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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 Shoung Ouyang, Pinnaduwa H. S. W. Kulatilake

Available literature on the topic is reviewed. Methods are suggested to improve the presently available techniques to perform probabilistic modeling of shear strength parameters for rock discontinuities. The Mohr-Coulomb model and a power law model are used as strength criteria to model shear strength of rock discontinuities. Use of various regression techniques for point estimation of shear strength parameters from direct shear data are discussed. Goodness-of-fit tests for bivariate beta and bivariate normal distributions are developed, and the applicability of them to represent the distribution of shear strength parameters is tested through examples. Both distributions seem to have potential to represent the statistical distribution of strength parameters.

Jan 1, 1986

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

This paper outlines a cutting-edge probabilistic resource modeling workflow tailored to the Round Mountain epithermal gold deposit. The primary goal is to craft a robust and modern simulation process that enables the quantification and comprehension of anticipated discrepancies during mining reconciliation, offering a more precise gauge of expected gold quantities compared to conventional estimation models.

Dec 1, 2023

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 J. H. Kempton, D. Atkins, W. Locke

The scrutiny given to model predictions of pit-lake water quality has focused attention on the uncertainty associated with long-term predictions. Although comparison of probabilistic predictive modeling of water quality in existing pit lakes suggest that short-term predictions can bracket most parameters, un¬certainties in wall-rock reactions and the stability of groundwater composition and climate remain unquantified This overview of the uncertainties associated with longer-term predictions is presented as support for those considering policy decisions that must be made in the absence of reliable estimates of future conditions.

Jan 1, 2000

By J. H. Kempton

The scrutiny given to model predictions of pit-lake water quality has focused attention on the uncertainty associated with long-term predictions. Although comparison of probabilistic predictive modeling of water quality in existing pit lakes indicates that short-term predictions can bracket most parameters, uncertainties in wall-rock reactions and the stability of groundwater composition and climate remain unquantified. This overview of the uncertainties associated with longer-term predictions is presented as support for those considering policy decisions that must be made in the absence of reliable estimates of future conditions.

Jan 1, 1998

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

standpoint. The effect on efficiency of collisions

Apr 1, 1995

By 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 Twin Cities Mining Research Center. This Bureau of Mines paper describes the simulation of the basic production system at the working face, which includes drilling, blasting, mucking, and roof bolting. 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 multiple location systems. 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, 1974

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

The current economic climate and demand for iron ore has resulted in mine operators being prepared to accept aggressive slope designs and associated failures provided that they can be quantified (ie volume of failure and clean up costs, etc) and incorporated into the mining costs, at a feasibility study level. This has numerous implications for pit slope design/geomechanics. Typically when geotechnical engineers conduct slope stability modelling a single value, usually the average or mean value for model input parameters (ie structural orientations, material properties and hydrological conditions) are chosen. The implications resulting from using a single value for model input parameters will vary depending on how the modeller has chosen the value, ie should the modeller choose a mean value from a log-normal distribution of material strengths an optimistic representation of the stability may eventuate, consequently if the designer decides to conservatively downgrade the values by a nominal factor, a pessimistic representation of slope angles may occur, which would result in excessive stripping and mine development costs. A more realistic and representative way to model the inherent variability of geological/geotechnical conditions would be to do so probabilistically. Whereby the modeller can assess the variability of the geological structure as observed/recorded during the core logging process and a similar approach for the material strength properties. The final model output would be a distribution of factors of safety in relation to overall slope angles, ie probabilities of failure for individual slope angles could be determined. This output (graph) could be modified by the mining engineer to incorporate mining costs as well as clean up costs for the respective slope angles and associated failure volumes, ie probabilities of failure. The author intends to provide a detailed overview of the processes involved in deriving a geotechnical design, ie; starting from the data collection phase (core logging/face mapping), through to the data interpretation and formulation of slope parameters; determining the variability and uncertainties associated with each of the process; ensuring that it is adequately captured in the model input parameters; and how the mining engineer could utilise this information to derive final feasibility study mining costs.

Jan 1, 2009

This study introduces a new probabilistic approach to seismic stability analysis of embankments and slopes. The approach is based on Sarma's solution, which is modified through presentation of the seismic force by its horizontal and vertical components; i.e. the force may have an arbitrary inclination. The probabilistic modelling includes Monte Carlo simulation of the shear strength parameters of the soil mass, which are assumed to have a normal distribution. The probability of failure is determined based on the seismic co-efficient, which is treated as a random quantity. The probabilistic approach is illustrated through a solution of a numerical example from an opencast coal Mine.

Jan 1, 1992

By Rossen A. Halatchev

This study introduces a new probabilistic approach to seismic stability analysis of embankments and slopes. The approach is based on Sarma's solution, which is modified through presentation of the seismic force by its horizontal and vertical components; i.e. the force may have an arbitrary inclination. The probabilistic modelling includes Monte Carlo simulation of the shear strength parameters of the soil mass, which are assumed to have a normal distribution. The probability of failure is determined based on the seismic co-efficient, which is treated as a random quantity. The probabilistic approach is illustrated through a solution of a numerical example from an opencast coal mine.

Jan 1, 1992

By D. S. Young

The random variable transformation technique was introduced to make probabilistic structural analysis simple for such structures as slopes, dams, foundations, or retaining walls, where two shear strength parameters are required to analyze their stability by deterministic engineering methods. The Gaussian transformation was performed by using the Hermite orthogonal polynomial function. This transforms the experimental histogram into the standard normal distribution, whose mean is zero with a variance of one. Then, the transformed standard Gaussian variable was used for the bivariate normal probability analysis on the structure. The Gaussian transformation technique and the Hermite polynomial functions were chosen because the bivariate joint normal distribution is well-known and easily available for engineers. The binormal probability analysis was made on the probability region of a certain confidence level by superposing the critical line on the same probability region that divides the region into two zones: stable and unstable zones. The critical line was determined from the back calculation of the deterministic engineering method of the structural design. Finally, the probability of structural failure at a desired confidence level was calculated by simply integrating the volume of the binormal density surface above the unstable zone in the probability region. A simple case of slope analysis is introduced to illustrate this probabilistic approach, and its effectiveness and simplicity is demonstrated.

Jan 1, 1987

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