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By Ross D. Lawrence

Suggestions have been made that the appraisal of mining assets using discounted cash flow techniques should be based solely on proven and probable reserves in reliance upon the widespread international recognition of uniform resource definitions. Following a review of generally accepted valuation principles, a survey of the literature and, most importantly, a review of real transactions in the open market, it is clear that valuators should not be constrained by the growing acceptance of modern mineral resource codes. On the contrary, valuation practitioners should be encouraged to examine all classes of mineralization and, after making due allowance for risk, to utilize all mineral resources as a basis for determining fair market value.

Jan 1, 2002

By D. Park, V. Gall

The three-dimensional finite element technique combined with a progressive failure approach were used to simulate stress distributions in a complete mine section that occur in response to a longwall mining operation. Due to the availability of a Cray supercomputer, a large-scale, three-dimensional, finite-element model was developed for the analysis. The Hoek-Brown failure criterion, which describes a realistic behavior of rock masses, was used for the simulation of progressive failure. A comparison of calculated and monitored stresses in the mine has shown that the model gives a good representation of stresses in the mine structure.

Jan 1, 1992

By Anna Marabini

This paper provides a summary of the studies performed over a period of more than fifteen years by the Italian National Research Council's Mineral Processing Institute in Rome to develop applications for the use of chelating reagents in the flotation of metallic minerals. A description is given of the various phases through which the studied progressed, starting with the combined use of commercial chelating reagents and a neutral oil and then moving on to the synthesis of new long-chain chelate collectors for the flotation of sulphide and oxidized Pb, Zn and Cu minerals. After a series of preliminary tests which confirmed the possibility of floating various metallic minerals with commercial reagents containing chelating groups exerting specific action on given cations, the studies were addressed to the development of a theoretical method of choosing chelating groups that exert selective action on one metallic mineral rather than others. The theoretical approach was based on thermodynamic data concerning the chemical equilibria in solution. The validity of the method has been proved in numerous cases by flotation tests on pure minerals. Subsequently the research was directed towards the design and synthesis of reagents with a mixed aliphatic-aromatic structure containing chelating groups for Pb and Zn and an alcoxyl chain of various length, position and configuration. The flotation results obtained on oxidized and mixed Zn-Pb ores provided interesting pointers for designing the nonpolar portion. The structural criteria identified via these studies were interpreted on the basis of chemical and steric considerations. A description is given of a new synthetic chelate collector which is effective in the selective flotation of Cu minerals from complex sulphides. The fact that this reagents is more selective than xanthate is demonstrated by comparative flotation tests on actual ores.

Jan 1, 1994

By Klaus Böde

Within the national and international strategy of the German based construction company HOCHTIEF, the majority of its business units is equipped with the comprehensive software package ARISTOTELES. This software is a powerful business information system for all accounting and controlling related processes in medium-sized and large construction and other related companies. Due to the complexity of the software, time constraints, and limited financial resources an implementation of this software package requires thorough project management. In this paper the relevant elements of project management are outlined based on practical experiences gained during this international IT - implementation project. Special emphasis is directed to the identification and management of potential risks. In this case particular acknowledgement was given to the multinational nature of the project and modernization of the business. This includes thorough reorganization of the company, significant changes of job requirements, and substantial trainings for its employees. At the same time key success factors like knowledge transfer, adoption of Czech legal requirements, commitment of management, networked thinking, and integrated project planning come into play. The costs for implementation had to be carefully evaluated because the software was implemented in a country with a considerably low cost I price level. All these impacts to the business had to be managed within the scope of transformation of business and political environment from socialist to market driven economy.

Jan 1, 2002

By Yongsik Jeong, Kwangmin Kim

Most tailings storage facility (TSF) failures occur in active, upstream-type TSFs, often due to extreme and unexpected weather conditions—specifically, heavy rainfall and strong winds. This case study of a TSF in southern Arizona examines the use of the optimum safe beach distance (Doptimal, the optimum distance between the crest and decant pond) as a tool for monitoring geotechnical stability and reducing catastrophic failures. A digital model of the TSF was used to determine the critical beach distance (Dcritical) under normal weather conditions, and Doptimal was then determined by adding incremental distances to account for the effects of heavy rainfall (Drainfall) and strong winds (Dwind). To overcome accessibility issues, a drone was used to map the TSF geometry and create a digital model. This model served as the basis for conducting a coupled stress-seepage, finite-element (FEM) analysis with a safety factor of 2.0 to assess geotechnical stability (Dcritical). The safe beach distance increments were determined using the PMP (probable maximum precipitation) and possible maximum wind speed. Based on this analysis, the optimal safe beach distance at the study site was identified as 202.2 m. Since the current beach distance (371 m) exceeds this value, the TSF was considered to be stable and satisfied the design safety factor of 2.0. However, this distance should be reassessed periodically to account for changes in the TSF geometry and other conditions. Furthermore, it applies only TSFs that are well-managed and feature a smooth, non-undulating beach surface with a consistent slope.

