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By Janusz S. Laskowski

Studies carried out over the last 10 years reveal that precipitating particles which may appear in alkaline solutions of long-chain amines and in acidic solutions of fatty acids exhibit clear isoelectric points around pH 10.6-1 1 for dodecylamine and around pH 2.5-3 for fatty acids. These colloidal species can accumulate at solid/liquid and liquid/gas interfaces and affect flotation. While the precipitate in solutions of fatty acids apparently can chemically interact with the mineral surfaces and is flotation-active if sufficiently long conditioning time is available, the cationic flotation of quartz in alkaline solutions is depressed by the colloidal precipitate. The experimental data available in literature on the adsorption, electrokinetic, contact angle and surface forces measurements in the solutions of the weak electrolyte collectors are analyzed and the role played by the precipitate is discussed. It is shown that these concepts allow for an explanation of the selective flotation of sylvite from halite with long-chain amines in potash ore flotation.

Jan 1, 1999

By J. A. Matar

Mineralization features at the Bajo La Alumbrera porphyry copper-gold deposit are discussed as they affect gold leaching and copper flotation behavior. Alteration-mineralization geological blocks are assigned in the zoned body, and each required its own geostatistical model. They extend horizontally outward from potassic to the phyllic-propylitic boundary, vertically from surface down to 300 meters, and include oxide, secondary enriched, and hypogene mineralization. Copper and gold values are calculated geostatistically from assays and all available geologic-mineralogic information. Reserves are classified for each geologic block and for each open-pit bench into leach or float ore according to metal grades, geologic characteristics, and supergene-hypogene relations. Finally ore extraction behaviour is briefly described, grouping gold and copper reserves into metallurgical families.

Jan 1, 1986

By Jack V. Hill

A unique type of grinding mill liner has been developed by Waagner-Biro A.G. of Austria. This liner system, termed an angular spiral lining (.ESL), was, successfully tested by Magma Copper Company's San Manuel concentrator in both their 10 Ft x 10 Ft (3.05m x 3.05m) and 12 Ft, 6 In x 14 Ft (3.81m x 4.27m) grate discharge wet grinding ball mills. Magma Copper's savings in power and grinding balls justified conversion of more than half of their twenty-six ball mills to the ESL system.1,2 The ASL system was provided by the Capitol Castings Division of Midland Ross Corporation, the exclusive licensee for such conversions. Capitol Castings proposed the following as expected benefits from installation of an ASL system in an 18 Ft x 21 Ft (5.49m x 6.40m) overflow discharge wet grinding ball mill at the Pinto Valley Operation of Cities Service Company: "(a) Reduction of power consumption per ton of ore milled = 12%, (b) Increased throughput = 6%, (c) Reduction of ball consumption = 6%."

Jan 1, 1982

By M. Z. Emad, M. U. Khan

"Coal mines opting for longwall mining or its variations rely on the main and tail gates for production. Stability of these entries or crosscuts is crucial in coal mining operations. Roof or strata failure can be fatal, may lead to property loss and delay in production. Failure of the gates depends upon many factors including the mining method, panel dimensions, pillar width, mine depth, caving rate, dimensions of gates and roof strength properties. In Pakistan coal is mined through a variation of longwall mining method with almost no mechanization while using timber as a primary support. Timber support as chock is very useful in coal mines especially in overhanging face. Similarly gate entries and coal faces are supported by chock supports throughout their length. In this paper the stability of the longwall gate is assessed for a typical coal mine in Pakistan by using finite element code. Numerical modelling considerations for gate entries are discussed. A model parametric study is performed for key factors. The results showed that the existing mining practice is not suitable and there is a need to review the mining approach. INTRODUCTION Main and tail gate entries leading to longwall mining panel play a crucial role in production cycle. Failure of any of these may lead to loss of life, property and production delays. The stability of gate entries depends primarily on the nature of loading and stresses incurred. It is relatively easier to assess the ground response to production for common longwall mining panel. In thin-seam coal mines the gate entries are generally supported throughout their length by timber made chock supports. The tailgates receive huge deformations and stresses during the mining and backfilling cycle. The chock supports are required to take care of rock falls leading to blockage of entries causing production delays and loss of capital. A number of supports are available for supporting the gate entries (Hoek and Brown 1980; Brady and Brown 1985). The support system can be selected based on load-deformation characteristics including the yielding behavior, pre- and post-yielding behavior (Barczak, 2003). The principal of support selection is that the support characteristics must match the ground response in order to maintain the gate entries (Mucho, et al., 1999). It has been observed that thin-seam mining (<1 m) is very challenging and it is necessary to develop an understanding of ground mechanics before the selection of an efficient support system Dolinar (2003). The chock supports have been tested for load-deformation characteristics in the laboratory (Barczak 2003). But the ground and support interaction, response and loads must be assessed for individual site. This can be accomplished by in-situ testing and observations at few locations. The generated data is generally insufficient for complete understanding. Numerical models can combine the data generated in the laboratory and on-site to fulfill the requirements."

