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By J. T. Berling, J. B. Conway

MANY studies have been devoted to the correlation of low-cycle fatigue behavior. Several of these have also been concerned with the identification of an effective approach to the prediction of low-cycle fatigue behavior from short-term tensile data. Perhaps the first such approach was that reported by coffin1 in the form: where is the plastic strain range, Nf is the number of cycles to failure, and c is a constant characteristic of a material. In this analysis by Coffin it was reasoned that in a short-term tensile test the value of Nf could be considered as equal to a , in which case the value of c is interpreted as the tensile ductility, f, measured in such a test. If, therefore, the Coffin equation is assumed to be applicable to a given material, it is a simple matter to predict the low-cycle fatigue behavior. Once the tensile ductility is known, this point is located at Nf = 1/4 on a log-log plot of vs Nf and a line is drawn through this point with a slope of to yield a prediction for the fatigue life. Actually, while this equation is quite useful it is not generally applicable, for experiment has shown that the value of —$ does not reflect the relationship between and Nf for all materials or even for a given material over all temperature ranges. An equation similar to the Coffin equation was prepared almost simultaneously by Manson.2 This expression had the form: In this case the exponent on Nf was not assigned any particular numerical value in accord with the various values of this exponent which had been observed for different materials and at different test conditions. Because of this characteristic it will be recognized that little use can be made of this expression in predicting low-cycle fatigue results. A fairly effective expression for use in predicting fatigue behavior was proposed by Manson3 based on a study of numerous sets of experimental results. This relation (Method of Universal Slopes) makes use of modulus of elasticity, ultimate strength, and tensile ductility, and assumes an exponent on Nf equal to 0.6 in representing the plastic strain range contribution to total strain range. While this equation of Man-Son does not yield completely accurate results it must be recognized as being the best means available at

Jan 1, 1970

By K. Hodgson, J. P. M. Hojem, N. G. W. Cook

Already about one-third of South Africa's coal is mined at depths exceeding 100 metres. Almost all this mining is done by the bord and pillar method. Conventional design procedures call for ever larger pillars as depths of workings increase, resulting in the loss of large amounts of coal and reductions in productivity. Barrier pillars are in general use to ensure against large collapses. The presence of these strong pillars would allow a more efficient design of the bord and pillar layout to yield improved extraction ratios by using smaller, yielding, pillars between the bords. Knowledge of the complete load- displacement curves for such pillars is a prerequisite for the design of such a system. A 100-MN, stiff jacking system for measuring the complete load-displacement curves of pillars with cross-sections of up to 2 m X 2 m is described. The jacks are installed in a slot cut across the central plane of symmetry of a pillar, thereby ensuring that the stress distribution in the pillar during a test, especially at its contacts with the roof and floor, is identical to that caused in a similar pillar by convergence across the seam. Preliminary results in the form of complete load-displacement curves for test pillars of about 1.5 metre square section are given.

By Charles R. Wraith

The property of the Roan Antelope Copper Mines, Ltd., is situated at Luanshya, north central part of Northern Rhodesia, and is connected with the main line of the Rhodesia Railways, Ltd., by a 24-mile branch line from N'dola. Most of the material and supplies that are not available in Africa are shipped into the country via Beira, on the East Coast of Africa, a distance of 1473 miles from Luanshya and the nearest ocean port. The output of copper is shipped by rail to Beira and thence by boat to the market. Passenger travel is mostly via Cape Town, a distance of 2162 miles from Luanshya. Excellent passenger trains operate on regular schedules between Cape Town and Northern Rhodesia. Luanshya is 13" south of the equator at an elevation of 4000 ft. above sea level, and has a mild healthful climate. During the rainy season, from October to March, the rainfall averages 53 in. The area is profusely covered with vegetation. An ample supply of water for industrial and domestic purposes is available throughout the year. The more important supplies for smelting purposcs, such as wood, coal, limestone, silica, quartzite, and clay for "dolly" mud, are conveniently available. Excellent grades of coal, coke and firebrick are obtained from the Wankie Colliery Co., Ltd., Southern Rhodesia. The Wankie colliery has just completed the erection of equipment for the manufacture of silica brick. An ample supply of quartzite of good grade is available for this purpose. Silica brick is also obtained from the Belgian Congo and from India. Limestone is quarried from a large deposit a few miles from Bwana Mkubwa, which is 30 miles by rail from the smelter. An abundant supply of clay for " dolly " mud and for lining launders is available within a short distance of the smelter. Metallurgy Copper is contained in the ore as chalcocite, chalcopyrite and bornite. Chalcocite predominates in the eastern end of the orebody almost to the exclusion of other copper minerals. The amount of chalcocite decreases with a corresponding increase of chalcopyrite and bornite toward the western extension, where the latter predominate.

