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By Dae S. Young

A new probabilistic approach is introduced for slope stability analysis including adverse impact of blasting vibrations. The material strength within a slope area is randomized in this bi-variate joint probability analysis. To be a completely general engineering method, the new probabilistic approach employs the random variable transformation technique; the Hermite model of the Gaussian transformation function, which transforms the experimental histogram of strength values to the standard Gaussian variables. Because bi-normal joint probability is analyzed on the true probability region projected on the Gaussian transformed variable plane, it is an exact solution of slope stability based on the available sample data. Details of the probabilistic approach are given through a case study on an iron ore mine. The case study demonstrated that the probabilistic approach is effective and simple enough to be a routine engineering practice for slope analysis.

Jan 1, 1984

By Betty M. Miller

INTRODUCTION In September 1974 the Resource Appraisal Group of the Branch of Oil and Gas Resources, U. S. Geological Survey, was asked to aid the Federal Energy Administration (FEA) in its legal responsibility to generate by June 1975 an independent appraisal of the undiscovered oil and gas resources of the United States, both onshore and offshore. As a result, the Resource Appraisal Group accelerated its ongoing efforts to develop sound appraisal methods and procedures that would permit the systematic collection and evaluation of basic data from petroleum provinces throughout the Nation. The results of this independent appraisal of the Nation's conventional oil and natural gas resources were published by the U. S. Geological Survey as Circular 725, June 1975 (1). The estimates in this report of undiscovered recoverable oil and gas resources for the United States were made: (1) by carefully re- viewing a large amount of geological and geophysical information gathered on more than 100 different provinces by over 70 geologists within the Survey; (2) by applying a variety of resource appraisal techniques to each potential petroleum province; and (3) by application of subjective probability procedures to group appraisals for each petroleum province. These methods provide a range of estimates which are summarized in terms of low, high and mean values for the various provinces and groups of provinces, or regions. The basic data and procedures used are documented and are being incorporated into a dynamic, data- intensive system that can be upgraded, updated and reevaluated periodically. These data are open to public inspection. In this study, the primary emphasis was placed on conventional crude oil and natural gas in the onshore provinces and the provinces on the continental shelf out to water depths of 200 metres; estimates

Jan 1, 1977

By S. Dessureault, Z. Gavelan

As globalization continues, sustainability and social responsibility has become essential in foreign mining investment. However this global trend and the increasing acceptability toward the globalization process, viability and sustainability are not always achieved. Viability and sustainability of mineral projects is dependant on the social and political environment of the region where the mining venture is located and is based on the interaction between the mining entrepreneurs, national-local government representatives, communities, grass-roots groups and independent civil organizations. These are the organizations, which play the acting roles on the viability of mining projects and are the main source of socio-political risks for the project. Throughout the decision-making process to invest in a mineral project, socio-political risks are quantified using a set of measurable variables. Nevertheless, these risk measures should be dependent on specific industries. Two mineral projects, even in the same mining district, may have significantly different political risk profiles based on their own socio-political variables. This paper describes a methodology that takes into account local social and political variables in defining a project-specific’s political risk profile. This contrasts with more typical political risk measures that focus on the country’s overall risk profile. Mining operations must operate on a local scale necessitating the development measure that considers more local variables.

Jan 1, 2004

By R. Trueman, D. B. Tyler

Numerical modelling was used to determine the magnitude and direction of stresses around drives both adjacent to and distant from open stopes in the South Crofty tin mine. Modelling predicted that drives near the stopes are situated in a stress-relaxed zone. The peripheries of drives that are sited in solid rock away from the influence of stoping are in compression. Key-block modelling was used to determine the typical geometries of critical blocks and distinct element modelling was used to determine block stability. The conclusions derived from modelling fitted the observational data. This indicated that key-block theory is a valid tool for analysing the stability of roadways in the South Crofty mine. The support requirements for drives located next to stoped-out areas were formulated using a risk analysis approach to key-block formation. The results were compared with support guidelines derived using empirical design methods. Good agreement was obtained for the roofs of the drives but not for the sidewalls. The concept of a critical excavation width was formulated: once an excavation is larger than the critical size the length of rockbolts need not be increased as the excavtion dimensions increase. This may be the case in all rock mases.

