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Journal articles on the topic 'Rock mechanics – Mathematical models'
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1
Zadhesh, Jamal, and Abbas Majdi. "MATHEMATICAL DETERMINATION OF ROCK JOINTS MORPHOLOGICAL PROFILE." Rudarsko-geološko-naftni zbornik 37, no. 5 (2022): 117–31. http://dx.doi.org/10.17794/rgn.2022.5.10.
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Determining the geometric or morphology and mechanical properties of joints and geomechanics of intact rock is a vitally important issue in predicting the behaviour of structures built inside or on rock masses. The joint morphology is significant because it affects the strength of the rock mass and controls the stability of the structures related to the rock masses. Until recently, joint morphology was introduced in a simple form which brought about models that are far from the inherent state of a rock joint. The work presented in this research introduces a new model to represent rock joint morphology which is very close to reality. For this research, Sarchawa marble mine joint systems are studied. According to this research, the morphology of each rock joint can be expressed as a mathematical equation. Using the output of this research, we can see a more realistic view of the rock masses. As a result, we can have better designs for structures correlated to rock masses, making the result better and more reliable.
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Petrakov, Dmitry, Kirill Kupavykh, and Artem Kupavykh. "The effect of fluid saturation on the elastic-plastic properties of oil reservoir rocks." Curved and Layered Structures 7, no. 1 (June 8, 2020): 29–34. http://dx.doi.org/10.1515/cls-2020-0003.
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AbstractBackground: The success of planning geological and technical measures aimed at intensifying oil production is of high importance.Methodology: To increase the efficiency of operations aimed at oil recovery enhancement, it is necessary to use mathematical models of the rock mass deformation, taking into account the physical and mechanical properties of the rocks.Results: Currently, the application of these models is difficult due to a lack of data. As a result, the use of simpler models is resorted to, which is not always correct in the practical application of these models. This article describes experimental studies aimed at determining the mechanical properties of rock and establishing the correlation between properties and the fluid saturation of the rocks. The study determined the physical-mechanical properties of the rocks (taking into account the stage of field development) and established the dependencies of the change in the oil reservoir rock properties on the saturation and type of load on a sample.Conclusions: The results show that the saturation of the rock with a liquid phase (hydrocarbon or water) decreases the strength of the reservoir rock, which in turn depends on the type of saturating fluid.
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Guzev, Mikhail, and Vladimir Makarov. "Principles of the non-Euclidian model application to the problem of dissipative mesocracking structures of highly compressed rock and massifs modelling." E3S Web of Conferences 56 (2018): 02001. http://dx.doi.org/10.1051/e3sconf/20185602001.
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New experimental results such as “zonal disintegration” around deep openings and “reversible deformations” of highly compressed rock samples cannot be described correctly from contemporary rock mechanics, which is based on the principals of classical Continuum Mechanics theory. A new approach to rock mechanics mathematical models consists of the application of non-Euclidian modelling to the problem of the description of anomalous experimental results. This leads to the formation of the “Geomechanics of Highly Compressed Rock and Rock Massifs” - a new branch of the existing theory of Geomechanics - in which framework a radical rise in geodynamical phenomena forecasting can be achieved. Principles of the geomechanics of highly compressed rock and rock massifs are discussed in this paper. The effectiveness of the application of non-Euclidian modelling to the anomalous experimental effects observed in research is demonstrated on two hierarchical geomedia block levels such as rock samples and rock massif around underground openings.
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Kononenko, Maksym, and Oleh Khomenko. "New theory for the rock mass destruction by blasting." Mining of Mineral Deposits 15, no. 2 (2021): 111–23. http://dx.doi.org/10.33271/mining15.02.111.
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Purpose. To develop a new theory for the rocks destruction by blasting using a description of the formation processes of zones with various mass state around the charging cavity. Methods. The new theory for the rock mass destruction by blasting has been developed based on the use of the well-known elasticity theory laws and the main provisions of the quasi-static-wave hypothesis about the mechanism of a solid medium destruction under the blasting action. The models of zones of crumpling, intensive fragmentation and fracturing that arise around the charging cavity in the rock mass during its blasting destruction, depending on the physical and mechanical pro-perties of the rock mass, the energy characteristics of explosives and the rock pressure impact, have been developed using the technique of mathematical modeling. Findings. Based on the mathematical modeling results of the blasting action in a solid medium, the mathematical models have been developed of the zones of crumpling, intensive fragmentation and fracturing, which are formed around the char-ging cavity in a monolithic or fractured rock mass. Originality. The rock mass destruction by blasting is realized according to the stepwise patterns of forming the zones of crumpling, intensive fragmentation and fracturing, which takes into account the physical and mechanical properties of the medium, the energy characteristics of explosives and the rock pressure impact. Practical implications. When using the calculation results in the mathematical modeling the radii of the zones of crumpling, intensive fragmentation and fracturing in the rock mass around the charging cavity, it is possible to determine the rational distance between the blasthole charges in the blasting chart, as well as to calculate the line of least resistance for designing huge blasts.
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ABETOV, Auez E., Abylay N. UZBEKOV, Nicolay N. GRIB, Andrey E. MELNIKOV, and Yury A. MALININ. "SPATIAL VARIABILITY OF PHYSICAL AND MECHANICAL PROPERTIES OF ROCK MASS IN CENTRAL KAZAKHSTAN." Periódico Tchê Química 17, no. 34 (March 20, 2020): 718–26. http://dx.doi.org/10.52571/ptq.v17.n34.2020.742_p34_pgs_718_726.pdf.
