Mining Problem Research Articles

Optimization of frequent item set mining parallelization algorithm based on spark platform

In this paper, we propose a new method that combines the parallelism of the Spark-based platform with fast frequent mining, called STB_Apriori. Previous research has shown that traditional frequent itemset mining algorithms have high overhead when faced with large datasets and high-dimensional data computation, and generate a large number of candidate itemsets; at the same time, when faced with diverse user requirements, they often generate very sparse and diverse data. In order to solve the problem of fast mining of massive data, our idea originates from the capability of Spark distributed computing and the common optimisation ideas in Apriori mining, by using the efficient operator BitSet to achieve transaction compression, bit storage and data manipulation by Boolean matrices, and at the same time by parallelising the processing and optimising the algorithmic logic to achieve fast and frequent mining. In experiments on real-world datasets, our model consistently outperforms five widely used methods by a significant margin on very large data and maintains its excellence in the remaining cases, proving its effectiveness on real-world tasks, while further analysis shows that increasing the number of distributed nodes also incrementally and continuously improves performance.

A Nonaxial-Type Swirling Cavitating Nozzle for Exploiting Natural Gas Hydrate

Summary Natural gas hydrates (NGHs) have garnered widespread attention in the new energy sector, owing to their efficient and clean combustion properties. NGHs are ice-like substances formed by methane and water under high-pressure and low-temperature conditions, abundantly deposited in seabeds and frozen soil of highlands on Earth. However, the rock shelves of NGH reservoirs are mostly fragile and sparsely colloidal. Traditional mechanical mining methods can easily cause rock-shelf collapses, leading to mining accidents. Long-term indoor experiments and pilot mining projects have shown that cavitating nozzles can provide a feasible solution to the problem of efficient mining of NGHs. To further improve the efficiency of cavitating nozzle mining for NGHs, we have optimized and designed a nonaxial-type swirling cavitating nozzle (NASCN) based on traditional swirling cavitating nozzles (SCNs). Both numerical simulations and indoor experiments have verified the higher mining performance of this nozzle. In the numerical simulation experiments, we analyzed the cavitation performance, erosion performance, and energy consumption characteristics of different cavitating nozzles using the mixture multiphase flow model and the renormalization group (RNG) k-ε turbulence model. In the indoor experiments, we utilized a jet erosion experimental device for NGHs to analyze the erosion effects of different cavitating nozzles on hydrate samples. The results of these experiments indicate that the NASCN reduces energy consumption by 12% compared with traditional nozzles when there is little difference in cavitation performance and erosion performance. Moreover, under similar energy consumption, the NASCN improves erosion efficiency by 35.2% compared with traditional nozzles. These results demonstrate that the NASCN has good application value in the mining engineering of NGHs.

Oligarchy of Power in The Management of C-Mine Resources in Noemuti, North Central Timor Regency

This paper raises the dynamics of oligarchic power relations in the management of C-quarry mining resources in the form of stone in Noemuti District, North Central Timor Regency. This research uses the oligarchy theory of Jeffrey Winters as a basis for analysis in looking at mining problems that seem to be deadlocked when dealing with power authorities in resource management in the regions. The practice of oligarchy in Winters' theory uses 5 main approaches. But in this paper, it only limits to two approaches, namely the concentration of wealth and the concentration of power. Facing the dynamics of oligarchy that strengthens in local resource governance, on the other hand, presents resistance from civil society to take part in the legitimacy of power in the context of equitable distribution of resource management policies. The practice of community resistance is based on Sidney Tarrow's theory of collective challenge, common goals, solidarity and collective identity and maintaining the politics of resistance.

Review of Major Influencing Factors Contributing to Persisting Safety Problems in Coal Mines: Addressing Systemic Challenges

The coal mining industry in Pakistan faces recurring fatal accidents due to data scarcity, lack of research, and technology adoption. This paper reviews the current status of coal mining, the ongoing energy crisis, the utilization of indigenous coal resources, and the prevailing safety challenges. By comparing coal mining safety standards in Pakistan with global benchmarks, this study proposes advanced mining technologies to improve productivity and safety. This study emphasizes the importance of investigating the underlying factors causing mining accidents in order to devise effective strategies to mitigate them. The lack of relevant data and the reluctance to adopt technology in the industry are identified as major obstacles to improving safety conditions. The proposed strategies for overcoming safety issues include improving data collection and analysis, increasing research efforts, and promoting the adoption of advanced technology. Thus, this paper highlights the urgent need to address safety concerns in Pakistan’s coal mining industry to avoid further loss of lives and resources.

