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By James R. Walpole

Less than 100 years ago the first major federal regulatory agency, the Interstate Commerce Commission was established (in 1887), and since that time literally hundreds of other federal agencies have been created. The regulations set by these agencies tremendously affect the individual citizens of this country as well as U.S. institutions. A few examples of the myriad agencies established include the Food and Drug Administration. (1907), the Bureau of Mines (1910), the Federal Reserve System (1913), the Federal Trade Commission (1914), the Tennessee Valley Authority (1933), the Securities and Exchange Commission (1934), the National Labor Relations Board (1935), the Small Business Administration (1953), the Federal Maritime Commission (1961), the Equal Employment Opportunity Commission (1965), the Farm Credit Administration (1971), etc., etc. Eight years ago, on December 2, 1970, still another federal agency was established by the reorganization plan of President Nixon -- the Environmental Protection Agency (EPA). The Administrator of EPA was given authority to regulate certain activities affecting the environ-ment, which were formerly within the jurisdiction of the Department of Interior, the Department of Health, Education and Welfare, the Federal Radiation Council, the Atomic Energy Commission, the Department of Agriculture, etc. Within weeks after the formation of this Agency, Congress began to enact legislation which would be administered by EPA. Over the last eight years a considerable number of such laws have been passed, a few of which include: the Clean Air Act (1970), the Noise Control Act (1972), the Federal Water Pollution Control Act (1972), the Marine Protection, Research, and Sanctuaries Act (1972), the Federal Insecticide, Fungicide and Rodenticide Act (1973), the Safe Drinking Water Act (1974), the Toxic Substances Control Act (1976), the Resource Conservation and Recovery Act (1976), the Clean Air Act Amendments of 1977, etc. It may be helpful to review, in a summary fashion, the major provisions in some of these statutes, and accompanying regulations, as they relate to water quality control in the mining industry. The Safe Drinking Water Act and the Federal Water Pollution Control Act contain provisions to be examined, as well as the Resource Conservation and Recovery Act and the Toxic Substances Control Act. One other law, the Surface Mining Control and Reclamation Act (1977), is not administered by EPA although it does contain many provisions related to environmental control, and it will also be dis-cussed because of its importance to the mining community.

Jan 1, 1978

By G. F. Livingston, F. K. Shelton, J. C. Stahl, R. E. Churchward

"INTRODUCTION An investigation of the metallurgy of cobalt from domestic ores has been in progress since February 1940 and has resulted in the formation of a hydrometallurgleal process for the production of electrolytic cobalt metal. Previous reports of these investigations have been given by F. K. Shelton; 7/ and Ruth E. Churchwrd, F. K. Shelton, and G. Knickerbocker. 8/ Briefly, the process, as applied to ores containing cobalt oxide, consists of leaching with H2SO3 or, preferably, with H2SO3 and H2SO4, to dissolve the cobalt. The cobalt solution passes through one or more purification stages to remove iron and elements of the copper group, and cobalt carbonate is precipitated under carefully controlled pH conditions. The cobalt carbonate is dissolved in on acid electrolyte containing sulfuric acid, boric acid, and sodium fluoride. The electrolyte then proceeds to electrolytic cells where cobalt is plated as a metal and sulfuric acid is regenerated.The present paper contains the results of several investigations signed to give a more complete chemical and engineering understanding of different unit processes involved in the electrowinning of colbat. Some work has been done to broaden the process to include arseniferrous cobalt ores as well as the oxide ores upon which the investigation was initiated. Most of the data presented herein have been obtained since the release of the previous reports; any changes suggested heroin that conflict with recommendations in earlier reports are based on more complete data and usually are preferable."

Nov 1, 1945

By L. T. Matthews, C. E. Loo, R. P. Williams

The behaviour of iron ores and fluxes in the high temperature zone of a sintering bed is extremely complex. Following a review of current knowledge, an attempt is made to define relevant terminology to describe the processes that occur in this part of the bed. A deformation temperature is used to quantify the initial formation of melt, which is produced predominantly by reactions between fine particles in the sinter mix. The subsequent assimilation of larger particles is considered to depend on the reactivity of the melt and the assimilation resistance of these particles. Novel laboratory experimental techniques are used to quantify these parameters. Results demonstrate that the properties of the raw materials used have an extremely important influence on the initial processes of melt formation and assimilation and also on the nature of the sintering reactions and sinter-bonding phases.