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The efficiency and quality of drilling and blasting operations in the development of mineral deposits largely depend on the variability of the properties of the rock mass. With a detailed study of various geological objectsmineral deposits or structural elements of the earth’s crust of any order, up to a single layer or block, it is possible to create three-dimensional digital models. The article considers the possibility of spatial variability of rock mass properties in Central Kazakhstan by means of mathematical modeling using data from the drilling process control file of the Aquila system of a DH-M drilling rig. To assess the structure and condition of the rock mass, it was constructed two-dimensional sections digital model, which shows the spatial variability of physical and mechanical properties. A pseudolinear approximation between the file vectors is chosen as a method for constructing twodimensional sections. The application of the mathematical method of pseudo-linear interpolation is shown, which allows with a sufficient degree of reliability to evaluate the physical and mechanical properties (PMP) of the rocks in the inter-well and inter-interval space of the rock mass. Based on the results of the study, the software was developed that provides an operational and effective assessment of the physical and mechanical properties of the rock mass with the visualization of the result. The developed approach and software can be used to improve the efficiency of drilling and blasting operations of existing mining enterprises, as well as in the implementation of scientific and industrial research on mathematical modeling of state of the rock mass.
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Xing, Guangchi, and Tieyuan Zhu. "A viscoelastic model for seismic attenuation using fractal mechanical networks." Geophysical Journal International 224, no. 3 (November 17, 2020): 1658–69. http://dx.doi.org/10.1093/gji/ggaa549.
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SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.
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Li, Changping, Longchen Duan, Songcheng Tan, Victor Chikhotkin, and Xiaohui Wang. "An Electro Breakdown Damage Model for Granite and Simulation of Deep Drilling by High-Voltage Electropulse Boring." Shock and Vibration 2019 (November 29, 2019): 1–12. http://dx.doi.org/10.1155/2019/7149680.
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Electropulse rock breaking has wide application prospects in hard rock drilling and ore breaking. At present, there are no suitable physical mathematical models that describe electropulse boring (EPB) processes under confining pressures. In this paper, a high-voltage electropulse breakdown damage model is established for granite, which includes three submodels. It considers electric field distortions inside the rock, and an electric field distribution coefficient is introduced in the electro-breakdown model. A shock-wave model is also constructed and solved. To simulate the heterogeneity of rocks, EPB rock breaking in deep environments is simulated using the two-dimensional Particle Flow Code (PFC2D) program. The solved shock wave is loaded into the model, and confining pressure is applied by the particle servo method. An artificial viscous boundary is used in the numerical simulation model. Using this approach, a complete numerical simulation of electropulse granite breaking is achieved. Breakdown strength and the influences of physical and mechanical parameters on it are also obtained. Time-varying waveforms of electrical parameters are obtained, and the effect of confining pressure on EPB is also described.
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Deng, Wubing, and Igor B. Morozov. "Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies." GEOPHYSICS 81, no. 4 (July 2016): D395—D404. http://dx.doi.org/10.1190/geo2015-0406.1.
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We have developed a macroscopic model for a two-phase medium (solid porous rock frame plus saturating pore fluid) with squirt flows based on Lagrangian continuum mechanics. The model focuses on improved physics of rock deformation, including explicit differential equations in time domain, causality, linearity, frequency-independent parameters with clear physical meanings, and an absence of mathematical internal or memory variables. The approach shows that all existing squirt-flow models can be viewed as microscopic models of viscosity for solid rock. As in existing models, the pore space is differentiated into compliant and relatively stiff pores. At lower frequencies, the effects of fluid flows within compliant pores are described by bulk and shear solid viscosities of the effective porous frame. Squirt-flow effects are “Biot consistent,” which means that there exists a viscous coupling between the rock frame and the fluid in stiff pores. Biot’s poroelastic effects associated with stiff porosity and global flows are also fully included in the model. Comparisons with several squirt-flow models show good agreement in predicting wave attenuation to approximately 1 kHz frequencies. The squirt-flow viscosity for sandstone is estimated in the range of [Formula: see text], which is close to field observations. Because of its origins in rigorous mechanics, the model can be used to describe any wavelike and transient deformations of heterogeneous porous media or finite bodies encountered in many field and laboratory experiments. The model also leads to new numerical algorithms for wavefield modeling, which are illustrated by 1D finite-difference waveform modeling.
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Li, Haoran, Ziheng Wang, Dekang Li, and Yajun Zhang. "Particle Flow Analysis of Macroscopic and Mesoscopic Failure Process of Salt Rock under High Temperature and Triaxial Stress." Geofluids 2021 (November 15, 2021): 1–15. http://dx.doi.org/10.1155/2021/8238002.
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In order to reveal the mechanism of thermal-induced deformation and fracture development of salt rock under high temperature, the particle flow program PFC2D was used to study the triaxial compression failure process of salt rocks under different temperatures; at the same time, a combination model of Burge and Linearpbond was proposed to simulate plastic deformation and heat conduction of salt rock. Finally, the simulation results were compared with the experimental results to verify the validity of the conclusion. The simulation results show that the elastic limit points of rock gradually descend, the dilatancy points rise gradually, and the plastic deformation characteristics of salt rock become more obvious with the increase of temperature. Due to the damage of the sample, the strong chains break and disappear, increasing the proportion of the weak chains, and the high temperature intensifies the rupture of the contact between the particles in the salt rock. As the temperature increases from 50°C to 120°C, the strong chains in the rock sample decrease significantly, and the damage gradually increases; when the temperature is 150°C, the contact force decreases sharply, and the damage of salt rock is significant. According to the particle displacement cloud diagrams, it is found that the expansion direction from the middle part of the rock sample to the left and right ends is 12.08°, 9.55°, 8.2°, 6.33°, and 0°, respectively. The displacement directions of the rock sample show obvious radial expansion tendency, and the higher the temperature, the more obvious the “drum-shaped” failure phenomenon in the middle of the rock sample. During the heating process, the thermal cracks are mainly tensile cracks, and transverse cracks are gradually formed in the middle of the model. The cementation failure points at the top and bottom of the model expand in an oblique direction and form oblique cracks of about 45°. From the three different mathematical models of macroscopic and mesoscopic views, it is concluded that the effect of temperatures on salt rock is more significant after 90°C. This research is important for exploring the macroscopic and microscopic mechanics evolution of salt rock and provides a reference for determining the long-term mechanical strength of salt rock.
