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By V. Svalbonas, M. Fresko

The present versions of the Welding Codes, such as BS7608, have long been known to be compatible with hand computations of membrane and bending stress, rather than detailed finite element solutions. However, in the last five years, in the mining industry, this incompatibility has been largely ignored, and the code interpretations have been pushed into the realms of ground welds, residual stresses, and even flaw growth. Such techniques have to be recognized as extrapolations not necessarily sanctioned by the original code documents. The safety of such extrapolations, as they are related to grinding mill fatigue design, is investigated herein.

Jan 1, 2002

By Krzysztof Kotwica

The steady demand for rock materials leads not only to on increase in mining but to the need for decreasing the loss of material in the process of exploitation as well. It brings about an increase in using of explosives in open pits and as a result an increase of after blasting gases volume, vibrations, the scattering (dispersion) of stone ect. All these factors affecting the environment lead to the research work for applying the electrohydrodynamic methods both in open casts and underground mines. In the article the authors describe the concept of this method and construction of equipment which recently have been successfully introduced in mining, the results obtained determine the possibilities of using this method and the future directions. The results of combined method with high-pressure water jets cutting and prototype equipment for separating rock blocks from the rock mass using special head with high-pressure water jets are also described.

Jan 1, 2006

Andesites are a major source of aggregate for much of the North Island of New Zealand. There are regional differences with respect to some important properties of the andesites. Some are reactive with cement and are designated as potentially deleterious or deleterious by the concrete industry. Other andesites, particularly those that are slightly altered or weathered, have rather high Plasticity or Clay Indices and perform poorly in road construction.   The performance of the andesites has been investigated and can be shown to be determined by: +        the chemistry of the rock which in turn determines the chemistry of the glass in the rock; +        the presence of large amounts of groundmass glass in the rock; and +        the nature of the superimposed alteration processes. Environment of extrusion and how rapidly the rock has been cooled or chilled are also important as they determine the fabric of the rock and how much glass will be present in the rock.   There are three main types of alteration that affect the quality of the aggregate: 1.   hydrothermal alteration, 2.   late magmatic alteration associated with the devitrification of glass, and 3.   weathering.   Each of these alteration types produces different alteration minerals. In fresh andesites the devitrification of glass has an important affect on the rockÆs properties. The Taranaki andesites are shown to have unusually (in comparison with other North Island andesites) high Na2O contents, held in the groundmass glass, which is the fundamental reason for the high alkali û silica reactivity of these andesites.

Jan 1, 2005

"The profile of the respondents was that of a professional responsible for communications, community relations or corporate social responsibility programs. By targeting a consistent professional profile it was possible to ensure that most respondents had a similar degree of responsibility and/or decision-making ability related to the application of communication technologies. The research attempted to be inclusive and attention was paid to interview respondents from both genders and from indigenous groups.4, 5 A codebook of 80 themes was developed that highlighted recurring topics; for example, codes were created to identify risks, benefits, policies and learning process of using social media and included topics that were repeatedly emphasized by respondents (i.e. age, efficiency and language). Both manifest coding (i.e. coding of the visible content, such as specific words) and latent coding (i.e. coding of underlying meanings) was undertaken (Creswell [13]). The codes were used in the qualitative analysis using ATLAS.ti software and network views were created to illustrate the relationship between major themes of this research. There are limitations to this research, largely related to the changing nature of the Internet and communication technologies. There is also a geographic limitation to the application of this research because most of the data was gathered primarily from Canadian sources.6 Different levels of Internet penetration, or limited access to computers or mobile devices, and low literacy rates may reduce the applicability of the research in countries with low Internet penetration. A more systematic process to selecting candidates may have helped bring balance to the final list of interview respondents. For example, most of the corporate respondents were from medium and large companies and there was not adequate representation of small mineral exploration companies. The research did not probe into social media applications by different business groups within the mining sector, such as smelting and processing."

Jan 1, 2011

By Robert M. Miller, Judy Milligan

A computerized "Decision Support System" was used to evaluate an "Underground Platform Approach to Oil Recovery". Over a billion calculations were required to model the mine layouts; learning curves for shaft, tunnel, and well drilling scenarios; detailed cost, schedule, and resource data; complex oil production and material balance data; varying reservoir parameters; and complex oil pricing curves. Simplified "optimum" solutions were defined in terms of muck hoisting capacity, barrels of oil per day, and present worth. Complex "optimum" solutions were defined in terms of minimal exposure scenarios during development followed by shortest time to full production.