Jan 4, 1992

By L. K. Weaver

The purposes of this Bureau of Mines report are to review the history of the domestic offshore hydrocarbon production; to project offshore oil and lease condensate production from 1971 through 1985; and to show the impact of offshore development on the onshore segment of the petroleum industry. Since 1954, offshore production has provided an increasingly larger portion of the domestic oil production. Domestic offshore oil and lease condensate production has increased from about 2.0 pct of the U.S. total in 1954 to 16.7 pct in 1970. Likewise, marketed gas production has increased from 1.0 pct of the U.S. total in 1954 to 15.0 pct in 1970. The past performance of exploration, leasing, development, and production of the offshore petroleum industry was used to make projections of offshore oil production. A comparison between onshore and offshore operations was also made. Assuming a tentative Department of the Interior offshore leasing schedule is completed by 1980, the authors estimate that by 1985, about 30 pct of domestic crude oil and lease condensate production from the lower 48 States will come from offshore areas. Currently, leasing of Federal offshore areas has been delayed due to environmental considerations. The rate at which off-shore hydrocarbons will enter the energy market will depend, to a large extent, on how soon environmental considerations are resolved. Assuming that offshore leasing will resume in the near future, U.S. offshore production of crude oil and lease condensate should be about 934 million barrels in 1985.

Jan 1, 1973

By Otto Ruhl

The zinc-lead ore reserves of the Tri-State district of Kansas, Missouri, and Oklahoma, as of December 31, 1947, are estimated at a total of 66,100,000 tons of crude ore containing 2.18 percent metallic zinc and 0.38 percent metallic lead. The Bureau of Mines began estimating the reserves in October 1945 and completed the' work December 31, 1947. A total of 38,900 acres of land representing approximately 5 percent of the area of the district is covered in this report. The work was confined for the most part to properties developed or partly developed by drilling and underground workings, and to acreage sufficiently drilled out to indicate ore of enough tonnage to make a commercial undertaking. The acreage in which ore reserves exist is widely distributed in all three States. A map of the Tri-State area is shown in figure 1. The remaining 95 percent of the area is not necessarily nonproductive but represents, possibilities for future exploration and development of additional mineral resources when and if economic conditions or national necessity encourage such work. Of the total reserves, 41 percent are in Missouri, 38 percent in Kansas, and 21 percent in Oklahoma.

Jan 1, 1949

By K. Wangerud, B. S. Caruso

A water balance model with deterministic and stochastic components was developed and used for the Gilt Edge Mine Superfund Site, South Dakota, to evaluate risks of contaminated runoff discharging to surface waters based on assumed water treatment plant (WTP) rates for different remedial alternatives. The objectives of the modeling were to use a stochastic approach for analysis of precipitation based on historic records, and for probabilistic estimation of annual and monthly runoff from primary disturbed/mining activity areas that currently requires, or will need, treatment at the WTP, water storage and changes in a major pit, and risk of contaminated water bypass of the WTP to a downstream drainage. Subareas/source areas generating contaminated runoff requiring treatment were delineated. A simple water balance model was used based on precipitation inputs and evapotranspiration and groundwater losses. Annual and monthly precipitation records for Lead, South Dakota were used to estimate precipitation at the mine site. A lognormal distribution was estimated for monthly precipitation. The stochastic software package/Excel add-in “@Risk” was used to generate random monthly precipitation values using a Monte Carlo method based on the distributions. The average annual and monthly distribution of pan and lake evaporation, and groundwater losses were also estimated for the site. Stochastic outputs from the model for the end of each month and year included contaminated runoff requiring treatment, water storage in mine pits and the risk of WTP bypass given different assumed WTP rates. The probability of the time required to dewater the pits was also modeled.