By Robert Dunne, John Angove

The physical properties of an ore body require determination for virtually all mining projects, new and existing. The extent and regularity of such determinations being subject to the size and homogeneity of the orebody. Such properties have an impact at the design stage of new plants, with respect to equipment specification, and thus effects capital costs; and also impacts on the operating costs of new and existing plants, with respect to power consumption, production levels and part replacements. All of these can severely alter the bottom line and can be the determining factor in the economic viability of many projects. This paper examines some of the most common properties that are measured, the procedures utilised in determining these properties, and their variability under conditions of reproducibil­ity, and to a lesser extent repeatability. The properties looked at were Impact Crushing Work Index, Abrasion Index, Bond Rod Mill Work Index and Bond Ball Mill Work Index. A number of testing laboratories throughout Australia and the US were utilised in the survey. The results showed up some interesting and important features of the procedures used, all of which have become accepted industry standards, and which had varying effects on the final result. Tests such as the rod and ball mill indices would appear to have reasonably robust procedures which allowed for the determinations of the respective index without the introduction of significant variations, although there were indications that variations could occur. The other tests gave a sufficiently different picture to be able to suggest that an argument could be made for a more intensive investigation to be undertaken, with the possible outcome that a modified test procedure or an alternative test is required.

Jan 1, 1997

By E. Varouchakis

Spartan Spatial Random Fields (SSRF?s) provide a new geostatistical framework (Hristopulos, 2003) with applications targeting environmental risk assessment and natural resources estimation. SSRF?s have the ability to incorporate constraints based on physical laws in the statistical description and have proved to be computationally fast in the analysis of synthetic data sets. This paper presents an application of a specific SSRF model and a new local-error spatial estimator (Hristopulos, 2005) in the mapping of environmental pollutants using a real data set. A detailed comparison of the local SSRF estimator with a classical kriging method is presented. It is shown that the SSRF approach provides a competitive alternative for spatial estimation.

Jan 1, 2005

By Y. Tao

The professional status and characteristics of mineral processing were discussed along with the importance of innovative personnel training for mineral processing engineering. Reform ideas and models for the mineral processing engineering education system were suggested to formulate and implement new training program for the mineral processing specialty. It is suggested to strengthen engineering training practices, cultivate the culture of innovation, improve innovative education system and insisting on the combination of teaching with production and scientific research as the important means of training innovative talents for mineral processing engineering.

Jan 1, 2010

By Gunnar Nord

Shifting ground conditions when tunnelling often call for different methods of attacking the tunnel face. In order to overcome problems with local unstable soft ground in a hard rock tunnelling project the Boodex method offers a cost effective alternative. Boodex and variants of it is a combination of two well-known techniques, drilling with Boomer rig using Odex gear. It will give a steel lined hole ready for grouting and the steel pipe has a load bearing capacity that means that a spiling effect is achieved. In this paper the method and some applications will be described with possibilities and limitations.

Jan 1, 2003

By Leon J. Jacobs, Kyle R. Ott

This paper discusses design and construction aspects of the tunnel, shaft and station for the Weehawken Tunnel and Bergen line Avenue Station. The project consists of a 1,269 m (4,156 ft) long existing railroad tunnel, which will be enlarged and equipped with a two-track light rail system. The project also includes construction of a deep underground station, with a large shaft connecting the surface station to the below ground station for access and ventilation purposes. Vibration and noise from blasting is a critical community issue and blasting adjacent to two 230-kV duct banks located in the tunnel invert required special blasting procedures.