Jan 4, 1993

By F. M. C. C. Vieira

There are many uncertainties that a mine designer should consider when selecting an optimal layout. Even though the inherent variability in the design parameters indicates that single-values are not representative of mining conditions, risk estimators such as ERR are often used without considering their statistical distributions. A probabilistic methodology has been developed to assess the influence of the extraction sequence and layout geometry on the rockburst risk associated with four ultra-deep mining layouts. The statistical distributions of incremental energy release rates and excess shear stresses at face elements are used as indirect estimators of rockburst risk in stopes, and the statistical distribution of the rock condition factor (RCF) is used as an indirect estimator of rockburst risk in tunnels and service excavations.

Jan 1, 2002

By Rodolfo Lagos, Nicos Pfeiffer, Ben Harding, Clayton V. Deutsch

This paper documents a probabilistic resource modeling workflow for the Round Mountain epithermal gold deposit. The set of categorical and continuous variable simulated realizations provides a model of variability and uncertainty given the current orebody knowledge. These realizations can be used to quantify and understand expected deviations in reconciliation during mining and provide a more accurate measure of expected gold than an estimated model. Gold mineralization at Round Mountain is primarily contained within tertiary tuff units, which dip gently to the west and thicken towards the southern part of the orebody. Domain boundaries are modeled as combinations of lithology and alteration; alteration domains are constrained to be within the tuffs. Large-scale geologic uncertainty is strongly influenced by parameter uncertainty, particularly the input histogram. The spatial bootstrap characterizes prior global uncertainty in the input histogram for categorical and continuous variables. Categorical models are generated using hierarchical truncated pluri-Gaussian (HTPG) simulation. Continuous variable simulation is carried out within the simulated domain boundaries using trend models to account for non-stationarity.

Aug 19, 2023

The modelling of lithological domains is a critical step in mineral resource and reserve evaluation. Deterministic models rely on an interpretation of the available drill hole data and expert knowledge, but do not account for the uncertainty in the spatial extent of the lithological domains. Instead, probabilistic models based on conditional simulation can be used to map the probabilities of occurrence of the domains within the deposit, which reflect the uncertainty in their presence or absence at unsampled locations. The mineral grade model is then obtained by weighting the predicted grades associated with each lithological domain by the probability of occurrence of this domain. Such an approach accounts for the continuity of the grades proper to each lithological domain and for the uncertainty in the spatial extent of these domains within the deposit. An application to a porphyry copper deposit is presented. Keywords: spatial uncertainty; plurigaussian simulation; geological control; kriging; geostatistics.

Jan 1, 2007

By W. Barnett

The Limpopo Metamorphic Belt is a complex geological terrane with at least three major deformational events. Tectonically juxtaposed lithology, open to isoclinal folding, crosscutting and re-activated shear zones and metamorphic gneisses and schists make pit slope design and maintenance a risky business. Venetia diamond mine?s Cut 3 is planned to reach 360 m by 2011. The difficult rockmass created problems in the original pit and a new more comprehensive slope design was necessary. Nearly 9 km of geotechnical drilling were undertaken to produce a new geological model and provide geotechnical information near the final Cut 3 face. All existing data from the pit were brought together into a database. SRK Consulting were brought into the project to audit the process and provide most of the manpower for the data analysis. Existing failures were back-analysed and the geotechnical domains identified. Analyses of only the southern domains are discussed in this paper. Geotechnical engineers can design slopes at any angle, but it is up to the managers at the mine to decide what risk they are willing to accept in a slope design. Once the issue of risk was discussed and settled in respect of the consequences of failure, each of the main geotechnical domains were analysed to produce a slope design at5% probability of failure with 15% above the first ramp. A risk assessment of the design was then undertaken to determine what risk the design placed on the equipment, personnel and the profitability of the overall mining operation. The risk assessment indicated minimal risk to the operation. One of the main assumptions of the final design is that the pit slopes will be dewatered. A project was immediately put in place to determine a groundwater model for the mine and to thereby determine the best dewatering procedure. However, it should be obvious that it is practically impossible to prevent benches from getting briefly saturated with water during storm conditions. It was therefore necessary to look specifically at supporting the crests of the ramps in the problematic southern domains to guard against the possibility of crest failure during heavy rains. The data available were re-analysed toward this objective. Spiles were recommended as the most cost-effective support system, and a probabilistic approach was used in the design. The final design has a 5% probability of failure, and the analyses indicate a strong sensitivity of the required spile spacing to the strength of the reinforcement material that will eventually be used. The pit slope parameters derived as per the discussion in this paper have just begun to be implemented at Venetia Mine.