Jan 1, 2002

By Adam Moore, Peter Radziszewski, Matt Gallimore

"Stirred mill technology dates back to 1928 where the idea to use “an agitator and spherical grinding media” was presented. In the context of the mining industry, interest in stirred milling technologies has grown over the last 20 years where the typical observation reported inDespite these developments, the tumbling mills are continuing to be used in fine and ultrafine grinding applications. The main reason for this, as communicated at the Canadian Mineral Processors roundtable discussion in 2013, is that the comfort level in understanding stirred milling technologies is not at the level of that of tumbling mills.At CMP 2014, one contribution was made to explore how mill design affects power and energy in a stirred mill. While the 2015 CMP paper explored the application of one scale-up methodology to the Gibraltar case. For the CMP 2016, the aim of this paper is to contribute to increasing the general comfort level with stirred milling technologies by developing a better understanding of the different scale-up methodologies used. This will be accomplished by first completing an overview of the scale-up models found in the literature followed by a review of the different testing and scale-up procedures. This review will be supported by a number of case studies found in the literature. The paper will close with a discussion on some of the challenges that these models and methodologies have and how future research might contribute to overcoming them.IntroductionStirred mill technology dates back to 1928 where the idea to use “an agitator and spherical grinding media” was presented (Stehr, 1988). The year 1948 saw the successful application of Du Pont’s “sand mill” for pigment grinding. Subsequent years have led to the development of different types of stirred mills spanning a number of industries that require fine and ultrafine grinding."

Jan 1, 2016

A good deal of experimental work has been done from time to time on the application of compressed air to the elevation of wet pulp. On account of the flat nature of most of our mill sites elevation of the pulp has to be provided for, and the various methods in vogue show considerable loss of time, in the replaceing of wearing parts. During the last two years the writer has carried out a great many experiments with a view of devising an elevator that will give continuous work with a minimum of wear.The results do not show a high efficiency for the power employed, but the lift is continuous in operation, very cheaply installed, and possesses no wearing parts. The lift was tried working in a bore hole of 8 in. diameter, but in many cases it is more convenient to sink a small well for the purpose. The result to date showed that the most efficiency was obtained when the depth of the wellwas not less than the height of the lift required. The pressure of air required in pounds per square inch was (approximately) half the number of feet to be lifted.In the majority of cases the lift required varied between 20 ft. and 50 ft. and the air pressure required between 10 lbs. and 25 lhs. per square inch. In most existing installations the air compressors in use were delivering air to the receivers at about four times that pressure, and when air so compressed was expanded to perform its work at a reduced pressure, it was apparent that the power exerted in origInally compressing the air above the working pressure required at the lift was absolutely lost.

Jan 1, 1901

By Paloma Lazaro, Moe Momayez

Heat-related illnesses (HRI) are relatively common in both hot surface and underground mining operations. When workers are exposed to extreme heat or strenuous work in a hot environment, they become prone to heat stress. Heat strain is the result of the body’s response to external and internal heat stress. It is therefore vital for the conditions leading to heat strain be detected and treated in a timely manner. Heat-related illnesses are manifested by exhaustion and heat stroke. The predicted heat strain (PHS) [ISO 7933 (2004)] model has been developed to predict the health condition of the worker in terms of core body temperature and water loss. The PHS model tested in this study is based on eight physical parameters that are measured at different intervals during a work shift. They include air temperature, humidity, radiation, air velocity, metabolic rate, clothing insulation, posture, and acclimatization. The model predictions are then compared with a direct physiological measurement, such as core body temperature. We present the results of an extensive study that monitored and predicted body’s response to heat stress under different environmental and working conditions. The PHS model provided reliable results in most instances in comparison with other prediction methods currently in use in the field.

By Paloma Lazaro, Moe Momayez

Heat-related illnesses (HRI) are relatively common in both hot surface and underground mining operations. When workers are exposed to extreme heat or strenuous work in a hot environment, they become prone to heat stress. Heat strain is the result of the body’s response to external and internal heat stress. It is therefore vital for the conditions leading to heat strain be detected and treated in a timely manner. Heat-related illnesses are manifested by exhaustion and heat stroke. The predicted heat strain (PHS) [ISO 7933 (2004)] model has been developed to predict the health condition of the worker in terms of core body temperature and water loss. The PHS model tested in this study is based on eight physical parameters that are measured at different intervals during a work shift. They include air temperature, humidity, radiation, air velocity, metabolic rate, clothing insulation, posture, and acclimatization. The model predictions are then compared with a direct physiological measurement, such as core body temperature. We present the results of an extensive study that monitored and predicted body’s response to heat stress under different environmental and working conditions. The PHS model provided reliable results in most instances in comparison with other prediction methods currently in use in the field.