Jan 1, 1934

By Alvin Kaufman

ANTHRACITE mining in the United States is concentrated in a 480 sq mile section of north- eastern Pennsylvania. The producing area is broken up into four fields, known as the Northern, Southern, Eastern Middle and Western Middle fields. These areas represent intricately folded coal measures in synclinal residuals left by erosional forces. Destruction by erosion has eliminated some 95 pct of the original coal. However, discounting the 5 billion tons removed to date, 8 billion tons are believed to be still recoverable.

Jan 3, 1953

By Gen-Hua Shi, Richard E. Goodman

In hard, discontinuous rocks, failure modes and stability are controlled to a great extent by the intersection of discontinuities with the excavated surface. We have solved the general problem of finding the shape and size of all blocks formed through the inter- section of any number of joints and excavation surfaces and will demonstrate a simple graphical method for determining which of these is the "keyblock." An example will explain this methodology applied to a simple open pit. The effects of slope curvature in plan or section, will be demonstrated. Finally, we will show how to determine the optimum orientations for the cut slopes. The methodology is based upon a powerful topologic theorem concerning the finiteness of spatial intersections. This paper is a companion to another dealing with underground openings in the Proceedings of the 22nd Symposium on Rock Mechanics (MIT) , July 1981. This paper discusses the rock blocks created by the intersection of discontinuities and excavation surfaces in a rock mass. It establishes principles and procedures by means of which those blocks that are finite and critically located can be identified and described. The main assumptions are the following: 1. The rock itself is assumed to be strong so that the only concern for stability is the movement of rock blocks them- selves.

Jan 1, 1983

By Clark J. Gilbert

The mining method at the Cannon mine uses heading and bench stopes, which are subsequently backfilled with cemented high-strength fill before pillar removal. The dimensions of the pillars are 7.3 m wide by 19.8 to 28.9 m high (24 ft by 65 to 95 ft). They require careful blasting in order to not damage the rock, compromising pillar strength and complicating later removal. Additionally, the proximity of dwellings makes vibration control a must for good neighbor relations. A blast monitoring study was conducted in order to optimize bench blasting practices to maximize fragmentation, reduce costs, and to minimize wall damage and ground vibration. The Cannon mine is a joint venture between Asamera Minerals (US) Inc., a 92% owned subsidiary of Gulf Canada Ltd., and Breakwater Ltd. Asamera is the operator. The mine is located at the south end of Wenatchee, WA, a town of roughly 45,000 people on the eastern flanks of the Cascade Mountains. Gold is the primary product at the mine. The rock is extracted using a sublevel end-slicing method on 15 m (50 ft) lifts, with subsequent backfilling and pillar removal. The stope widths, dictated by rock conditions at 7.3 m (24 ft), are the same in the primaries as in the pillars, or secondaries.

