Block Size Distribution Research Articles

Models Development for Prediction of Blast Efficiency and Total Charge in a Typical Quarry

The prediction of blast efficiency is usually achieved by using models; this in turn, gives better and more efficient rock fragmentation. However, the accuracy of the prediction often times relies on the model development validation. In this study, models were developed and compared upon validation for predicting the blast efficiency and total charge required for efficient fragmentation using artificial neural network (ANN). Rock samples were gathered from the study are, and the uniaxial compressive strength (UCS) test was carried out on all the samples based on international standard. The average UCS obtained from the rock samples at the Eminent quarry (EQ) is 153.61 MPa. The dimension of in-situ rock mass considered in the study area is 60 m x 40 m, and the in-situ block sizes obtained vary from 2.02 m2 to 3.20 m2. The average percentage value of F50 obtained from the Split-Desktop image analyses is approximately 72.44 cm. The various results obtained from the UCS, in-situ block size distribution, image analysis of the blasted rocks and the total charge were used to develop the models for the prediction of blast efficiency. The key issue of concern about these models is that they are mostly site specific and the fact that if they perform well in a location does not guarantee the other. Hence, the validation and suitability of these models on the mine site. The blast efficiency prediction using ANN is compared with measured efficiency and the value of coefficient of determination, R2 obtained is 0.9733. The value of the coefficient of determination, R2 obtained from ANN by comparing the prediction of the total charge and the measured total charge is 0.9773. The findings showed that, the proposed ANN based mathematical models are suitable and thus, give better prediction to blasting efficiency and the possible total charge.

Numerical Study on the Characteristics and Control Method of Coal Leakage between Supports in Integrated Mining of Extremely Loose and Soft Coal Seams

Extremely loose and soft coal seams, with a Platts coefficient of less than 0.3, are easy to break in the process of integrated mechanized roof coal mining and are prone to spilling and piling up between the hydraulic supports, which is a safety hazard for the movement of equipment. The coal particles must be cleaned up manually, resulting in reduced resource recovery rates and lower mining face efficiency. To effectively mitigate and control the problem of coal spillage accumulation amidst hydraulic supports, this study utilizes discrete element numerical simulation to examine the characteristics of block size distribution and the spilling process during the crushing of highly loose and soft top coal. By taking into account various parameters associated with shelf spacing, this research identifies key factors for controlling arching and self-stopping phenomena in top coal particles. The study findings suggest that the uppermost coal layer undergoes significant fragmentation during the integrated mining process of loosely packed and soft coal seams, resulting in a higher probability of coal leakage issues observed near the rack’s coal wall side and at the end of the roof control area. The key factors contributing to the self-arresting of spilled coal particles include inherent characteristics of the coal body, particle diameter, and stand spacing. In this specific mine under investigation, an arch formation naturally occurs to prevent further leakage when the distance between stands is less than eight times the diameter of particles, and after process correction, the average time saving for a single shift of manual floating coal cleaning at the working face is about 2 h, and the proportion of time saving is more than 50~75%.

Determination of meaningful block sizes for rockfall modelling

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rockfall blocks are often fragmented due to the preceding fall process. The in situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in situ block size distributions with many blocks within the whole range of block sizes. In the current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model synthetic rock masses on the basis of discrete fracture networks. They statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine in situ block size distributions. We wanted to know whether the in situ block size distributions derived from the synthetic rock mass models can be described by probability distribution functions, and if so, how well. We fitted various distribution functions to three determined in situ block size distributions of different lithologies. We compared their correlations using the Kolmogorov–Smirnov test and the mean-squared error method. We show that the generalized exponential distribution function best describes the in situ block size distributions across various lithologies compared to 78 other distribution functions. This could lead to more certain, accurate, verifiable, holistic, and objective results. Further investigations are required.

Stochastic Process Leading to Catalan Number Recurrence

Motivated by a simple model of earthquake statistics, a finite random discrete dynamical system is defined in order to obtain Catalan number recurrence by describing the stationary state of the system in the limit of its infinite size. Equations describing dynamics of the system, represented by partitions of a subset of {1,2,…,N}, are derived using basic combinatorics. The existence and uniqueness of a stationary state are shown using Markov chains terminology. A well-defined mean-field type approximation is used to obtain block size distribution and the consistency of the approach is verified. It is shown that this recurrence asymptotically takes the form of Catalan number recurrence for particular dynamics parameters of the system.

