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A discrete fracture network (DFN) model based on non-parametric kernel density estimators (KDE) and directional-linear statistics is developed. The model provides a characterization of the fracture network with distributions of fracture orientation and size jointly. A solution to the Bertrand paradox is used for the calculation of disk sizes from trace lengths, the latter calculated from the intersection of disks and highwall faces by triangulation. A Poisson point process is applied for the generation of the model, with fractures assumed to be flat and circular in shape, the number of fractures per unit volume (P30) adjusted to match the experimental length of fractures per unit area (P21). Length censoring of traces due to the surface dimension is considered in the calculations by including semi-bounded traces, i.e., traces censored in one of their ends. Orientation and size biases are corrected with a weighting function in the random sampling. The truncation effect whereby no traces shorter than some cut-off length are recorded, is addressed by a randomized optimization algorithm. The joint fracture orientation-size distribution model developed is tested with trace maps of discontinuities measured from photogrammetric models of twelve highwall faces of quarry benches, with outstanding results. Computational advantages over traditional parametric fracture models are addressed.

The modelling of discontinuities in rock mass is undertaken with different measurement techniques and used to determine the in situ block size distribution (IBSD). Two monitoring techniques are employed: televiewer logging of boreholes and photogrammetry of highwall faces in a quarry bench; televiewer performs at the borehole diameter scale, while photogrammetry surveys at the entire bench scale. Ground sampling distances were, respectively, about 1 and 8.5 mm. The discontinuities are modelled as a stochastic discrete fracture network (DFN), with the number of discontinuities used in the simulation calibrated by the intensity per unit length (P10) on the televiewer data, or by the fracture density (P21) on the photogrammetry data, leading to different fracture networks. From the discontinuity network models, the IBSDs are calculated and discussed as function of the sampling scale (i.e. televiewer or photogrammetry data source) and of the fracture density. The goal is to compare the results from both techniques for rock mass structural characterization, to assess their limitations and shortcomings, and to show their potential complementarity at different sampling scales. The televiewer data provides smaller block sizes than the photogrammetry, following the higher number of fractures observed in the former. All volumetric distributions obtained are extremely well represented by Gamma with a power law tail distribution. Despite different location parameters, it is particularly remarkable that all distributions present very similar Gamma shape parameters. The constant log–log slopes of the tails provide evidence of multi-scale validity and a scaling invariant structure (more than two orders of magnitude) of discontinuities of the rock mass. The IBSDs and the scale effect are discussed in the light of the fragment size distributions from blasts carried out in the area characterized.

Currently, the charging procedure for sublevel caving mining is carried out with no prior information of the rock mass condition. Thus, engineers are blindsided to unexpected rock conditions and ill-prepared to address issues associated with collapsing boreholes . This results on charging problems and, as consequence, bad fragmentation of the rock after blasting which difficult ore loading and transportation as the gravity flow of the rock is reduced. This paper builds up the work done by Ghosh et al. (IJRMMS, 2018), to classify the geotechnical rock condition into five classes (solid rock, fractured rock, cave-in, minor and major cavity). From it, two applications based on the Measure While Drilling (MWD) technique have been developed: one for geotechnical rock condition of orebodies and the other for predicting the risk of collapse in boreholes. The work of Ghosh et al. has been improved into a geotechnical rock condition block model to simplify the quantitative assessment and automatic recognition of rock trends. A thorough correction of the MWD parameters has been also applied to minimize external influences other than the rock mass. From it, the risk of borehole collapses model has been developed by comparing different combinations of the geotechnical rock condition block-model with the charging length of 102 production fan-holes. The assessment of the number of collapsed and non-collapsed blastholes and the charging length/blasthole length ratio has been used to assign high, medium or low risk of collapse to each combination. The results predict collapses in the first half of the fan-holes for the high risk, collapses in the second half of the fan-hole for the medium risk and no collapses along the hole for the non-risk holes. The two models have been applied in large scale for two orebodies in the Malmberget mine, Sweden, which comprises 20 drifts and 5060 fan shape long-holes.

