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Adaptive processing is often related to the mineral composition of the mining block currently processed. The portions of waste, ore and secondary product minerals considered are always positive and typically sum to 100% (i.e. a composition). A typical solution to predict block averages of spatially dependent quantities would be block kriging. However, kriging is based on spatial correlations and it has been repeatedly shown that correlations of compositional data are spurious and blurred by the constant sum constraint. Aitchison (1982) proposed a general solution for compositional problems, based on transforming the compositional data to a set of logarithms of ratios of components, and analysing the transformed scores. The transform is chosen to be invertible to ensure that no information is lost in the process. This methodology avoids spurious correlation problems and ensures coherence between results obtained with different subcompositions. Pawlowsky-Glahn and Olea (2004) adapted the approach for point-support geostatistics, allowing the prediction of point compositions from spatially neighbouring data, without the artefacts induced by standard multivariate cokriging. Unfortunately upscaling the results of this approach with block cokriging is not straightforward, because of the nonlinearity of logratio transforms. Furthermore, we have to consider those nonlinearities created by the dependence on the block composition of extraction efficiency and processing costs of the possible processing choices. This paper proposes a solution for predicting the conditional expectations of the benefit of processing the block with each processing choice using geostatistical simulations of the local values of the composition and the resulting block integrals. The computation for a large number of blocks can be done efficiently using Cholesky decomposition. The approach also allows the calculation of prediction errors for expected compositions and expected benefit at almost no additional computational cost. Such compositional approach is necessary, for example when processing choices depend on proportions of certain minerals after other components have been removed; or if processing alters the composition in a multiplicative way, by partially removing a portion of some components.

Aug 1, 2013

By G. W. MacLeod

The iron ore question in this country has been widely discussed for many years, but only recently has its real significance becoming generally understood. The exhaustion of the old Helen mine, in 1918, marked the last phase of hematite production in Ontario, and with the closing of the Magpie mine in 1921 , Canada ceased to be a producer of iron ore. For the past three years every ton of ore used in Canadian blast furnaces has been imported. In a recent issue of the Engineering and Mining Journal-Press, Arthur B. Pearsons, Assistant Editor, makes the following statement : Iron dominates the world. Some contend that coal is more vital. be-cause heat is needed to make iron and steel. But there are other sources of energy, more convenient and less costly and it is only a question of time when progress in hydro-electric development will have reached the point where coal will be but an incidental source of power and heat. Even more direct means than the generation of electricity by hydro-power eventu-ally will be developed by making available the latent energy of the sun. But iron; Science gives not the vaguest suggestion that anything will dis-place iron and steel as the most essential material tool of modem civiliza-tion. ? Hardness, tenacity, malleability-it possesses all these in unique de-gree. These are some of the qualities that make steel and iron indispensable in modern industry. The domestic consumption per inhabitant of the United States has climbed uniformly from 0.18 tons in 1900, to 0.36 tons in 1922. New kinds of machines and new types of structures are being devised every year; and steel or iron is the basis of most of them." It is unlikely that the Ontario Government were actuated by this motive when they appointed the Iron Ore Committee to investigate and report on the iron ore situation, nevertheless, these facts must have influenced them in some degree.

