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By S. Dixon

The Phelps Dodge - PD/PERI Heap2D Model is a phenomenological stockpile leaching model that has been used to investigate the best operating practices for leaching chalcocite. The model was used to investigate the interrelationships of raffinate application rate, aeration rate, raffinate iron grade, acid cures, lift height, crush size, bulk density, air injection spacing and raffinate drip emitter spacing.

Jan 1, 2006

By Nader Golchinfar

The V-shaped breakout zones around excavation boundary have been captured by a variety of numerical methods such as FEM and DEM methods and failure criteria such as linear Mohr-Coulomb and non-linear Hoek-Brown failure criteria. Diederichs (2007) used Hoek-Brown parameters in his spalling parameter approach; however, it is convenient to use the Mohr-Coulomb failure criterion in numerical modeling because the material parameters can easily be determined from triaxial tests. It is shown in this study that when peak and residual strength parameters as well as dilation angle are properly defined, the brittle Mohr-Coulomb failure criterion can be used to model depth of failure near underground excavations satisfactorily.

Jun 1, 2012

By Trevor Saldanha, Stephen Grano

A key uncertainty in flotation modelling is determining, a priori, the proportion of each mineral which will develop a certain rate constant for different feeds of variable liberation and hydrophobicity. First and foremost is the ability to predict the proportion of minerals that will not be recovered, even at very long flotation times, and which therefore report to the tailing stream as the non-floatable fraction (i.e., having a zero rate constant). Recent empirical evidence has shown there are at least two factors which contribute to heterogeneity in flotation rates and, in particular, the appearance of a non-floatable fraction - heterogeneity in the distribution of adsorbed collector amount on a particle-by-particle basis, even for the same liberated mineral in the same size fraction, and the existence of a critical contact angle below which the bubble-particle union is unstable. In this paper, inferred measures of the critical contact angle for liberated particles are compared with stability model calculations. This has demonstrated that the dependency of the critical contact angle with particle size and mineral specific gravity are explicable by bubble-particle stability considerations. This argument is further extended to the flotation behaviour of composite particles, as a function of liberation class, in which the wetting perimeter of the attached bubble on the composite particle surface is constrained by the presence of a surrounding hydrophilic domain for the case of simple binary composites. Reasons for the different flotation behaviour of composite particles having different textures, as noted in the literature, are also discussed in terms of the stability of the bubble-particle union.

Jan 1, 2014

MODELLING FOR DESIGN AND CONTROL AT KALGOORLIE NICKEL SMELTER Modelling at KNS has been driven by a need to have better tools to answer questions about control, design and optimisation of the plant. This paper describes a number of modelling tools developed for use at KNS and how the development of modelling tools fits with a design and control strategy. In the area of control, a thermodynamic model has been developed to allow process parameters to be calculated. The model allows for the automatic selection of data from a laboratory data base, desired operating set points are input and the operating parameters are calculated. The model has the ability to adjust the burner efficiency and the furnace heat loss depending upon conditions. To assist with the testing of proposed furnace design changes, various mathematical models of the burner and shaft have been created using PHOENICS. These models are particularly well suited to combustion heat transfer and flow aspects of both the burners and shaft. Validation of these models have been based on novel sampling and measuring techniques in the shaft and also by using scale and cold models. Overall plant energy and cost structures can be analysed using a flowsheet simulation, developed to evaluate potential alterations to the plant flowsheet. This model system allows the global evaluation of process changes.

Jan 1, 1993

By Donald Thompson, Jessie Bonner, Ileana Tibuleac

Predicting ground motion from complicated mining explosions is important for mines developing blasting programs in regions where vibrations must be kept below certain levels. Additionally, predicting ground motion from explosions in complex 3D media is important for source size estimation for nuclear treaty monitoring. Both problems have been addressed under the development of a new series of programs including: 1) Generalized Fourier Methods to generate synthetic seismograms (Green’s functions) in 3D media for a moment tensor source implementation and 2) MineSeis3D, a program that simulates seismograms for delay-fired mining explosions with a linear relationship between signals from small size individual shots. To test the programs, three-component seismic recordings of three production shots at an iron mine in northern Minnesota were compared to synthetic waveforms in 3D media. Comparison of the observed and synthetic waveforms shows promising results. The shape and arrival times of the normalized synthetic and observed waveforms are similar for most of the stations. The synthetic and observed waveform amplitude fit is best for the vertical components in the mean 3D model but not as promising for the transversal components. The observed effect of spall on the waveform spectra was weak in the case of fragmentation delay-fired mining explosions. Commercial applications of the code could provide data needed for designing explosions that do not exceed ground vibration requirements posed by the United States Department of Interior, Office of Surface Mining.

