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By J. C. Jaeger

The study of brittle fracture of rocks has been a much neglected subject until quite recently and now is in a state of transition and rapid development. Historically, three methods of testing were used by engineers: uniaxial tension, bending, and, by far the most common, uniaxial compression of cubes. This latter was probably adequate for engineering requirements, but from the last century onwards there has been a demand from geologists for a study of the properties of materials under conditions comparable with those at depth in the earth's crust. King1 remarked that "in engineering practice a cube of the material is put into a testing machine and the stress required to crush the cube is measured. This gives the limiting stress difference for the material so long as the boundary conditions are similar to those existing during the test . . . this may by no means be the case when the boundary conditions are very different from those existing in the test, for instance, in the case of rupture in the neighbourhood of a cavity. . . ." Despite this very clear statement of principle, many writers until recently (e.g. Jeffreys2 used the uniaxial compressive strength as a measure of the 'strength' of rock. In the last century (Becker 3, it was both conjectured and, for some rocks, known qualitatively, that plastic deformation could occur under confining pres- sure; the demand from geologists has been for the study of flow rather than fracture of rocks.. From the time of von Karman (1911) and Böker5 (1915) onwards, apparatus has been built which could provide confining pressures sufficient to make some rocks plastic. Many experiments tended to be made on rocks such as marble, which readily become plastic, and the general tendency was to make relatively few experiments in the brittle range. This is particularly true of many experiments on combined stresses. As a result of this, there is not sufficient data to provide adequate information

Jan 1, 1967

By John M. Dealy, Robert D. Pehlke

Values for interaction parameters in nonferrous systems, as calculated from published data, are tabulated and discussed. The influence of temperature on the parameter is derived and compared with the results of the literature study. Wagner's relationship between the interaction parameter and the self interaction coefficients is compared with the tabulated data. A problem which has been of considerable interest in the field of metallurgy is the prediction of the effect of one alloying element present in dilute concentration on the thermodynamic properties of another dilute alloying element. Ultimately, the prediction may be accomplished entirely from statistical mechanical considerations. At the present, however, the problem remains unsolved since liquid solution models which are simple enough for analytical treatment are inadequate for such purposes. Thus, we desire some means of organizing the information on dilute systems which will serve as a guide for further study on interactions in dilute alloys, and also provide a basis for the utilization of thermodynamic data in the engineering design of alloys.

Jan 1, 1963

By F. N. Lewis

HOPPERS may be divided into three classes accord-ing ing to type, namely; round, suspension, and square or rectangular. The round hopper is the most simple of the three and is the most easily understood by laymen. The bursting pressure in these hoppers is resisted by the shell as a round tank resists the pressure of water. They are perfectly stable as long as they retain their cylindrical shape. In holding water or other liquids the pressure on the sides is always the same, but with ore this is seldom true. These round hoppers for ore are usually filled from one side and frequently drawn off from the opposite side. A considerable amount of fine material is deposited on the side of filling, while the coarse particles run over to the far side. This con-dition of filling causes the ore to flow out unevenly, sometimes drawing out completely on one side. After a time the remaining ore breaks down and the shock of this falling ore, sometimes many tons, is very severe and has a tendency to distort the hopper from its true shape; consequently a round hopper holding ore should be stiffened to resist such shocks as this. For these reasons round hoppers have never been popular with engineers for holding ore. They also have a trait of welling. up worse than the square hoppers. I have known of round hoppers holding fine ore, 25 ft. diam-eter, that had a tendency to well up until there was ,only a round hole about 6 ft. diameter leading to the gate. The suspension or catenary type of hopper is well adapted to conditions requiring only small capacities. The selection of this type of hopper should be done with considerable care. The theory of the design is that the loads are carried entirely in tension in the bottom plate, just as a hammock carries a load, and it must be remembered that the bottoms of these hoppers are con-stantly changing form with the changing loads. Take a hammock, for example, if a person stands up in it, the bottom goes down and the sides approach a straight line; if the person lies down then the bottom comes up and the sides go down. It is this constant changing of the form that has a tendency to break the connections.