Jan 1, 1990

By P. Huttagosol

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

Jan 1, 1989

By John T. Norton, Matthew J. Donachie

Residual lattice strai?zs were produced in 2024 aluminum and ingot iron by uniaxial tensile deformation. These strains were rneasured on the original surface and ulith depth below the surface. The strains conformed approximately to those from a macroscopic stress distribution but they were not truly macroscopic in nature. The exact mechanism which apparently causes the coherently difi9,acting region of each grain to behave as if macroscopically stressed was not determined. MACROSCOPIC stresses in metals produce strains in the lattice which result in X-ray line broadening and line displacements. The latter effect can be utilized in a technique for determining stresses in metals as first shown by Lester and born.' Subsequent advances in technique have enabled the X-ray method of stress measurement to be satisfactorily applied to many problems involving residual stresses of a macroscopic nature, such as those due to welding, grinding, shot-peening, and so forth. In the case of stresses such as those described above, the correlation of X-ray- and mechanically determined data has been generally good. However, plastically extended polycrystalline metals have sometimes been reported2 to show line displacements upon release of the applied tensile load, yet the nature or origin of the residual lattice strains, rls, producing these displacements has never been clear. As will be pointed out, this lack of clarity regarding the macroscopic or microscopic nature and origin of these stresses casts doubt on the validity of results achieved by the commonly accepted techniques of X-ray stress measurement. This anomalous behavior requires clarification to remove the doubts concerning X-ray stress measurement. The present paper is the result of an investigation of the interesting behavior of such plastically extended polycrystalline metal bodies. The studies were originated to carry out the following tasks: 1) Observe whether a residual lattice strain is produced as a result of plastic extension and show whether any residual lattice strains produced can be related to the usual concept of a macrostress. 2) Examine the origin of any residual lattice strains observed. 3) Consider the implications or consequences of the existence of such residual lattice strains on the problem of X-ray stress measurement. THEORY 1) Lattice Strains. The theoretical developments necessary for the treatment of lattice strains and their relation to stresses follow from the classical theory of elasticity and have been adequately covered by arrett. For an isotropic solid under homogeneous deformation, it can be shown that, for uniaxial stresses where Dl is the macrostress acting in the longitudinal direction; E$L is the lattice strain in the plane defined by the surface normal and the longitudinal direction at an angle, , from the surface normal; ET is the similar strain in the transverse plane; E is Young's modulus; and v is Poisson's ratio. Eq. [2] is independent of angle + and Eq. [I] is a linear function of sin2, see Fig. 1, and can be solved analytically for DL if E and u are known and EL is measured. Thus, a uniaxial macrostress will be indicated by a linear E,L vs sinZ plot and a

Jan 1, 1962

By R. E. Hall

When the criterion for control of scale prevention on the evaporating surfaces is made the conditions in the concentrated boiler water, then this control becomes an exact operation amenable to an accuracy commensurate with all other operations in the boiler room. The responsibility in boiler water conditioning, however, includes more than clean surfaces. Corrosion in feed lines, economizers and the boiler is a function of the condition of the later, and must be controlled. Steam line and turbine blading deposits must be obviated by the system of conditioning. By the chemical treatment employed, the amount and character of noncondensable uses in the steam must be controlled in accordance with the intended use of the steam. All. in all, the responsibility in boiler crater conditioning ends not with the entrance of the water into the boiler but with the passage from the boiler nozzle of steam, the dryness and rarity of which are defined by the uses to be made thereof. A clearer conception of the scope of boiler water conditioning can be obtained by reference to a diagram of the surfaces (Figure 1) at which it functions. Consideration of this diagram leads to the following outline for the problems of boiler water conditioning: (a) Prevention of scale formation on surfaces (1) In contact with water but at which no evaporation occurs. (2) At which evaporation is occurring.

Jan 1, 1926

The Electricity Commission of New South Wales operates three power stations located on Lake Macquarie and Lake Munmorah. Coal for these power stations is supplied by three collieries operated by the Electricity Commission, three operated by the State Mines Control Authorityrand one privately owned. Most of the coal used in these power stations is won from the Great Northern seam which lies at depths of up to 220 ft at Awaba and at depths of the order of 600 ft at the remaining mines on the southern end of the field.

Jan 1, 1972

By M. Omneya El-Hussaini, M. Galal Abdel Wahab, A. Mohamed Mahdy, M. Fathi El Shahat