Jan 1, 2003

By James E. Kolesar

An essential prerequisite to expanding the application of longwall mining techniques in the United States is the development of a better understanding of the mechanics of rock mass deformation near the mined seam, in the inter- burden and at the surface. The results of studies of this type will provide a basis for the development of empirical and/or numerical modeling techniques to predict the rock mass response to mining both near and far from the mined seam. This will lead to improved gate and panel design, resulting in maximum recovery, increased productivity, as well as provide a mechanism for assessing likely surface effects induced by long- wall mining. Presented here is the instrument plan to be used at Kitt Mine No. 1 in the study of rock mass response to two adjacent longwall panels.

Jan 1, 1982

By J. L. Schroder, William J. Halvorsen, Wiliam W. Lyons, Kent C. Ware, Sheridan A. Glen, Donald C. Simpsom

The prospects for near-term growth in coal demand are exceptional: the federal government recently targeted 141 oil- and gas-fired generating units for mandatory conversion to coal; coal-to-synfuel developments are proceeding at a steady clip, with construction of a $1.2 billion gasification plant to begin this year in Beulah, ND; uncertainty over nuclear power and stratospheric oil prices enhance the steam coal market; the export market is ripening; and an influential new political force (the Senate Coal Caucus and Congressional Coal Group) is flexing its muscles on Capitol Hill. But the rosy picture is muddled by signals, often conflicting, sent out by federal agencies. Although EPA can be credited with relaxing its grip on the Clean Air Act, its sulfur dioxide control strategy is still often at odds with the Administration's call for domestic energy (coal) development. B. R. Brown, president of Consolidation Coal Co., sums up the situation: "Every mule is pulling in a different direction." Often in the midst of the fray is the small operator who has been hardest hit by the stagnation of coal markets. Layoffs, shortened work weeks, and mine closures were rampant in the eastern and midwestern coal fields, even among large producers. The longstanding boom in western coal was tempered during 1979 by a noticeable slowdown in announcements of new mine construction. The prognosis: Eastern coal will remain in the doldrums for quite a while to come as it works off some 90 Mt of overcapacity. Midwestern coal will fare no better due to the regulatory-influenced appetite of midwestern utilities for low-sulfur western coal. This displacement should ease, though, as new power plants equipped to burn high-sulfur coal come on line in the years ahead. In the West, the National Coal Association projects production to increase a healthy- 10% this year, although mine-to-market transportation looms as the single largest stumbling block to marketing efforts. Fatalities Up 40% in 1979 The National Coal Association estimated total coal production in 1979 at 671 Mt, an increase of 13% over 1978. Of this total, the East and Mid-west accounted for 476 Mt (71%) and the West produced 195 Mt (29%). With the consistent rise in western production playing against flat outputs in the East and Midwest, underground mining's share of total production continues to slip and is expected to account for only 38-39% in 1980. Incidence of deaths and injuries at US coal mines soared in 1979 over 1978 rates. MSHA figures (still subject to final adjustments) reveal a death rate of 0.07 per 200 000 man-hours, up 40% over 1978's 0.05 figure. MSHA chief Bob Lagather attributed the death incidence to the large number of new coal mines put on line in 1978, which he estimated at between 350 and 400. Nonfatal injuries rose to 8.48 per 200 000 man-hours, up about 15% from a 1978 rate of 7.35. In absolute numbers, MSHA counted 144 fatalities and 18 111 lost-day injuries during the 1979 calendar year. The 144 coal mining deaths in 1979 is the highest number of coal fatalities at US mines since 1975.

Jan 5, 1980

By Dan Plazak

Discussion by Dan Plazak The authors are to be congratulated for presenting a simple and practical tool for quick estimates of ground water flow rates. At the risk of detracting from the simplicity of the method, I would like to suggest a slight refinement to the equation as presented. As the authors noted, the Jacob-Lohman equation (1952) assumes confined-aquifer conditions. To use confined-aquifer equations in water-table aquifers, Jacob (1963) presented a correction to convert water-table aquifer drawdowns [Ahw] to equivalent confined aquifer drawdowns [Ah,: 2] [Ah Ah = Ah - w(1) Cw 2H where: Ah, = Drawdown in confined aquifer: Ahw = Drawdown in water-table aquifer and H = Original saturated thickness of aquifer] Substituting the above in equation ( I) of Hanna. Azrag and Atkinson [4nT Ah - 2H ) Qj2.25 T t(2) 1 nr2 S W] Since the above expression predicts lower pump rates, it causes the Jacob-Lohman equation to agree more closely with appropriate analytical and numerical models. Figure 1, adapted from Fig. 5 of Hanna. Azrag and Atkinson, illustrates the closer agreement of the modified equation to their numerical model, as reflected in Qm/QJL ratios closer to unity. The agreement improves particularly as drawdown [Ah] becomes large in relation to aquifer thickness H. An additional advantage of the modified equation is that Hanna, Azrag and Atkinson's correction factor C is much more stable as pit depth increases. Assuming, as did Hanna, Azrag and Atkinson, that their numerical model is an accurate predictor, it is clear that the modification incorporated in equation (2) improves the accuracy of preliminary estimates of ground water flow to a pit.[ ] References Jacob, C.E and Lohman. S. W.. 1952, "Nonsteady flow to a well of constant drawdown in an extensive aquifer." Transactions, American Geophysical Union. Vol, 33, No. 4. pp. 559-569. Jacob. C. E.. 1963, `Determining the permeability of water-table aquifers,' USGS Water-Supply Paper 1536-1, pp. 245-271