Jan 1, 1924

By John Wilson

"The Rietveld numerical method was used to calculate the relative abundances of phases in both synthetic binary mixtures and synthetic and natural ores, using X-ray diffraction data. The results were compared with those of image analysis and a chemical method. The ranges of the relative errors were estimated. The Rietveld method is found to be acceptable for determining the abundances of major and minor phases and the amorphous component of partially crystalline samples. In complex mixtures, where there are several trace phases (~<2 wt%) present, the technique becomes less accurate. It is most useful as an alternative technique to image analysis when sample preparation is problematic or sample particle sizes are sub-micron. It is a manual method which requires user input during the fitting process, but is both simpler and faster than image analysis due to the reduced set up time and sample preparation required. It is now implemented at CANMET as a technique for quantitative analysis.INTRODUCTIONUntil recently, the Applied Mineralogy group at CANMET used only image analysis and chemical techniques to determine phase quantities. An effort to develop quantitative X-ray diffraction (XRD) has been on-going for several years. Initially, the reference intensity ratio (RIR) method with external standards was tried with some success (Szymanski and Petruk, 1989). The main difficulty with this technique was finding adequate standard material for each phase present in the sample. This shortcoming made the method ultimately impractical, given the wide variety of materials which come to the laboratory for analysis.The Rietveld refinement method of quantitative XRD (Hill et al 1993, Mumme et al 1996), in contrast, requires no standards and requires minimal sample preparation and therefore a more rapid turnaround compared to image analysis. The Rietveld method also has advantages over image analysis in that it can identify and quantify polymorphs, ultra fine materials and many types of hydroxide products. As well, it is useful for analyzing materials such as bauxite or talc, which do not polish well enough for making mounts of the quality required for image analysis. To quantify amorphous material and phases which are present in amounts below the detection limit of XRD, the addition of a standard material is still required. However, in such cases only one standard is needed, which is alumina."

Jan 1, 2003

By H. H. Claudet

PROBABLY the first flotation mill for treating molybdenite ores was put into operation .in Norway during 1913, when the writer was employed to introduce and apply the Elmore vacuum flotation process at a mine in southern Norway. These operations proved successful and led to other similar installations in that country. It remained, however, for Norwegian engineers themselves to iron out their difficulties and establish the molybdenum industry on a basis which ultimately attained world importance. Just as today, an urgent demand for molybdenum arose during the world war of 1914-18. By 1916, many molybdenite properties were in operation in Canada and several small concentrating mills were under construction. At one of these, in the Ottawa Valley district, the opportunity came for applying the Elmore vacuum flotation process, using a flow-sheet similar to that adopted in Norway. Later, as one of the staff of the General Engineering Company, who had already developed a highly efficient flowsheet for treating molybdenite ores, using the Callow pneumatic flotation process, the writer devoted considerable time to research work and investigations on a number of molybdenite projects and deposits in eastern Canada. The bulk of Canada&apos;s production of molybdenite was coming at that time from the Moss mine at Quyon, Que., where concentration of the ore was effected by water-film flotation. It is of interest to note that this process, based on the principle of surface tension, had been developed and introduced by the late Henry E. Wood, of Denver, Colorado- one of the original owners of the Moss mine-at the time he was investigating the Elmore vacuum process in his Denver plant. The process, with certain modifications, was used at several other properties in eastern Canada, and notably in the ore dressing laboratories of the Department of Mines at Ottawa and in a plant at Renfrew, Ont., in both of which ore from deposits in various parts of Canada was treated, with recovery of very appreciable amounts o much needed molybdenite. During the summer of 1917, the water-film flotation mill at the Moss mine was dismantled and the plant was re-modelled by the General Engineering Company to include the Callow system. This installation, using improved flotation methods, was highly successful both as to recovery and grade of concentrate, and proved a decided advance in molybdenite concentration, a recovery of upwards of 90 per cent being obtained, with a concentrate grading over 90 percent MoS2.

Jan 1, 1944

By P. J. Sylvester, D. H. C. Wilton, R. I. Wheeler, M. A. E. Huminick, D. Evans-Lamswood