Jan 1, 2001

Optimizing production scheduling in open pit mines is important for managing cash flows of mining operations. This paper describes a new, probabilistic, mixed integer programming (MIP) formulation which has been developed to minimize the risk of not achieving planned production targets, in terms of metal production and ore tonnage feed for the mill during production, while considering maximization of total discounted economic value. The new MIP model also recognizes that to minimize movement of excavators over long distances and accommodate equipment access, the blocks scheduled for mining within a period cannot be spread too widely. The model is applied to a laterite nickel-cobalt deposit, as an example of multi-element deposits that have complex ore quality constraints. The results show that the proposed model generates feasible schedules. When compared with traditional optimization techniques, the new model is superior in terms of minimizing the risk of not meeting production targets, especially at the early stages of production, and in terms of generating practical scheduling patterns.

Jan 1, 2006

By A. P. Whittlestone, J. D. Johnson, R. J. Pine, M. E. Rogers

standpoint. The effect on efficiency of collisions

Apr 1, 1995

By A. Aly Selim, Bruce D. Hanson

A computer model capable of simulating the basic production system in a variety of underground mining methods has been developed at the U.S. Bureau of Mines Twin Cities Mining Research Center. The simulation of the basic production system at the working face, which includes drilling, blasting, mucking, and roof bolting, is described in this paper. The model is event-oriented; that is, the status of the system is updated at the occurrence of an event. All event or activity times, including failure and repair of equipment, are treated as stochastic variables. A location dimension, in addition to the time dimension, is used, allowing the simulation of systems with a number of stopes or faces. To aid the user in determining the efficiency of his system, the model provides several reports. An event or activity report gives the frequency of occurrence, total active time, and cumulative delay statistics for each event. An equipment report delineates the availability and utilization of all equipment. A production report provides information on various performance measures such as tons produced and holes drilled. The cost report gives the cost of various elements in the system. Operating data from an actual mining situation were used in validating the model. In addition to the description of the model, examples of simulation experiments which were performed on a room-and-pillar mine system are given. Use of the model to determine methods for improving the efficiency of the system is discussed.