Jan 7, 1928

By John H. Harden

The Koepe system of winding from shafts is the invention of Mr. Frederick Koepe, Manager of the Hanover Coal Mine, Westphalia, one of the collieries worked by Krupp, the well-known German ironmaster. The first trial of the system was made at the Hanover

Jan 1, 1889

By B. F. Bush

The coal-fields of Missouri, situated in the northern and western portion of the State, are distributed, in whole or in part, over 57 counties, embracing an area estimated by Mr. Broad-head' to be practically 23,000 sq. miles, including small detached beds and outliers in St. Louis, St. Charles, Lincoln and Warren counties in the eastern part of the State. This area includes about 8,000 sq. miles of Upper or Barren Measures, 2,000 sq. miles of exposed Middle, and 12,420 sq. miles of exposed Lower Measures. In a general way, the Missouri coal-field is bounded on the east by an imaginary line entering the northern part of the State just east of the 92d Meridian and passing across the State in a southwesterly direction to a point on the Kansas-Missouri line a little below the southern boundary of Barton county. An important part of the field overlaps this line and extends down the northern side of the Missouri river, underlying the greater part of Randolph, Howard, Boone and Audrain counties. In all, 34 counties produced coal during the year 1903. Fig. 1 shows the position of the coal-fields in Missouri. Geological Features. The Coal Measure formations, all of the Carboniferous age, rest unconformably upon the rocks of the sub-Carboniferous or Mississippian series, and, in some cases, upon the rocks of the Devonian and Silurian ages. From their outcrop on the eastern and southeastern borders of the field, the Measures dip west to northwest at the rate of 10 ft. per mile, reaching a maximum thickness estimated by

Jan 1, 1905

By Charles A. Ashburner

DURING the early part of August, 1880, I was directed by Prof. J. P. Lesley, State Geologist, to assume charge of the geology and mapping. of the Second Geological Survey of the anthracite codfields. I visited the region uninaumbered by any instructions other than this,—that I should submit a plan for making the sur-

Jan 1, 1881

By J. S. Blakemore, E. O. Hall

SERRATED yielding, commonly called the Portevin-Le Chatelier effect, is known to occur in a wide range of alloys where the moving dislocations are considered to be locked by the diffusion of solute atoms to them. From the work of Cottrell,1 an approximate relationship between strain rate, E, dislocation density, p , and solute diffusion coefficient, D, giving rise to serrated yielding is: e =Dp

Jan 1, 1969

By A. E. Beasley, Ike McKinney

Scale is a broad term which includes many types of mineral deposits which have limited solubility in water. These mineral components precipitate when combinations of scale-forming cations and anions exceed their solubility. Scale deposits are tightly bound to each other and to the metal surfaces of a water system. Precipitates that do not readily adhere to each other or to metal surfaces are known as sludges. Sludges are easily removed from a system by flushing. For example, a sludge is formed in the internal treatment of boiler waters with orthophosphates where the calcium is purposely precipitated as hydroxyapatite. Calcium phosphate would have a tendency to adhere to the boiler tubes except for the addition of tannins or lignins. These sludge conditioners maintain the precipitated calcium phosphate as a sludge which can be readily removed by boiler blowdown.

Jan 3, 1973

By J. N. Hummel

THE methods of electrical prospecting, which employ contact electrodes to produce an electric field in the ground, furnish information concerning the constitution of the material beneath the surface, as indicated by the distortion of this artificially produced field and anomalies therein. To reveal the distortion of such field of known character, it is only necessary to measure qualitatively the direction of the field, using sensitive compensation methods. In such a case, the survey is relatively simple, and that is an important factor from a practical point of view, The distortion of the normal field thus determined permits an easy interpretation and gives approximate information as to the subsurface conditions, without the necessity of a thorough theoretical knowledge of the electrical field. The true field of application of the equipotential lines and search-coil methods, which are based on this principle of directional determination of the electrical field in the ground, is that of search for deposits of economic minerals for the mining industry, although they can also be used in solution of other problems; for example, in the determination of the strike of anisotropic beds. The distortion of the electric field as represented by the picture of equipotential lines or other measured curves is striking only when bodies having conductivities different from that of the country rock are embedded in the underground, or when the underground is anisotropic.