Jan 1, 2005

By Y. J. Wang

In the mathematical analysis of electrical networks, the electrical devices are often modeled using idealized network elements such as current sources, voltage sources, and resistors. An analogous approach is outlined here for the modeling of mine ventilation networks, which can be considered nonlinear resistive networks. The modeling technique proposed uses five basic (non-reducible) elements: the H element, the Q element, the D element, the R element, and the N element. These elements are characterized by their (a) pressure gain or loss, (b) air quantity, and (c) pressure-versus-quantity relationship, each of which may be known or unknown. In addition to the definition of the basic elements, the necessary conditions for which there exists a unique solution are discussed. This is performed using theoretical developments derived from electrical circuit theory and illustrated in example networks. The proposed procedures are useful in the solution and characterization of mine ventilation networks.

Jan 1, 1996

By C. V. Deutsch, D. A. Silva

The geologic modeling of multiple domains is required for the prediction of mineral resources and reserves. In general, explicit methods have wide acceptance among modelers due to the ability to manually add deemed important trends and geological features into the models. As an alternative, implicit geologic modeling techniques are increasingly adopted to reduce professional time requirements. These methods aim for objective, repeatable and flexible models by replacing the manual time-consuming interpretation of sections with the interpolation of signed distance values. These techniques, however, have been developed for the binary case of two domains at a time. The current paper presents an algorithm that extends the binary case to multiple domains. The method is able to transfer large-scale geological features from data to geologic models. A case study illustrates the benefits of the algorithm and practical implementation considerations.

Jan 1, 2016

By Raj K. Rajamani, Nikhil Dhawan

"Agglomeration has become common pre-treatment step to improve heap leach percolation thereby recovery, the fundamental understanding of the agglomeration process for crushed ores is still lacking. Agglomeration is required for ores which either contain excessive amounts of clay or an excessive quantity of fines generated during mining and crushing. Numerous experiments have been carried out in laboratory scale batch drums using different ores. It has been found out that experimental agglomerate size distributions exhibit self-preserving spectra. The self-preserving/ similarity distribution of the agglomerates is found to be independent of operating conditions and is uniquely determined by the size enlargement mechanism. An empirical model based on the absolute difference between moisture applied and optimum moisture was developed. This model uses self-preserving spectra in the form of a Rosin-Rammler distribution function to predict size distribution at different operating conditions. The empirical model was considerably easier to work with plant scale agglomeration drums. Also, a test known as dip test is developed which improves fundamental understanding of the agglomerate formation and growth mechanisms. This test also provides the progeny size distribution of each agglomerate size. The progeny size distribution was analyzed with a model that partitions the particles into a host and guest category. The ensuing partition coefficient identifies the behaviour of a particle as a host for other particles or a guest layering on other particles. This concept helps in identifying the type of agglomerate that would result for a specific feed size distribution. INTRODUCTIONHeap leaching is one of the hydrometallurgical processes that have served as a green and economically viable process for the treatment of low grade complex ores of copper, uranium, nickel, silver and gold (Dhawan et al., 2013). Heap leaching appears to be a favorable candidate for the least energy consuming process for low grade ores. In heap leach operations nowadays a pretreatment step known as crushed ore agglomeration has been implemented (Dhawan et al., 2013). A bed of agglomerates improves the uniform percolation of solution through the heaps of ore. Therefore, it was possible to treat wastes and mill tailings via agglomeration and heap leaching. Agglomeration pretreatment is required for ores which either contain excessive amounts of clay or an excessive quantity of fines generated during mining and crushing (Bouffard, 2005; Dhawan et al., 2013).While agglomeration has become common practice pretreatment step in heap leach operations, the fundamental understanding of the crushed ore agglomeration process is still lacking. The author reviewed publications up to 2012 on the crushed ore agglomeration process and did not come up with modeling studies on the topic (Dhawan et al., 2013). Some of the possible reasons can be the stochastic nature of the process, experimental difficulties, and lack of instrumentation for fundamental studies."