Cloud detection algorithm based on point by point refinement

In order to limit the interference of cloud noise on ground scene information, cloud detection has been a hot issue in research on remote sensing image processing. Cloud detection labels the clouds in remote sensing images at the pixel level. The majority of early cloud detection systems rely on manually created feature and threshold segmentation with limited generalizability. Remote sensing cloud detection based on deep learning has improved in accuracy and speed thanks to the quick development of convolutional neural networks, but it is still unable to satisfy practical application requirements when dealing with sceneries with variable cloud block size and sparse distribution. To this end, this study proposes a cloud detection algorithm based on point-by-point refinement based on the idea of coarse to fine. Specifically, firstly, the residual module is introduced in the U-Net network to extract more features; secondly, the point-by-point refinement module is designed to filter out the areas in the remote sensing images where the clouds are easily detected wrongly for optimization and re-prediction, and then produce finer-grained and more accurate cloud detection results. The quantitative and qualitative experiments validate the effectiveness of the proposed method.

Genetic characterisation of the Connemara pony and the Warmblood horse using a within-breed clustering approach

BackgroundThe Connemara pony (CP) is an Irish breed that has experienced varied selection by breeders over the last fifty years, with objectives ranging from the traditional hardy pony to an agile athlete. We compared these ponies with well-studied Warmblood (WB) horses, which are also selectively bred for athletic performance but with a much larger census population. Using genome-wide single nucleotide polymorphism (SNP) and whole-genome sequencing data from 116 WB (94 UK WB and 22 European WB) and 36 CP (33 UK CP and 3 US CP), we studied the genomic diversity, inbreeding and population structure of these breeds.ResultsThe k-means clustering approach divided both the CP and WB populations into four genetic groups, among which the CP genetic group 1 (C1) associated with non-registered CP, C4 with US CP, WB genetic group 1 (W1) with Holsteiners, and W3 with Anglo European and British WB. Maximum and mean linkage disequilibrium (LD) varied significantly between the two breeds (mean from 0.077 to 0.130 for CP and from 0.016 to 0.370 for WB), but the rate of LD decay was generally slower in CP than WB. The LD block size distribution peaked at 225 kb for all genetic groups, with most of the LD blocks not exceeding 1 Mb. The top 0.5% harmonic mean pairwise fixation index (FST) values identified ontology terms related to cancer risk when the four CP genetic groups were compared. The four CP genetic groups were less inbred than the WB genetic groups, but C2, C3 and C4 had a lower proportion of shorter runs of homozygosity (ROH) (74 to 76% < 4 Mb) than the four WB genetic groups (80 to 85% < 4 Mb), indicating more recent inbreeding. The CP and WB genetic groups had a similar ratio of effective number of breeders (Neb) to effective population size (Ne).ConclusionsDistinct genetic groups of individuals were revealed within each breed, and in WB these genetic groups reflected population substructure better than studbook or country of origin. Ontology terms associated with immune and inflammatory responses were identified from the signatures of selection between CP genetic groups, and while CP were less inbred than WB, the evidence pointed to a greater degree of recent inbreeding. The ratio of Neb to Ne was similar in CP and WB, indicating the influence of popular sires is similar in CP and WB.

Determination of the Effective Blasting Region by Using Fragmentation Analysis: A Field Study

Fragmentation, the most common method for assessing blast efficiency, provides significant benefits to post-blast operations. The most important parameter affecting fragmentation in blasting is geological formation characteristics. This study aimed to investigate the blasting efficiency on different geological units in the blasting area using WipFrag fragmentation analyses and to suggest ways to increase of blasting efficiency. With this aim, 30 blasts were observed in the Caldag raw material field of Adana Cement Turkish Inc., which has very heterogeneous geological features. The study field was examined by dividing it into 3 geological units as “limestone,” “clayey limestone,” and “clayey limestone + marl.” During the observations, scaled images were taken in each blasting area for in situ block size distribution before blasting and muckpile size distribution after blasting. In situ block size distribution and muckpile size distribution were evaluated using WipFrag software, and the fragmentation index of each blast was determined. One-way analysis of variance (ANOVA) was performed to determine the differences in the fragmentation index in the field. As a result of ANOVA analysis, there were differences between the geological units in terms of fragmentation index, and of the unit with the highest blasting efficiency was the “Clayey limestone + marl” unit.