At present, modern jumbos equipped with MWD (Measure While Drilling) provide the position of the blastholes collar and, from the drill length and the azimuth and inclination angles (monitored outside the blasthole), the theoretical end position of the blasthole. Since the trajectory of the hole during the drill is not measured, deviations are not accounted with the result that the actual spatial position of the blasthole is unknown. This paper investigates the quality of the drilling in underground blasting operations with a view to quantify the distance of the position assessed by the MWD system with respect to the actual end position of the blasthole logged. For that, a Pulsar Micro Probe Mk3 has been used to measure the actual trajectory of several production blastholes, drilled in semi-automatic mode, by measuring inclination and azimuth values at 1 m intervals. The results indicate significant deviations between the actual end position of the blastholes and the end position given by the MWD system. Deviation measurements are compared with the MWD parameters. This points out that possible disturbance zones in the rock, indicated by peaks and drops in the variability of the rotation pressure and in the signals of feed and hammer pressure, are correlated with changes in the blasthole trajectory.

Blasting performance is influenced by mechanical and structural properties of the rock, on one side, and blast design parameters on the other. This paper describes a new methodology to assess rock mass quality from drill-monitoring data to guide blasting in open pit operations. Principal component analysis has been used to combine measurement while drilling (MWD) information from two drill rigs; corrections of the MWD parameters to minimize external influences other than the rock mass have been applied. First, a Structural factor has been developed to classify the rock condition in three classes (massive, fractured and heavily fractured). From it, a structural block model has been developed to simplify the recognition of rock classes. Video recording of the inner wall of 256 blastholes has been used to calibrate the results obtained. Secondly, a combined strength-grade factor has been obtained based on the analysis of the rock type description and strength properties from geology reports, assaying of drilling chips (ore/waste identification) and 3D unmanned aerial vehicle reconstructions of the post-blast bench face. Data from 302 blastholes, comprised of 26 blasts, have been used for this analysis. From the results, four categories have been identified: soft-waste, hard-waste, transition zone and hard-ore. The model determines zones of soft and hard waste rock (schisted sandstone and limestone, respectively), and hard ore zones (siderite rock type). Finally, the structural block model has been combined with the strength-grade factor in an overall rock factor. This factor, exclusively obtained from drill monitoring data, can provide an automatic assessment of rock structure, strength, and waste/ore identification.

A semi-analytical full-field solution for the radiation of seismic waves has been developed and applied to calculate the near-field vibration from blasting. The shape of the source function applied to the blasthole wall has been obtained from numerical modelling of detonation, with a peak value determined as the shock matching pressure of the detonation products and rock. Particle velocity and acceleration signals from four blasts have been recorded and used for the purpose of determining the quality factors (Q) of the rock mass, expressed as functions of the radial distance to the blasthole. The model consistency has been validated by verifying that the resulting peak particle velocity at the blasthole wall coincides with the particle velocity obtained from the explosive-to-rock shock matching calculation. Fracture zones are identified using a failure criterion based on principal stresses of the resulting Cauchy's stress tensor and uniaxial compressive and tensile strengths. Two variants of the industry-standard Holmberg-Persson approach have been compared with the full-field solution.

The mutual relation between Measurement While Drilling (MWD) parameters in percussive-rotary drilling is investigated in order to limit the number of MWD variables, and to select the more significant ones, that are required for a sound rock mass characterization. Cross-correlation of the MWD signals is used to determine their relations, the analysis of which brings a thorough understanding of the way that the rig control system governs the different parameters. Data recorded from six drilling machines, working in semi-automatic and manual mode, on three different rock types with different logging interval, have been analyzed. The results point out the feed pressure as the lead parameter that drives the adjustment of the other variables to optimize the drilling, thus being the upfront response to variations in the rock mass. Control parameters that limit this adjustment to minimize disturbances during the operation are also discussed. Finally, the influence of the rock mass condition on the MWD parameters response is studied.