Jan 1, 2016

By F. Andrieux

"Extruded aluminum profiles are increasingly used for lightweight vehicle construction. Since fracture strains of aluminum profiles are relatively low, damage modeling is crucial for reliable crash simulation. For aluminum profiles, not only the stress state but also the orientation influenced both the deformation and damage behavior. For the material characterization smooth tensile tests were performed in six orientations, both stress-strain curves and r-values were registered. Moreover notched tensile and shear-tension tests were performed in three directions. Finally punch specimens were tested to investigate biaxial loading. Digital image correlation (DIC) analyses were performed to determine local strain values such as critical values at failure. Numerical investigations were conducted with the strain based damage model GISSMO, which is well suited and widely applied for crash simulation. For a strain based failure model the choice of the deformation model is crucial. Deformation models with increasing complexity were investigated to find the best compromise over all experiments. It was found that there is still a great requirement on development of a material model which describes the orientation dependence of the hardening behavior over all stress states in order to be able to use a strain based failure model reliably.INTRODUCTION Weight reduction is an important step for less energy consumption and as a consequence aluminium is increasingly used in automotive parts. An important field of application is the well-established aluminium extrusion which allows the realisation of quite complex shapes of profiles required for an innovative lightweight design with integrated functions. Typical applications are chassis parts, bumpers, crash elements, air bags, etc. Especially the Al–Mg–Si medium strength alloys of the 6000 series can be easily extruded to form complex profiles and prevail for extrusion. Since fracture strains of aluminum profiles are relatively low, damage modeling is crucial for reliable crash simulation. For aluminum profiles not only the influence of the stress state but also the orientation with respect to the extrusion direction have an influence on both the deformation and damage behavior and need to be characterized. The effect of orientation on deformation behavior has been intensively investigated in the last decades and material models haves been proposed (e.g. Barlat & Lian, 1989; Barlat, Lege, & Brem, 1991; Barlat et al., 2003) to describe accurately anisotropic behavior. However it can be noticed that the parameters of anisotropic material models often rely on the yield stress in different directions, which means that the effect of strain hardening is not automatically accounted for. The accuracy of the models at large deformation is not guaranteed and has to be verified. In contrast to deformation models both the characterisation and the modeling of anisotropic damage behavior are not systematically studied. Isotropic failure models based on a critical strain as function of stress triaxiality (ratio of the hydrostatic stress to von Mises equivalent stress) are widely used for crash application (e.g., Bai & Wierzbicki, 2010; Sun, Andrieux & Feucht, 2009; Sun et al., 2013). The mechanisms of failure are manifold and not fully understood; to develop an anisotropic failure model it is mandatory to also have experimental data in different orientations for loading scenarios other than uniaxial tension, e. g. shear, biaxial tension, which implies an extensive experiment plan. This makes the development of failure models more challenging than deformation models for which it is possible to develop a reasonable anisotropic model using the framework of yield function and calibrate the material parameters based on results of tensile tests in different directions. Moreover the development of deformation and failure models are intricate as the variables governing the damage evolution are predicted by the def"

Jan 1, 2018

By A. Datta

An appropriate scale-up methodology is very useful for ball mill design and optimization of the grinding circuit. To date, the scale-up is based on the selection and breakage function model using lab mill data. However, a major drawback of that approach is that the charge motion in a lab mill is vastly different from that in a large industrial mill. Therefore, in the methodology proposed here, first the energy of individual collision in the mill is computed employing the discrete element method (DEM). Then the breakage of particles as a function of collision energy is studied in a separate experiment. Together, this information constitutes what is known as collision energy based population balance model. The appropriateness of this model is shown for different batch grinding mills.