Bi-objective Optimization in Role Mining

Role mining is a technique that is used to derive a role-based authorization policy from an existing policy. Given a set of users U , a set of permissions P and a user-permission authorization relation UPA ⊆ U × P , a role mining algorithm seeks to compute a set of roles R , a user-role authorization relation UA ⊆ U × R and a permission-role authorization relation PA ⊆ R × P , such that the composition of UA and PA is close (in some appropriate sense) to UPA . Role mining is therefore a core problem in the specification of role-based authorization policies. Role mining is known to be hard in general and exact solutions are often impossible to obtain, so there exists an extensive literature on variants of the role mining problem that seek to find approximate solutions and algorithms that use heuristics to find reasonable solutions efficiently. In this paper, we first introduce the Generalized Noise Role Mining problem (GNRM) – a generalization of the MinNoise Role Mining problem – which we believe has considerable practical relevance. In particular, GNRM can produce “security-aware” or “availability-aware” solutions. Extending work of Fomin et al., we show that GNRM is fixed parameter tractable, with parameter r + k , where r is the number of roles in the solution and k is the number of discrepancies between UPA and the relation defined by the composition of UA and PA . We further introduce a bi-objective optimization variant of GNRM, where we wish to minimize both r and k subject to upper bounds \(r \le \bar{r} \) and \(k\le \bar{k} \) , where \(\bar{r} \) and \(\bar{k} \) are constants. We show that the Pareto front of this bi-objective optimization problem (BO-GNRM) can be computed in fixed-parameter tractable time with parameter \(\bar{r} +\bar{k} \) . From a practical perspective, a solution to BO-GNRM gives security managers the opportunity to identify a mined policy offering the best trade-off between the number of policy discrepancies and the number of roles. We then report the results of our experimental work using the integer programming solver Gurobi to solve instances of BO-GNRM. Our key findings are that (a) we obtained strong support that Gurobi’s performance is fixed-parameter tractable, (b) our results suggest that our techniques may be useful for role mining in practice, based on our experiments in the context of three well-known real-world authorization policies. We observed that, in many cases, our solver is capable of obtaining optimal solutions when the values of either k or r are small.

A secure Multi-Frequency Computation Protocol in 2-Part Fully Distributed Setting

Secure frequency computation protocols have been researched and applied to address various privacy-preserving problems in machine learning, data mining, and data analysis. However, these protocols only allow for the calculation of a single frequency value in one execution. In this paper, we propose a protocol for calculating multiple secure frequency values concurrently for the 2PFD data model, which is a relatively new distributed data model that has appeared in many practical problems but has not received much attention. The proposed protocol not only maintains the accuracy of the output results and a high level of security but also exhibits good performance.

Production of low-sulphur tailings by hydrocycloning

Acid mine drainage (AMD) is an environmental problem in gold mines containing sulphur minerals. The potential for acid drainage in tailings facilities must be considered when studying their dry closure. Therefore, controlling the sulphur content in the final layer of tailings deposition has the potential to prevent AMD after closure. In this context, the rougher flotation tailings were hydrocycloning in a pilot plant in a gold mining company to assess the potential for generating modified tailings with low-sulphur content. A total of 10 samples were composited over one hour of pilot plant operation. The hydrocyclone overflow showed an average reduction of 36.2% in sulphur content and an average metallurgical recovery of 20.0%. The underflow had an average increase in sulphur content of 16.8% and 80.0% metallurgical recovery. These results demonstrated the possibility of generating modified tailings with reduced sulphur content through hydrocycloning.

Research on Gas Extraction Effect of High Gas Mines Based on Stereoscopic Cross Directional Drilling Technology

Based on the advantages of three-dimensional cross drilling technology and directional drilling technology, a gas extraction technology of "three-dimensional cross + directional" drilling is proposed. The advantages, applicability, and key influencing factors of this technology are analyzed, and on-site gas extraction experiments are conducted at the 2210 working face of the No. 2 coal seam in a certain coal mine. The research results show that after adopting the stereoscopic cross directional drilling technology and extraction technology, the gas extraction effect of the 2210 working face has been significantly improved compared to using ordinary extraction drilling, and the stereoscopic cross directional drilling technology can effectively increase the gas extraction volume and concentration. This technology has obvious advantages in improving gas extraction rate and ensuring operational safety, providing a certain reference for solving gas control problems in high gas mines.