Jan 1, 2017

By J. M. Wempen

Booster fans in underground coal mines are often located using the concept of a neutral point. Normally, intake airways are maintained at higher absolute pressure than return airways; therefore, air leaks from intake to return. By adding a significant pressure force to a region of a ventilation system, booster fans installed in a return airway can increase the pressure in the return so that air leaks from return to intake. This is commonly referred to as recirculation. The neutral point occurs at the location in the system where the pressure difference between [ ] the intake and the return airway is zero. At this point, there is no leakage or recirculation. Ideally, placing a booster fan near the neutral point minimizes leakage and recirculation. However, in practice, the position of the neutral point is not static and it changes as the ventilation system parameters change. Booster fans have the potential to increase the capacity and efficiency of coal mine ventilation systems. However, these fans add a significant pressure source to ventilation systems and can create areas where the pressure in the intake is less than the pressure in the return causing recirculation. In systems with multiple booster fans, there may be multiple recirculation paths and, as the capacity of these fans increases, recirculation is more likely to occur.

Jan 1, 2012

By S. R. Clark

"INTRODUCTION Of all the natural resources being taxed by the needs of the modern world, perhaps the most important is the continually expanding demand for water resources. As water becomes scarcer, and increasingly important, new technologies are needed to find innovative ways to preserve this precious resource. In Chile, for example, the mining industry is investing billions of dollars to build desalination plants and pipelines; bringing ocean water as far as 200 kilometers inland to meet their demand and maintain operations. It is a full-blown crisis for that nation and a top priority for their government and economy. It has been reported that world water consumption will increase by 40 percent in the next 10 years, representing nearly exponential growth. In the U.S., as more and more communities continue to be built, more drain on the current water infrastructure is created. For 25 percent of people and operations that rely on water from aquifers, this source is being consumed at a rate that will create significant problems meeting the demand in as few as two generations.1 A PROACTIVE APPROACH When it comes to controlling dust at your operation, whether a landfill, a transfer station, a haul road or another ancillary area, what are the options? We know watering is not the answer, but at the same time, we need to prevent dust from flying to ensure a safe environment and keep our skies clear of pollution, for both regulatory requirements and neighbors. Creating a Dust Mitigation Program instead of looking to buy the first dust control product off the shelf is a first step to conserve water and, at the same time, maintain the operational demands and environmental standards for a given site. The program concept is straightforward enough. However, the process of effectively constructing and executing a program is quite involved. When undertaking a program, each manager needs to work with their team and their partners/vendors in analyzing the following elements: 1. Site Expectations—It is important to understand how to balance your internal standards with your regulatory requirements, as well as how to keep your neighbors satisfied. 2. Site Aggregate—Variations in native soil, such as clay content or gravel levels, greatly affect the approach that will yield the highest results. 3. Climate—Relative humidity and seasonal variations are critical to achieving predictable results through product choice, application frequency and timing. 4. Daily Traffic—The type and frequency of traffic is an essential variable for site management. 5. Environmental Responsibilities—If you have additional, specifically defined responsibilities, the approach to your site may vary. 6. Budget—While efficiency is the goal of any program, some sites will have more stringent restrictions than others. 7. Current Usage Rates—Document and understand where you’re starting from, both with water, supporting products, and maintenance so that effective measurement of results is possible."