Jan 1, 1931

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957

By B. F. Tillson

HAVING been asked to talk about recent devel-opments in mining equipment, I chose the sub-ject of small units of storage-battery locomo-tives which recently have been developed with the idea of motorizing transportation in the mines as far as possible, replacing the manual labor of hand-tramming. Metal mines are probably less advanced in this field than coal mines, where transportation of large ton-nages on any one level is quite common. Of course, metal mines, where large tonnages are handled on any one level, are as advanced as coal mines, and storage-battery locomotives for main haulages are used quite commonly in such metal mines, but the mines having levels at many intervals in the depth of the orebody, or a number of intermediate levels in which a consider-able amount of hand-tramming has to be done, and small metal mines in which the size of the orebody does not seem to warrant the initial capital expenditure for the driving of main haulage levels and installation of rock and ore chutes and raises for the delivery of the broken ore and rock to the cars have been at consider-able disadvantage in replacing manual labor by some mechanical means of transportation. Several years ago the field was canvassed among the manufacturers of electric-locomotive equipment and the conclusion was reached that the art had not been devel-oped to the advantage of metal miners who desire to replace small units of labor by locomotive equipment. The need for such small locomotives is all the more em-phasized by the development in the past few years of mechanical mucking-machines (loading equipment for filling the cars from muck piles on the level). Any me-chanical loader is a liability instead of an asset unless means are also provided for keeping the material away from the loading-machines. Therefore the transporta-tion system must be equal to the capacity of a loading-machine, otherwise the latter is idle such a large per-centage of its time as to prove an unprofitable invest-ment. So there is a need for portable, small haulage units to handle small mine cars in many metal mines, and, naturally, units are desired which can be so readily shifted from level to level as to facilitate their free use. Of course, in mines in which each level comes to the shaft it is not such a difficult problem, but many mines have a great many intermediate levels which must be approached through raises, timber slides or other small openings required to transfer ore and to get timber and other supplies to those levels.

Jan 5, 1927

By L. G. Austin

If S (x) is the specific rate of breakage of size x and B (x, y) (see Table 1 for Nomenclature) is the cumulative breakage distribution function, the Herbst Fuerstenau2 assumption is that Inserting this assumption into first-order grinding equations it has been shown" that there are then simple analytical solutions to the grinding equations, as shown in Table 2. In this context "plug flow" is defined as all material passing through the mill in the same length of time, the residence time t. The term "n fully-mixed" means that the mill has a residence time distribution" which can be treated as if the mill were n equal fully mixed sections in series. In addition it has been shown that the assumption of Eq. 1 also leads to simple analytical solutions for closed-circuit, steady-state grinding with an ideal classifier at the mill exit returning oversize to the mill feed. The solutions are also given in Table 2, with µ as the ideal classifier cut size, C the circulation ratio, and Q (x) the size distribution of the circuit product. The specific surface area of these size distributions is where the density-shape factor k. is assumed to be constant with size. In practice, most methods of size analysis or area [ ] measurement have a finite lower limit, so that the integration is really performed from xm, to xm, For a realistic degree of grinding the value of So is dominated by the fine sizes because of the 1/x factor. Consider batch grinding of a feed of size y to y + dy. The batch grinding solution given in Table 2 is then [ ] The fresh surface area produced is the area of the fines plus the area of the original material remaining minus the area of the original material, [ ] Little error is introduced by neglecting the last term on the right-hand side since at t = 0 it is zero, and when t is significant the first term dominates because of the fine sizes produced. In addition, the form of P (x, t) for [ ] realistic values of S (x) 2t ax° is such that the major fraction of fresh surface produced is contained within the bottom 10% of weight of broken material, that is, for sizes for which P(x, t) < 0.1 (providing y is not near x.,). Thus for surface area purposes Eq. 3 can be approximated by [ ] becomes providing again that the feed sizes are coarse relative to xmi. Then the fresh area production is and W is the mass in the mill. The rate of surface production is WK, and the specific surface is Kt. From Table 2, the specific energy is mt/W so surface production per unit energy is [ ] Surface produced per unit energy input = KW/m (8) where m is the energy input of the mill. Clearly, identical reasoning applies to open-cycle, plug-flow grinding, with t replacing t, and Eq. 8 is obtained again. Considering open-cycle, fully mixed grinding, similar reasoning gives P(x) - t S(x) for surface area purposes, and