When the HSE Act was introduced in New Zealand in April 1993, one of the prime aims of the Government was to signal to the industry. The Government's recognition of the employer as the key person responsible for safety and health in the workplace and to actively encourage employers to self manage the health and safety function. Because of the significant change in the philosophy behind the new legislation, and because of the inherently conservative nature of the mining industry, it has taken some years for both the industry and the regulators to reach the stage of considering the framework in which a controlled degree of self management can proceed.   In this paper, some of the issues relating to the legitimacy of the process are considered, some of the questions raised in the minds of those charged with implementing the legislation are discussed, and the views of some eminent authors are examined.   The latter part of the paper focuses on a programme called the Reduced Site Surveillance Programme, which grew out of Goal 2 of the New Zealand Mining Inspection Group's 5-Year Strategic Plan. The programme is described in some detail, and the criteria applied at each stage of the programme is discussed. The paper concludes with the author's expectations of the longer term outcomes of the programme.

Jan 1, 1997

By G. L. Oldright

By means of a technique developed in cooperation with the Eagle-Picher Mining & Smelting Co. and outlined in the first report of this series (R. I. 4333 ), it was possible to take many thermocouple readings with base-metal couples at temperatures over 2300° F with unsupported protection tubes for over half the lengths of the Henryetta retorts. -This technique made it possible to avoid the use of the usual optical pyrometer, which gives temperatures dependent upon the luminosity of the flames, and which is not conveniently usable to read temperatures for the lengths of the retorts from the front of the furnace. The temperatures of the retorts themselves were necessary in order to set upper limits for safe operation; the lower limits of operating temperatures are set by the zinc content of the retort residues. The zinc content left in the retort residues for various sections of length also varies with retort temperatures rather than with flame temperatures. The variations in temperature along the retort can then be used as guides to distill more zinc from the residues, to avoid fluctuations in the rates ,of flow of zinc vapor into the condenser and to employ lower temperatures if such rates become high enough to cause losses of uncondensed zinc.

Jan 1, 1948

By J. W. Thompson

SALE AND CONVEYANCE. DEED BY INDIAN ALLOTTEE OF UNSOUND MIND-BONA FIDE PURCHASER. The deed of an Indian allottee whose mind was unsound, but who was not entirely without understanding, is voidable if made before the grantor's incapacity has been judicially determined; and a purchaser of the original grantee who interposes the defense of a bona fide purchaser has the burden of showing a purchase for value and on failure to do so can not claim the benefit of a bona fide purchaser. Adams Oil & Gas Co. v. Hudson (Oklahoma), 155 Pacific, 220, February. 1916. PURCHASER OF MINING CLAIM-RIGHT TO FIXTURES. The purchaser of a mine equipped with an electric hoist, placed in the mine under a rental contract with the owner of the hoist and under an agreement to return it to the owner at the expiration of the term of hiring, can not claim and hold the hoist as against the owner where the agent of the seller explained to the purchaser that the hoist was not owned by the owner of the claim. Montana Electric Co. v. Northern Valley Mining Co. (Montana), 153 Pacific, 1017. p, 1018, October, 1915. AUTHORITY OF GRANTEE TO EXTEND LEASE. A deed conveying lands subject to an oil and gas lease under which the lessee had the right to drill or pay money in lieu of drilling at his option, and reserving to the grantor a share of the royalties under such lease, and expressly authorizing the grantee to lease the land for oil and gas purposes and to take the rentals, authorizes the grantee to extend the existing lease before the expiration thereof in consideration of the annual payment of money in lieu of drilling, as contemplated by the lease.

Jan 1, 1916

By G. B. Shea

"INTRODUCTION Much of the recent progress in increasing the efficiency of oil-well performance can be attributed to advancements in the art of cleaning wells. Through research and development by operators and service companies during the past decade, significant improvements in the application of engineering and chemical principles to well-cleaning technology have widened greatly the scope of ""clean-out"" methods to the end that greater ultimate recovery of oil will be attained.This report reviews recent improvements and developments on this important problem in California; it describes also the use of various methods and tools for cleaning wells to stimulate or revive their productivity. Developments in preventing and removing mud sheaths in well-completion operations also are described. The report is based on a field survey, supplemented by data from the technical and patent literature and from manufacturers' catalogs, which contain much valuable information.In preparing the material for publication as a Bureau of Mines report, the author has been fully aware of certain limiting conditions that attend the discussion of a subject such as that treated in this report. The following are examples:1. To a considerable extent, well cleaning in California is done with tools rented from service companies, and their representatives and employees are specialists in jobs of this type. They usually have working experience with their own equipment and methods which greatly exceeds that of persons whose interest has been casual or who have had no opportunity to study the subject in detail in actual practice. Many of the tools and methods are covered by letters patent for the protection that may be in developing and successfully applying these mechanical and chemical means of increasing the production of wells. Frequently several years have been required to perfect a given tool or technique, requiring relatively large investments to establish a service that is remunerative to those who have primary interest in a certain development and at the same time attractive enough to the operators of producing properties (because of greater quantities of oil delivered into the flow tanks) to warrant employment of or contractual agreements with a particular service group."