Jan 1, 1995

By A. Cordonnier, Ch. Obry, R. Evrard

In spite of the large annual expenditures and the vast field of activity covered, it cannot be said that many new grinding machines have actually come to light and modified the existing market for more than half a century. Manufacturers have mainly made advances in increasing machine sizes, efficiency and reliability, and in machine automation. The relatively recent emergence of roller presses is the only exception to this homogenisation of machine ranges. The development of roller presses in pregrinding has shown the advantages of compression grinding over the ball mill from the power consumption point of view. But classical roller presses still have maintenance problems due to the high grinding pressure. The FCB Research Centre has carried out much work in this field and in particular has studied the advantages of this process in pregrinding and integral grinding. These researches lead to the development of two new compression grinding machines. The first one, HOROMILL®, presented for the first time on the 8th European symposium on comminution at Stockholm, finds its application in the field of fine to very fine grinding in dry process. The second one, RHODAX®, presented at INTERMAT in Paris, covers the field of secondary and tertiary crushing and the first stage of grinding for most of the minerals in dry or wet process. Its high reduction factor permits to do with only one machine the work realised today with two or three crushing/milling stages. These two complementary machines offer a wide range of combination summarised on [Figure 1].

Jan 1, 1995

By H. L. Bourne

This paper describes six basic stages between perception and production for a new sand and gravel deposit. Sand and gravel, like many of our natural resources, is taken for granted. It is assumed by John Q. Public that because sand and gravel is ubiquitous that it is available whenever and wherever needed - so long as it does not have to be mined in his neighborhood. This idea illustrates one of the enigmas of the industry, the fact that sand and gravel is abundant; however, its availability is another matter. Another problem is that this resource falls in the category of high volume, low profit materials; therefore, transportation costs are critical. Transportation roughly doubles the cost of these materials. It is not difficult to find sand and gravel, at least in Michigan. The problem is to locate a new source close to a market, near an adequate transport route (usually a highway) and in an area which will allow mining.

Jan 1, 1970

By Harold L. Kike

Until recently sulphur uses were so broadly based that economists used sulphur consumption to measure industrial activity. However, sulphur use patterns are changing and the manufacture of phosphate fertilizers presently accounts for approximately 65% of the world's sulphur consumption compared with only 25% in 1960. This has encouraged the development of new agricultural and industrial uses for sulphur. Major emphasis has been placed on its use as a fertilizer and in the manufacture of paving materials, specialty concretes and coatings. Some of these uses could have a significant impact on future sulphur usage.

Jan 1, 1986

By E. O. Dearden

In the ten years since its discovery the Lac Tio ilmenite-hematite deposit has become one of the world's largest sources of titanium ore. The deposit lies 25 miles north Havre St, Pierre, a fishing village on the north shore of the St. Lawrence River some 400 miles northeast of Quebec City. In 1941, J, A, Retty made a reconnaissance survey of the region for the Quebec Department of Mines. His results, published in 1942 and 1944, described a number of small ilmenite occurrences on the shores of four lakes within the area. Several of these were staked by Montreal and Toronto interests, Two of the claim groups were later optioned by Kennco Explorations, (Canada) Ltd, and a third by the New Jersey Zinc Company, During a detailed exploration program in 1946, Kennco geologists discovered eight ilmenite deposits, one of which was Lac Tio, the largest known body of ilmenite-hematite ore in the world. Quebec Iron and Titanium Corporation owned two-thirds by Kennecott and one-third by The New Jersey Zinc Company as organized in 1948 to equip and operate the new mining property. A railroad 27 miles in length was built (completed in 1950) to transport the ore to the St. Lawrence River at Havre St. Pierre, An electric furnace treatment plant, yielding a high purity iron and slag containing 70 m 75 percent Ti02, to process the ore was built at Sorel, Quebec, 550 miles up the river from Havre St. Pierre.