Jan 1, 1987

By Morgan L. Race, Matthew R. Glisson

"Most driven pile projects have plumbness limits from 0.25 in/ft (21 mm/m) to 0.5 in/ft (42 mm/m) to control bending stresses. For two projects, the project teams performed static load testing to evaluate performance of piles with sweep. One project, located in Grand Forks, North Dakota, used 9.625-inch (244-mm) diameter piles with a wall thickness of 0.395 inch (10 mm) and lengths ranging from about 130 to 160 feet (40 to 49 m). Measured pile sweep (lateral offset distance of the pile toe from the pile top) was between 12 and 17 inches (305 to 432 mm). Static load testing indicated that the piles could support the design load with axial deflection of less than 1 inch (25 mm) but only provided about 80 to 90 percent of the ultimate resistance at axial deflections of about 1.9 to 1.7 inches (49 to 43 mm), respectively. The other project, located in Shakopee, Minnesota, used 9.625-inch (244-mm) diameter pile but with a wall thickness of 0.352 inch (9 mm) and lengths around 50 to 90 feet (15 to 27 m). The measured sweep varied between about 20 and 63 inches (508 and 1,600 mm) for 9 of 214 piles driven at the site. Load testing indicated that these piles could provide the required design resistance with less than 0.3 inch (8 mm) of axial deflection and support the required ultimate resistance with about 0.5 to 0.6 inch (13 to 15 mm) to of axial deflection.INTRODUCTIONAnyone who has observed a significant number of piles has seen that, inevitably, the pile is not perfectly straight after driving. In spite of the best efforts of contractors, there are a whole host of reasons for piles to end up out-of-plumb or to have a curve, sometimes referred to as pile sweep. Most project specifications set limits for plumbness typically between 0.25 in/ft (21mm/m) and 0.5 in/ft (42mm/m) (USACE, 1991; PDCA, 2007; MnDOT, 2016; MoDOT, 2016). Closed-end pipe piles, including monotube or tapertube, are the only pile type that allow actual measurement of the final alignment of the pile.As Nadeem, et al. (2015) note, buckling failure of long, slender piles is the predominant mode of pile failure in soft soils. Pile sweep is just one source of buckling failure in long, slender piles. The nonlinear buckling analysis showed that increasing slenderness ratio and/or increasing degree of curvature decreases the loadcarrying capacity of a driven pile. Nadeem, et al. (2015) considered solid, steel pile with lengths from 24 to 66 feet (7.5 to 20 m), diameters from 9.75 to 26 inches (244 to 660 mm), initial bends from 2 to 6 inches (50 to 150 mm), and half- and quarter-sine shapes."

Jan 1, 2017

A research project was commissioned by the Australian Coal Association Research Program (ACARP) to improve the understanding of tailgate strata mechanics and to provide a more rigorous engineering basis for tailgate support design. A deformation mechanism termed æskew roofÆ was defined which relates the regional influence of differential horizontal strata movement (shear) about longwall extraction to gateroads. Confirmation of the mechanism was achieved by field investigations which included measurement of the shear displacement along weak interfaces. Under geological and mining conditions where the skew roof mechanism operated, strata units were found to move progressively further towards the goaf with height into the roof. 3D numerical modelling was used to assess the major geotechnical factors controlling the mechanism and to determine appropriate support strategies within a æskew roofÆ environment including the role of cables versus standing supports. The skew mechanism is considered relevant to; all roadways in the vicinity of longwall extraction including the faceline itself, chain pillar design, and support design.

Jan 1, 2005

By N. Kuyucak

"Acid mine drainage (AMD) is one of the most significant environmental challenges facing the mining industry worldwide. It occurs as a result of natural oxidation of sulphide minerals contained in mining wastes at operating and closed/decommissioned mine sites. AMD may adversely impact the surface water and groundwater quality and land use due to its typical low pH, high acidity and elevated concentrations of metals and sulphate content. Once it develops at a mine, its control can be difficult and expensive. If generation of AMD cannot be prevented, it must be collected and treated. Treatment of AMD usually costs more than control of AMD and may be required for many years after mining activities have ceased. Therefore, application of appropriate control methods to the site at the early stage of the mining would be beneficial.Although prevention of AMD is the most desirable option, a cost-effective prevention method is not yet available. The most effective method of control is to minimize penetration of air and water through the waste pile using a cover, either wet (water) or dry (soil), which is placed over the waste pile. Despite their high cost, these covers cannot always completely stop the oxidation process and generation of AMD. Application of more than one option might be required.Early diagnosis of the problem, identification of appropriate prevention/control measures and implementation of these methods to the site would reduce the potential risk of AMD generation. AMD prevention/control measures broadly include use of covers, control of the source, migration of AMD, and treatment. This paper provides an overview of AMD prevention and control options applicable for developing, operating and decommissioned mines."