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Deng, Wubing, and Igor B. Morozov. "Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity." GEOPHYSICS 83, no. 6 (November 1, 2018): MR345—MR352. http://dx.doi.org/10.1190/geo2017-0821.1.
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The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we find that Cole-Cole spectra naturally arise from conventional mechanics with nonlinear internal friction (non-Newtonian viscosity). The Lagrangian mechanical formulation is applied to a finite body (a rock sample in a laboratory experiment) and a wave-propagating medium, in both cases providing rigorous differential equations of motion and revealing the time- and frequency-independent material properties. The model also leads to a generalized Cole-Cole (GCC) model with multiple internal variables (relaxation mechanisms), similar to the generalized standard linear solid (GSLS). As a practical application, the GSLS and GCC models are compared on interpretations of recent P-wave attenuation and dispersion measurements on bitumen-sand samples in the laboratory. The GSLS and GCC models can be used to predict the observed strain/stress ratios with adequate accuracy. However, each of these models offers certain advantages, which are the linearity (for GSLS) and potentially smaller number of dynamic variables and broader peaks in attenuation spectra (for GCC). Therefore, additional experiments focusing on linearity of internal friction are required to establish which of these models may be preferable for rock. The Lagrangian approach provides a simple and physically meaningful way for comparing all types of observations, formulating numerical modeling schemes, and predicting the propagation of waves and behavior of other deformations of earth media.
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Xu, Liqi, Xiaoli Xu, Yiming Sun, and Tianci Lu. "Evaluation of Rock Brittleness Based on Complete Stress–Strain Curve." Mathematics 10, no. 23 (November 26, 2022): 4470. http://dx.doi.org/10.3390/math10234470.
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As a basic mechanical property of rocks, brittleness is closely related to the drillability, wellbore stability, and rockburst characteristics of reservoir rocks. Accurate evaluation of rock brittleness is of great significance for guiding oil and gas production and reservoir reconstruction. This paper systematically introduced the commonly used brittleness evaluation methods based on the stress–strain curve and analyzed their theoretical background and mathematical models. Combined with practical engineering application, the characterization effect of commonly used brittleness indexes in various rock samples is verified and optimized, and it is obtained that the brittleness index (B17 in this paper), based on the stress–strain curve and considering energy conversion, has the best characterization result for rock brittleness, which has good differentiation for different rock samples. At the same time, considering that the stress–strain curve under high confining pressure may result in a significant yield plateau phenomenon before and after the peak strength, the endpoint of the plastic yield plateau is used to replace the peak point as the starting point for the drop of bearing capacity. The revised brittleness index is consistent with the changing trend of the original curve, which verifies the reliability of the model. Finally, the method for characterizing the brittleness of Class II curves is supplemented, and the combined brittleness index of rock is established, which verifies the rationality and correctness of the index and provide a more general evaluation method for rock brittleness in engineering.
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BONDARENKO, N. K., and O. L. TIUTKIN. "CRITICAL ANALYSIS OF APPROACHES TO DETERMINING THE STRESS-STRAIN STATE OF THE "HORIZONTAL WORKING – LAYERED MASSIF" SYSTEM." Bridges and tunnels: Theory, Research, Practice, no. 22 (December 7, 2022): 5–11. http://dx.doi.org/10.15802/bttrp2022/268182.
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Purpose. To perform a critical analysis of approaches to determining the stress-strain state of the "horizontal working – layered massif" system. Obtain informed decisions for applying a specific approach to the case of a layered massif. To substantiate the metric of finite element models of the system "horizontal working – layered massif". Methodology. To achieve the purpose, the peculiarities of approaches to determining the stress-strain state of the system "horizontal working – rock massif" were analyzed. It has been proven that layering is the most important structural feature of the surrounding rock massif. A detailed analysis of mathematical methods for solving elastic-plastic problems for rock massifs was performed. Findings. During the analysis of solving the problem of determining the stress-strain state of the system "horizontal working – layered massif", two approaches were identified, each of which has its own set of methods. These approaches are analytical one and numerical, each of them has special features. It has been confirmed that recently the studies of the system "horizontal working - rock massif" are mostly based on the numerical approach, leaving only a small share of the total volume to the analytical one. It was determined that the introduction of numerical methods, in particular, the method of finite elements in specialized software complexes, allowed to change the concept of research in geomechanics and mechanics of underground structures, shifting the focus to mathematical and simulation modeling. Originality. Based on the results of the critical analysis of the approaches, the use of numerical analysis based on finite-element models is scientifically substantiated. It is this approach to determining the stress-strain state of the "horizontal working – layered massif" system that allows for layering to be taken into account without additional assumptions. Practical value. In the course of research, it has been proven that a spatial finite-element model from a flat prototype, but limited to a thickness of 0.1 or 1 m, is adequate for the given task, provided that plane deformation is considered.
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Skrzypkowski, Krzysztof, Waldemar Korzeniowski, Krzysztof Zagórski, and Anna Zagórska. "Adjustment of the Yielding System of Mechanical Rock Bolts for Room and Pillar Mining Method in Stratified Rock Mass." Energies 13, no. 8 (April 21, 2020): 2082. http://dx.doi.org/10.3390/en13082082.