Characterization of a fractured rock mass using geological strength index: A discrete fracture network approach

Rock mass contains siginificant heterogeneity due to the presence of structural discontinuities. The failure in the rock mass may cause a serious concern to road and rail transportation. Rock mass characterization is a first step towards preliminary investigation for road or tunnel excavations. Different field-based methods have been developed to characterize the rock mass conditions. The Geological Strength Index (GSI) is a simple and commonly adopted method with wide applicability in rock engineering. Traditional approaches are limited to 2D exposures for mapping purposes, but block formation or joint intersection is a 3D parameter. The advancement in computational techniques led to significant involvement of numerical modeling techniques such as those backed with discrete fracture network (DFN). The remote sensing techniques render the data with high precession potential not accessible with conventional methods. The stochastic DFNs generated based upon the statistical distribution of the input parameters can represent the natural fracture system in 3D. The developed synthetic fracture network can be used to examine the rock mass characteristics. This work addresses the incorporation of the Discrete Fracture Network (DFN) in the estimation of the Geological Strength Index (GSI) of the rock mass. The work compares the results of DFN generated using aggregate and disaggregate approaches in block size distribution (BSD) and rock quality designation (RQD) measurements for a fractured slope. The calculated BSD and RQD using DFN and field-estimated joint condition parameter are used to estimate GSI of the rock mass. A machine learning based python GUI tool was developed to find GSI from block volume and joint condition parameters. The prediction of GSI from input parameters using machine learning has led to systematically digitizing the standard GSI chart.

Age and recurrence of coseismic rock avalanches in Sierra de la Sobia (Cantabrian Mountains, Spain)

Dating of rock avalanche clusters along faults may provide paleo-earthquake data for locations where direct fault-rupture evidence is rare. This study focuses on the rock avalanche cluster preserved in the western slope of Sierra de la Sobia (Cantabrian Mountains, Spain), where evidence of Quaternary faulting was previously reported at the Marabio Fault segment, a splay of the long-lived León Fault. In a previous study we interpret this cluster as seismically induced based on the kinematic analysis of local fault structures, the block size distribution analysis of several rock avalanche accumulation bodies, and the stability analysis of current slopes. In this new study we date these deposits to assess the timing of the recurrent events and evaluate a paleo earthquake record. We determine the ages of 20 boulders from the coarse carapace of two calcareous rock avalanche deposits using the 36Cl Cosmic Ray Exposure dating technique. Our results indicate that the youngest instability event occurred 8.5 ± 0.6 ka ago and was simultaneously recorded by the recent lobes of the two rock avalanches and could correspond to the latest severe earthquake striking this area. The analysis of boulder age clusters in the middle and distal lobes of both rock avalanches reflects up to four additional coseismic instability episodes between ∼22.0 and ∼10.9 ka, with a recurrence interval of ∼3.7 ka on average. Extending this chronological analysis to other rock avalanche clusters could improve our understanding on landscape evolution and its potential for developing regional paleo-earthquake catalogs for the Cantabrian Mountains and other similar contexts.

Effect of uncertainties on block volume estimation

The combination of the aleatory nature of the rock mass structure and the epistemic errors related to the survey methods make rock mass characterization a challenge despite the remarkable evolution of the survey tools and the research on the subject. In particular, significant uncertainties affect block volume estimation: the need for simplification connected to the engineering approach to rockfall problems, for instance, risks to mask the ripple effect of uncertainties on the reliability of the results. Even considering a simplified shape of the block created by three sets of discontinuities (i.e., a prism), the uncertainties on the geometrical characteristics of the discontinuities (orientation, spacing, and persistence) greatly influence the resulting volume distribution. It is a fact that a single value of the volume cannot be representative of the rock mass: the In Situ Block Size Distribution (IBSD) should be built to describe the variability of block volumes. Many statistical distribution functions can be used for fitting spacing data (i.e., gamma, negative exponential, log-normal, Weibull). The choice of the function must follow a rigorous evaluation of the goodness of fit. This research aims to assess the influence of the uncertainties related to the discontinuities sets, with particular reference to spacing samples, on block volume estimation. Through numerical examples and a case study, this research shows that a reduction of uncertainty can be reached by rigorous statistical processing of the data.

Ejecta blocks around the Kings Bowl phreatomagmatic crater in Idaho: An indication of subsurface water amounts with implications for Mars

The Kings Bowl lava field, associated with the Craters of the Moon National Monument and Preserve on the Great Rift in Idaho, U.S.A., contains many explosive pits, the largest of which has a substantial field of ejecta blocks. These features were formed when lava supply diminished, the fissure was evacuated, and ground water entered. We have documented the properties of the ejecta block field: crater shape, the ejecta field to the west and the tephra field to the east, the vesicularity and density of the blocks, the block size distribution and the number of blocks per unit area as a function of distance from the crater, and the aspect ratios of the blocks. To the degree possible we compare the data to those of ejecta blocks at other phreatomagmatic craters on rifts especially, Deception Island, South Shetland Islands, and White Island, New Zealand, and find them similar. Many of the Kings Bowl ejecta characteristics can be described by relationships that have previously been published to describe ejecta blocks around impact craters. We have also performed ballistic and energy calculations to derive ejection velocities for the blocks consistent with our data. The “velocity exponent” b in the relationship d ​∝ ​vi-b where d is ejecta size and vi is the initial ejecta velocity for our data is around −3.0 and in the range previously observed for impact ejecta (−3.7 to −0.32), although at the small end.