Jan 1, 1974

By G. T. Smith, R. C. Moyer

L. P. DAVIDSON*—In the analysis of the cadmium sponge how is the sample prepared ? M. M. NEALE*—The analysis of the cadmium sponge? L. P. DAVIDSON—You gave a very high percentage of metallic cadmium, 2 pet zinc, 2 pet lead and say 93 pet

Jan 1, 1950

By Eric Jette

THE alloys of gold and iron were investigated in 1907 by Isaac and Tammann,1 who determined the thermal diagram for the entire system by thermal analysis and microscopic examination. They also reviewed the previous literature. Since that time the present authors have been able to find only two additional references. Guertler and Schulze2 examined the electrical resistance of iron alloys containing up to 40 per cent by weight of gold between 0° and 200° C.; the alloys were in the form of wires. The main result of this work was to confirm the solid solubility limit found by Isaac and Tammann; namely, about 20 per cent Au. More recently, Shih3 has examined the magnetic properties of gold alloys containing up to 10 weight per cent iron and particularly the range below 5 per cent. The alloys in the lower range were found to be paramagnetic; the 10 per cent alloy was ferromagnetic. The present investigation was undertaken to determine the solid solubility limits at various temperatures, particularly below the a-y transformation point of iron, since these solubilities are of some impor-tance in connection with the working of the alloys in the manufacture of certain "grey" and "blue" golds.

Jan 1, 1934

By Howard I. Epstein, John R. Buzek

Thickeners are simply large tanks, usually circular in shape, which are designed to allow settling of solids and to operate with continuous overflow of clear water and underflow of thick pulp. The dimensions of the thickener are usually such that dewatering of very fine pulps may be accomplished while still overflowing clear water. Some thickeners such as the Center, Hardinge and Hydrotator types combine thickening with filtering2 while others such as the Dorr type are pure thickeners. l .2 , 3 A schematic diagram of the traction type Dorr thickener is shown in [Fig 1]. This type is appropriate for tanks over 15 m (50 ft) in diameter. This tank employs a rotating raking mechanism which moves the settled material toward the central discharge. For this and other thickeners, it is common to have a shallow conical tank bottom in order to conform to the geometry of the raking mechanism, and it is often desirable to elevate the tank for ease of access to the product. When the tank does not rest on the ground, the forces resisted by the cone are large, and thick plates must be employed. The fabrication of these tanks requires temporary supports in order to erect the cone. A flat-bottomed tank could also be used because the settled material would soon form a hardened conical surface. However, because of the presence of large bending forces, even larger plate thicknesses are required than for the conical bottom. Significant cost savings often can be realized by the use of a scalloped-bottomed tank such as the one partially shown in [Fig. 2]. The particular scalloped bottom discussed in this paper employs radial beams forming the outline of the cone-shaped bottom. These beams are supported directly by columns. Cone segments are hung between adjacent beams. The exact geometry of these segments depends upon the cone angle and radius, the number of radial beams, and their inclination. The geometry is chosen to satisfy certain clearance restraints and to utilize the material as efficiently as possible. The resulting thickness of these segments is significantly less than that of the equivalent plate for the tank with a conical bottom. This result, along with the simpler fabrication procedures required, accounts for the cost savings associated with this design. The raking mechanism employed may be the same as for the conventional conical bottom since the settled material soon forms a conical surface. Determination of the internal force mechanism for the scalloped bottom leads to designs that utilized material efficiently and thus maximize the cost savings. The complicated geometry of these bottoms along with the difficulty in analyzing the structure are factors which may have limited the use of scalloped-bottomed tanks to date. When such tanks have been built, the uncertainties associated with the internal forces have led to designs that are somewhat inefficient. In this paper, equations relating the geometric parameters are presented along with simplified closed-form solutions for the internal forces in the cone segments, from which the loads applied to the beams and the loads carried to the cylindrical tank shell can be deduced. An example is presented to show the magnitude of the savings which may be realized with this configuration.