"Abstract — Systematic characterization of the mineralogy of massive sulfide ore deposits can provide valuable insights into ore genesis and metallurgical processing that would not be apparent otherwise. We describe a method wherein (1) normative mineral abundances are calculated from whole-rock chemical assays using an algorithm, (2) the results are cast in block models, (3) the results are then verified with automated image analysis of a subset of samples prepared as grain mounts by backscattered electron imaging and X-ray mapping on a scanning electron microscope, and (4) those verified results are integrated with textural data determined by optical microscopy.The technique is applied to the magmatic Ni-Cu-Co sulfides of the Ovoid orebody, based on geochemical assays of 3175 whole-rock samples. Three principal ore zones are defined in the Ovoid. Type I ore occurs in the center of the deposit; it is magnetite-rich and pyrrhotite-poor with intermediate contents of pentlandite and chalcopyrite. Type II ore surrounds Type I ore and is pentlanditechalcopyrite- rich with intermediate contents of pyrrhotite and magnetite. Type III ore occurs at the base and along the outer periphery of the northern part of the orebody; it is pyrrhotite-rich and chalcopyrite- poor with an intermediate content of pentlandite, and a low-to-intermediate content of magnetite."

Jan 1, 2012

Up to thirty years ago, coal preparation in western Canada, except at four plants, had not included actual coal washing. The exceptions were at Nanaimo and Royston, B.C., where tub washers and wet tables were in use; at Hosmer, B.C., using. Robinson cones; and at Leitch Collieries, Passburg, Alta., using a feldspar jig. The two last named collieries had a short life and were not operating in 1920. The industry was divided, as at the present day, into two sections, steam (bituminous) coal and domestic (largely sub-bituminous) coal, the first generally supplying industrial needs and the second householcl and other heating requirements. The two sections overlap to some small degree today as prepared sizes, chiefly stoker, and briquettes, from steam coal are shipped for house-hold use, and domestic slacks are used in certain industrial plants. The .domestic operator, for reasons shown later, was not primarily concerned with actual coal washing as a phase of coal preparation, and bent his efforts to improvement of screening and loading plants, with hand-picking of coarse sizes. The bituminous operator, on the other hand, felt it necessary by 1920 to consider coal washing. When the mines were comparatively young, coal quality could be controlled to a considerable degree by selective mining, by leaving behind some of the seam or by-passing districts in a mine where the coal was of inferior quality to that in other districts. This obviously had its limitations, and so the next step was coal washing.

Jan 1, 1952

By Gordon Jackson

"There are two accomplishments of air and gas drilling: a new series of economic and mechanical challenges; and, acceptance as a standard drilling and completion tool.The new challenges are related to the concept of using a gaseous circulating medium in drilling for oil or gas. For purposes of discussion, a two part division has been made: the challenge of fluid invasion control and that of equipment and tools. Great strides have been made in the development of materials and techniques to combat formation fluid invasion. Chemicals and the ""mist drilling"" technique, now in use, have the versatility to cope with a wide range of downhole fluid entry conditions.Equipment and tools have been developed to meet the challenges of better, more economic drilling and completion possible with a gaseous circulating fluid. Economic and operational challenges remain.Acceptance of air and gas drilling as a normal operating tool was reached with difficulty. It is now established as a means of reducing costs in exploratory and develop-mental well drilling, exemplified in a recent study of 226 wells covering 419,407 feet of hole in the United States. Air reached the projected depth in 85 per cent of the operations, although formation water was encountered in 48.7 per cent of the holes. Slim hole bit performance and cost all compared for overall bit averages as part of analysis."