Jan 1, 1999

By K. Baris

Methane (CH4) present in coal seams, generally known as Coalbed Methane (CBM), Coal Mine Methane (CMM) or Coal Seam Gas (CSG), is a major energy source, as it is the primary constituent of natural gas. At the same time, released methane is a potent greenhouse gas (GHG) and a major safety hazard in underground mining operations. Therefore, a considerable effort has been undertaken to develop coal bed methane extraction and utilization technologies that can achieve both environmental and safety benefits. Countries with significant coal reserves and gassy seams, i.e., USA, Australia, Canada, China, India, Poland and Germany have developed mature methodologies and practices to extract, before and during mining, and utilize significant amounts of methane from coal seams. Nevertheless, on a global scale, methane recovery remains untested and many technical and economic challenges require urgent attention. The research presented in this paper, sponsored by the United States Environmental Protection Agency (EPA), is focused on the Zonguldak Basin, the only hard coal region in Turkey. The basin is known to contain very gassy coal seams and consists of three major regions: Armutcuk, Zonguldak and Amasra. Among the three, the Amasra coalfield is considered as the most favorable for CBM recovery, as it comprises of deeper coal seams and where a private company, Hema Enerji A.S. (Hema) is already developing coalbed methane production facilities. This study aims at developing a reservoir model to predict the potential CBM recovery from the CBM-2 well, the only producing CBM well drilled by HEMA Enerji A.S in the Amasra coalfield. History matching was utilized to model the 15-day production data and uncertainty analysis was performed to estimate the optimum values for the reservoir parameters. The produced model yielded an average production rate of 143 m3/day for 10 years. The total amount of CH4 to be produced during this period was 0.53 million m3. Furthermore, the total amount of GHG to be avoided was estimated at 6585 tCO2e.

Aug 1, 2013

By A. Sand

Within stamp-charged coke making a large volume of coal is compacted to one single coal cake before entering the coke oven chamber. This is done by means of several falling stampers in a stamping machine having a mold nearly of the oven?s dimensions. Producing a high quality coke also from inferior coals requires a cake density of approximately 80% of the coal density. Besides that the industrial stamp-charging process demands a minimum mechanical strength of the coal cake to move it from the stamping mold into the oven chamber without failure. Densification and the build-up of cake strength were investigated earlier in stamping tests using a micro-stamping device. The quantities derived from these tests (as e.g. cake density or porosity) represent average values for the entire cake. Statements describing the local compaction state at different heights are difficult to achieve without destructing the cake. In order to gain better insight into the densification process and the inner structure of the coal cake a computational model based on the discrete element method (DEM) has been set up using 2 and also 3-dimensional simulation software. The stamper?s position and velocity as well as the force acting on the stamper were monitored and the model?s response was compared against measurement data from laboratory stamping tests. It was possible to reproduce the force and displacement pattern of the stamper in response to the viscoelastic properties of the cake using standard DEM bonding and contact models. Furthermore, the rearrangement of particles in response to the compaction by the stamper was tracked by calculating their displacement at the point the stamper hit the coal surface. The latter can also be used as indicators of particle deformation or breakage. By defining control points at different heights the particle displacement, stress and strain rates, porosity could be studied at different heights. Keywords: coke making, coal stamping, compaction, agglomeration, DEM, simulation

Sep 1, 2012

Many investigators believe that column flotation cells offer significant advantages over standard mechanical machines for the flotation of fine particles. However, because of their unique design and operation, conventional techniques for flotation cell scale-up and design cannot be applied to columns. In an attempt to help alleviate this problems a population balance model based on first principles has been developed for fine particle flotation in a column. Two different terms have been considered in the model, i.e., transport and rate. Transport terms, incorporating fluid flow and bouyancy, are used to describe the movement of air bubbles, unattached particles and bubble-particle aggregates along the length of the column. Rate terms, which describe the bubble-particle attachment process, have been derived from first principle considerations. Because the model is based on first principles, it can be useful for the design, control, optimization and scale-up of column flotation cells.