Jan 1, 1976

By Neil T. Russo, Peter M. Kandaris, Jogi S. Gadok

"Assessment of subsurface data for foundation design in support of long high voltage electric transmission lines is best accomplished using a probabilistic strategy since only a small portion of structure locations are typically sampled. Probabilistic approaches provide a tool to evaluate site uncertainty in a systematic and rational manner. This paper provides a case history of a risk-based design approach for a recently completed 191-mile long 69/161/345kV steel monopole transmission line traversing Central Iowa. The project owner made available limited subsurface information at project initiation, requiring the design team to obtain additional data within a constrained budget for 1067 large diameter, laterally-loaded deep drilled shaft reinforced concrete piers. The team commissioned a geologic desktop study to reduce uncertainty in subsurface evaluations and aid in selecting additional sample sites. In total, investigation programs tested approximately 15 percent of structure sites. The paper details the probabilistic approach used to estimate foundation geotechnical design parameters, with information from the various studies categorizing strata both laterally and with depth. Low-bound parameters were estimated via a statistical approach at a predetermined reliability level. Significant savings resulted from this approach when compared to conservative deterministic processes. Project QA/QC logged subsurface soil conditions during foundation excavation, then compared as-found conditions to the conditions assumed for design. The team redesigned foundations if either a non-conservative variance in soil conditions was observed or if bedrock elevation differed significantly from design assumptions. As a result, only 22 out of 1067 foundations required modification during construction (2% variance from initial design) with negligible impact on the construction budget and schedule.INTRODUCTIONFoundation design for long high voltage transmission lines presents a unique challenge in that the assessment of subsurface conditions typically requires substantial data that may or may not be obtainable. Investigations are usually performed well in advance of construction, often with limited access to structure sites and typically in remote areas. Probability and risk-based investigation and design strategies offer an opportunity to systematically estimate subsurface profiles and geotechnical design properties with limited data. Risk can be further reduced with dedicated field inspection of foundation construction along with good field and design team communication during construction. This paper presents a case history of probabilistic methods used for the investigation and design of electric transmission line foundations."

Jan 1, 2017

By C. O. Swanson

CALCULATING the average grade of a gold deposit is a problem that presents certain unique difficulties. Particularly troublesome is the fact that the average of the samples taken from a deposit is likely to be higher than the grade of the ore that is eventually mined, even when allowance is made for dilution and other factors resulting from the mining operations. It would seem that this situation is due to the presence in the deposits of structural peculiarities which have not been properly taken into account, since estimating the average grade of the broken ore produced from the deposits does not present the same difficulty. It is therefore evident that structural considerations are of prime importance in estimating the grade of a deposit. This fact is clearly realized and taken into account in cases where the boundaries of the orebodies and the variations within them are easily recognized. But in many gold deposits this condition is not satisfied, a circumstance which can be regarded as the main source of difficulty. Lacking definite information concerning the structure, we are apt to use certain procedures which are either empirical or based on general probabilities.

Jan 1, 1945

In the stability assessment of open pit walls, geotechnical engineers have to deal with uncertainty related to structural geology, rock mechanical parameters, groundwater and so on. This uncertainty will immediately and significantly impact on wall stability assessment and therefore. influence mineral recovery and ultimately the financial return of open pit mining. However, the conventional factor of safety applied to measure the stability of slopes and the relevant analytical computer packages cannot quantitatively consider the variability or uncertainty of the input data. As a supplement, therefore, geotechnical engineers have begun to apply probability to the stability assessment of open pit walls over the last two decades. To-date unfortunately, no powerful computer package is available to geotechnical engineers to conduct the probability analysis of slope stability. This paper presents a computer package of probability analysis for rock and soil slope stability. In this computer package, the strength parameters of rock and/or soil material such as cohesion, friction angle and unit weight of the different rock and/or soil type domain in a complex structural geology environment can be considered as the basic input random variables. Groundwater level can also be taken into account as a random variable in this package. Two `rigorous' limit equilibrium solutions, the Morgenstern/Price method and the Sarma method, can be used to calculate the factor of safety during Monte Carlo Simulation applied in this program. Five types of probability distribution are included in this package for the user to simulate basic input random variables. Two realistic cases from BHP Iron Ore are used to illustrate this package.

Jan 1, 1997

By W. E. Roscoe

The probability of making an exploration discovery in Canada can be calculated from Derry's (1970) data on exploration expenditures and number of discoveries over the last nineteen years. Considering an average exploration "try" to be $30,000, the probability of a discovery with one try has decreased tenfold from about 0.01 in 1951 to 0.001 in 1969. A plot of these probabilities can be extrapolated to the future, giving a 1969-71 three-year average probability of 0.00096 with 90 per cent confidence limits of 0.00042 and 0.00153. Using this probability, various calculations can be made, such as (1) the probability of making at least one discovery for any given exploration expenditure, (2) the probability of ultimate ruin or survival of the exploration investment process and (3) the expected value of an exploration investment. There is a critical minimum amount per discovery that must be re-invested in exploration, no matter how large the original investment is, for exploration to survive at all in the long run. Currently, this critical minimum is $31,200,000 with 90 per cent confidence limits of $19,600,000 and $71,400,000.

