These cases are being yearly
more and more evaded by the ingenuity of engineers in charge. The
author believes it soon will be recognized that the situation is
rare indeed where complete square-setting is necessarily without an
economical alternative. An objection is sometimes raised to filling
in favor of timber, in that if it become desirable to restope the
walls for low-grade ore left behind, such stopes could only be
entered by drawing the filling, with consequent danger of total
collapse. Such a contingency can be provided for in large ore-bodies
by installing an outer shell of sets of timber around the periphery
of the stope and filling the inside with waste. If the crushing
possibilities are too great for this method then, the subsequent
recovery of ore is hopeless in any event. In narrow ore-bodies
with crushing walls recovery of ore once left behind is not often
possible.
The third sort of timber constructions are cribs, a "log-house" sort
of structure usually filled with waste, and more fully discussed
under artificial pillars (Fig. 31). The further comparative merits
of timbering with other methods will be analyzed as the different
systems are described.
FILLING WITH WASTE.--The system of filling stope-excavations completely
with waste in alternating progress with ore-breaking is of wide
and increasingly general application (Figs. 32, 33, 34, 35).
Although a certain amount of waste is ordinarily available in the
stopes themselves, or from development work in the mine, such a
supply must usually be supplemented from other directions. Treatment
residues afford the easiest and cheapest handled material. Quarried
rock ranks next, and in default of any other easy supply, materials
from crosscuts driven into the stope-walls are sometimes resorted
to.
In working the system to the best advantage, the winzes through
the block of ore under attack are kept in alignment with similar
openings above, in order that filling may be poured through the
mine from the surface or any intermediate point. Winzes to be used
for filling should be put on the hanging-wall side of the area to
be filled, for the filling poured down will then reach the foot-wall
side of the stopes with a minimum of handling. In some instances,
one special winze is arranged for passing all filling from the
surface to a level above the principal stoping operations; and
it is then distributed along the levels into the winzes, and thus
to the operating stopes, by belt-conveyors.
[Illustration: Fig. 32.--Longitudinal section. Rill stope filled
with waste.]
[Illustration: Fig. 33.--Longitudinal section. Horizontal stope
filled with waste.]
[Illustration: Fig. 34.--Longitudinal section. Waste-filled stope
with dry-walling of levels and passes.]
In this system of stope support the ore is broken at intervals
alternating with filling. If there is danger of much loss from
mixing broken ore and filling, "sollars" of boards or poles are
laid on the waste. If the ore is very rich, old canvas or cowhides
are sometimes put under the boards. Before the filling interval,
the ore passes are built close to the face above previous filling
and their tops covered temporarily to prevent their being filled
with running waste. If the walls are bad, the filling is kept close
to the face. If the unbroken ore requires support, short stulls
set on the waste (as in Fig. 39) are usually sufficient until the
next cut is taken off, when the timber can be recovered. If stulls
are insufficient, cribs or bulkheads (Fig. 31) are also used and
often buried in the filling.
[Illustration: Fig. 35.--Cross-section of Fig. 34 on line _A-B_.]
Both flat-backed and rill-stope methods of breaking are employed in
conjunction with filled stopes. The advantages of the rill-stopes
are so patent as to make it difficult to understand why they are
not universally adopted when the dip permits their use at all. In
rill-stopes (Figs. 32 and 34) the waste flows to its destination
with a minimum of handling. Winzes and ore-passes are not required
with the same frequency as in horizontal breaking, and the broken
ore always lies on the slope towards the passes and is therefore
also easier to shovel. In flat-backed stopes (Fig. 33) winzes must
be put in every 50 feet or so, while in rill-stopes they can be
double this distance apart. The system is applicable by modification
to almost any width of ore. It finds its most economical field
where the dip of the stope floor is over 45°, when waste and ore,
with the help of the "rill," will flow to their destination. For
dips from under about 45° to about 30° or 35°, where the waste
and ore will not "flow" easily, shoveling can be helped by the
use of the "rill" system and often evaded altogether, if flow be
assisted by a sheet-iron trough described in the discussion of
stope transport. Further saving in shoveling can be gained in this
method, by giving a steeper pitch to the filling winzes and to the
ore-passes, by starting them from crosscuts in the wall, and by
carrying them at greater angles than the pitch of the ore (Fig.
36). These artifices combined have worked out most economically
on several mines within the writer's experience, with the dip as
flat as 30°. For very flat dips, where filling is to be employed,
rill-stoping has no advantage over flat-backed cuts, and in such
cases it is often advisable to assist stope transport by temporary
tracks and cars which obviously could not be worked on the tortuous
contour of a rill-stope, so that for dips under 30° advantage lies
with "flat-backed" ore-breaking.
[Illustration: Fig. 36.--Cross-section showing method of steepening
winzes and ore passes.]
On very wide ore-bodies where the support of the standing ore itself
becomes a great problem, the filling system can be applied by combining
it with square-setting. In this case the stopes are carried in
panels laid out transversally to the strike as wide as the standing
strength of the ore permit
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