Jan 1, 1987

By Troy Williams, Chris Preston, Ian Lipchak

"Underground blasting operations are challenging from the standpoint of the distribution of explosivesenergy representative of ring blasting. Energy from both shock and pressure regimes of commercialexplosives may appear concentrated in the collar region of a typical ring blast and diluted at the toes of holes due to the oblique geometries of blastholes. The non-homogenous nature of ore in whichexplosives are distributed via drillholes, adds to the complexities of generating particulate profiles from fragmented material with consistencies that are predictable from blast pattern to blast pattern - well suited for specific underground handling equipment and mill processing. In an ideal world, it would be the blasting operations themselves that represent the primary crushing mechanism, or at least mitigate mechanical crushing that can comprise a large component of the cost in generating suitable muck. This paper presents a dynamic break view in 3D that allows a planner to visualize the potential break zone around a blasthole generated by an explosive load using a Kleine field. Simple as it sounds, this methodology provides information that can be used in conjunction with cavity monitoring surveys (CMS) to potentially judge dilution due to overbreak as well as recovery for a typical blast. As examples, there are two break geometries that are examined regarding circular breaks and elliptical breaks around blastholes. Using a Kleine field to define break, a planner generated isosurface can be generated and compared to CMS data for calibration and prediction, using AEGIS 3D ring design software."

Jan 1, 2016

By C. Tan, C. Detournay

Wellbore stability is a major concern for drilling in naturally fractured formations. The infiltration of drilling mud into the fractures is a factor, which may compromise wellbore integrity due to the loss of strength experienced by the fractures. The reduction in the fracture frictional and cohesive properties is attributed to weakening of the infill materials and lubrication of fracture asperities by the mud filtrate. One way to investigate the influence of mud infiltration on wellbore stability in fractured formations is to use a numerical modeling approach. A requirement for the numerical model is the ability to predict the region of mud infiltration. This paper describes a numerical technique to model the extent of mud infiltration for application in coupled fluid-mechanical simulations in densely fractured rock masses using the computer code, UDEC. Several factors are considered including fracture pattern, in-situ stresses, reduction in joint frictional angle and cohesion, viscosity of the mud filtrate and fracture plugging. Results of numerical simulations are presented to illustrate the technique and show the influence of these factors on the extent of mud infiltration. Un des problèmes importants posés par le forage en milieu fissuré saturé, est celui du maintient de la stabilité du puit. L’infiltration de boue de forage dans le massif peut avoir pour effet de réduire les propriétés frictionnelles et cohésives des fractures et de compromettre ainsi la stabilité du puit de forage. Le radoucissement des propriétés des fractures est attribué à la dégradation du materiau de remplissage et au pouvoir lubrifiant des boues. L’analyse numérique offre un moyen d’investiguer l’influence jouée par l’infiltration de boue sur la stabilité du puit. Un des critères de sélection du modèle numérique sera son pouvoir de prédiction du domaine d’infiltration de boue. Cet article décrit une technique numérique permettant de modéliser l’infiltration de boue de forage dans le cadre de simulations hydro-mécaniques, en milieu à haute densité de fractures, effectuées avec le logiciel de calcul UDEC. Parmis les facteurs tenus en compte, on trouvera la nature du réseau de fractures, les contraintes in-situ, le radoucissement en friction et cohésion des joints, la viscosité de la boue et le bourrage des fractures. Des résultats de simulations sont présentés pour illustrer la technique et montrer l’influence de ces facteurs sur la taille du domaine d’infiltration de boue. Bohrlochstabilität ist ein wichtiger Aspekt für das Bohren in geklüfteten Gebirgsformationen. Das Eindringen der Bohrlochstützflüssigkeit in die Klüfte kann die Bohrlochintegrität wegen des Verlustes der Festigkeit des Kluftsystems gefährden. Die Reduktion der Reibung und kohäsiven Eigenschaften ist der Schwächung der Kluftfüllung und der Schmierwirkung der eingerungenen Stützflüssigkeit in Bezug auf die Kluft-Asperities geschuldet. Numerische Berechnungen sind ein Weg zur Untersuchung des Einflusses der Infiltration der Bohrlochstützflüssigkeit auf die Bohrlochstabilität in geklüfteten Gebirgsformationen. Eine Voraussetzung für numerische Modelle ist die Fähigkeit den Bereich der Infiltration der Stützflüssigkeit zu prognostizieren. Diese Publikation beschreibt ein numerisches Verfahren, um die Reichweite der Infiltration von Stützflüssigkeiten mittels fluid-mechanisch gekoppelter Simulationen im engständig geklüfteten Gebirge mit dem Programm UDEC zu modellieren. Verschiedene Faktoren, wie Kluftmuster, Gebirgsspannungszustand, Reduktion von Kluftreibungswinkel- und kohäsion, Viskosität der Stützflüssigkeit und Rissabdichtung wurden untersucht. Ergebnisse numerischer Simulationen werden präsentiert, um die Vorgehensweise zu illu