Estimating rockfall and block volume scenarios based on a straightforward rockfall frequency model

Rockfall causes a large number of accidents and fatalities in steep environments. A realistic quantification of rockfall risk is thus crucial for an effective prevention of damages and loss of lives. The estimation of rockfall and block volumes for different return periods thereby remains a major challenge. In this paper, we present a straightforward rockfall frequency model (RFM: Rockfall Frequency Model) and its application at 8 different sites at 7 locations in the Swiss Alps. The RFM assumes that the magnitude-frequency relationships of rockfall events and blocks follow a power law. The parameters of this distribution are estimated based on a simple classification of rock structures and on field inventories. Beside the block volume frequency, which is very sensitive to the consideration of large rockfall events, the frequency of rockfalls with at least one block with a minimum volume, is determined. The block size distributions measured in this study were well captured by power laws. The rockfall and block volumes calculated with the RFM were generally slightly higher than the scenarios of the official hazard assessments. The uncertainty analysis, however, revealed a high variability of the release scenarios with respect to the parameters of the RFM, increasing with the return period. Both, the rockfall volumes and the block volumes, are particularly sensitive to the estimated exponent of the power law distribution of the rockfall events. Nevertheless, the proposed RFM provides an objective and transparent approach to derive magnitude-frequency relationships of rockfall events and individual blocks even if historical inventories are missing or insufficient and is thus a promising alternative to merely expert-based approaches.

Determination of prior austenite grain-and martensitic substructure size from metallographic etchings using a multi-step image processing algorithm

Abstract State-of-the-art modelling algorithms allowing for prediction of macroscopic properties of martensitic steels are primarily based on microstructural parameters such as prior austenite grain size as well as martensite packet-and block size distribution. The latter are usually obtainable via electron backscatter diffraction (EBSD) measurements. However, determination via light microscopy would present a more cost-effective determination method. This work presents a python-based multi-step image processing algorithm capable of separating the grain boundaries and the martensitic substructure from etched micrographs. Additionally, the viability of a characteristic mean free path parameter λ of the martensitic substructure for comparison of different martensitic microstructures is tested. To this end, a microstructure variation of PH15-5 was performed using different heat treatments and the specimens were analyzed using EBSD and electrolytically etched micrographs.

On the Influence of Sampling Scale on the In Situ Block Size Distribution

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.

Multi-multifractality and dynamic scaling in stochastic porous lattice

In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we choose to be a square of unit area for convenience. We then define a generator that divides the initiator or one of the blocks, picked preferentially with respect to their areas, to divide it either horizontally or vertically into two rectangles of which one of them is removed with probability $q=1-p$. We find that the remaining number of blocks and their mass varies with time as $t^{p}$ and $t^{-q}$ respectively. Analytical solution shows that the dynamics of this process is governed by infinitely many hidden conserved quantities each of which is a multifractal measure with porous structure as it contains missing blocks of various different sizes. The support where these measures are distributed is fractal with fractal dimension $2p$ provided $0<p<1$. We find that if the remaining blocks are characterized by their respective area then the corresponding block size distribution function obeys dynamic scaling.

Study on the Fractal Characteristics of the Pomegranate Biotite Schist under Impact Loading

In order to study the fractal characteristics of the pomegranate biotite schist under the effect of blasting loads, a one-dimensional SHPB impact test was carried out to test the dynamic compressive strength, damage morphology, fracture energy dissipation density, and other parameters of the rocks under different strain rates; besides, sieve tests were conducted to count the mass fractal characteristics of the crushed masses under different strain rates to calculate the fractal dimension of the crushed rock D . Finally, the relationships between fractal dimension and dynamic compressive strength, crushing characteristics, and energy dissipation characteristics were analysed. The results show that under different impact loads, the strain rate effect of the rock is significant and the dynamic compressive strength increases with the increasing strain rate, and they show a multiplicative power relationship. The higher the strain rate of the rock, the deeper the fragmentation and the higher the fractal dimension, and the fractal dimension and rock crushing energy density are multiplied by a power relationship. By performing the comparative analysis of the pomegranate biotite schist, a reasonable strain rate range of 78.75 s-1~82.51 s-1 and a reasonable crushing energy consumption density range of 0.78 J·cm-3~0.92 J·cm-3 were determined. This research provides a great reference for the analysis of dynamic crushing mechanism, crushing block size distribution, and crushing energy consumption of the roadway surrounding rock.