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The article presents a novel yielding mechanism, especially designed for the rock bolt support. Mechanical rock bolts with an expansion head and equipped with one, two, four and six dome bearing plates were tested in the laboratory conditions. Furthermore, in the Phase2D numerical program, five room and pillar widths were modeled. The main aim of numerical modeling was to determine the maximal range of the rock damage area and the total displacements in the expanded room. The models were made for a room and pillar method with a roof sag for copper ore deposits in the Legnica-Głogów Copper District in Poland. Additionally, in the article a load model of the rock bolt support as a result of a geomechanical seismic event is presented. Based on the results of laboratory tests (load–displacement characteristics), the strain energy of the bolt support equipped with the yielding device in the form of dome bearing plates was determined and compared with the impact energy caused by predicted falling rock layers. Based on the laboratory tests, numerical modeling and mathematical dynamic model of rock bolt support, the dependence of the drop height and the corresponding impact energy for the expanded room was determined.
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Neskromnykh, Vyacheslav, Marina Popova, A. Golovchenko, P. PETENEV, and Liu Baochang. "Method of drilling process control and experimental studies of resistance forces during bits drilling with PDC cutters." Journal of Mining Institute 245 (December 2, 2020): 539–46. http://dx.doi.org/10.31897/pmi.2020.5.5.
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A rational, theoretically proved and empirically verified control system is a condition for optimal management of the drilling process in compliance with the criteria for minimizing the cost of time and material resources. A new generation of rock-cutting tools using PDC cutters (polycrystalline diamante cutters), which are extremely effective when drilling wells for various purposes in medium-hard rocks, dictates the need to develop methods and criteria for optimal control of the drilling process using this tool.
The paper presents an analysis of the force interaction between rock-cutting elements, face rock, and drilling mud saturated with slam, highlights the influencing factors and provides dependencies for determining the parameters of rock failure. Empirical verification of the theoretical propositions was carried out based on the data analysis from experimental bit drilling of marble with PDC cutters with a diameter of 76.2 mm, processed using the method of full factor experiment to obtain mathematical models of factors and their graphical interpretation.
The method of controlling the drilling process based on the optimal ratio of the tool rotation frequency, axial weight and deepening per one turnover is considered, which allows determining the rock failure mode at the well bottom by indirect signs and choose the optimal values of the drilling mode parameters that correspond to the most optimal conditions in terms of achieving the maximum mechanical drilling speed in conjunction with the rational mode of rock-cutting tool operation. A scheme is presented that contains possible variants of the bit run mode and ways to recognize them by the ratio of the deepening per turnover and the rotation frequency of the rock-cutting tool.
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Mirenkov, Valery. "CAUCHY PROMLEMS IN GEOMECHANICS." Interexpo GEO-Siberia 2, no. 4 (2019): 176–81. http://dx.doi.org/10.33764/2618-981x-2019-2-4-176-181.
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Proposal about linear stress field of virgin solid and necessity for calculation stress-strain behavior near workings at actual mining cause to development analytical and numerical methods of the calculations. One-dimensional, two-dimensional and three-dimensional models of solids with relaxations, which are placed to the class of Couchy problems, for which Cauchy initial data are formulated, has been occurred. It is related to the fact that in rock mechanics plane with relaxation or space with cavity, for which there are infinitely remote points, are considered. There are known solutions, when boundary conditions represented by constants, determined by initial stress field adopted for concrete solid, are formulated on the infinity. In condition of numerical calculation, the software usually gives some result, accuracy of which does not control. Worldwide scientific schools represent same results which are in antimony with theory of equals of mathematical physics, which have outlined class of Cauchy problems for that with cancelled out boundary condition on the infinity. In the work, problems of rock mechanics for the plane relaxed with random holes are considered. The necessity to carry out points of the theory is proved. Method of solving of such problem class based on getting so-called additional solution formulated in class of Cauchy problem is proposed.
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Mader, Thomas, Magdalena Schreter, and Günter Hofstetter. "An advanced constitutive model for transversely isotropic rock - Evaluation of two different regularization approaches." IOP Conference Series: Earth and Environmental Science 1124, no. 1 (January 1, 2023): 012115. http://dx.doi.org/10.1088/1755-1315/1124/1/012115.
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Abstract The mathematical description of the material behavior of rock is a demanding task in engineering practice. Rock is classified as a frictional cohesive material characterized by highly nonlinear mechanical behavior with irreversible deformation, strain hardening, strain softening and degradation of stiffness. In addition, depending on the origin of a particular rock type, the orientation of minerals and grains as well as the formation of stratification planes lead to inherent anisotropic behavior. Especially in stratified rock types like shales or phyllites, often the special case of transversely isotropic material behavior is encountered. In a previous work, a novel continuum-based material model for describing both, the highly nonlinear and transversely isotropic material behavior of rock, denoted as TI-RDP model, was presented. By means of the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, an established isotropic damage plasticity model for rock was extended. In this contribution two different regularization approaches, which are well established for isotropic models, i.e., the mesh-adjusted softening modulus and the implicit gradient-enhancement, are adopted for the TI-RDP model. Based on uniaxial tension and triaxial compression tests considering different orientations of the principal material directions with respect to the direction of axial loading, their capabilities are assessed in terms of predicting the direction-dependent mechanical behavior in a mesh-insensitive manner.
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Malanchuk, Z. R., A. O. Khrystyuk, S. Ye Stets, V. V. Semeniuk, and L. O. Malanchuk. "Substantiation of research results on energy efficiency of basalt crushing." Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 6 (December 25, 2022): 41–46. http://dx.doi.org/10.33271/nvngu/2022-6/041.