Experimentation of Heat-Insulating Materials for Surrounding Rocks in Deep Mines and Simulation Study of Temperature Reduction

With the increasing depletion of shallow resources, mining has gradually shifted to deeper levels, and the high-temperature problem of deep mining has restricted the efficient and safe development of mining. In this study, five types of thermal insulation materials for surrounding rocks with different ratios were produced using tailings, P.O.32.5 clinker, aluminum powder, glass beads, quick lime, and slaked lime as test materials. Based on the uniaxial compression test, the thermal constant analysis test, and numerical simulation analysis technology, the change rule of mortar compressive strength and thermal conductivity was analyzed, and the cooling effect of surrounding-rock thermal insulation materials with different ratios was discussed. The results showed that the compressive strength of the surrounding-rock thermal insulation materials ranged from 0.39 to 0.53 MPa, and the thermal conductivity ranged from 0.261 to 0.387 W/(K·m), with the compressive strength of ratio E being the largest and the thermal conductivity of ratio A being the lowest. In the numerical simulation analysis results, the thermal insulation layer thickness was taken as a value of 10 cm when, at this time, the best thermal insulation effect and economic benefits involved a temperature reduction of 0.9 K. In the case of changing the thermal conductivity and inlet wind speed, the original temperature of the rock temperature reduction was also very clear, with maximum reductions of 0.92 K, 0.92 K, and 1.42 K.

Geospatial Analysis of the Socioeconomic and Demographic Effects of Historic Coal Mining in the Greater Pittsburgh Region, Pennsylvania, USA

A geospatial model was developed to statistically assess the socioeconomic effects of coal mining in the greater Pittsburgh, Pennsylvania area by integrating home sale data, abandoned mine lands (AML) inventory “problem area” sites, and census demographic information. Results indicated that homes located within problem areas sold for an average of 28% ($58,600) less than homes outside of these regions. Demographic data revealed a notable disparity in the population distribution within Allegheny County mining problem areas as having a statistically significant larger Black population. This same trend was even more pronounced in urban areas. The study also established that areas influenced by past mining activities had a higher proportion of individuals without formal postsecondary education. Logistic regression models were created to analytically evaluate the relationship between predictor variables, specifically home sale price and Community Needs Index, to the probability of being situated within mining problem areas. The home sale analysis indicated a negative correlation between sale prices and the likelihood of residing in a mining-affected zone, implying that properties with lower prices are more commonly situated in these impacted areas. The CNI logistic regression model revealed a correlation between the probability of living in a mining problem area and overall higher community needs.

Research on controlled mining of end slope fire-burned area in open-pit mine

To solve the problem of controlling mining in the open-pit mine end slope fire-burned area, applying multivariate function fitting to the roof and floor modeling of multi-coal seam open pit mines, introducing the factor of coal quality changes in the fire-burned area, determining coal quality information at each location through proximate analysis of coal, to establish the net profit model of the mining area, it is determined the net profit of each mining position by numerical integration, the final mining position was determined without failure by calculating the slope stability based on the numerical simulation of strength reduction. Taking the Dananhu No. 2 open-pit mine in Hami, Xinjiang, China as the engineering background, the fire-burned area III within the southern end slope boundary of the first mining area is 240 m. It was finally determined that the optimal mining position is when the advancement degree is 182 m, the ultimate pit slope angle is 25°, the three-dimensional slope stability is 1.305, the profit is 671.96 million yuan, The deep boundary of the southern end slope fire-burned area of the slope is reduced by 58 m. This paper solves the problem of end slope mining in Dananhu No. 2 mine, and maximizes its net profit under the condition of ensuring safe production.

Swin-chart: An efficient approach for chart classification

Charts are a visualization tool used in scientific documents to facilitate easy comprehension of complex relationships underlying data and experiments. Researchers use various chart types to convey scientific information, so the problem of data extraction and subsequent chart understanding becomes very challenging. Many studies have been taken up in the literature to address the problem of chart mining, whose motivation is to facilitate the editing of existing charts, carry out extrapolative studies, and provide a deeper understanding of the underlying data. The first step towards chart understanding is chart classification, for which traditional ML and CNN-based deep learning models have been used in the literature. In this paper, we propose Swin-Chart, a Swin transformer-based deep learning approach for chart classification, which generalizes well across multiple datasets with a wide range of chart categories. Swin-Chart comprises a pre-trained Swin Transformer, a finetuning component, and a weight averaging component. The proposed approach is tested on a five-chart image benchmark dataset. We observed that the Swin-Chart model outperformers existing state-of-the-art models on all the datasets. Furthermore, we also provide an ablation study of the Swin-Chart model with all five datasets to understand the importance of various sub-parts such as the back-bone Swin transformer model, the value of several best weights selected for the weight averaging component, and the presence of the weight averaging component itself.The Swin-Chart model also received first position in the chart classification task on the latest dataset in the CHART Infographics competition at ICDAR 2023 - chartinfo.github.io.