Jan 1, 2002

By David C. Oyler, Dennis R. Dolinar, Christopher Mark, Craig S. Compton

Fully-grouted roof bolts comprise more than 80% of the primary roof supports used in U.S. coal mines. However, nearly 1,500 MSHA reportable, non-injury roof falls occur each year, and most of these are attributable to failure of the roof bolt system. Anchorage failure is one failure mechanism for fully-grouted bolts. As roof deformation works its way upward, the bolts can become heavily loaded near their upper ends. If the applied load exceeds the anchorage, the bolts will simply pull out. Research dating back 30 yrs indicates that this type of anchorage failure is most likely when the roof rock is weak, just where roof support is most critical. In soft shale or coal roof, the small amount of data available in the literature indicates that 20-30 in of resin anchorage may be required to achieve the full capacity of the bolt. In other words, the “full resistance zone” of a 60 in bolt may actually be just 30-40 in. Despite its potential importance, there is no widely accepted anchorage test for fully grouted bolts. Standard pull tests have sometimes been employed, but they provide no information on the anchorage near the top of the bolt. An alternative, first described more than 25 yrs ago in the U.S., is the short-encapsulation pull test (SEPT). With this test, the bolt is installed with only a short (1 ft or less) tube of resin. In recent years variations of this test have become international standards. v

By N. Mulaudzi, S. Archer

"Direct cobalt electrowinning was developed to produce unrefined cobalt metal as an alternative to producing a mixed hydroxide product (MHP), which is the common cobalt intermediate product in African Copperbelt operations. MHP is preferred due to the high cost of producing high-grade cobalt cathode. Direct cobalt electrowinning test work results have shown that the purity of the unrefined cobalt metal produced from a low-grade copper solvent-extraction raffinate stream was ~97% (w/w), which is significantly higher than the MHP purity (up to 45% (w/w) Co). The current study investigates whether direct cobalt electrowinning would increase the profitability of African Copperbelt copper–cobalt oxide operations, when compared with the MHP flowsheet. An order-of-magnitude economic evaluation was conducted using dynamic differential discounted cash flow models on a “bare-bones” basis, using a 10% discount rate. Three variables were evaluated, namely; reagent utilisation extents, precipitation extents and filter-press wash efficiency. Multivariable risk analysis was also conducted using the Monte Carlo simulation technique to understand the impact of key project drivers. The financial study results indicated that a direct cobalt electrowinning flowsheet could potentially result in a higher mean net present value (NPV) compared with the MHP flowsheet. Cobalt recovery was found to have the most significant impact on the NPV. In addition to increased profitability of African Copperbelt operations, direct cobalt electrowinning has the potential to reduce the environmental footprint of operations as well as addressing the Democratic Republic of Congo government’s drive towards export of higher value metal products instead of low-grade intermediates."

Jan 1, 2015

Q: It is May 1961 at Bill Wrather's Washington house. Bill, think back to your first job after college. Wrather: Perhaps I ought to go back a little bit further than my first job. I entered the University of Chicago with the idea of studying law. My intention was to take a 4-yr liberal arts course and superimpose a law degree on that. But during my undergraduate work I fell under the influence of R. D. Salsbury. He decided I had some talent as a geologist and influenced me to take a geological course. Nevertheless, I did not give up the idea of law. While in school I took a spell of typhoid fever and almost died. The doctor recommended outdoor exercise, so a geological job seemed logical. W. H. Emmons was a graduate student in the University and he interceded with Dr. Hayes of the USGS. I went on the payroll as assistant packer at $60 a month. I had one of the most glorious summers I ever spent in my life. That fall and the following year I took law courses and became thoroughly convinced that I was cut out for a geologist rather than a lawyer. I finished up my law work in 1908 while waiting for a job with Bill Emmons, who was doing a careful study of Goldfield and Tonopah.