Jan 1, 2018

By E. F. Klein, R. L. Eacret

Introduction In contrast to the general type of crushing mechanism in which the crushing surfaces alternately approach and withdraw from each other, described earlier in this section, and continuous-pressure break¬ers such as rolls and roller mills that will be described in a later chapter, impact crushers load by striking pieces of rock while in free fall and hurling them at high speed against stationary surfaces. Because the impact crusher depends for its effectiveness upon high velocity, wear is greater than in the slower-moving jaw and cone¬type wear parts, and for this reason its use is strictly limited to rela¬tively soft, friable, and sticky rocks that are characteristic of many nonmetallic mineral deposits. A few of these are phosphates, lime¬stone, barite, clay, asbestos rock, and coal. However, several examples of their use on soft lead-zinc and precious metal ores have been known. Although the use of impact crushers is expanding today into the range of ores containing as much as 15-18% silica, Taggart16 set the practical limit at 5%, and in the 1940s and 1950s several installa¬tions in the US and western Europe exceeded the limits of economical maintenance and were quickly superseded by the slower-moving, con¬ventional crushers. A rock that tends to be plastic or bouncy in a jaw or gyratory crusher when the force is applied slowly to reach ultimate strength, may become brittle with rapid loading and thus increase the effective¬ness of the applied forces. For this reason it is to be expected that as the quality of hammers, grates, plates, and cages improves with advances in steel technology, the use of high-speed crushers of this kind will increase. Terminology Modern usage differentiates between the impactor and the hammer mill, the former relying primarily on the impact of hammers (fixed or free-swinging) and secondarily upon pieces striking one another or steel surfaces; the hammer mill relies on both the centrifugal impact force of free-swinging hammers and the attrition and shear action between these hammers and well-placed grates suspended at the bot¬tom just below the hammer circle. The hammer mill, because of its grate discharge, restricts discharge of oversize rock to the grate open¬ing, while at the same time providing a trap for removal of tramp iron or other uncrushables. The impactor discharges free, so generally works with a screen to control product sizes. The question of terminology, impactor vs, hammer mill, creates difficulties because the similarities appear to outweigh the differences by far; if one were to list the similarities in order of importance and then the differences, he would be forced to conclude that they would best be dealt with as a single kind of crusher. Taggart16 gave it four names and added "as it is variously known," but it must be remembered that in 1945 the machine was nearly exclusively of the flailing-hammer type, while today the fixed-hammer rotor is also com¬mon. In this chapter the terms impactor and hammer mill will be used where they seem to apply. It is perhaps unfortunate that this terminology is being confused with rock breaking at the mine, usually with hand-held tools, e.g., the article "High-Energy Impact Rockbreaking" by Grantmyre and Hawkes, CIM Bulletin, August 1975. General Description Impact breakers, impact crushers, and hammer mills accomplish material breaking and reduction primarily through impact action of the material with fixed or free-swinging hammers revolving about a central rotor. The material to be crushed enters through an opening at the top or top side known as the "feed opening" or "hopper opening" and falls into the path of rotation (hammer circle) of the hammers. Initial breakage is accomplished in midair by collision of the dropping feed material with high-speed hammers. The second stage of breakage occurs when the pieces hit plates or breaker bars which line the crusher boxlike frame. Hammer mills rely further on a shearing and attrition action between free-swinging hammers and grid bars or grates at the crusher bottom which restrict discharge of oversize material until it is broken sufficiently to pass through the grid opening. The term hammer is used in reference to the piece which strikes the material, whether it is fixed on the rotor or free-swinging. It

Jan 1, 1985

By S. Veeramasuneni

The sign of the surface charge for alkali halides in their saturated brines has been established from non equilibrium electrophoresis measurements and on this basis the flotation response of alkali halides was explained based on the adsorption of oppositely charged collector colloids by heterocoagulation. These surface charge results for alkali halides are generally as expected from simplified lattice ion hydration theory with some exceptions, specifically LiF, KCI, NaCl, KBr, RbBr, KI, and Rbl .The presence of natural oxygen defect states in the crystal lattice and the inaccuracies involved in the gaseous ion hydration free energy values used appear, in past, to be responsible for these deviations. The presence of natural oxygen defect states in KCI, KBr, RbBr, and Rbl as characterized by UV Nis absorption, was found to account for their anomalous surface charge. Further, other positively charged alkali halides, LiF, NaCl and KI, were found to be free of oxygen defect states. Nevertheless, oxygen defects can be created in these alkali halides to make them negatively charged and has been demonstrated for NaCl. Such negatively charged NaCl can be readily floated with positively charged amine collector colloids thus confirming the surface charge/collector colloid adsorption theory.