Jan 1, 1961

By C. H. Lau, I. T. Ng

Uniaxial Compressive Strength (UCS) of rocks is an important mechanical parameter for many civil engineering and rock engineering applications such as tunnel excavation, slope stability and foundation design. Macau is one of the world's fastest growing and most densely populated cities, many large and important infrastructures have been being continuously built using pile foundations which are designed to be supported by granitic bedrock. In Macau, the UCS of the granitic bedrock is required almost for every project involving pile foundations and is always measured directly from UCS test in the laboratory. However, direct measurement of UCS requires high quality rock core sample which is not only time-consuming and expensive but also requires high level of operating skill. In view of this fact, estimation of UCS using some empirical correlations will be more practical and efficient because they are relatively fast and economical compared to the direct measurement from UCS test. In the past, some empirical correlations had been established and widely used for estimating UCS of rocks in common engineering practice. However, it has been well recognized that the rock properties are generally varied with sites or geological regions in other words an empirical correlation developed from one region or one country may not be applicable for other regions or countries. Due to the reason that the empirical correlations for predicting UCS for granite are scarce in practice, in this study an extensive experimental program has been performed and a large database containing data such as UCS, Point Load Index (Is50), Schmidt Rebound Hardness (RL), porosity (?), water absorption (S), specific gravity (Gs) and dry density (?d) has been developed. An attempt has been made for developing a new empirical correlation for estimating the UCS of Macau granite. Accordingly, a comprehensive statistical analysis for correlating UCS with Is50, RL, ?, S, Gs and ?d has been performed and a local empirical relationship based on the developed database is proposed for obtaining reliable estimation of UCS for the granite of Macau. Finally, the performance of the proposed correlation is accessed by using another independent testing database developed in this study. It indicates that Is50, RL, ? and S have strong correlation with UCS whereas Gs, ?d have poor correlation with UCS. This study not only proposed a proper predictive empirical correlation for UCS determination for Macau granite but also provides detailed statistical information which is beneficial to engineers for obtaining better characterization of Macau granite.

Jan 1, 2015

The writer presents a concise summary of eleven recent discoveries made in the Maritime Appalachian area, with suggestions for fur the research. This information may prove helpful to geologists working in other fields and to students contemplating further avenues of research in mining geology and exploration. INTRODUCTION THIS paper is not intended as a research study on the subject, but i. merely a brief review of eleven discoveries that have been made in the Canadian Appalachian area. Furthermore, this is not a critical analysis of the merits of any one geophysical method, but it is an un-prejudiced observation of how these discoveries were actually made and what techniques were apparently most fruitful. Some generalizations are attempted whicl1 may suggest further avenues of research in the field of mining exploration. The writer wishes to thank his colleagues in the field for their comments, which he was able to in-corporate into this paper. In particular, he is grateful to Dr. Paul Bevan and

Jan 1, 1963

By C. R. Kato, G. Proulx

"Within the continuous scenario of reduced aluminium price and plants production costs increase, the energy consumption optimization in the aluminum electrolytic pots continues as the main focus for the producers. Energy consumption was chosen as a key performance indicator to drive the efforts and actions for improvements. Alcoa improved the energy consumption by approximately 3% from 2005 to 2015. This improvement was a result of best practices implementation, new technologies introduction, strategic actions with plant curtailments and management practices. The main objective of this paper is to highlight the importance of the management practices for planning and operational improvements beyond the technology changes. About 10 years ago, Alcoa reorganized its approach to retain knowledge in the Smelters by using a Best Practices format. For each specific subject, a skilled team defined the minimum requirements and the Best Practices for several aspects of operation and maintenance, which affect the environment, safety, cost, customers and performance. These Best Practices were deployed to all Smelters combined with training sessions to process and operation professionals. We will describe how the Best Practices were organized, the deployment strategy used, and the approach to measure the plants’ success. We will describe the management approach that includes Manufacturing Analyses focused on 3-year potential, annual planning, and weekly monitoring of plant stability. A manufacturing analysis is organized at select plants with cross-functional participation of specialists from technical, operational, procurement and finance. The output of a manufacturing analysis includes a roadmap of enablers to improve energy efficiency. A quarterly follow-up of enabler deployment is held with the plant and resources that participated in the analysis. Annually, there is a Planning Process where energy consumption enablers are selected to be implemented during the next 3 years for each plant. A monthly critical analysis is made by the plants with regional best practice support. On a weekly basis, key performance indicators are reviewed with determination of a stability index for each plant. Any deviation signal of unstable condition is alerted and supporting resources are diverted to the plant to reverse trend with countermeasures.INTRODUCTIONDue to factors like excess aluminum in the market and lower consumption in China, the LME price is declining along the last years, as showed in Figure 1. In 2011, the price peaked at US$ 2,400/ton and since then, continues to trend down and approaching the lowest level at US$ 1,500/ton in the last 5 years."