In order to clarify the requirements for satisfactory coupling on rock, six methods to monitor vibrations with blasting seismographs are investigated in the longitudinal component of the vibratory motion. The methods studied consisted on placing the geophone mount on a granite surface freely (loosely), held with a sandbag, and attached with an anchor (the center of the geophone's mount was fixed with a plastic anchor, a bolt and a nut), thermal adhesive (glue), gypsum plaster (used as an adhesive) and double-sided tape. For each measuring condition, transmissibility in two mounts was assessed on a vibration shaker from 2 to 190 Hz at one or two vibration levels (5, 20 mm/s). The main findings of this work are: (1) Transmissibility varies with coupling method. It is flat at low frequencies and has a maximum at higher frequencies; in some trials mainly with anchored, glued and plastered such peak occurs outside the frequency range studied. (2) The frequency of the first maximum of transmissibility shifts towards smaller frequencies as the peak velocity increases when the bonding conditions are weak, as for free and sandbagged mounts. However, if the bonding is stiff enough, as for anchored or plastered mounts, transmissibility values at 5 and 20 mm/s are very similar. (3) The frequency of the first peak in the measured transmissibility provides a preliminary estimate of the performance of each method, so that its conditions of use should be defined upon frequency and velocity of the imposed motion, rather than using the anticipated peak acceleration, as it is currently made. These have been defined for the methods under study. (4) Anchoring and plastering provide the best performance, the later with smaller errors at high frequencies (>128 Hz). (5) The seismograph itself (not the coupling) is another source of error that should not be neglected specially for measurements in the low frequency range; large errors, exceeding by one order of magnitude those from coupling are obtained in the 2‒4 Hz band.

The damage from blasting to the remaining rock mass is analyzed with the purpose of developing a drilling index from measure while drilling (MWD) parameters, able to predict high risk of potential over- and under-excavated zones produced by blasting in the contour of a tunnel. A new methodology based on the comparison of scanner profiles of the excavated sections with the position of the contour blastholes, has been developed to obtain the excavated mean distance (EMD) between the blasthole and the excavated profiles at each MWD record position, which may be considered as a damage measure. MWD parameters, that describe the in-situ rock mass properties before the blast, are thoroughly normalized to remove external influences that may hide the actual response of the rig to rock mass properties and lead to wrong interpretations. 54 blasts, which comprise around 1700 contour blastholes, have been compared with more than 4000 excavated sections. A non-linear multiple-variable power-form model has been developed to predict the excavated mean distance as function of the normalized penetration rate, hammer pressure, rotation speed, rotation pressure and water flow parameters, and the lookout distance. These parameters combine the rotational, hydraulic and percussive mechanisms of the drill, and the confinement of the explosive charge with depth. Sources of uncertainty, unavoidable in the harsh condition in which the data were measured, such as drilling deviations, the scaling and primary support prior to scanning the excavated section, possible variations (unrecorded) in the explosive linear density, etc., have been assumed to be of random nature.

This paper investigates fragmentation in an aggregate quarry in the light of the fragmentation-energy fan concept. Six blasts were monitored, located one behind the other in the same quarry area. The rock structure was blocky, the water level and the usage of explosives were variable within and between the blasts; however, the distribution of explosive energy in the blocks was relatively uniform and the performance of both explosives per unit mass appeared to be similar. The powder factor above grade was between 0.28 and 0.44 kg/m3. Fragmentation of the plant feed was measured using an online digital image analysis system and three belt scales in the crushing plant. The oversize material that was not directly fed to the plant after the blast corresponds to 3–9.3% of the total. Data from image analysis was used to build the size distribution in the coarse range (fragments above 120 mm), and the passing fractions at 120 and 25 mm obtained from belt scales data were used in the range 120–25 mm. The non-dimensional percentile sizes between 10 and 90% for each blast are described through power functions of the powder factor above grade; the model coefficients (i.e. nine prefactors and nine exponents) are statistically significant. From them, using the principles of the fragmentation-energy fan and the Swebrec distribution properties, the fragmentation can be expressed in terms of the powder factor by means of five parameters: the fan focus coordinates and the three parameters of a function of the exponents versus the percentage passing. The model shows a good capability to describe fragmentation from 10 to 90 percentile sizes, with an expected error below 6% and a maximum likely error less than 15%.