Jan 1, 1958

By Vanessa M. Torres, Lafayette C. L. Freitas, Evandeo C. Silva

This paper shows two applications of artificial intelligence models in process development. In the first application, a heuristic fuzzy correlation can predict flotation behavior in bench scale based on feed characteristics for a high variability copper ore, as well as to predict plant performance for a feasibility project evaluation, minimizing its risk. The second case study shows the use of neural networks to model the iron ore sintering, correlating ore characteristics and operational parameters with sinter properties. With this application, CVRD aims to establish a new step on iron ore product evaluation and customer support.

Jan 1, 1998

By Fritz Kleiner, Walter Meintrup

On Nov. 4, 1981 A/S Sydvaranger's 1-kt/h (1,100-stph) wet-process, iron ore ball mill completed its first four months of uninterrupted, full-load operation in Kirkenes, Norway. This 6.5-m-diam (21-ft-diam) mill is driven by a gearless ring or wraparound 8.1-MW (10,860-hp) motor at 13.1 rpm-a first of a kind in this segment of industry. This article examines reasons for selecting this type of drive over more conventional schemes, lists specific advantages of such large mills, and describes the installation in Norway. History For almost a decade, good operating experiences have been gained with 28 gearless ring motor drives in the cement industry, driving 2.5 to 4-m-diam (8.2 to 13-ft-diam) tube mills with drive powers ranging from about 3-4 MW (4,000 - 8,000 hp). Why then did the mineral ore processing industry hesitate until 1980 to adopt this successful concept for similar applications on ball, semiautogenous, and autogenous mills? There are a number of good reasons in the eyes of conservative mill builders and operators, the most commonly cited ones are: • No operating experience in this segment of specialized industry. • More severe environmental conditions in the wet ore grinding process. • An indifferent attitude of mill builders and electric motor manufacturers towards new drive technologies. • Limited confidence in solid-state power supply systems, such as frequency converters of the required size. There have been and still are numerous problems associated with low-speed geared mill drives of any kind, especially with individual motor/gear sizes approaching or exceeding about 4 MW (5,360 hp). Every mill builder knows about them, but operators learn to accept them as inevitable. The Decision to Change Three things combined to break this technological stalemate: the courage and progressive spirit of one major iron ore processor in Scandinavia, the cooperation of three experienced manufacturers, and an unusual application problem that could not be solved by any conventional approach. The last factor was surely the decisive one, but the first one does not come as a surprise either. The Swedes near Kiruna and the Norwegians around Kirkenes are experienced ore miners and processors, and much credit goes to them for technological breakthroughs in the industry. At A/S Sydvaranger in Kirkenes, above the Polar circle at about the latitude of Alaska's northern tip, the existing grinding facilities, with a total of 14 100 to 240-t/h (110 to 264-stph) ball mills, can not be expanded. Nevertheless, to increase mill throughput, only installing a larger mill in place of an existing smaller one was a practical alternative. For this replacement, the owners set requirements that seemed impossible to meet: • The old 100-t/h (110-stph) ball mill should be replaced with a new ball mill with 10 times the rated throughput, without significantly impairing the operation of the remaining mills, and without significantly changing the mill building. • The new mill should have a variable-speed drive to ultimately optimize the grinding process by means of a closed-loop process¬computer-controlled grinding cycle, and to minimize the specific energy consumption. • Availability, efficiency, and life expectancy of all new components must be higher than those being replaced. • Inrush-current and harmonic loads on the rather weak electric supply line must be minimized to ensure safe plant operation. All old ball mills at A/S Sydvaranger are the geared type, using single synchronous and wound-rotor, slow-speed motors with ring-and-pinion gears. Operators are familiar with the limitations and problems associated with such drives, and they are aware that the following items become major concerns when drive powers are drastically increased: • Gears are subject to wear and tear, require frequent maintenance, and eventual replacement of major parts. • Gears are sensitive to misalignment, overload, and thermal distortion, limiting their useful life. • On dual or quadruple drives, load-sharing and torque oscillations between motors can be a major reason for concern. • At these speeds, ring-and-pinion gears reach their torque transmission capabilities altogether at around 4 MW (5,360 hp) per motor/pinion. To obtain the desired variable-speed performance of the new drive, the only practical and economical conventional solution would have been a frequency-controlled, low- or medium-speed dual motor drive with about 8 MW (10,720 hp) of power. This, however, was not feasible because of limited floor space. Therefore, bids were solicited for the alternative drive method, the gearless ring motor. General Considerations Why are such large mills considered? After all, one could avoid all the problems by simply staying with smaller mill unit sizes. Under competitive pressures of free markets, however, grinding efficiencies and specific energy consumption become key factors in selecting new equipment. Specific energy consumption of ball mills decreases with increas-

