Vitali Shekov

This paper examines the undesirable yet inevitable influence of loading system compliance on specimen deformation measurements during testing—a problem that has become typical and remains consistently relevant in the field of mechanical materials testing. Of the two possible approaches to addressing this issue—increasing the stiffness of the loading system or applying corrections to the measurement results—this work focuses primarily on the latter. A mathematical model describing the interaction between loading system components was developed using mixed additive-multiplicative scaling, and a cost-effective method for neutralizing the effect of loading system compliance was proposed. It is demonstrated that applying this method is theoretically equivalent to conducting tests on a virtual machine with infinite loading system stiffness. The method utilizes load-displacement data obtained from two compression tests performed under identical conditions: one with the specimen and one without it. The method was validated using aluminum specimens by comparing the calculated elastic modulus (75.6 GPa) with the established reference range (72–75 GPa). Additionally, the method was used to determine the elastic modulus of amphibolite and to generate corrected load-displacement diagrams. A comparative analysis revealed a source of error inherent in the traditional compliance summation method. Overall, the proposed approach, model, and method—based on additive-multiplicative correction of compression test results—offer a structured and interpretable supplement to traditional techniques, opening new avenues for enhancing the accuracy of both direct and indirect measurements of material properties.

This study investigates the application of the Pure Random Orthogonal Search (PROS) method, introduced in the literature in 2021, for approximating force and displacement measurement data obtained from rock specimen testing, using granite as a case study. The primary objective is to simplify the data approximation procedure and improve the accuracy of experimental data analysis by reducing the influence of subjective factors within a predefined protocol. The research focuses on determining the maximum value of the tangent modulus of elasticity during the pre-peak deformation stage of granite specimens under uniaxial compression. The study employs methods of mathematical modeling of rock mechanical behavior and experimental data analysis. To approximate the experimental data, a modified two-parameter S-curve equation is proposed. The optimal parameter values are determined using the PROS method, which reduces the problem to solving a two-dimensional objective function minimization task. The dimensionality of this optimization problem remains independent of the number of experimental data points, thereby enhancing computational efficiency. A systematic computational procedure is developed for the automated calculation of the approximating equation’s parameters and the determination of the maximum tangent modulus of elasticity. In the context of challenges associated with accurately measuring displacements using conventional testing machines, a numerical correction procedure is proposed and implemented to account for the compliance of the loading system. The results of the study are consistent with both the literature-reported experimental data and the data obtained in this work. The methodology and findings can be adapted for analyzing the properties of concrete as an artificial analog of natural rock materials.

The aim of this work is to study the influence of Poisson's ratio on the crack depth in the surface layer of cylindrical samples of frozen soil depending on axial compression. The initial data include values of Poisson's ratio from the range of its possible values from 0.05 to 0.5. In this paper, two variants of an algorithm for modeling the conditions for the occurrence of a crack in the surface layer of a cylindrical sample of frozen soil under uniaxial compression are proposed. The thickness of this layer is equal to the depth of the crack. The simulation showed that the initial stage of crack formation in materials with low Poisson's ratio occurs more slowly than in materials with high Poisson's ratio, but the final stage of crack formation in materials with low Poisson's ratio occurs at a higher rate than in materials with high Poisson's ratio. These observations lead to a model with a sigmoidal function of the thickness of the damaged surface layer on the axial load. The results of the study are of practical interest to developers of assessments of the bearing capacity of frozen soils as a brittle material. Further research may involve taking into account the dependence of Poisson's ratio on load.

The article describes the mechanism of occurrence and gradual development of the tension fractures in the surface layer and the shear fractures in the core of the rock supports (pillars) under uniaxial compression. This model differs from the existing ones because it identifies two stages of the failure process: during the first stage, tensile stresses initiate fracture formation, and during the second stage, shear stresses cause shear fractures. This approach does not rely on preliminary assumptions about the presence or absence of fractures before the deformation begins, which expands the scope of its application. Our previous studies have shown that the tensile stresses in the core of the pillar negatively correlate with the thickness of the surface layer containing newly formed radial cracks. When the tensile stresses do not exceed the tensile strength, the thickness of this layer does not increase, which determines the transition to the second stage of failure. During the second stage, tangential stresses continue to increase, which causes the shear failure of the pillar core. Case study shows that after the first stage of failure, the pillar retains its load-bearing capacity only partially, since the damage significantly reduces the area of its cross-section, for example, to 42% of the original value in the example considered. The results of the modeling are consistent with the known studies and conclusions that when designing rock supports it is extremely important to consider the gradual failure and reduction in the bearing capacity during their operation to ensure the safety of mining operations. The risk indicators of the rock pillar failure are vertical tension fractures, spalling and transformation into the hourglass shape. The shear fractures that develop during the second stage and are oriented at angles close to the internal friction angle are more hazardous. The simulation results are consistent with the known data. However, variability of the physical and mechanical properties of rocks and the external influences to which they are exposed indicates the need for further research on this topic.

This article considers the effect of constant and variable Poisson’s ratio on cracking in concrete and rock specimens under uniaxial compression using mechanical systems modeling methods. The article presents an analysis of the data confirming the increase in Poisson’s ratio under specimen loading. A system of equations for modeling the effect of Poisson’s ratio on cracking under uniaxial compression is proposed. The comparison showed that the model with a constant Poisson’s ratio predicts a thickness of the surface layer with cracks that is underestimated by approximately 10%. In practice, this means that the model with a constant Poisson’s ratio underestimates the risk of failure. A technique for analyzing random deviations of Poisson’s ratio from the variable mathematical expectation is proposed. The comparison showed that the model with a variable Poisson’s ratio leads to results that are more cautious, i.e., it does not potentially overestimate the safety factor. The model predicts an increase in uniaxial compression strength when using external reinforcement. An equation is proposed for determining the required wall thickness of a conditional reinforcement shell depending on the axial compressive stress. The study contributes to understanding the potential vulnerability of load-bearing structures and makes a certain contribution to increasing their reliability.