"Lead-zinc mineralization is distributed in Egypt along the Red Sea coast between El Qusier and Ras Banas. A representative sample from Um Gheig was collected and ground to -60 mesh for the mineralogical study. It contains hemimorphite (Zn2SiO4.H2O), sphalerite (ZnS), galena (PbS), calcite (CaCO3) and dolomite (CaMg(CO3)2) beside the gangue minerals gypsum (CaSO4.2H2O) and hematite (Fe2O3). Cadmium seems to be incorporated in the crystal structure of the zinc-lead minerals. The chemical analysis of Um-Gheig representative sample revealed that, it contains 16% zinc combined with 0.1% cadmium, 2.3% lead and 0.1% boron beside other elements.Pug and agitation leaching were performed on samples ground to -200 mesh to achieve the maximum dissolution efficiency of cadmium with respect to other elements. Cadmium leaching efficiency reached 90% by using 40% H2SO4 at S/L ratio 1/2 and stirring time 2 hours at 80o C. Cadmium was then separated as yellow precipitate of CdS from the sulfate leach liquor containing 0.9 g/l Cd, 145 g/l Zn, 0.15 g/l B and 0.01 g/l Pb. Separation of cadmium was carried out by direct precipitation using Na2S as well as H2S. The recovery of 94% cadmium free of zinc was achieved.IntroductionLead-zinc ores occur in Egypt in a few localities distributed along the Red Sea coast between El Qusier and Ras Banas. Um-Gheig Pb-Zn ore is a replacement deposit in limestone and calcareous sandstone in the basal series of the Middle Miocene rocks. The reserve of the ore deposits has been estimated by Soviet and German Experts to be about 900,000 Ton, Bishai [1]. As has been mentioned, zinc is a common element and cadmium is comparatively rare in almost zinc minerals. It was estimated that zinc is 200 times as abundant as cadmium. According to Bodas [2] about 2.1% of cadmium was carried by the Zn mineral hemimorphite (15.3% Zn) in Thailand. Also, Onal et al., [3] found that 164 g/t Cd was carried by Pb–Zn ore sample containing 10.17% Pb and 10.98% Zn from Aladag in Turkey. Cadmium metal has gained great importance due to its wide applications in civil and navy purposes as well as in nuclear field. It is characterized by its ability to absorb thermal neutrons during the chain reaction inside the nuclear reactors. It is also used in the manufacture of sheets which directed the chain reactions [4]."

Jan 1, 2008

MINING; SOLUTION U.S. 4,066,297 - In the solution mining of uranium from an underground deposit of uranium ore using an alkaline leaching solution, precipitation of alkali metal salts is avoided by maintaining the Injected leach solution of an alkaline carbonate or bicarbonate and an oxidant undersaturated with respect to carbonates Undersaturation is effected by use of a water softening unit or by bleeding a portion of the recycled alkallne leach solution. A P. Spence, assigned to Atlantic Richfield Co Jan. 3, 1978 4 pp. (299-4). Filed: 6-1-76 (69 1,344)

Jan 1, 1979

By G Giles

One of the main tools used by mining operations to mitigate the risk of rock burst is the installation of a so-called ædynamic resistantÆ support system. Such systems are designed to absorb the impact of shockwaves created by mine-induced seismic events. Dynamic support must be strong and capable of sustaining high loads and, at the same time, they have to be flexible and accommodate large deformation. A dynamic support system is therefore a system capable of absorbing a high quantity of energy. Ground support systems are composed of rock reinforcement (rock bolts or cable bolts) and surface support (mesh or shotcrete). In terms of surface support, fibre-reinforced shotcrete is increasingly seen as the industry preferred solution when difficult ground conditions are experienced, including areas of high seismic hazard. A thick layer of shotcrete is certainly strong but it is by no means flexible. Normal weld-mesh has some flexibility, but it is not very strong. The Australian Centre for Geomechanics (ACG), in collaboration with Onesteel Reinforcing Pty Ltd, is currently working on a new high-energy absorption mesh that combines strength and flexibility. The new mesh can be installed with a jumbo, in a similar way as the widely used sheet of weld-mesh. This paper describes the development of this new mesh system.