The capacity of 17 functions to represent the size distribution of fragmented rock is assessed on 1234 data sets of screened fragments from blasted and crushed rock of different origins, of sizes ranging from 0.002 to 2000 mm. The functions evaluated are Weibull, Grady, log-normal, log-logistic and Gilvarry, in their plain, re-scaled and bi-component forms, and also the Swebrec distribution and its bi-component extension. In terms of determination coefficient, the Weibull is the best two-parameter function for describing rock fragments, with a median R2 of 0.9886. Among re-scaled, three-parameter distributions, Swebrec and Weibull lead with median R2 values of 0.9976 and 0.9975, respectively. Weibull and Swebrec distributions tie again as best bi-component, with median R2 of 0.9993. Re-scaling generally reduces the unexplained variance by a factor of about four with respect to the plain function; bi-components further reduce this unexplained variance by a factor of about two to three. Size-prediction errors are calculated in four zones: coarse, central, fines and very fines. Expected and maximum errors in the different ranges are discussed. The extended Swebrec is the best fitting function across the whole passing range for most types of data. Bimodal Weibull and Grady distributions follow, except for the coarse range, where re-scaled forms are preferable. Considering the extra difficulty in fitting a five-parameter function with respect to a three-parameter one, re-scaled functions are the best choice if data do not extend far below 20% passing. If the focus is on the fine range, some re-scaled distributions may still do (Weibull, Swebrec and Grady, with maximum errors of 15–20% at 8% passing), but serious consideration should be given to bi-component distributions, especially extended Swebrec, bimodal Weibull and bimodal Grady.

Ten functions (Weibull, Swebrec, Gilvarry, Grady and Lognormal, and their bi-component versions) are fitted to 448 sets of screened fragment size data from blasted and crushed rock. The ordinary least squares criterion has been used for the fits and two minimization techniques have been tested, in both cases running the problem repeatedly with different initial values of the unknown parameters in order to ensure a global minimum. There is a distinct behavior of errors across the passing range, which has been divided in four zones, coarse (>80%), central (80%–20%), fine (20%–2%) and very fine (

A model for the calculation of the productivity of cyclic excavators is developed. The production rate results as a product of an ideal, maximum, productivity rate (one of the coefficients of the model) times an operating efficiency. The latter is described as a function of three variables (rock strength, nominal bucket capacity and explosive energy concentration) and three more coefficients. The coefficients of the model have been obtained from field measurements in twenty production blasts at two open pit mines, for which mechanical properties of the rock, blasting characteristics and mucking rates were carefully measured. The model is statistically significant and explains up to 90 % of the variance of the production rate measurements.

Size distributions of fragments of crushed rock in conveyor belts and of blasted rock in a muckpile obtained by sieving are compared with the size distributions obtained by digital image analysis of photographs of the same materials taken on-site. Several calculation methods are tested, based on the raw distribution of fragment areas and on the volume-transformed ones. The influence of the calibration of the system on the results and the performance of the system in a non-calibrated mode are evaluated. The capacity of some distributions (Rosin-Rammler, Swebrec and lognormal) to fit the data in the coarse region (where particles can be delineated, i.e. discriminated individually) and to extrapolate to the non-delineated fines (where particles cannot be outlined and their contour delineated) is assessed. The error between the sizes measured and the sizes of the reference distributions (determined by sieving) increases from the coarse to the fines region. The maximum error at a given size depends primarily on its value relative to the fines cut-off (FCO) of the image analysis. In general, at sizes greater than the FCO, where the system is able to delineate fragments reliably, both volume and surface-based, calibrated, calculations can determine the sizes with maximum error expectancy of about 30%. Below the FCO, only the calibrated, volume calculation maintains a maximum error of 30%, down to sizes of about one fourth the FCO, rapidly increasing for smaller sizes. Where the calibration is done based on data above the FCO, errors can be large below this point, in excess of 80% at sizes half the FCO. In the fines range (sizes smaller than 0.2 times the FCO) the maximum errors can be close to or greater than 100% for most of the calculations and function fittings. Of the distributions tested, all of them are acceptable at sizes above the FCO; below that, the Swebrec function seems to adapt better towards the fines than the Rosin-Rammler and lognormal. Validerad; 2009; 20080826 (ysko)