Jan 1, 2003

By S. P. Mehrotra, P. C. Kapur

A phase-species classification is suggested for the mathematical models of flotation kinetics. Important models are discussed and the structure of their rate constants and parameters is analyzed. Split or enhancement factors are formulated for different kinetic models. The steady state dynamics of the flotation circuits can always be described in terms of these factors. For simulation of circuits, feed is characterized in a formal manner starting from a multivariate distribution of particles in flotation rate, size and mineral content. Synthesis of optimum circuits which simultaneously searches for the best process variables and structural parameters from a generalized master network is described. Trends in the areas of search algorithms, role of middlings and feed identification etc. are indicated.

Jan 1, 1989

By Murali Thirukkonda, Rahul Shah, Srinivas Tangrila, Shankar Rachakonda, Jan Kajuch, Arthur Gurson

"High-temperature superconductors have potential for a variety of applications such as power generators, superconducting magnets for mine sweepers or ship propulsion motors, and magnetic levitation transportation systems. Interest in the use of superconducting wires and tapes increased dramatically after the discovery of high-critical-temperature (high-Tc) oxide superconducting compounds, which offer operating temperatures above that of liquid nitrogen. Several techniques have been proposed to produce commercially viable high-Tc oxide based superconducting wires. One of the promising methods involves multi-pass powder-in-tube (PIT) wire drawing followed by rolling and heat treatment. This work focuses on the development of a numerical model to simulate the PIT drawing process for fabrication of long lengths of silver sheathed Bi-2212 superconducting wires. The finite element based model was used to predict densification of the oxide powder, wire drawing forces, and silver sheath thickness during drawing. A cap-type pressure dependent constitutive equation was implemented in the model to simulate the powder behavior. The model incorporated experimentally obtained material data for the silver and powder. Results indicate that powder densification is increased by decreasing the initial silver thickness and increasing the silver strength. Data from wire drawing experiments were used to verify model predictions. IntroductionSuperconducting wires and tapes can be used to carry large dc currents with no measurable loss due to resistivity. When used in superconducting magnets for power generators, motors, levitation devices, magnetic detectors, or energy storage devices, they could potentially result in significantly reduced energy losses. In the past, most prototypes were tested in liquid helium at 4.2K [1]. However, the necessity to provide liquid-helium cooling systems proved to be a serious limitation in commercialization. In 1986 high-critical-temperature (high-Tc) oxide superconductors were discovered [2], which could allow for higher operating temperatures above liquid nitrogen (77 K). Since then, both academia and industry have concentrated their efforts on the development of high-Tc oxide superconducting wires, tapes and coils. As yet, large scale fabrication of long lengths of these wires with the required current carrying capacity and mechanical properties remains an enormous challenge."