Crushed stone is widely used as a versatile aggregate in construction. The growing demand for high-quality aggregates underscores the importance of assessing the strength properties of both the rock and the crushed product during exploration and subsurface studies. Understanding how processing affects these properties is crucial for optimizing crushed aggregate production. This study aims to investigate the shape characteristics of crushed stone particles and evaluate their influence on the physical and mechanical properties of the final product. The findings indicate that different stages of gabbrodolerite processing significantly impact its properties. Specific particle shapes were found to improve the strength characteristics of the crushed stone, providing new insights into the effects of crushing processes. An improvement in the quality characteristics of gabbrodolerite after primary crushing with a JC 1600 crusher was observed when compared to the original samples (post-explosive fracturing). The key particle shape characteristic, the flakiness index, was reduced by 2 to 2.5 times after the third stage of processing with the HP4 A and Barmac B9100SE crushers. Crushed stone subjected to three stages of crushing exhibited improved strength, as evidenced by reduced mass loss when establishing crushability decreased of 1.5 to 2 times, losses by micro-Deval decreased on the average by 2.4 %. Simulations of particle wear demonstrated changes in shape, with an increase in roundness and a reduction in surface roughness and flatness, while elongation remained nearly unchanged. A study of the physical and mechanical properties and shape characteristics of crushed stone has revealed certain patterns that indicate which types of stone are best suited for different construction tasks. The research was funded by the federal budget to fulfill the state assignment for the Institute of Geology of the Karelian Research Center of the Russian Academy of Sciences.

This paper presents a model for predicting the thickness of the cracked surface layer in rock specimens subjected to axial compression with lateral pressure. The study focuses on radial cracks that are most prominently open on the lateral surface, manifesting as axial (or longitudinal) cracks on this surface. The research employs methods for analyzing mechanical and geotechnical systems. The proposed model determines the conditions under which damage to the surface layer decreases depending on Poisson’s ratio and lateral pressure. Radial cracks typically precede spalling, making it crucial to examine the conditions of their initiation and the potential for influencing their development, and this holds significant importance for mining and underground construction practices. A comparison indicated that the predicted values and those reported in the literature for the thickness of the damaged surface layer in rock pillars are within a similar range, varying from 44% to 70% of the initial cross-sectional radius. Although this study focuses on rock materials, the proposed model also offers potential applications in examining crack formation in cement and geopolymer concretes, serving as artificial analogs of rock, thereby helping to mitigate the risk of structural failure in building systems.

This paper discusses modeling the behavior and prediction of fracture of brittle materials. Numerous publications show that progress in this area is characterized by the emergence of a number of new models that meet the requirements of the mining industry, construction and other engineering practices. The authors focus only on one class of models, paying special attention to the compromise between simplicity of solution and versatility of the model. A new version of the model is proposed, taking into account the advantages of previous models. We present a differential energy criterion for brittle fracture substantiated, according to which, fracture occurs at a certain ratio of dissipated and stored (elastic) energy. Fracture is considered as the end of the deformation process with a virtual transformation of the initial material almost without cracks into a real material with cracks. The highest and lowest elastic moduli are analytically determined, respectively, on the ascending and descending branches of the stress–strain curve. A graphical version of the algorithm for determining the brittle fracture point on the post-peak branch of the stress–strain curve is proposed. The modeling results are consistent with the experimental data known from the literature.

In addition to mining, underground space is widely used for various purposes - tunnels, underground storage facilities, etc. Very often, such structures are built specifically taking into account their use, less often they use the developed space. At the same time, the museum space is perceived "as is."The main difference between the museum mining space and other uses of mining is the conflict between the maximum preservation of the interiors of these workings (it should be authentic, that is, to contain previously used in this space technological, historical, cultural content) and safe, i.e., the geotechnical state should correspond to the safe stay of visitors. That is why the study of the sustainability of mining is becoming the number one task in such studies. The problem is compounded for abandoned mining operations, the operation of which was discontinued many years ago.Some solutions were proposed during the study of the abandoned Rogoselga mine, located near a high-traffic highway 135 km from the city of Petrozavodsk, 4 km from the village of Kolatselga, Republic of Karelia, Russian Federation. Underground production appeared in the process of hematite extraction, as the main raw material for the local ironworks in 1898. Mining was stopped in 1903 and, after several attempts to restore, was closed. This complex of workings is a valuable monument to the whole era of iron ore production in the southeastern part of the Fenno-Scandinavian Shield, in terms of historical and cultural points of view. The underground space includes the remnants of preparatory rollbacks, as well as the remnants of the wasting chambers, the ore of which went by itself in the rollbacks and then on the gallery was delivered to the surface. The total length of the workings does not exceed 300 meters, with a diameter of 2 meters, and the thickness of the ore body in the chambers up to 3 meters.Over more than a century, the underground area has been slightly transformed by the collapses of individual parts but has retained but some areas are in good condition. To evaluate the workings, some methods for assessing the underground space were proposed, including modern approaches to documenting the workings, assessing the sustainability of the vault, and individual preparatory works. The result is the development of a geological and information model of the underground space, allowing to study stability by modern methods, including the finite elements method (FEM).The small size of the work predetermined the methods used. The methodology used in photogrammetry has been adopted as a general technology of 3D modeling. The work has led to the development of several solutions for small-diameter imaging and lighting technology, as well as to identify "weaknesses" in production and the possibility of using geotechnical techniques to assess the stability of the array.