Attention-based fuzzy neural networks designed for early warning of financial crises of listed companies

Developing an early warning model for company financial crises holds critical significance in robust risk management and ensuring the enduring stability of the capital market. Although the existing research has achieved rich results, the disadvantages of insufficient text information mining and poor model performance still exist. To alleviate the problem of insufficient text information mining, we collect related financial and annual report data from 820 listed companies in mainland China from 2018 to 2023 by using sophisticated web crawlers and advanced text sentiment analysis technologies and using missing value interpolation, standardization, and data balancing to build multi-source datasets of companies. Ranking the feature importance of multi-source data promotes understanding the formation of financial crises for companies. In the meantime, a novel Attention-based Fuzzy Neural Network (AFNN) was proposed to parse multi-source data to forecast financial crises among listed companies. Experimental results indicate that AFNN exhibits significantly improved performance compared to other advanced methods.

Enhancing the performance of integer models for addressing the long-term production planning problem in open pit mines by decision variable fixation based on parametric analysis of the final pit limit

Enhancing the performance of integer models for addressing the long-term production planning problem in open pit mines by decision variable fixation based on parametric analysis of the final pit limit

Investigating critical metals Ge and Ga in complex sulphide mineral assemblages using LIBS mapping

Elemental imaging using Laser-Induced Breakdown Spectroscopy (LIBS) mapping is increasingly applied to a wide range of materials. In geomaterials, phase identification and characterization (mineralogy) are crucial for solving a variety of problems in earth sciences and mining industry.Here we applied LIBS mapping to ore samples from the world-class Kipushi deposit, Democratic Republic of Congo, because these ores are known for their great mineral complexity and economic value, especially for their high potential in critical metals such as Ge and Ga.The mineralogy of the samples was reconstructed by combining two approaches: 1) element colocalization in LIBS maps that were selected based on the knowledge of occurring mineral species at the site and 2) correlation maps obtained by applying the Interesting Features Finder (IFF) algorithm. Reconstructed minerals include chalcopyrite, bornite, chalcocite, sphalerite, galena, pyrite, tennantite-(Zn), renierite, tungstenite, betekhtinite, carrollite, gallite, and a series of non-sulphide gangue minerals (quartz, carbonate and clay minerals). SEM-EDS was used to confirm the LIBS-derived mineralogy, especially for sub-pixel inclusions.Among other results, Ge and Ga are hosted as major elements in renierite and gallite, respectively, and also as trace-elements in chalcopyrite, bornite and tungstenite (for Ge), and chalcopyrite, bornite, sphalerite and renierite (for Ga). Particular attention was paid to iron interfering with gallium at 417.20 nm, for which simple background-corrected peak intensities were compared to a more advanced chemometric method (MCR-ALS). All the results were obtained with minimal time and efforts and, while only qualitative in nature, they already provide essential information about ore texture, mineralogical composition and trace-element distribution across the ore.

Jaccard-constrained dense subgraph discovery

Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence, it is natural to consider the question of finding dense subgraphs in a temporal network that are allowed to vary over time to a certain degree. In this paper, we search for dense subgraphs that have large pairwise Jaccard similarity coefficients. More formally, given a set of graph snapshots and input parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, we find a collection of dense subgraphs, with pairwise Jaccard index at least α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, such that the sum of densities of the induced subgraphs is maximized. We prove that this problem is NP-hard and we present a greedy, iterative algorithm which runs in Onk2+m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {} \\left( nk^2 + m\\right)$$\\end{document} time per single iteration, where k is the length of the graph sequence and n and m denote number of vertices and total number of edges respectively. We also consider an alternative problem where subgraphs with large pairwise Jaccard indices are rewarded. We do this by incorporating the indices directly into the objective function. More formally, given a set of graph snapshots and a weight λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, we find a collection of dense subgraphs such that the sum of densities of the induced subgraphs plus the sum of Jaccard indices, weighted by λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, is maximized. We prove that this problem is NP-hard. To discover dense subgraphs with good objective value, we present an iterative algorithm which runs in On2k2+mlogn+k3n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {}\\left( n^2k^2 + m \\log n + k^3 n\\right)$$\\end{document} time per single iteration, and a greedy algorithm which runs in On2k2+mlogn+k3n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {}\\left( n^2k^2 + m \\log n + k^3 n\\right)$$\\end{document} time. We show experimentally that our algorithms are efficient, they can find ground truth in synthetic datasets and provide good results from real-world datasets. Finally, we present two case studies that show the usefulness of our problem.