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Purpose. To experimentally determine the main design and operational parameters of the influence of rock mass properties on the Roller Crusher performance when processing basalt rock mass. Methodology. The crushing and grinding of basalts are studied by the methods of mathematical statistics in order to identify the results obtained and determine the dependences of technological parameters on the mechanical impact factors. Experimental studies are carried out on the example of basalts from the Rafalivskyi quarry in the Rivne region. Findings. It has been revealed that the elemental composition of rocks in the benches of basalt quarries has a different mineral composition. Experimental studies of the rock crushing results have determined the efficiency of using screening for crushing basalts. The experimental dependences of the roller crusher performance in crushing and grinding modes on the properties of the rock mass have been obtained. Originality. The value of crushed rock fractal joints has been found, when using cone and centrifugal crushers, which is characterized by the shape factor and fractal dimension D. For cone crusher Kf=2.15.0 and D=1.4. For centrifugal crusher Kf=1.51.8 and D=1.17. These parameters testify to the energy feasibility of using centrifugal crushers. The high value of the multiple correlation coefficients R2 and Fisher criterion F, whose value at a significance level of 0.05 is higher than the critical one, indicates a sufficient convergence between the experimental and theoretical results and the accuracy of the obtained analytical dependences. Practical value. The generalized models for determining the Roller Crusher performance, obtained for each rock type, based on significant factors, greatly facilitate the choice of parameters for crushing and grinding processes, and also allow choosing a rational mode of crusher operation.
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Deng, Jia, Jiujiang Li, Lan Zhang, Fuquan Song, Dong Wang, and Hongjian Wang. "CH4 transport in micro–nano porous media associated with supercritical CO2 flooding." Physics of Fluids 34, no. 7 (July 2022): 076112. http://dx.doi.org/10.1063/5.0100762.
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Injecting supercritical CO2 into tight gas reservoirs to displace CH4 is an extremely promising technology of unconventional gas exploitation. However, Darcy's law cannot describe the gas flow due to ultra-low permeability and micro–nano porosity of tight rock. The present work is an analytical approach to investigating the nonlinear seepage characteristics of CH4 displacement by supercritical CO2. Moreover, considering the steady and unsteady state conditions, mathematical models for planar linear flooding, planar radial flooding, and single well and one-well injection/one-well production types are presented, computed, and verified. Their equipotential and streamline charts are first determined by implementing the model. Additionally, by investigating variables such as formation pressure, producing pressure drop, permeability, temperature, well spacing, and mass flow, their contributions to gas production rate are determined. Finally, an approach for improving the gas recovery efficiency is obtained based on the obtained results.
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Xie, Shijie, Hang Lin, Yixian Wang, Yifan Chen, Wei Xiong, Yanlin Zhao, and Shigui Du. "A statistical damage constitutive model considering whole joint shear deformation." International Journal of Damage Mechanics 29, no. 6 (January 23, 2020): 988–1008. http://dx.doi.org/10.1177/1056789519900778.
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The whole shear deformation of rock joints significantly affects the long-term behavior and safety of engineering projects. In this paper, a new damage constitutive model related to the Weibull distribution and statistical damage theory is proposed. This model considers the shear stiffness degradation, post-peak softening, and residual phase of rock joints in the whole shearing process. Main works include the three following aspects: First, the phase of initial damage is determined on the assumption that the joint shear failure is regarded as a result of damage evolution, according to the typical joint shear curve and the three-parameter Weibull distribution. Then, a statistical damage evolution model for the whole joint shearing process is introduced to make this model be capable of describing the residual phase of rock joints. Finally, a statistical constitutive model for the whole joint shearing process is proposed by statistical damage theory, and the calculated results of the models are compared to the experimental results. The results indicate that the proposed model shows a good agreement with the experimental examples, and the proposed model can distinctly reflect the effects of residual stress, peak stress, and shear stiffness. In addition, the model parameters can be mathematically confirmed and have distinct physical meanings.
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Zhang, Ligang, Xiao Fei Fu, G. R. Liu, Shi Bin Li, Wei Li, and Sining Qu. "Models for evaluating craters morphology, relation of indentation hardness and uniaxial compressive strength via a flat-end indenter." Open Geosciences 10, no. 1 (July 25, 2018): 289–96. http://dx.doi.org/10.1515/geo-2018-0022.
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AbstractIn this work, the intensive theoretical study and laboratory tests are conducted to evaluate the craters morphology via the flat-ended indenter test, relationship of indentation hardness (HRI) and uniaxial compressive strength (UCS). Based on the stress distribution, failure process and Mohr–Coulomb failure criterion, the mathematical mechanical models are presented to express the formation conditions of “pulverized zone” and “volume break”. Moreover, a set of equations relating the depth and apex angle of craters, the ratio of indentation hardness and uniaxial compressive strength, the angle of internal friction and Poisson’s ratio are obtained. The depth, apex angle of craters and ratio of indentation hardness and uniaxial compressive strength are all affected by the angle of internal friction and Poisson’s ratio. The proposed models are also verified by experiments of rock samples which are cored from Da Qing oilfield, the percentage error between the test and calculated results for depth, apex angle of craters and the ratio of HRI and UCS are mainly in the range of –1.41%–8.92%, –5.91%–3.94% and –8.22%–13.22% respectively for siltstone, volcanic tuff, volcanic breccia, shale, sand stone and glutenite except mudstone, which demonstrates that our proposed models are robust and effective for brittle rock.
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Boreiko, D. A., A. A. Lutoev, and D. Yu Serikov. "Theoretical studies on the nature and conditions of interaction of heel and peripheral nose cones of offset roller cone bits with a bottom hole." Gornye nauki i tekhnologii = Mining Science and Technology (Russia) 7, no. 3 (November 5, 2022): 231–39. http://dx.doi.org/10.17073/2500-0632-2022-3-231-239.