May 1, 1943

By Yaw Boadi, Andrew McCallum, Sandy Gray, Yavuz Atasoy, Peter Wemyss

"Various full-scale test programs and installations of the InLine Pressure Jig (IPJ) have provided evidence that pre-concentration of the difficult to leach sulphide mineral through gravity can provide significant increases in economic recoveries. The continuous gravity concentrates are intensively treated either by re-grinding or Intensive Cyanidation. Data from various mine sites worldwide is presented. Treatment of complex ore bodies with this low cost methodology may render previously uneconomic ore bodies financially viable and assist in the recovery profile of transitional ore.INTRODUCTIONThe use of gravity is made extremely attractive in complex ore situations due to the low cost of operation, typically a few cents per ton operating cost and lack of chemicals.Gold mines which suffer from poor recovery due to complex mineralogy such as Stibnite, Arsenic, Carbon, Telluride, Silver and other pacifying agents such as Iron, which can form coatings, can all benefit from the process proposed in this paper. The key issue is not overall recovery as much as one of economic recovery. The key to this is maximised recovery at the lowest possible capital and operating cost. Other options such as flotation are reviewed but are not seen in many instances to be the panacea due to issues discussed in the paper. The use of the InLine Pressure Jig in the re-circulating load of the milling circuit is a cost effective means of recovering a sulphide/gold concentrate containing the complex mineral assemblages which require re-grinding and intensive leaching for optimised gold recovery.The benefits of Jig Assisted Grinding (JAG) are many and the challenge over the past years has been developing, understanding, implementing and evaluating the benefits of various flowsheet models. This has involved the reconciliation of results in plant scale trials back to the original laboratory test program. The following paper outlines the insights gained in this area through extensive work carried out by many people across both laboratories and plant sites in Australia and overseas. The examples in this paper are some of the work carried out on a few selected sites but similar work has been carried out on other sites such as Penjom, Granny Smith and Agnew. This work has eventuated in several installations which we believe have great importance in the future of the gold processing industry. They will lead the way forward to the modern all-gravity plants of the future.Compared to flotation, for the recovery of sulphides, gravity is a simple option. The simplicity generally translates to low capital and operating cost."

Jan 1, 2004

By Panagiota Tsolis-Katagas, Basilios Tsikouras, Tassos A. Grammatikopoulos, C. Katagas

"Mineralogical techniques including microscopic methods, reflected and transmitted light microscopy, Cathodoluminescence (CL) and Scanning Electron Microscopy equipped with an Energy Dispersive Spectrometer (SEM-EDS), are useful in determining the quality of industrial minerals. They are essential for studying ores and metallurgical products including the evaluation of physical characteristics of the mineral, paragenetic relationships, associations with possible deleterious contaminants (e.g., sulphides), spatial distribution within the ore zones and liberation characteristics. The methods are inexpensive, and provide quick identification and distinction among the industrial minerals and the gangue minerals in a section. Additionally, SEM is necessary to reveal complex textural sequences and 3-D measurements of minerals and quick semi-quantitative analysis.Common analytical methods include Electron Microprobe Analyses (EMPA) and Whole Rock Analysis (WRA) (commonly with XRF and ICP) for major and trace elements. The EMPA analyses of industrial minerals provide information on the purity of the analyzed grains as opposed to the bulk chemical analyses that may be misleading due to contamination by other associated common “gangue” minerals. These techniques have been implemented for the case studies of wollastonite, V-magnetite and muscovite. Therefore, these methods can provide extremely useful information and lead to the implementation of a successful pilot-testing programme.MINERALOGICAL EVALUATION OF DEPOSITSDespite their considerable and increasing economic importance, industrial mineral deposits have traditionally been neglected by economic geologists, and are only rarely the subject of the detailed analysis widely lavished on metallic mineralization. Moreover, in that they generally represent concentrations of “normal” rock-forming minerals, albeit commonly with particular textural and/or geochemical features, they have tended to fall between the mainstream of petrogenetic studies and mineral deposit research (Grammatikopoulos 1999). For many industrial minerals, little attention has been paid to the factors responsible for their local concentration as large and high-grade bodies. This comparative neglect has particularly been the case for minerals such as talc and wollastonite, widespread in metamorphic rocks, in which they are reasonably interpreted as components of assemblages derived, respectively, from pelitic sediments, ultramafic igneous rocks and siliceous limestones."