Jan 1, 1996

By M. Polat

Variations in flotation rate by particle size and specific gravity have been investigated for three different bituminous coals. The flotation rates for various components were determined by separating the products of bulk flotation into size-specific gravity fractions. The effects of feed size and reagent addition on the flotation response of individual size-specific gravity fractions were evaluated.

Jan 1, 1994

By Robert A. Jankowski, George E. Niewiadomski

INTRODUCTION The utilization of longwall mining technology in the United States has steadily increased since the first longwall plow system was installed in 1952. At the errs of FY 1992, some 76 coal mines were employing longwall mining systems for coal extraction, and approximately 78 shearer and 3 plow faces are operating nationwide at any given time. Although the number of operating longwalls has remained relatively constant over the last five years, longwall production levels have increased significantly during this period. During the same timeframe, the number of continuous miner sections has decreased by 13 pct., from approximately 1438 in FY 1988 to less than 1250 in FY 1992. According to Mine Safety and Health Administration (MSHA) data, the average production of longwall sections increased from approximately 2400 tons per shift (tps) in FY 1988 to more than 3100 tps FY 1992. In fact, the average production has more than tripled since 1978, when it was only 850 tps. Approximately 25 pct. of operating longwalls are capable of producing in excess of 4000 tps. Longwall production currently accounts for nearly 36 percent of U.S. underground coal production, compared to 4 pct. in 1978. These improvements are attributed to improved longwall equipment and increased availability, larger longwall panels and automation. While longwalls are highly productive and offer other advantages, operations employing this method of mining continue to experience dust compliance problems more frequently than other mining system. Although dust levels have remained relatively unchanged over the past five years, averaging 1.6 mg/m3 and 1.9 mg/m3 based on results of operator and inspector sampling, respectively, during FY 1992, approximately 25 pct. of the operating longwalls were in noncompliance during any given bimonthly sampling cycle. Although modest gains in longwall dust control technology have been made, these have been overshadowed by significant increases in production rates. As more coal is mined, more dust is generated (Figure 1). Therefore, the increase in longwall productivity has meant that far more dust is being produced which must be controlled. [ ] In view of the current compliance record, any efforts to further increase longwall output, as has been forecasted, must be accompanied by: (1) the reduction of dust levels at existing operations through the proper installation and maintenance of suitable engineering dust controls; and (2) the advancement of dust control technology for today&apos;s and future longwalls that will enable all face personnel o work in an environment that is free of excessive levels of respirable coal mine dust. MSHA&apos;S RESPIRABLE DUST CONTROL PROGRAM Since 1972, federal regulations have required each coal mine operator to continuously maintain the average concentration of respirable dust in the mine atmosphere during each shift in the active workings at or below 2.0 mg/m3 through the application of environmental dust control methods. The regulations provide for further reduction in the dust standard whenever the