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An offset of roller cone rotation centerlines is used to increase the mechanical penetration rate while drilling in soft rocks. This enables increasing the area of a cutting structure teeth contact with a bottom hole. The analysis of offset cone drill bit (cutting structure) teeth wear showed that particularly significant wear is characteristic of the transition zone from the heel cone to the nose cone; which leads to significant reduction in the mechanical rate of penetration and a rapid decrease in the hole diameter. The purpose of this paper is to conduct a theoretical research on the nature and conditions of interaction between heel and peripheral nose cones of offset roller cone bits with a bottom hole; which is aimed at improving the efficiency of rock cutting by offset roller cone bits. To achieve the purpose; the authors analyzed data on the nature and causes of wear of existing offset roller cone bit cutting structure (teeth); developed a mathematical model in a cylindrical coordinate system allowing to determine the location and geometric parameters of the gage cone contact area with the hole wall for different roller cone bits sizes; developed a computer solid model for checking the adequacy of the mathematical model by comparing these two models; prepared recommendations for further improvement of the design of existing offset roller cone bit cutting structure (teeth). The research was carried out by the method of mathematical simulation of geometric figures and bodies corresponding to roller cones and a hole. The research has revealed that significant adjustments need to be made to the geometry of the roller cone teeth (currently being patented). This would allow decreasing the areas of cone heel blunting by 15–20 % as well as providing more prolonged contact of base and gage cones with bottom hole and wall surfaces. This allows to reduce wear of teeth in the transition zone of the generatrix from the peripheral nose cone to the gage (heel) cone of the roller cone and to maintain the required specific pressure on the cut rock for a longer period of time and; as a result; to increase both the mechanical penetration rate and the service life of the drilling tools.
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Khan, Naseer Muhammad, Kewang Cao, Muhammad Zaka Emad, Sajjad Hussain, Hafeezur Rehman, Kausar Sultan Shah, Faheem Ur Rehman, and Aamir Muhammad. "Development of Predictive Models for Determination of the Extent of Damage in Granite Caused by Thermal Treatment and Cooling Conditions Using Artificial Intelligence." Mathematics 10, no. 16 (August 11, 2022): 2883. http://dx.doi.org/10.3390/math10162883.
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Thermal treatment followed by subsequent cooling conditions (slow and rapid) can induce damage to the rock surface and internal structure, which may lead to the instability and failure of the rock. The extent of the damage is measured by the damage factor (DT), which can be quantified in a laboratory by evaluating the changes in porosity, elastic modulus, ultrasonic velocities, acoustic emission signals, etc. However, the execution process for quantifying the damage factor necessitates laborious procedures and sophisticated equipment, which are time-consuming, costly, and may require technical expertise. Therefore, it is essential to quantify the extent of damage to the rock via alternate computer simulations. In this research, a new predictive model is proposed to quantify the damage factor. Three predictive models for quantifying the damage factors were developed based on multilinear regression (MLR), artificial neural networks (ANNs), and the adoptive neural-fuzzy inference system (ANFIS). The temperature (T), porosity (ρ), density (D), and P-waves were used as input variables in the development of predictive models for the damage factor. The performance of each predictive model was evaluated by the coefficient of determination (R2), the A20 index, the mean absolute percentage error (MAPE), the root mean square error (RMSE), and the variance accounted for (VAF). The comparative analysis of predictive models revealed that ANN models used for predicting the rock damage factor based on porosity in slow conditions give an R2 of 0.99, A20 index of 0.99, RMSE of 0.01, MAPE of 0.14, and a VAF of 100%, while rapid cooling gives an R2 of 0.99, A20 index of 0.99, RMSE of 0.02, MAPE of 0.36%, and a VAF of 99.99%. It has been proposed that an ANN-based predictive model is the most efficient model for quantifying the rock damage factor based on porosity compared to other models. The findings of this study will facilitate the rapid quantification of damage factors induced by thermal treatment and cooling conditions for effective and successful engineering project execution in high-temperature rock mechanics environments.
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Wiercigroch, Marian, Marcin Kapitaniak, Vahid Vaziri, and Krishnan Nandakumar. "Complex dynamics of drill-strings: Theory and experiments." MATEC Web of Conferences 211 (2018): 01002. http://dx.doi.org/10.1051/matecconf/201821101002.
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We investigate complex drill-string dynamics in a downhole drilling where strong nonlinear interactions between various types of vibration take place. First, we present a low dimensional model of the downhole drilling where a drill-bit cutting a rock formation has a strong coupling between torsional and axial oscillations. The model can be used to study drilling stability as an example results are given. Then we introduce a new experimental rig developed by the Centre for Applied Dynamics Research at the University of Aberdeen, capable of reproducing all major types of drill-string vibration. One of the most important features of this versatile experimental rig is the fact that commercial drill-bits, employed in the drilling industry, and real rock-samples are used. The rig operate in different configurations, which enables the experimental study of various phenomena, such as stick-slip oscillations, whirling and drill-bit bounce. It also allows to determine mechanical characteristics of the drill-bits, which are used to calibrate mathematical models.
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Zhuravkov, M. A., and V. V. Kolyachko. "The construction of solutions for some model problem classes with resolvent equations of a fractional order." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 58, no. 1 (April 4, 2022): 60–70. http://dx.doi.org/10.29235/1561-2430-2022-58-1-60-70.