Multiscale matrix-fracture transfer functions for naturally fractured reservoirs using an analytical, infinite conductivity, discrete fracture model

Fracture matrix transfer functions have long been recognized as tools in modelling naturally fractured reservoirs. If a significant degree of fracturing is present, models involving single matrix blocks and matrix block distributions become relevant. However, this captures only the largest fracture sets and treats the matrix blocks as homogeneous, though possibly anisotropic. Herein, we produce the steady and transient baseline solutions for depletion for such models. Multiscale models pass below grid scale information to the larger scale system with some numerical cost. Instead, for below block scale information, we take the analytic solution to the Diffusivity Equation for transient inflow performance of wells of arbitrary trajectory, originally developed for Neumann boundary conditions, and recast it for Dirichlet boundaries with possible internal fractures of variable density, length, and orientation. As such, it represents the analytical solution for a heterogeneous matrix block surrounded by a constant pressure sink, we take to be the primary fracture system. Instead of using a constant rate internal boundary condition on a fracture surrounded by matrix, we segment the fracture and, through imposed material balance, force the internal complex fracture feature to be a constant pressure element with net zero flux. In doing so, we create a representative matrix block with infinite conductivity subscale fractures that impact the overall drainage into the surrounding fracture system. We vary the internal fracture structure and delineate sensitivity to fracture spacing and extent of fracturing. We generate the complete transient solution, enabling new well test interpretation for such systems in characterization of block size distributions or extent of below block-scale fracturing. The initial model for fully-penetrating fractures can be extended to 3D, generalized floating fractures of arbitrary inclination, and internal complex fracture networks.

An experimental investigation of shear strength behavior of a welded bimrock by meso-scale direct shear tests

Bimrocks have been rarely studied due to their inhomogeneous properties, challenges related to specimen preparation and tedious in-situ tests. This study was undertaken in an attempt to determine the shear strength parameters as well as the deformation behavior of a highly welded bimrock using laboratory meso-scale direct shear tests. In addition digital image processing analyses (DIP) and fragmentation fractal dimension (DF) calculations were made to quantify the geometrical and structural properties of the bimrock. It was concluded that the block size distribution of Sille bimrock is scale-invariant and shows fractal fragmentation. Moreover the block sizes have power-law distributions and there is evident skewness in normal distribution. The test results demonstrated that with the increase of volumetric block proportions (VBP), the internal friction angle (ϕ) of the bimrock increases whereas its cohesion (c) decreases. Strain softening behavior was observed after attaining the peak shear stress for all normal stresses and the VBP values. It is revealed that the normal stress is more effective than the VBP on the development of dilatation/contraction behavior. Lastly, the negative correlation between the DF and the peak shear stress indicated that the shear strength of the bimrock increases while the proportion of relatively small blocks in the specimen decreases.

Quantifying the Relative Influence of Railway Hump Classification Yard Performance Factors

Single-railcar freight shipments that move in multiple freight trains and are sorted at several classification yards between origin and destination remain an important source of traffic and revenue for North American railways. Despite the role of both mainlines and yards in freight rail transportation performance, little attention is devoted to investigations of classification yard performance, and few yard capacity models and tools are available. To address this need, this paper seeks to quantify the relative influence of different factors on several yard performance metrics. Simulation experiments conducted with YardSYM, a discrete-event simulation model developed specifically to analyze hump classification yards, examine varying the volume, number of blocks, block size distribution, number of outbound trains, train departure distribution, train arrival time variability, and arriving block volume variability. In addition to the expected sensitivity of yard performance to railcar throughput volume, the most influential factors change depending on the particular yard performance metric, emphasizing the criticality of matching performance metrics to railroad business objectives. The results of this research serve to screen variables for the future development of multivariable yard performance models and facilitate more informed business decisions regarding yard operating plans that make more efficient and economical use of existing yard capacity.

Comparison between methods for calculating the volume of rock blocks

Many methods for calculating the volume of rock blocks have been developed in the last decades. The first attempts to estimate such crucial quantity produced analytical equations to calculate the mean and variance of volume, considering blocks created by three discontinuity sets with a certain spacing probability distribution. From then, the research community followed three kinds of approaches for calculating block volume: the fully analytical one (e.g., Palmstrøm’s formula), the fully probabilistic one (e.g., Discrete Fracture Network generators), and the mixed one (e.g., In Situ Block Size Distribution). In this paper, a comparison among the different methods is presented, supported by numerical examples, highlighting their strengths and disadvantages in terms of reliability and repeatability.