Jan 1, 2016

By George J. Thompson

This pa per deals with the internal characteristics of steel and its response under cold northern temperatures. General maintenance procedures and specific repair techniques are covered.

Jan 1, 1973

By R. C. Fernandes, F. L. Santos

Aluminum alloys in particular, have certain limitations when subjected to welding process. This is mainly present because aluminum alloys have high thermal conductivity, high contraction in solidification and high hydrogen solubility. Taking this into account, the FSW process has great potential for this application, since it is autogenous, held without metal melting and without the use of slags or shielding gases. From this concept, the aim of this study is to evaluate the joining of thin sheets of aluminum alloy 3105 H26 with 0.7 mm of thickness. To performing of the tests, some parameters were analyzed, such as: tool penetration in the sheets, attack angle, the type of welding tool and penetration control mode (position or force). The results indicated that the force control mode is most suitable for thin sheets, and the transient state at the beginning of welding was the most critical part to control the welding quality.

Jan 1, 2015

By E. C. Roper

THE Britannia Mining & Smelting Company, Limited, have been operating their property at Britannia Beach, B.C., continuously for nearly forty years and have mined over 33,000,000 tons of ore from orebodies within a belt of highly sheared rocks, five miles long by 2,000 feet wide. The property is in the Coast Range mountains, about twenty miles due north of Vancouver. The mountains rise abruptly from sea level to elevations of 4, 500 feet within a horizontal distance of 7,000 feet. The topography has enabled the orebodies to be developed by adit tunnels. The active mining levels are connected to the adits by incline and vertical service shafts. The main service adits are the 2200, 2700, and 4100 levels (see Figure 1). The mine surface shops, three bunk-houses, and over one hundred dwellings form the townsite camp at the portal of the 2200 level adit. A small camp of one bunk-house and a few dwellings is situated at the 2700 level portal. The beach surface shops and camp, adjacent to the 4100 level adit, service the mill, foundry, and other beach installations as well as the mining from the 4100 level. The ore mined from the various orebodies is delivered to the 4100 main haulage level through a system of rock raises and intermediate tramming levels and is hauled on the 4100 level to the mill.

Jan 1, 1945

By D. J. Cheung, V. N. Kazakidis

ABSTRACT Seismicity and rockburst problems in hard-rock mines negatively impact safety and profitability. The authors propose a design risk methodology as a relative risk assessment for underground excavations vulnerable to rockburst damage. It considers rock mass conditions relating to mininginduced stress, geological structure, rock mass properties, and mining influence. Application of the methodology to rockburst cases involving seismically active fault zones at the Craig mine in Sudbury, Ontario, Canada, demonstrates that design changes can reduce exposure and economic risks. Mines with high geotechnical risk can use the design risk methodology to evaluate design alternatives as a risk management strategy.

Jan 1, 2014

By H. J. lgner

Hydraulic fills are widely used in the tabular, steeply dipping stopes of the South African gold and platinum mines as an integrated process within a daily cycle of drill and blast. There is therefore only a small time window in which to fill the geotextile bags used as primary fill containment, without the risk of loosing production. Consequently, mines tend to increase the flow rate to the stopes, although this compromises adequate drainage, consolidation and strength development during filling. Recent underground measurements inside the geotextile bag have revealed that at high rates of rise and at 25 degrees dip, the backfill can remobilise within a limited area inside the geotextile bag during filling. This sudden downward surge of backfill exerts, for only a few seconds, additional loading on the geotextile, its supporting mesh and the props. This unstable behaviour poses a serious threat as it can push props out of place, thereby damaging the geotextile bag and causing a mud slide in the stope. To reduce the risk of accidents, the phenomenon of sudden slumping was further investigated for various filling conditions in the laboratory. The results confirmed that the maximum pressures associated with the sudden slumping can be more than five times those experienced during steady-state consolidation. Based on this new insight, the current best practice for hydraulic backfilling was critically reviewed. A practical approach to implementing meaningful standards is presented to ensure safe operations in relation to the consistency of the backfill quality and the appropriate matching of geotextile characteristics with backfill properties.