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In this paper, we represent new examples of constructing model problems of the mechanics of a deformable solid using a fractional differentiation apparatus. The solutions to boundary problems of mechanics are found, in which the defining differential equations have a fractional order. In particular, such problems as a model of a “fractal” oscillator, a model problem on the dynamic of wave propagation in rock, model problems on the deformation of wave propagation in deformable viscoelastic media (a semi-infinite viscoelastic rod) for various viscoelasticity models are considered. When building the solutions, the Mainardi algorithm and the Laplace transformation are used. Model solutions for the considered problems are built. Asymptotic solutions of wave propagation equations in viscoelastic media under different viscoelasticity models are obtained.
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Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1279–81. http://dx.doi.org/10.1115/1.3143691.
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Mechanical failure of machine parts, structures, and microelectronic components has a strong negative impact on the safety, security, and productivity of our people. Prevention of these failures is a principal focus of solid mechanics, which uses analysis, experiment, and computation to provide the understanding necessary for failure reduction through improved design, fabrication, and inspection. Experimental mechanics plays a critical role in this effort since it provides the data base for the calculations and the means for testing the validity of proposed theoretical models of failure. Current trends in experimental mechanics show increased use of optical methods for monitoring the displacements, velocities, and strains of surfaces. This trend has gained impetus from the attractiveness of noncontact methods for hostile environments and dynamically loaded bodies. Advances in laser technology have enhanced the instrumentation associated with these methods. Another trend is the investigation of material behavior under more complex loading conditions, made possible by the availability of servo-controlled testing machines with computer interfaces. Still another trend is the increased attention given to defects, such as inclusions, cracks, and holes, because of their importance in failure mechanisms. Opportunities for future contributions from experimental mechanics appear to be great and to occur across a broad range of technological problems. A central theme of future research appears to be increased emphasis on measurements at the micron and submicron scale in order to advance the understanding of material response and failure at the micromechanical level. Increased attention will also be given to internal measurements of defects, deformations and residual stresses because of their importance in developing a fundamental understanding of failure. Automated data reduction and control of experiments will greatly increase the information obtained from experiments and its usefulness for the development of mathematical models. Other important research directions include improved methods for measurements of in situ stresses in rocks, improved measurements of displacements and physiological parameters in biological systems, capability for long-term monitoring of the integrity of structures, and improved sensors for feedback control of mechanical systems.
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Kessai, Idir, Samir Benammar, Mohamed Zinelabidine Doghmane, and Kong Fah Tee. "Drill Bit Deformations in Rotary Drilling Systems under Large-Amplitude Stick-Slip Vibrations." Applied Sciences 10, no. 18 (September 18, 2020): 6523. http://dx.doi.org/10.3390/app10186523.
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In oil and gas industry, rotary drilling systems are used for energy exploration and productions. These types of systems are composed of two main parts: mechanical and electrical parts. The electrical part is represented by rotating motor called top drive; however, the mechanical part of the system is composed of tool string with many pipes, at the bottom end of these pipes the bit is attached to cut the rock during their contact. Since the bit is in a direct contact with rock characteristic variations, it can be under risk for heavy damage. The latter is principally caused by the fact that the rock–bit interaction term is highly nonlinear and unpredictable. In literature, many mathematical models have been proposed for rock–bit interaction, but they do not reflect the dynamic of the bit under vibrations since torsional and axial vibrations are strongly coupled and synchronized with it. In industrial development, the design of drill bit has faced many improvements in order to overcome these vibrations and mitigate unpredictable phenomena. Even though, the practical use of these drill bits confirmed that there are still many failures and damages for the new designs; moreover, bits’ virtual life become shorter than before. The objective of this study is to analyze the drill bit deformations caused by the stick-slip vibration phenomenon which is characterized by high-frequency high-amplitude in rotary drilling systems. The obtained results were validated through a case study of MWD (measurement while drilling) data of well located in a Southern Algerian oil field.
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Kolesnikov, Gennady, and Timmo Gavrilov. "Sandstone Modeling under Axial Compression and Axisymmetric Lateral Pressure." Symmetry 14, no. 4 (April 11, 2022): 796. http://dx.doi.org/10.3390/sym14040796.
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The problems of the mechanical state of rocks and other brittle materials are studied from different sides in a large number of publications, the flow of which does not weaken with time, which is explained by the relevance and complexity of these problems. Quantitative values of strength and other characteristics of such materials can be obtained experimentally or using numerical and analytical models. This work is aimed at developing an analytical model for analyzing the state of brittle material on the example of sandstone under axial compression and axisymmetric proportional lateral pressure. The research uses methods of modeling mechanical systems based on the basic ideas of fracture mechanics. For axial compression with proportional lateral pressure, the equation of the load–strain curve is obtained, and the functions of residual life and damage are justified; effective stresses and effective modulus of elasticity are determined; a calculation algorithm and examples of its application are given. The results of the simulation are consistent with the experimental data known from the literature. The results obtained to a certain extent clarify the understanding of the mechanism of rock damage and destruction under axial compression with lateral pressure.
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Sun, Chuang, Yunhe Ao, and Laigui Wang. "The Research on Strain-Softening Characteristics and Local Fracture Law of Deep Granite Roadway." Complexity 2020 (June 22, 2020): 1–13. http://dx.doi.org/10.1155/2020/1064016.
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The complex mechanical properties of deep surrounding rocks during excavation and unloading have always been a concern in engineering communities. Based on deep roadway engineering, the mechanical properties of granite strain-softening were investigated by laboratory tests. An exponential relationship between granite peak softening modulus and confining pressure was obtained using a nonlinear fitting method. A strain-softening model was developed based on plasticity theory for granite which took into account the nonlinear dilatancy angle and confining pressure. A mathematical model was developed using FLAC3D as platform. By developing a numerical model for a deep roadway, the local fracture characteristics of deep surrounding rocks under strain-softening conditions were evaluated. It has been found that the postpeak failure of granite had a tendency for brittle-ductile transformation. Under high confining pressure conditions, granite exhibited brittle failure characteristics during the postpeak period, and the postpeak softening modulus was decreased with the increase of confining pressure. From FLAC3D numerical calculations, it was found that the numerical models of different mesh densities had basically the same characteristic curves of surrounding rocks, which showed that the local cracking phenomenon had little effect on calculation results when the convergence constraint method was applied for the calculation of the stability of supporting structures and surrounding rocks. It was seen from the numerical simulation analyses of surrounding rock local fracture properties in deep roadways that plastic shear strain appeared in the local areas of roadway vault and arch foot, which basically coincided with the damage location and depth of surrounding roadway rocks.