Jan 4, 1964

Background Chronology 2008 Positions May 8, 2010 Summit Going Forward Say one thing and do another ??Genuine passion to see our customers succeed?, ?A passion for exceeding our customer?s expectations? Self serving actions to gain competitive advantage at the expense of the customer No single supplier or technology can manage the overall mine and its integrated operation - April 2005: Informal meeting at Toronto CIM 2004 -Unanimous interest - July 2005: Formal Calgary Meeting, developed: - Scope and vision statement , - OEM/OTM communication plan, - industry communication plan - Aug?Nov 2005: Aligned with SMART - Nov 2005?May 2006: Direct OEM, OTM communication - May ?Sept 2006: Developed baseline standards - Sept -April 2007: Developed SMART document - Sept 2007: Document distribution and request OEM OTM response - Jan ?May 2008: Acquired OEM OTM feedback and positions May 2008: Results presented to SMART and discussions on next steps

May 1, 2010

By G B. Arehart, S J. Mathews, J L. Mauk

The banded nature of the quartz veins which form the Empire lode at the Golden Cross mine, is perhaps their most striking feature. Petrographic studies show that significant differences occur between the bands in terms of textures, quartz grain size, calcite, adularia and kaolinite content, and the form, concentration and mineralogy of sulfide phases.   The d18Oquartz values of individual bands within the vein material range from 7.3-10.9ë. Calculations show that the d18Oquartz values can be adequately explained by temporal variations in the system temperature, boiling and/or variations in the systems fluid/rock ratios.

Jan 1, 1995

By D Brouwer, P Wild, B Belle

Due to the steep geo-thermal gradient in Bowen Basin area, as underground coalmines reach increased depths of extraction, the Bulk Air Cooling (BAC) requirements will increase as opposed to cooling the workplace using the ventilation means alone. One such mine has already been using a 4 MW surface BAC plant for the last six years to manage the working temperatures with reduced cooling efficiency as the mine expands. Due to the horizontal nature of the longwall mine layout, distances from the working face to intake shafts are rapidly expanding to over 6 km as opposed to the vertical mine layout of a hard rock mine. To improve the positional cooling efficiency, reduced panel pressure differentials, improved rib emission gas management, and intake dust management, small diameter intake shafts were located on the inbye end of production panels and halfway up the development panels with localised mobile small BAC plants. This paper summarises the results of extensive underground data of this innovative cooling concept for development and retreating longwall face heat management compared to a larger remote BAC plant.CITATION:Belle, B, Brouwer, D and Wild, P, 2017. The use of mid-panel ventilation shafts to improve positional cooling efficiency in a Bowen Basin longwall mine – a case study, in Proceedings Australian Mine Vent Conference 2017, pp 217–224 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 28, 2017

By J. J. Bezuidenhout

The waste-heat boiler is used within the Sulphide flash smelting process as the main dust and energy recovery unit. The large volume of off-gas discharged from the flash smelter is at a very high temperature (1350°C) and contains a significant dust load that subjects the downstream waste-heat boiler to tough and demanding conditions. The boiler cavity is especially prone to dust accretions, fouling, and corrosion caused by accumulation of molten particles and precipitation of sulphuric acid. Computational fluid dynamics (CFD) is applied within a qualitative study to model the flow and heat transfer distribution throughout the waste-heat boiler. The commercial CFD package, Fluent 6.2.16, was applied to a modified waste-heat boiler (23 m ×11 m ×5.4 m) within the Outokumpu flash smelting process. This investigation focuses on the geometric modifications to the typical boiler design, which includes elevation of the ceiling, placement of flow-obstructing baffles and radiation plates parallel within the flow path. Also investigated were various boiler operating conditions such as the circulation of process off-gas, air leakage from the dust discharging hoppers and variation in inlet gas composition. The geometric modifications had the desired effect of increasing the volumetric utilization and therefore enhancing heat transfer between the boiler surface and the gas stream and dust segregation. Introducing circulated off-gas at a rate of 20 m/s and at a 45° angle to the front of the waste boiler further enhanced cooling while reducing the high impact of the furnace-uptake gas-stream on the boiler ceiling. The placement of radiation plates was found to be very effective in enhancing the heat transfer surface and distributing gas flow within the boiler. These results present recommendations towards an improved waste-heat boiler design. Keywords: flash smelting, waste-heat boiler, CFD simulation, off-gas cooling.