Jan 1, 1979

By Arthur West

It is the purpose of this paper to describe briefly some recent large power stations for blast furnaces, where the blast is exclusively supplied by gas engines using furnace gas. The stations are given in the chronological order in which they were designed, in order to indicate the various improvements suggested by experience. Fig. 1 shows the blowing-engine station of the Bethlehem Steel Co. at Bethlehem. Although the picture shows only five blowing engines, the house now contains 11 engines. In the diagrammatic plan the arrow shows the position and direction of camera. This station handles five modern blast furnaces of 450 to 500 ions capacity each. In this, as in all the other stations described in this paper, each furnace is blown by two single tandem gas engines. Ten engines are thus required for five furnaces, leaving one single tandem spare engine. This spare capacity has been shown by several years&apos; experience at Bethlehem to be adequate to insure continuous operation. The engines in the Bethlehem station are right hand and left hand, arranged in pairs. The outboard bearings of each pair are close together so that there is not room for passageway between them. On the right of the picture are shown the inclined drums communicating with the cold-blast lines outside of building, so that any engine may be operated on any furnace. The illustration shows four cold-blast gate valves with pipes passing through wall, but since the photograph was taken the drums have been extended to take care of a fifth valve for a fifth furnace. At the extreme back of the picture can be seen the tubs of three twin vertical-horizontal Southwark steam blowing engines, which, although of modern design and as good as new, are not operated because of the greatly reduced blowing cost shown by the gas blowing engines. The next station built is shown in Fig. 2. This is the plant of the Minnesota Steel Co. at Duluth, Minn., and is at present constructed for five engines, to handle two furnaces, with one spare engine. The engines are of practically the same size as those at Bethlehem. Instead of being arranged in right-hand and left-hand pairs, as at Bethlehem, all the engines are of the same hand; this arrangement has some ad-

Jan 1, 1915

By R. W. Raymond

Under the names of Conservation, Social Justice, the New Nationalism, and Progressive Democracy, many earnest reformers are calling for a new system of Federal government to replace the one which they ascribe to our fathers, and declare to have been outgrown. They are proposing the lease by the United States of certain natural resources on the public domain, for the profit of the U. S. Treasury, instead of the sale of such resources to private citizens or associations of citizens. In the present paper, I shall try to show that this notion is neither new nor good. It is clear that the United States is owner, as well as sovereign, of public lands acquired through conquest or purchase from other nations, as it was owner of the public lands expressly ceded to it by the original thirteen States. Its policy with regard to such lands involves, therefore, two entirely distinct questions: What shall it do as owner ? and, What shall it do as sovereign ? The latter question, it must be confessed, has played but a small part in our history. All the prerogatives of sovereignty which were not explicitly conferred upon the Federal government by the original States were retained by them. The ownership or control of precious or other metals or minerals in the earth, for instance, was thus reserved to the several sovereign States. New York, South Carolina, and other States have passed laws on this subject, without regard to Federal authority. As new States have been successively admitted to the Union, the tacitly accepted theory has been, that they thereby acquired all the reserved rights of the original States. These newer States largely outnumber the first thirteen; and it is inconceivable that they would submit to any deprivation of sovereignty based on historical grounds. One of them—Texas—came into the Union by its own voluntary