Jan 9, 1982

By Michael M. Carroll, Zhu-ping Duan, Han-ping Chin

INTRODUCTION The inelastic stress-strain behavior of rocks has urged engineers to seek for the possible application of plasticity to engineering pro¬jects such as tunnels, oil wells, dams, etc. for a long time. Early efforts in this direction have tentatively used the classical theories to solve some axisymmetric problems, in which the rocks were treated as perfectly plastic and nonfrictional materials (Talobre, J. A., 1957). Meanwhile, one of the fundamental assumptions is that the volume strain of elastoplastic material is purely elastic. Drucker and Prager (1952) developed a perfectly plastic and frictional model with a generalized form of Mohr-Coulomb law, which serves as both failure criterion and yield criterion. Although the associated flow rule gives unacceptably large dilatancy, this model is a very important step to deal with the frictional behavior of geological materials. As a further step, Roscoe et al (1963) and Schofield and Wroth (1968) proposed a Cam-clay model, which accounts for the yielding before the material reaches a failure envelope and reflects the plastic volume strain as a strain hardening factor, and the open end of the Drucker-Prager envelope is capped by a family of yield surfaces, the envelope is made conforming with crit¬ical void ratio line. The proposed shapes of the cap have been based on experimental data and on convenience of mathematical descrip¬tions. Drucker, Gibson and Henkel (1957) introduced a spherical cap for soils, while in Cam-clay model the cap is semi-logarithmic yield function derived from the result of triaxial tests. DiMaggio and Sandler (1971) proposed an elliptical model for sand, in which the hardening function depends exponentially on plastic strain. Sandler et al (1976) used a plane cap model to express the behavior of a wide range of geological materials of which the nonlinear hysteretic nature is significant. Mizuno and Chen (1982) illustrated the physical mean¬ing of cap models and their adaption to finite element calculation. In recent years, Carroll et al (1972, 1980) have studied the com¬paction of porous materials under hydrostatic pressure and discussed the mechanism of the nonlinear response thoroughly. Analytical and numerical analysis of the hollow sphere model by Curran and Carroll (1979) predicted an initial yielding surface, dependent on the initial porosity, and showed a strong coupling between hydrostatic and deviatoric effects. All these main features from the abovementioned theoretical research are visualized by the experimental data on Boise sandstone (1984). The combination of such previous work would be logically the construction of a plasticity model for porous rocks which, following the tradition of assigning the name of birthplace to a special model, is called Cal-Rock model (Carrol, M. M., 1984). The results of triaxial tests along different loading paths reveal the compaction characteristics for deviatoric and hydrostatic stress separately. the fitting of the nonlinear stress-strain curves leads to a construction of yield surfaces. Moreover, an uniaxial strain test gives the strength envelope which is the critical state line. The whole model is composed in the frame of elasticity theory. The concept and representation of plasticity used here are in the spirit of Naghdi¬Casey theory (Casey and Naghdi, 1984 and 1984, Naghdi and Trapp, 1975). In order to find the way of using such a plasticity model in engineering problems, the stress field in a thick-walled cylinder of porous material is calculated. This is an axisymmetrical problem with plane strain, which is an idealization of oil well in an infinite medium. Because the constitutive relation is highly nonlinear, a numerical method has been utilized to obtain the solution. CONSTRUCTION OF CAL-ROCK MODEL (1). Elastic-plastic constitutive equations The basic assumption is that the yield surface in stress space depends on one parameter, namely the plastic volume strain, as the data on Boise sandstone suggested. Starting from this point, the theory formulated in stress space and in strain space by Naghdi and his co-workers (1975, 1981) can be simplified. The simplified yield function is

Jan 1, 1986