Ten production blasts and one single-hole confined blast have been monitored in two quarries in order to assess the measurable forms of energy in which the energy delivered by the explosive is transformed in rock blasting. The seismic field from seismographs readings, the initial velocity of the blasted rock face obtained from high-speed video camera records, and the fragment size distributions from image analysis of the muckpile material are used to determine the seismic wave energy, the kinetic energy and the fracture energy, respectively, transferred in the blasting process. The blasting data and the methods of calculation of the energy terms from those are described in detail. Heat of explosion and useful work to 100 MPa have been used as descriptions of the energy of explosives. The maximum total energy measured accounts for not more than 26% of the available explosive energy if this is rated as the heat of explosion, though lower figures are usually obtained. The values measured for each of the energy components range from 2% to 6% of the total energy available for the fragmentation energy, 1–3% for the seismic energy and 3–21% for the kinetic energy. For the confined shothole, the seismic energy was 9% of the heat of explosion. The uncertainty of the calculated energies is analyzed from the variability of the measured data. Particularly important influential parameters are the treatment of the fines tail of the fragment size distribution in the determination of the fragmentation energy, and the use of P or S wave velocity values, and whether these are determined from in situ or from laboratory measurements, in the calculation of the seismic energy.

The operation of a digital image analysis system in a limestone quarry is described. The calibration of the system, required in order to obtain moderately reliable fragmentation values, is done from muckpile sieving data by tuning the image analysis software settings so that the fragmentation curve obtained matches as close as possible the sieving. The sieving data have also been used to extend the fragment size distribution curves measured to sizes below the system’s optical resolution and to process the results in terms of fragmented rock, discounting the material coming from a loose overburden (natural fines) that is cast together with the fragmented rock. Automatic and manual operation modes of the image analysis are compared. The total fragmentation of a blast is obtained from the analysis of twenty photographs; a criterion for the elimination of outlier photographs has been adopted using a robust statistic. The limitations of the measurement system due to sampling, image processing and fines corrections are discussed and the errors estimated whenever possible. An analysis of consistency of the results based on the known amount of natural fines is made. Blasts with large differences in the amount of fines require a differentiated treatment, as the fine sizes tend to be the more underestimated in the image analysis as they become more abundant; this has been accomplished by means of a variable fines adjustment factor. Despite of the unavoidable errors and the large dispersion always associated with large-scale rock blasting data, the system is sensitive to relative changes in fragmentation.

A microspheres-sensitized emulsion explosive, to be used in rock blasting tests, is characterized by means of the cylinder test. This test measures the expansion of a copper tube upon detonation of an explosive charge inside. Eight cylinder tests have been made with two different diameters (50 mm and 100 mm) and two different densities (1180 kg/m3 and 1030 kg/m3) in a 2 × 2 × 2 test matrix. The expansion energy is affected by the density but not by the test diameter, which suggests that this explosive, at the densities studied, behaves close to ideal already at 50 mm. The explosive velocity of detonation had been also measured within the trials. In addition, velocities of detonation were measured in six production blasts and reported here. The Jones–Wilkins–Lee (JWL) equation of state parameters have been obtained for this emulsion at the densities and diameters tested. The calculation method includes a radial expansion function, with a non-zero initial velocity at the onset of the expansion. The equations reflecting the CJ state conditions and the measured expansion energy were solved for the JWL parameters by a non-linear least squares scheme. These parameters have been validated with three different LS-DYNA models (Lagrangian-Lagrangian, Smooth Particle Hydrodynamic-Lagrangian, Arbitrary Lagrangian Eulerian-Lagrangian). All models show a good correlation with the test results when comparing them against the detonation pressure, the cylinder wall expansion, the Gurney limit velocities and the radial wall velocities. The Smooth Particle Hydrodynamic is the best numerical model for replicating the detonation pressure, the Lagrangian for the cylinder wall expansion radius and velocity history, and Arbitrary Lagrangian Eulerian on the overall performance. Arbitrary Lagrangian Eulerian and Smooth Particle Hydrodynamic techniques are widely used to describe the materials subjected to large deformations, such as explosives, on full-scale simulations for civil and mining applications. The good agreement between numerical and experimental results justifies the use of these methods to model the expansion of detonation products.