Jan 1, 2008

By Louis J. Cabri

"Mineralogical evaluation of ores containing platinum-group elements (PGE) is fraught with difficulties because of the low grades (often 1-3 g/t PGE), dispersal of PGE (usually as finegrained platinum-group minerals [PGM]), as well as occurring in solid solution in some base metal sulphides (BMS) such as pentlandite and pyrrhotite. Mineral processors not only need to know how the PGE are distributed, that is, their mineralogical distribution, but the grain sizes of the PGM, and especially the associated minerals.After obtaining a representative ground sample, common approaches include studying a large number of polished or polished thin sections, concentration of the PGM and sulphides by different gravity methods (e.g., heavy liquids, elutriation, micro-panning) and study of the produced concentrates. Unfortunately, these methods often do not produce concentrations that are sufficiently representative of a particular ore. The newly developed patented technology of hydroseparation (Rudashevsky et al., 2002) is especially effective at making concentrations of PGM over a wide range of concentrations (down to <300 ppb Pt+Pd+Au) and size fractions, including <45µm (down to a few micrometres in size), a size range not possible by other techniques. This water-based environmentally friendly laboratory technique provides a large amount of data from samples, which can range from 5 to 1000g, giving confidence to extrapolation of results to bench-scale and larger test work, especially when combined with quantitative image analysis to determine modal percent of major minerals and mineral liberation data, needed to predict the minimum (K80) and optimum (K40) grinds. INTRODUCTIONThe invention of the electron microprobe in the early 1960’s and scanning electron microscopes (SEM) with energy dispersive spectrometers (EDS) in the 1970’s presented mineralogists with powerful tools permitting them to obtain chemical and surface area data on minute amounts of minerals in situ, in a non-destructive manner. An area of process mineralogy that has very much benefited from this new technology was the characterization and understanding of PGM species, resulting in rapid growth of newly characterized species (Figure 1). Recognition of the first PGM may be ascribed to the Spanish explorer Ulloa in 1748, who described native platinum from South America. The second PGM (laurite, RuS2) was only recognised in 1866 by Wöhler in placer samples from Borneo (now Kalimantan) and the third (sperrylite, PtAs2) by Wells in 1889 from the Sudbury Ni-Cu sulphide deposits. The discovery of the important Pt-Pd deposits in the Bushveld Igneous Complex led to the characterization of the important Pt-Pd sulphides (cooperite, PtS2 in 1928 and braggite, (Pt,Pd)S2 in 1932). By the early 1960’s, only about 20 PGM were recognised, and many later proved to be poorly or incompletely characterized. Thus, the introduction of electron probe microanalysis (EPMA) led to a 50% increase of known PGM, as shown in a 1972 review on PGM (Cabri, 1972). At the time of the next review in 1981 (Cabri, 1981) the number of known PGM had grown to 75 and as of 2002, it had increased to 109 (Cabri, 2002). However, it is the author’s experience that less than about 25 PGM may be considered to be “common”, i.e., found in many different deposit types, as shown in Table 1, but usually only some of these occur in any one particular deposit."

Jan 1, 2004

By P. J. D. Lloyd

The widely employed IPCC models for the release of methane from underground coalmining operations are reviewed, and put in the context of the South African National Communication on greenhouse gas emissions. Then attempts to calibrate the model via measurements on South African coalmines are described. These attempts failed because it rapidly became clear that the IPCC model, involving methane adsorbed by the coal and released (a) by the depressurization of the strata caused by mining, (b) from the broken coal and (c) from coal remaining in roof, floor, pillars or goaf after mining, was not valid. Instead, measurements showed that the methane release was very variable, sporadically falling to zero. Carbon dioxide concentrations were monitored at the same time as methane, and followed methane concentrations. An alternative model was developed, in which methane was largely displaced from the coal and held in fissures, cleats and pores, which, when intersected by mining, released methane into the ventilation stream. In a key test of this hypothesis, methane concentrations around a continuous miner were monitored both during operation and after shutdown. Even during operation, methane became undetectable. It is hypothesized that heating of the South African coal-seams during the emplacement of the igneous dykes that cut so many of the seams caused displacement of the methane from the coal into the pores. This fissure-held methane, or free methane, is released rapidly once a pathway through the coal into the mine atmosphere is established. In contrast, methane adsorbed in the coal, and measured as the seam gas, desorbs relatively slowly. Measurements suggest that on average about 50%of the adsorbed methane is lost one day after mining. By that time, the coal will have left the mine, so that the remaining seam gas will be released to the atmosphere outside the mine. Attempts to measure methane emissions from surface coal-mining operations showed very little detectable methane. Coal from surface operations, which was milled and exposed to atmosphere, adsorbed gas from the air. It is concluded that methane release from surface operations is probably less than 3Gg/a. It is estimated that the total methane release from the coalmining industry amounts to about 72 Gg/a, as opposed to the National Communication estimates of 323 Gg/a in 1990 and 317 Gg/a in 1994. However, there are large errors associated with these estimates, and it is recommended that the methodology outlined in this report be extended to as many mines as possible to reduce the errors that are inherent in the physical processes underlying the release of methane from South African coalmines.