Jan 1, 1993

By J. Grubb

"The undertakings described in the paper titled “Study on correlation of quantified coal rank with self-heating temperature” by Wang and Luo in the November 2015 issue of Mining Engineering (Wang and Luo, 2015) are mathematically sustainable and an acceptable extension of work performed by Smith and Lazzara (1987) for the U.S. Bureau of Mines. The paper is not an accurate explanation of the currently accepted leading practice for determining the propensity of a coal seam for spontaneous combustion. The paper could lead a practitioner to an oversimplified conclusion on how to determine the propensity of a coal seam to spontaneously combust.The spontaneous combustion of coal is a complex and not fully understood reaction. What is understood is that many more factors other than selfheating temperature (SHT) and coal rank are required to sufficiently evaluate the risk of spontaneous combustion in a particular coal seam. A superficial assessment can lead to an improper response to the risk. Some statements on the next steps through an appropriate literature search would have made the authors’ conclusions more credible.The SponCom 2.0 software, updated by the National Institute for Occupational Health and Safety (NIOSH) in 2011, provides a path for evaluating the susceptibility of a coal seam to spontaneous combustion. In addition to proximate and ultimate analyses to establish coal rank, and therefore an estimate of SHT, the program includes the history of heatings, friability, seam thickness, overburden thickness, rider seam presence, pyrite presence, face and butt cleat densities, geothermal source presence and other geological features in the assessment. Mining conditions including floor heave, rib sloughage and rate of advance are also assessed to conclude a propensity for spontaneous combustion."

Jun 1, 2016

By William Gleason

"On April 4, 2017, the largest earth-pressure-balance tunnel boring machine (TBM) ever built finally completed its 2.7-km (1.7-mile) journey beneath Seattle, WA, nearly four years after it began boring the SR-99 tunnel that will eventually replace Seattle’s Alaskan Way Viaduct.By now, readers of this publication are familiar with the ordeal that began on Dec. 6, 2016, when the machine overheated and shut down. Until that point, the TBM, named Bertha, had grabbed headlines for being the largest in the world with a 17-m (57.6-ft) diameter face. But after the incident that stopped the progress, the headlines suddenly stopped focusing on the engineering marvel of the tunnel project and began asking what went wrong. Just 300 m (1,000 ft) into the tunneling journey the machine was stuck, unable to move forward and impossible to retract.The project’s contractors, Seattle Tunnel Partners,(STP JV) – a design-build consortium comprised of Dragados - USA, Tutor Perini, say a 20-cm (8-in.) steel well-casing buried in the path of the machine caused the problems that halted the TBM. The Washington State Department of Transportation (WSDOT) disagrees, and the issue over who ultimately pays for the repairs is now with the courts.Eventually, engineers determined the best way to get Bertha back to work was to dig a 36-m (120-ft), deep concrete lined shaft pit in front of the machine and lift the 1.8-kt (2,000-st) cutterhead out for repairs. The repairs took two years but eventually the machine resumed mining in January 2016. In April 2017, the TBM finished building the tunnel, breaking through at the tunnel’s north end near Seattle’s Space Needle, with little to no ground surface movement measured on the entire alignment.While the cause of the TBM breakdown and who should pay for repairs was debated above ground, the work below ground continued. David Sowers, deputy program administrator, engineering and program management with WSDOT, told Mining Engineering during the 2017 Cutting Edge Conference in Seattle that in addition to the technical marvel that the tunnel became, the fact the parties involved were able to work through the unprecedented challenge is a great example of how to overcome challenges on massive projects."

Jan 12, 2017

By Luther W. Hyde

Ground water, one of Florida&apos;s most valuable resources, is also one of its most abundant. The State is fortunate to have several prolific ground- water reservoirs that yield tremendous quantities of water to wells and to some of the world&apos;s largest springs. These ground-water reservoirs, or aquifers are of two types artesian and nonarteaian. Ad artesian aquifer is one that contains water under sufficient pressure to rise above the top of the oontaining formation. A nonartesian aquifer is one that contains water which is not confined, and the upper water surface (water table) is free to rise and fall. The principal source of ground water in Florida is the artesian Floridan aquifer which supplies most of the water users in the State. Nonartesian sources include the Biscayne aquifer of southeastern Florida, the sand-and-gravel aquifer of extreme western Florida, and a shallow aquifer which lies at depths of less than 100 feet over much of the State. The accompanying map shows the approximate areas where these aquifers are the main source of supply; however, the boundaries do not represent the areal extents of the aquifers. For example, the Floridan aquifer extends beyond the southern boundary shown on the map, but it is not of great economic significance there because the water is highly mineralized. Aquifers other than the four described occur in the State, but they are, for the most part, of minor significance. One of these is an artesian aquifer which is formed by permeable zones that occur locally within the confining beds above the Floridan aquifer.