Jan 1, 2003

Site specific geotechnical data, deposit characteristics and method of mining are key factors when assessing an appropriate slope design philosophy. Mining geotechnics should be viewed as an iterative design process linked closely with mine planning, development and operational safety constraints. This case study presents geotechnical investigations for slope design at Macraes Flat Gold Mine using kinematic, probabilistic and economic analyses tempered with knowledge of site specific conditions. The recommended designs not only reduce early waste stripping tonnages but also provide data to optimise final walls.

Jan 1, 1992

The Development of a Non-Roasting Technology for Polymetallic Gold and Silver-Bearing Sulfide Concentrates Treatment

Sep 13, 2010

By Michael Young, Josh Rubenstein, Michael Cooper, Tom Shouldice, Dan Curry

"Xstrata Nickel Australasia’s Cosmos plant in Western Australia is currently implementing a debottlenecking project to increase nickel output while maintaining metallurgical performance and a low unit cost for production. Mineralogical analyses indicated that the processing bottlenecks could be removed by simply reconfiguring portions of the circuit as well as adding capacity with technical advancements – notably an IsaMill™, Jameson Cell, Wemco® SmartCell™ and Larox Filter.The Wemco® SmartCell™, which is particularly suited for coarse mineral flotation, and Jameson Cell, which is particularly well suited for fast floating and fine minerals, combine as rougher scalpers to complete the main stream portion of the flotation circuit. Addition of the two new cells meet the required flotation capacity to handle the forecast increase in nickel feed grade and tonnage.The addition of an IsaMill™ for regrinding allows the SAG mill to produce a coarser primary product, thus enabling increased throughput. The advantages offered by the IsaMill™ include operation in open circuit (internal classification), an inert grinding environment (ceramic media) for better downstream flotation (“clean” new surfaces), compact footprint (easy to retrofit into existing plant) and energy efficiency. With the new rougher capacity addition, the remaining original plant cells were reconfigured to suit the new regrind mill and cleaning requirements. The existing 24 m2 Larox pressure filter was replaced with a larger 32 m2 unit to dewater the increased concentrate output.The paper describes the upgrade at the Cosmos concentrator with particular emphasis on the mineralogical data and metallurgical benefits associated with the changes.INTRODUCTIONThe Cosmos concentrator is located 680 km northeast of Perth in Western Australia. The deposit’s development and operations were started in 1999 by Jubilee Mines NL, Cosmos’ previous owner, with the first production of nickel concentrate in April 2000. The Cosmos concentrator treats a komatiite hosted high grade nickel sulphide ore, with sulphides being predominantly pentlandite and pyrrhotite with lesser amounts of pyrite and chalcopyrite."

Jan 1, 2010

By Yuting Xue, Danqing Gao, Brijes Mishra

Heterogeneity and discontinuity significantly affect rock strength. For accurate stability prediction, intact rock behavior is imperatively included in rock mass behavior. However, past research largely used arbitrary scaling approaches to produce rock strength. This paper considers a stochastic approach in order to determine the strength of a rock. Based on the laboratory data, a MATLAB® with extreme value stochastic model generates a database for each physico-mechanical property. Then FLAC® simulates laboratory-sized rock specimens. The grids developed in the numerical model can in turn develop random material properties in MATLAB®, which researchers then applied to the final FLAC® model. Model runs simulate the approach performed in the laboratory. The results from the model indicate that a stochastic approach produces strengths that are lower than a deterministic approach. Failure modes for each specimen are different, similar to observations in the laboratory. In addition, random density also influences the failure mode, highlighting the importance of stochastic analysis in rocks.