Jan 1, 2005

By Venda Oliveira P. J., Correia A. A. S., Danisi C. M.

"AbstractA laboratory study has been undertaken to establish common understanding of the creep phenomenon of a Portuguese soft soil chemically stabilised with binders. In order to study the effect of different stress levels on the strength and on the creep behavior of the stabilised soil, oedometer creep tests and unconfined compressive tests were performed at different curing times. Results show that the creep stress level does not influence the unconfined compressive strength. In addition, the creep phenomenon increases the unconfined compressive strength of the treated soil. Two different secondary compression indexes were recognized from the one-dimensional compression curve which increase with an exponential trend with the creep stress level.IntroductionConstruction on soft soils requires a mandatory soil stabilization work to improve mechanical characteristics of the natural soil. Deep mixing method is a worldwide employed ground improvement method, nevertheless the creep phenomenon hasn’t been yet thoroughly analyzed. Most of the published papers have focused on the analysis of the compressibility and the strength of the soil-binder mixtures without considering the creep phenomenon. However, numerical results (Venda Oliveira et al. 2009) have shown that although settlements that occur during the creep stage (namely creep strains) are less in case of treated columns, they are still important especially due to the high loads applied to the stabilised soil. The few published studies about creep behavior of soil-binder mixtures reveal that the stabilization of an organic soil with cement induces a reduction of creep deformations, which is related to the amount of cement used and that the increase of the organic matter of the soil has a negative impact on soil stabilization, further inducing a slight increase in the creep deformations (Venda Oliveira et al. 2012).As part of the current research the effect of different stress levels on the creep behavior of a soft clayey-silt soil was studied. The binder mixture used to enhance the properties of the soil had a specific composition and quantity. Unconfined compressive strength tests (UCS) and UCS creep tests were carried out at pre-set curing times in order to analyze the creep behavior of the soil-binder mixture. In particular five different creep stress levels were studied to understand its influence on the strength and on the compressibility of the stabilised soil. In addition, considerations about the secondary consolidation index are also presented."

Jan 1, 2014

By Rudolph G. Wuerker

THE Krupp-Renn Process,[1] has been successfully used to treat low-grade iron ores, laterites, titaniferous sands, and other minerals, and before World War I1 25 units were built by the Krupp-Grusonwerk, Magdeburg, Germany. J. J. Howard[2] has shown theoretical advantages of the pyro-metallurgical treatment over conventional approaches; and the process was described by R. Durrer[3].

Jan 1, 1951

By M. J. Mullikin, J. B. Conway

for use in describing combined first- and second-stage creep data. In the above ?o represents the instantaneous strain on loading, ?t the limit of transient creep, ?S the steady-state creep rate, t the time, and ? a constant leading to the exhaustion rate of transient creep. It was noted that this equation was similar in form to that proposed originally2 by McVetty. This type of equation was also suggested by Andrade and Aboav3 in studies of the shear strain of cadmium. Calculation of the constants ?o, ?t, ?, and ?s, in Eq. [ l] is somewhat involved due to the slight complexity of this relationship. In the paper by Garofalo a computer approach based on a least-squares analysis was recommended. Such an approach involves a trial and error solution but when a computer facility is available the difficulties in this calculation are of little consequence. It does mean however that the evaluation of this type of equation would become quite tedious if computer facilities were not available. Some recent studies have identified a fairly straightforward method for calculating the constants in the Garofalo equation. While not leading to a least-squares evaluation the approach is accurate and is recom-

Jan 1, 1967