Jan 1, 2008

By B. Yarar, J. Kaoma

[Introduction The critical surface tension of wetting of hydrophobic materials has been investigated extensively by Zisman et al. (1973) and relates the spreading of a liquid on a solid to the surface tension of this liquid. Thus, the Zisman ap¬proach shows that a plot of Cos 0 versus ?LV where, 0 is the contact angle and ?LV is the surface tension of that liquid in contact with its own vapor at equilibrium, produces a straight line which can be extrapolated to Cos 0 = 1. The intercept corresponds to a given ?LV, termed the critical surface tension of wetting. In instances, however, Cos 0 - ?LV plots show deviations from linearity. Alternative approaches have also included the plotting of adhesion tension (YLV COs 0) versus ?LV that can be interpreted in terms of critical surface tension data (Lucassen-Reynders, 1963). It has, on the other hand, been customary to correlate contact angle (0) with flotation data, although it is recognized that surface inhomogeneities and related contact angle hysteresis limit the interpretations pertaining to solid surface structures purely based on contact angle measurements. It is nonetheless true that 0 = 0, when the liquid is water, corresponds to a hydrophilic solid. Determination of ?c by contact angle measurements in conformity with the Zisman approach can encounter experimental difficulties, especially when solids are in a powder form. Following the reasoning that 0 = 0 corresponds to the hydrophilic state of a solid, froth flotation experiments can be expected to produce critical surface tension of wetting values for powders. The technique that consists of plotting recovery (% R) versus YLV data and extrapolating the linear part of the curve to % R = 0, has been described elsewhere (Yarar and Kaoma, 1984). This paper describes some of the results obtained by the extrapolation technique mentioned above, using various sulfide minerals. Experimental Materials Molybdenite (MoS2), sphalerite (ZnS), chalcopyrite (CuFeS2), chalcocite (Cu2S), and galena (PbS) were handsorted from massive samples and ground by mortar and pestle, and the -147 Fan fraction used in experiments; sulfur (S) was a C.P. Fisher Scientific Co. product. Method One gram powder samples were conditioned for three minutes in methanol-water solutions of predetermined surface tension values and the percents recovered by flotation using a Partridge-Smith Cell (Partridge and Smith, 1972), were plotted against each ?LV value. Results and Discussion The percent recovery versus ?LV for two naturally hydrophobic solids, i.e., natural molybdenite, MoS2 and sulfur are given in Fig. 1 where it is seen that ?c for sulfur is obtained as 31.5 mNm-1 whereas for MoS2, it is 26 mNm-1. Figure 1 also shows that the new flotation technique described, for estimating ?c is in good agreement with the Zisman method. Curves obtained by the same method for the minerals Cu2S, PbS, and ZnS are given in Fig. 2, where it is seen that for Cu2S, ZnS, and PbS, the extrapolation to % R = 0 produces ?c values of 36, 39, and 49 mNm-1, respectively. CuFeS2, on the other hand, gives a curve that does not permit such an extrapolation to obtain a ?c value with certainty. Nonetheless, treatment of the powder with 8.95 X 10-5 molar Na2S solution followed by washing with distilled water prior to flotation effects the curves as shown in the insert of Fig. 2. The type of curves given in Fig. 1 appear to be typical of hydrophobic solids as can also be observed in Fig. 3. The composition of solid and minute quantities of inclusions seem to play an important role as regards the surface properties of solids as reflected by the slope of the linear part of the % R - ?LV plot and thus the value of ?c obtained by this technique. For example, MoS2 of three different stoichiometric compositions produced the data given below. [MoS2MoS2.14Mo1.002S2 ?c mNm-126.029.031.0 dR/d?8.95.23.0]]

Jan 1, 1985

By A. C. Spencer, H. F. Bain, E. C. Harder, Sidney Paige, C. M. Weld, W. Lindgren

At a meeting of the New York Section, on May 23, 1918, the sole subject of discussion was the nature and occurrence of iron ores in certain parts of the world." Owing to the importance of this subject, it has been deemed advisable to publish the remarks made at that meeting in the form of a paper, for presentation at the Milwaukee Meeting. The remarks related to the following districts: Page Brazil. By E. C. Harder................................. 116 Scandinavia. By Waldemar Lindgren..................... 120 Cuba. By C. M. Weld.................................. 124 Southern Europe. By A. C. Spencer...................... 130 China. By H. Foster Bain............................... 132 Alsace-Lorraine. By Sidney Paige......................... 135 Brazil BY E. C. HARDER† During the years immediately preceding the war, the iron ores of Brazil were attracting the attention of iron operators both in Europe and in the United States. This was due to the large quantities of practically undeveloped ore available, and to its great purity. It is reasonably safe to state that had capital not been diverted from the exploitation of these deposits to war purposes, Brazilian iron ores would probably now be offered in European and American markets. It is certain that after the war these ores will play a prominent part in the economic reconstruction of Europe and perhaps in the development of America. The Brazilian iron-ore field ranks among the six great iron-ore districts of the world, the others being: (1) The Lake Superior district of the United States; (2) the Lorraine ore field of northern France and southern Germany; (3) the magnetic deposits of northern Sweden; (4) the ore fields of Oriente, Cuba; and (5) the Wabana ores of Newfoundland. It is doubtless the greatest known undeveloped iron-ore district in the world. The Brazilian iron ores are situated in the State of Minas Geraes, the center of the district being located about 250 miles in a direct line west of

Jan 1, 1920

By Stephen J. Navin, Francis P. D. Navin

Long-distance movement of various materials by conveyor is becoming common; therefore, it is no surprise that conveyors are frequently found in very long tunnels. In such long tunnels, there is a continual controversy between the tunnel operator's requirement for a maximum of clear space for the conveyor and vehicles and the investor's wish to make the minimum capital investment for excavation. This analysis shows that the question becomes more pressing as the tunnel becomes longer. The result given in this paper is a straightforward method by which an economic and operational optimal tunnel width may be selected for any specified tunnel length. Detailed computational formulas are developed relating costs of construction, vehicle operation, vehicle accidents, and conveyor downtime to both tunnel width and length.