May 1, 2007

By Douglas C. Fraser

A DIGHEM survey was flown in the Belford-Montcalm Township area of Ontario in November 1975. This 600-linemile survey resulted in the detection of 134 EM anomalies. The Montcalm Township copper-nickel discovery yielded a single-line anomaly having a conductance of 154 mhos. This anomaly was highly visible because (a) it had the highest conductance in the survey area, (b) it correlated with a 175-gamma thumbprint-shaped magnetic anomaly and (c) it was isolated from long conductive bands. The deposit is a copper-nickel pyrrhotite body which occurs in gabbro and strikes north-south, parallel to the flight lines. The DIGHEM survey was flown north-south, because the exploration program was primarily concerned with locating copper-zinc sulphides in the east-west-striking felsic volcanics. The flight line passed close to the deposit and yielded a 9-ppm anomaly on the chart record. The computer analysis showed that a deposit of exceptionally high conductance (154 mhos) caused the relatively weak (9 ppm) anomaly. The ground follow-up program of magnetics and EM led quickly to the discovery drill hole, which penetrated the orebody in September 1976. Subsequent geophysical surveys consisted of horizontal-loop EM, pulse EM, magnetic and induced polarization surveys over an area of about 8 claims. In addition, a detailed DIGHEM" airborne survey was flown at a line spacing of 100 m to evaluate the entire property of 620 claims. This detailed survey yielded EM conductor maps and contour maps of resistivity, magnetics and enhanced magnetics.

Jan 1, 1978

By H. C. Rickaby

Introduction The township of Swayze, from which the Swayze gold area derives its name, is in the Sudbury mining division, approximately 150 miles northwest of Sudbury. The gold area may be regarded as situated at the southwest corner of a triangular area whose northeast and southeast corners are at Porcupine and Shiningtree, respectively, and whose sides are between 70 miles and 90 miles in length. On a geological map, it would be found that belts of Keewatin greenstones and sediments form the sides of this triangle, and that they surround a large granite mass. Prior to the summer of 1931 the Swayze corner of this triangle had probably been less prospected than the other parts and comparatively little was known of it from the standpoint of gold mining possibilities. The extensive belts of iron formation to the south and west of Swayze received some attention about the year 1909, and during the years 1927 and 1928 some prospecting was done in the townships of Greenlaw and Cunningham, south of Swayze, but chiefly for base-metals- copper, zinc, and lead. In the summer of 1931 a very promising discovery of gold-bearing quartz was made by J. G. and J. L. Kenty, working for the Brett-Trethewey Mines, Ltd., in association with Northern Canada Mining Corporation, and Northland Prospectors, Ltd., and this property, now known as the Kenty Gold Mines, Ltd., has been actively developed with very encouraging results. Following this discovery a6d during the summer of 1932 much prospecting took place in the area, as a result of which a number of other discoveries of gold were made, chiefly to the west of the original find. They are distributed over a wide area, which includes the townships of Rollo, Raney, Swayze, Denyes, Halcrow, and Greenlaw.