Study of Slope Stability of the Mining Wall in an Open-Pit Coal Mine by the Paste Cut-and-Backfill Method

According to this study’s findings, slope stability problems in open-pit coal mines can be avoided, and mine wall collapse can be effectively mitigated by the use of cut-and-backfill mining techniques. The main research results are as follows: (1) The stope and waste rock’s geotechnical, physical, and mechanical characteristics were gathered and examined; the geotechnical and mechanical characteristics found in this study largely satisfy the criteria for slope stability analysis. (2) Cemented paste backfill (CPB) materials were made of mine waste rock and fly ash at a desired ratio, mixed with cement as a bond material, and were tested in the laboratory, using a combination of cement percentages of 6%, 8%, and 10% for the cement content and 25%, 30%, 35%, and 40% for the fly ash content, to determine the ideal mix for artificial ground support in underground mines, taking into account both economic and performance factors. (3) By using this model, the changes in CPB strength were investigated under various factors influencing the cement ratio, and limit equilibrium modeling was used with the FLAC-Slope 8.1 program with different cement paste backfill ratio to calculate the factor of safety for each cement percentage after 1 day, 3 days, 7 days, and 28 days of curing time (CT) to obtain the optimum compressive strength and shear straight of cemented paste backfill with high paste fill shear strength on the slope. (4) The research results are of great significance for the safety of important facilities in open-pit mines and provide a basis for the design and safety implementation of open-pit slope engineering.

A road network traffic flow data imputation method based on the fusion of spatiotemporal features and adversarial networks

In response to the problem of missing traffic flow data on highways, to solve the problem of insufficient mining of traffic flow characteristics using existing spatiotemporal correlation repair methods, a missing data repair method based on spatiotemporal fusion adversarial network is proposed based on analyzing the spatiotemporal characteristics of traffic flow, this method utilizes the fusion of GRU and GCN to capture the fine-grained spatiotemporal relationships of traffic flow, optimizes the generator and discriminator of the adversarial network, and achieves accurate repair of missing data. Experiments based on real data have shown that under various missing modes and rates, the model can learn the topological relationships of the road network, capture the temporal regularity and spatiotemporal correlation in the data, and effectively impute missing data.

A Secure Parallel Pattern Mining System for Medical Internet of Things.

In this paper, a new generic parallel pattern mining framework called multi-objective Decomposition for Parallel Pattern-Mining (MD-PPM) is developed to solve challenges in the Internet of Medical Things through big data exploration. MD-PPM discovers important patterns by using decomposition and parallel mining methods to explore connectivity between medical data. First, a new technique, the multi-objective k-means algorithm, is used to aggregate medical data. A parallel pattern mining approach based on GPU and MapReduce architectures is also used to create useful patterns. To ensure complete privacy and security of the medical data, blockchain technology has been integrated throughout the system. Several tests were conducted to demonstrate the high performance of two sequential and graph pattern mining problems on large medical data and to evaluate the developed MD-PPM framework. From our results, our proposed MD-PPM has achieved strong results in terms of memory usage and computation time in terms of efficiency. Moreover, MD-PPM performs well in terms of accuracy and feasibility compared to existing models.

Об одной новой схеме применения метода конечных элементов в горных науках

At the moment a large number of research papers are being published in the field of mining sciences, utilizing FEM (finite element method) in one way or another. The vast majority of these papers are devoted to solving various engineering problems in mining using different software products such as ABAQUS, PLAXIS, etc. It has been determined that almost all existing works in this field follow the typical scheme for the application of FEM. Materials and methods. The analysis showed that the typical scheme for the application of FEM in mining sciences contains a fundamental error related to the inadequate consideration of the representative volume of rocks during the construction of a continuous medium model and the formation of a discrete model. This leads to a significant degree of inaccuracy in the modeling results. Results and discussion. To resolve the fundamental error, a new scheme for the application of FEM in mining sciences is proposed. It differs from the typical scheme by introducing a new intermediate model between the rock mass and the continuum model. This model, named ‘rock mass body’, represents a set of geoparticles. The sizes of the geoparticles are determined according to the representative volume of the structural or textural components of the rock mass. Comparative analysis has shown that, unlike the typical scheme for the application of FEM, the use of the proposed scheme allows to get solutions with a high degree of accuracy when researching rocks with coarse-grained and medium-grained structures. Conclusion. An analysis of the typical scheme for the application of FEM identified a fundamental error in its use for rock mass modeling tasks. A new scheme has been proposed to correct this error. Suggestions for practical application and direction of future research. The research results can be used to improve the accuracy of finite element models of rock masses. Further research should focus on improving methods for determining the shape of finite elements in relation to the symmetry of the structural and textural components of the rock mass. At the same time, it is necessary to take into account the fracturing of rocks.