Jan 1, 1913

By Norman Maxwell

There was more activity in crude production in northwestern Pennsylvania in 1935 than for several years before, resulting in an increased oil production and also in the number of wells completed. Crude -production approximated 16 million barrels for the state, an increase of about one million barrels over 1934. Demand, indicated by refiners&apos; runs to stills, increased proportionally, leaving stocks of available crude at the end of the year at the lowest point since the middle of 1934, when they reached an all-time low. The price of crude varied during the year from a low of $2.02 to a high of $2.27 at the end of the year for Middle district oil. The price of Bradford and southwest Pcnnsylvania oil changed accordingly. The average for the year would be a lower price than in 1934. A summary of the production data for the year 1935 is given in Table 1. In making up this table, 1935 figures were simply added to the table published by S. H. Cathcart last year1. A list of important wildcats is given in Table 2. Bradford Field Approximately 10,000 acres of the proven producing area of the Bradford field is in Cattaraugus County, New York, and it is possible, by differences, to distinguish the Pennsylvania production from the New York portion. The listed production for the Bradford field includes only that portion of the field situated in Pennsylvania, but also includes production from a small pool, locally known as the Mt. Jewett-Kanesholm pool, where the Bradford sand is being developed and flooded in precisply the same manner as that of the Bradford field itself. The Mt. Jewett-Kanesholm pool is not, strictly speaking, an extension of the Bradford field, but inasmuch as it is so closely allied with the Bradford field-—that is, the sand is the same and the production methods are the same—the production and drilling figures include this area.

Jan 1, 1936

By Norman Maxwell

There was more activity in crude production in northwestern Pennsylvania in 1935 than for several years before, resulting in an increased oil production and also in the number of wells completed. Crude -production approximated 16 million barrels for the state, an increase of about one million barrels over 1934. Demand, indicated by refiners&apos; runs to stills, increased proportionally, leaving stocks of available crude at the end of the year at the lowest point since the middle of 1934, when they reached an all-time low. The price of crude varied during the year from a low of $2.02 to a high of $2.27 at the end of the year for Middle district oil. The price of Bradford and southwest Pcnnsylvania oil changed accordingly. The average for the year would be a lower price than in 1934. A summary of the production data for the year 1935 is given in Table 1. In making up this table, 1935 figures were simply added to the table published by S. H. Cathcart last year1. A list of important wildcats is given in Table 2. Bradford Field Approximately 10,000 acres of the proven producing area of the Bradford field is in Cattaraugus County, New York, and it is possible, by differences, to distinguish the Pennsylvania production from the New York portion. The listed production for the Bradford field includes only that portion of the field situated in Pennsylvania, but also includes production from a small pool, locally known as the Mt. Jewett-Kanesholm pool, where the Bradford sand is being developed and flooded in precisply the same manner as that of the Bradford field itself. The Mt. Jewett-Kanesholm pool is not, strictly speaking, an extension of the Bradford field, but inasmuch as it is so closely allied with the Bradford field-—that is, the sand is the same and the production methods are the same—the production and drilling figures include this area.

Jan 1, 1936

By Z. T. Bieniawski

The importance of understanding the phenomena associated with rock fracture has long been fully appreciated in rock mechanics. This is clearly apparent from the special attention paid to rock fracture in the comprehensive papers published within the past four years.l-5 These papers present a picture of how the knowledge of brittle fracture of rock was gradually enriched and also show that what was often taken for granted three or four years ago is no longer considered as valid today. The Griffith hypothesis,6 thought in the past to predict the strength of rock, is now known to be applicable to fracture initiation only. The knowledge of a failure criterion for fracture initiation is not sufficient, however, as after fracture initiation the rock is still a useful material even possessing increasing load-bearing ability. The importance of the fracture propagation process, subsequent to fracture initiation, is thus obvious. Yet, relatively little attention has so far been paid to brittle fracture propagation in rock. As it is now realized that understanding of this process is a prerequisite for practical rock mechanics applications, studies of propagation of brittle fracture in rock constitute an important aspect of rock mechanics research. It has been pointed out 4 that it is essential that the failure mechanism is fully understood before a failure criterion is postulated. Many failure criteria have been propounded in the past on the basis of theoretical reasoning alone and could not be verified by experimental evidence. Recently, a hypothesis for the mechanism of brittle fracture of rock was propounded, 4 describing the events taking place in the rock from the initial application of gradually increased load to complete disintegration of the material.

Jan 1, 1972