Jan 1, 1933

By J. S. Fox

Major-element data for unaltered, unmineralized felsic host rocks from a number of stratigraphically simple, massive volcanogenic Zn-Cu(-Pb) sulphide deposits of low metamorphic grade have been compiled. The petrochemical affinities of these host rocks have been determined (by standard means and by discriminant analysis) and compared. This comparison indicates that volcanogenic deposits in felsic terrains are not restricted to the classical calc-alkaline rock association as previously thought, but can actually be hosted by rocks showing a range of iron content. There is a positive correlation between differentiation trend and are tenor. Zn-Cu ores usually have iron-rich felsic hosts (most Canadian Shield deposits); Pb-Zn -Cu ores have iron-poor felsic hosts (Japanese, Iberian and Tasmanian deposits). This parallels the antipathetic relationship between iron content and background lead levels evident in young, unmineralized, island arcs as well as in many older belts. Correlations between differentiation trend on one hand and massive ore mineralogy and the relative proportions of various rock type (including rhyolite, quartz-porphyry and coarse pyroclastic rocks) on the other are also evident. It is concluded that the recognition of a calc-alkaline differentiation trend cannot be used as a prospecting guide, as has previously been proposed. However, in view of the above correlations, the recognition of a given trend may aid in the formulation of an effective exploration philosophy.

Jan 1, 1979

By K. Fagerlund, L. Rosenback, T. Mäkinen, Y. Anjala

This paper deals with the nickel smelter and refinery concepts Outokumpu has applied at Harjavalta and several other plants. Also other process routes and modifications developed and tested by Outokumpu during the recent years are highlighted. Outokumpu started nickel production in Harjavalta in 1959. Until 1995 the Flash Smelting - Peirce-Smith (PS) converting route was applied. High grade nickel matte from the converting step was further refined by means of leaching and electrowinning to produce cathode nickel. In 1995 the nickel production capacity was increased from 17 000 t/a to 52 000 t/a based on the Direct Outokumpu Nickel Smelting Process (DON). In the DON process PS converting is eliminated and high grade nickel matte with low Fe-content is directly produced in the flash smelting furnace (FSF). Metal values from the smelting slag are recovered in the electric furnace (EF) as iron containing Ni-matte. The DON process can be operated with either two matte concept, where high grade FSF matte and EF matte are produced, or a single matte concept, where EF matte is recycled to the smelting furnace and thus only one type of high grade matte is obtained. The additional refinery capacity at Harjavalta is based on hydrogen reduction producing.

Jan 1, 2005

By J. P. Harrison, K. Gao

It is well known that in situ stress measurements at a given site will generally display significant variability. However, it appears that a robust analysis of such measurements – i.e., one that is faithful to the tensorial nature of the data – is not available. Despite the fact that stress is a tensor, stress magnitude and orientation have long been analyzed separately using classical statistics. In earlier work we demonstrated the applicability of tensor statistics to the analysis of stress variability. Here, we investigate further the difference between tensor and classical statistics with respect to the stress tensor correlation matrix. Our analysis commences with the selection of a series of valid correlation matrices. Then, assuming that standardized tensor components follow the multivariate standard normal distribution, these correlation matrices are used to generate marginal probability distributions of the eigen-parameters (i.e., principal stress magnitude and rotation angle). From these, random stress tensors are generated, their eigenparameters determined, and the probability density distributions of these obtained using both classical and tensor statistics. Our results indicate that, for all correlation matrices, both methods give practically identical distributions for principal stress magnitude. However, the discrepancy between the two methods with regard to probability density distribution of rotation angle is highly dependent on stress component correlation. This discrepancy is usefully quantified in terms of the integral, with respect to orientation, of the difference between the two probability density distributions. This parameter, which we term Area Difference, is closely linked to the magnitude of the correlation matrix determinant, which itself is related to the normal stress correlation coefficient (i.e., ?x ,?y ??). Assuming that Area Difference should not exceed 0.1, we identify the critical determinant for any particular value of normal stress component correlation coefficient. Thus, using published in situ stress data and the obtained critical determinants, we show that for a specific normal stress component coefficient, when the correlation matrix determinant is less than its critical determinant, the more precise tensor statistics should be used to calculate the distribution of rotation angle. These results demonstrate that the customary analysis of stress measurement data may lead to erroneous results, and that tensor statistics appears to be preferred approach.

Jan 1, 2015