Jan 1, 1985

By John V. Beall

Probably the only hotel in the world with near 100% occupancy at all times is the modern Hotel Indonesia in Djakarta. However, there is little gaiety among the scores of business men who occupy the hotel because they fret as days grow into weeks in seemingly interminable negotiations with government officials. As one man put it, "time is a dimension that they [Indonesians] have never grasped." But the visitors still come in droves to investigate business opportunities in this sprawling nation of tropical islands which is, with 120 million people, the fifth largest nation in the world. Approximately $300 million is being spent each year in Indonesia by foreign companies and governments. Aid grants from the latter are derived about one third from the United States, one third from Japan and the remainder from many nations. Djakarta is a far cry from pleasant colonial Batavia, as the city was called under the Dutch. The orderly colony of prewar days was managed as an agricultural and trading dependency of Holland. The Dutch did little about educating the people. The islands were controlled by the Japanese during World War II and afterwards there was a war for independence--which was attained in 1949. In the ensuing years, President Sukarno devastated the economy by squandering money on a gigantic scale. A Communist-attempted coup in 1965 resulted in a military takeover and the extermination of Communists. The new government under Suharto, which took over all power in March 1966, found itself in a situation where bare survival was the first consideration.

Jan 1, 1970

By John F. Myers

Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity.

Jan 8, 1958

By Maurice Rey, Victor Formanek, Paul Chataignon

IT is found when floating oxidized lead ores by sulphidization, that the presence of calcium salts in the water is usually detrimental and lowers the recovery. This effect is particularly marked in dry countries such as North Africa, where the waters often carry large amounts of calcium sulphate and where the ore may even contain gypsum. This effect is particularly marked in dry countries such as North Africa, where the waters often carry large amounts of calcium sulphate and where the ore may even contain gypsum. The effect of calcium salts is readily visible. Whereas in their absence cerussite is quickly stained brown and then .black by sodium sulphide, in their presence the mineral remains very light in color. A similar- effect is produced when barium sulphide is used as a sulphidizing agent instead of sodium- sulphide. Magnesium salts have little or no effect and even tend to reduce the detrimental effect of calcium salts. A study of this phenomenon indicates that it is due to the precipitation of calcium or barium carbonate in contact ,with the mineral simultaneously with the formation of lead sulphide.

Jan 1, 1950

By H. C. Heard

The review by Professor J. C. Jaeger (Chapter 1) briefly summarizes and discusses a select group of papers by various workers dealing primarily with aspects of fracture in brittle rock materials. Professor Jaeger's treatment is primarily concerned with the correlation of phenomenological and theoretical failure criteria with empirical results from short duration tests at ambient temperatures and generally at low lithostatic and interstitial fluid pressures. As engineering rock mechanics becomes more concerned with new techniques of mineral exploration and production at increasingly greater depths in the crust, it is well to be aware of the effect of the environment -that of the superposed stress field upon the lithostatic and interstitial fluid pressure, the temperature and the duration of the loading upon the failure of rocks either by fracture or flow. All results to be discussed here are from laboratory tests on small homogeneous samples, thus caution should be used in the direct extrapolation of these results to large inhomogeneous rock masses having quite different boundary conditions in the earth. The purpose of this supplement is to briefly point out the major effects of these parameters as examined singly, with all others held constant, and to cite some recent results which apply to the main theme on the brittle failure of rocks. The total stress field imposed upon a small volume of porous and permeable rock in the earth's crust may be thought of as the sum of an applied differential stress, plus a lithostatic pressure, plus an interstitial fluid pressure. The differential stress portion may be completely specified by nine components, six shear and three normal. If the small volume element is in rotational equilibrium, by suitably choosing our coordinate axes we may resolve these nine components into the three principal com-

Jan 1, 1967