Jan 1, 1971

By A. F. Silva, R. Dockendorff, J. M. Girao Sotomayor, V. F. Navarro Torres, C. Castro

This paper shows the importance of performing probabilistic analyses in open pits, especially for mine planning, which can lead to more efficient ore extraction and meeting the acceptability criteria for safety in mine slopes. Three-dimensional stability analyses were performed to evaluate the future geometry of a large open pit for iron ore extraction in Brazil. The strength parameters of the lithologies were calibrated using ruptures in the pit walls. After determining the factors of safety (FoSs) from the calibrated parameters, probabilistic analyses were performed using the total range of values of each parameter under different field conditions to verify the reliability of the initial analysis. In this sense, it was possible to plot the probability of failure (PoF) and the FoS on the graph of slope height versus slope interramp angle (IRA) for the future pit in each lithology. IRA recommendations are made for two scenarios: (1) the best scenario: dry without ubiquitous joints and (2) the worst scenario: the water table at 10 m depth with ubiquitous joints in the most unfavourable direction. The results show that probabilistic evaluation is an important tool for establishing alert mechanisms in slopes that can be termed stable.

Jul 2, 2022

By John G. Kovac

A computer simulation has been developed to estimate the chances of a miner making a successful escape while wearing a SCSR. The model takes into account: (1) training in the use of SCSRs, (2) apparatus integrity, and (3) the oxygen cost of a mine escape. This Bureau of Mines report examines survival odds for a prototypical escape, and illustrates how these odds change when SCSR training is improved.

Jan 1, 2009

By Calvin L. Stevenson

The probability of a particle passing through a maze is predictable and consistent. This principle may be utilized to effect a particle size separation of materials by presenting a physical maze to a stream of material that will allow the fine particles to pass, while deflecting the coarse particles. A maze is effective even though all apertures encountered are many times larger than the particles being separated. By designing a machine that allows the probability parameters to be controlled and varied without changing physical dimensions, probability sizing becomes a useful tool for the separation of granular materials.

Jan 1, 1967

INTRODUCTION TO PROBABILITY THEORY The mathematical theory of probability provides the foundation for the interpretations and inferences that can be made from statistical techniques. Probability theory is a broad field of study in itself, and can only be touched on here in order to provide the necessary back- ground for a more complete understanding of statistical analysis. Probability is concerned with the outcome of random events. It had its beginnings in the theory of games of chance which were of great interest to European mathematicians during the last half of the 17th century. The outcome of a random process or experiment is defined as an event. The collection of all mathematical points associated with each event is called the sample space for an experiment. Consider a random experiment having a finite number, n, of possible outcomes, some of which have a characteristic A. What is the probability that A will result from a single

Jan 1, 1980

By G. Pan

The production data of many mines have not reconciled geostatistical estimations based on exploration and development drilling. The discrepancies in recovered metals are sometimes as large as 30%. A number of factors are responsible for such unpleasant outcomes. A major cause, however, is the lack of geological controls in the implementation of geostatistical techniques. Geological modeling establishes geological constraints and mineralization/ore envelopes. Geological constraints are usually established through drill hole interpretation. Mineralization and ore envelopes have been delineated manually based on assay grades. The issues associated with manual methods are: •Time requirements . •Inconsistent dilution. •Uncontrollable implementation variance. Although the time issue may not be a big concern for some companies, the other two have been responsible for many undesired estimation errors. A new geostatistical approach described in this study is designed on the basis of indicator and ordinary kriging. The central component of the method is the procedure for automatic delineation of mineralization and ore envelopes. The method, referred to as probability assigned constrained kriging (PACK), is demonstrated on a Carlin-type gold deposit. The estimation results are compared to blast-hole based production panels, showing that the estimated tonnage is about 2.1 % higher than the actual production, and the average grade is about 2.4% lower.

Jan 1, 1995