Jan 1, 1966

By D. Shuck

Incorporation of a 2,727 mtpd, $5.7 million flotation circuit into the Mclaughlin flowsheet was completed in November 1991. This capital addition reduced overall operating costs and improved the gold recovery of the low grade refractory reserves over that expected for direct cyanidation. In addition, flotation provided a means to generate a sulfide concentrate which is utilized to supplement feed to the pressure oxidation circuit.

Jan 1, 1994

By R. Pinksen

The IOC Mining and Operations Departments expressed an interest in reducing the amount of oversize material (>1.0 m x 1.0 m x 1.0 m; 39 inches x 39 inches x 39 inches) being produced and its subsequent downstream effects including in-pit sorting and reduction, damage to mobile equipment, and significant delays in the loading pockets and the primary crushers. To achieve this goal an oversize reduction project was undertaken by the mine and to date has significantly improved upon baseline measures. One key approach used to reduce the amount of oversize was the implementation of thicker emulsion. The introduction of a thicker emulsion provided more resistance to the forces created by dynamic water and reduces the infiltration of the emulsion into the cracks and fissures of the rockmass. Reduced amounts of oversize and more consistent fragmentation throughout the muckpiles has been a result. Additionally, a significant reduction in nitrates leached into the mine water discharge has been realized. To determine the effectiveness of the oversize reduction project, IOC used a of first-of-kind technology to assess fragmentation presented to the shovel at the digging face. A Digital Vision System (DVS) was installed on one of the shovels to capture images that were stamped with GPS locations. A large population of digital images were analysed to produce a robust fragmentation distribution baseline that was used as one of the mine key performance indicators (KPI). Changes to blasting practice were subsequently measured against the baseline KPI to assess effectiveness.

Jan 1, 2011

By J. Boldy

The discovery of the Delbridge massive sulphide deposit in the Noranda district of Quebec resulted from an appreciation of the significance of a mercury leakage halo as a litho-chemical pathfinder to blind ore, coupled to its location relative to a geologically inferred ore-bearing horizon within complex volcanic stratigraphy. Systematic sampling of micro-fractures present in outcrops delineated a diagnostic anomaly, drawing attention to an area considered prospective for buried ore. The massive sulphide deposit was subsequently found to be blind and topped at the 110 metre level.

Jan 1, 1984

By L. P. Meade

The need to feed an established talc mill from a crude are source located closer to the mill prompted the drilling in 1986 of a previously mapped talc-carbonate deposit. This talc-bearing rock had never been considered as a potential source of crude talc are because of the high carbonate content and other deleterious minerals that were observed in outcrops. Selective mining, in-pit grade control and creative processing has allowed this deposit to be developed into an orebody. By definition, an orebody has to be a source of positive cash flow. With industrial minerals, this is determined as much by market acceptance as by are tenor.

Jan 1, 1992

By A. Bruynesteyn

Results are presented from a series of tests designed to determine the beneficial effects of the microorganism Thiobacillus ferrooxidans upon the leaching of uranium from a pyritic uranium ore. Minus 1-inch (-25mm) 0.0711 percent uranium containing, pyritic ore from the Rio Algom Mine at Elliott Lake, Canada was leached with lixiviants of various Eh and pH as well as being subjected to a biologically-assisted ferric iron leach. In all cases, the biological leach gave superior extraction. At pH 1.6, the biological leach gave 100.6 percent extraction and the ferric iron leach 69.8 percent. This improvement in extraction is associated with a relatively rapid biological breakdown of the pyritic material, thus liberating uranium mineralization associated with these pyritic materials and regenerating the ferric sulphate lixiviant in situ.

Jan 1, 1981

By R. D. Stewart

Abstract. Induced fluorescent sorting is a means of beneficiating an ore by selective labeling with a reagent combination which fluoresces when activated by ultraviolet light The reagent combination normally consists of a surface active compound and a fluorescent dye. The surfactant adheres selectively to a specific surface and carries the dye with it. Upon activation with ultraviolet light, the labeled pieces, in the size range 1.27 cm to 20 cm (0.5 to 8 in.), are detected during free fall by photosensitive cells and ejected by water jets. Either ore or gangue may be labeled.

Jan 1, 1980

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