Jan 1, 1994

By Anil Saigal, Jr. Fuller, Said Jahanmir

"All-ceramic crowns, including glass-infiltrated spinel composites, are coming into widespread use because of their superior aesthetics and chemical inertness. This study investigates the residual stresses that are developed in these composites as a result of cool down from the glass-infiltration temperature to room temperature due to slight mismatch in the coefficients of thermal expansion and its effect on the mechanical behavior of these composites. Two-dimensional finite element simulations were performed using an object oriented finite element program OOF. The OOF program is a combination of two programs. The first program, PPM200F, is designed to read an image file such as a micrograph. The individual pixels that constitute the micrograph may be collected into groups and their material properties assigned. PPM200F is then used to create the finite element model/mesh that OOF then reads. The average residual stresses are found to be tensile in the spinel matrix and compressive in the infiltrated-glass. There is large variation in residual stresses and strains from location to location with presence of locations at which the glass is under tensile stress. The crack initiation and initial propagation in glass-spinel composites is at the glass-spinel interface in both the glass and the spinel. The presence of residual stresses can lead to lower crack initiation stresses and degrade the mechanical properties of the composites.IntroductionGlass-infiltrated spinel ceramics are in clinical use as core materials in all-ceramic crowns and as inlays and onlays (1-3). Advantages of ceramic composites include near net-shape forming with high strength in the infiltrated state. Besides, spinel is quite translucent and may potentially be used without a veneer. However, these ceramic composites are subject to damage accumulation from repeat oral contact loading and often fail after a few years of use (4). This paper examines the residual stresses that are developed in these composites, after cooldown from the glass infiltration temperature to room temperature, due to the slight mismatch in the coefficients of the thermal expansion of the two phases."

Jan 1, 2001

By Jaime Herrero, Santiago Gómez, Pablo Segarra, José Ángel Sanchidrián

This paper presents a mathematical model for the study of the 2D movement of blast bench faces based on the high-speed video analysis of three blasts at El Aljibe quarry (Spain) recorded at 2,000 frames per second. In these blasts, a set of bags of 0.75 × 0.75 m were placed in front of a selected blasthole defining a reference plane in which to study the kinematics of the movement. The burdens range from 3.86 m to 5.54 m, with a bench height of 12–13 m. An affine transformation system was calculated to convert coordinates from the video images into actual spatial coordinates. The problem is established from a multi-objective minimization approach in order to simultaneously optimize two defined objectives: trajectory fitting using Total Least Squares regression, and time–displacement regression using Ordinary Least Squares. Muti-objective minimization formulation produces Pareto plots of non-dominated solutions, i.e., optimal combinations of initial velocities and response times, (i.e. time between detonation and the onset of bench face motion). From the Pareto frontier, the most balanced solution is selected. Blast response time lasts only a few milliseconds and appears so brief at the frame rate used that it is difficult to detect visually. In this context, the bi-objective optimization-based approach proves to be a more robust tool than frame-by frame survey for quantifying such a rapid event while also maintaining a strong performance in the trajectory fitting task. Root Mean Square Error (RMSE) for the two minimizations average 0.22 m and 0.13 m, respectively. The initial velocities obtained range from 4 to 17 m/s, and the response times 0.7 ms to 21.7 ms. An analytical model is also presented for predicting fragments initial velocity and response time as functions of blast geometry and rock mass properties, explaining approximately 87% of the total variability.

Jan 26, 2026

By D. D. Bolstad, S. M. Dar, T. W. Smelser, H. C. Pettibone

The use of roof bolt supports has reduced the number of fatal and nonfatal roof fall accidents in coal mines. Roof fall accidents, however, still occur far too frequently. Roof bolting plans are based almost entirely on trial and error, which inevitably leads to underdesign or overdesign with regard to bolt length, spacing, tension, and bolt type for the specific conditions. Underdesign poses safety problems, and overdesign leads to unnecessary costs. Guidelines are needed to select and design optimum roof-bolt plans that will maximize safety and minimize cost. Despite the use of 100 million roof bolts per year, the theory of roof bolting remains underdeveloped. Underground tests designed to provide this knowledge have been only partially successful owing to the many uncontrollable geologic variables present in underground mining situations. The Bureau of Mines believes that the best approach is to conduct a laboratory model study in correlation with finite-element analysis (FEA) and field verification, where these variables can be tightly controlled and measured. A physical model allows precise performance measurement of different bolt types as a function of a wide range of precisely measured parameters. Although the model being used is idealized and limited in size, it serves as a reliable basis for confirming the mechanism of rock reinforcement by bolting and the accuracy of the computer FEA approach to modeling mining problems.

Jan 1, 1984