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Ivins, Erik R., Lambert Caron, Surendra Adhikari, and Eric Larour. "Notes on a compressible extended Burgers model of rheology." Geophysical Journal International 228, no. 3 (October 30, 2021): 1975–91. http://dx.doi.org/10.1093/gji/ggab452.
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SUMMARY Constitutive theory for viscoelasticity has broad application to solid mantle or ice deformations driven by tides, surface mass variations, and post-seismic flow. Geophysical models using higher order viscoelasticity can better accommodate geodetic observations than lower-order theory, typically provided by tensor versions of Maxwell, 4-parameter Burgers or standard linear (Zener) rheology. We derive, for the first time, a mathematical description of a compressible version of the extended Burgers material (EBM) model paradigm which has a distribution function of relaxation spectra. The latter model is often used for parametrizing high temperature background transient responses in the rock physics and mechanics laboratory setting and have demonstrated application to low frequency seismic wave attenuation. A new generalization of this practical anelastic model is presented and applied to the glacial isostatic adjustment momentum equations, thus providing useful guidance for generating initial-value boundary problem-solving software for quite general coding strategies. The solutions for the vertical motion response to a suddenly imposed surface load reveal a short-term transience of substantial amplitude.
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Morozov, Igor B., and Wubing Deng. "Macroscopic framework for viscoelasticity, poroelasticity, and wave-induced fluid flows — Part 2: Effective media." GEOPHYSICS 81, no. 4 (July 2016): D405—D417. http://dx.doi.org/10.1190/geo2014-0404.1.
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Sedimentary rocks possess complex microstructures and require simplified descriptions in terms of averaged, or effective mechanical properties. Most conventional approaches to effective media use the concept of viscoelastic moduli to describe the frequency-dependent wave velocities and attenuation. However, for rock containing pore fluids, a single pair of bulk and shear moduli does not account for slow P- and S-waves and for reflections and conversions in heterogeneous media. To overcome these limitations, we use the general linear solid (GLS) theoretical framework to derive multiphase models of effective media. Two types of models are considered. First, for sandstone containing thin layers saturated with brine and gas, two-phase effective-medium relations are derived in a (relatively) closed form for the density and elasticity, and the parameters of internal friction are inferred by fitting the dispersion spectra of both fast and slow P-waves. In the second application, we consider the generalized standard linear solid (GSLS) medium, which is broadly used in numerical simulations of seismic wavefields. The GLS point of view suggests that (petro)physical significance should always be sought for the mathematical variables usually assumed in GSLS models. Inertial effects and interactions between internal variables cause additional wave modes in a GSLS medium. Contrary to what is often thought, with inertial effects and fuller interactions between the internal variables, near-zero or negative velocity dispersion can occur in a medium with band-limited attenuation.
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Madejski, Paweł, Paulina Krakowska, Edyta Puskarczyk, Magdalena Habrat, and Mariusz Jędrychowski. "Permeability determination in tight rock sample using novel method based on partial slip modelling and X-ray tomography data." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (May 24, 2019): 3053–63. http://dx.doi.org/10.1108/hff-11-2018-0711.
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Purpose The purpose of the paper was the application of computational fluid dynamics (CFD) techniques in fluid flow using Maxwell’s equation for partial slip modelling, estimating the flow parameters, and selecting tangential momentum accommodation coefficient (TMAC) for tight rock samples in permeability calculations. Design/methodology/approach The paper presents a numerical analysis of fluid flow in a low-porosity rock sample by using CFD. Modelling results allowed to determine mass flow rates in a rock sample and to calculate permeability values using a modified Darcy’s equation. Three-dimensional (3D) geometrical model of rock sample generated using computed X-ray tomography was used in the analysis. Steady-state calculations were carried out for defined boundary conditions in the form of pressure drop. The simulations were applied taking into account the slip phenomenon described by Maxwell’s slip model and TMAC. Findings Values of permeability were calculated for different values of TMAC, which vary from 0 to 1. Results in the form of gas mass flow rates were compared with the measured value of permeability for rock sample, which confirmed the high accuracy of the presented model. Practical implications Calculations of fluid flow in porous media using CFD can be used to determine rock samples’ permeability. In slip flow regime, Maxwell’s slip model can be applied and the empirical value of TMAC can be properly estimated. Originality/value This paper presents the usage of CFD, Maxwell’s equation for partial slip modelling, in fluid flow mechanism for tight rock samples. 3D geometric models were generated using created pre-processor (poROSE software) and applied in the raw form for simulation.
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Niu, Zihao, Zhende Zhu, and Xiangcheng Que. "Constitutive Model of Stress-Dependent Seepage in Columnar Jointed Rock Mass." Symmetry 12, no. 1 (January 13, 2020): 160. http://dx.doi.org/10.3390/sym12010160.
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Columnar jointed rock mass (CJRM) is a highly symmetrical natural fractured structure. As the rock mass of the dam foundation of the Baihetan Hydropower Station, the study of its permeability anisotropy is of great significance to engineering safety. Based on the theory of composite mechanics and Goodman’s joint superposition principle, the constitutive model of joints of CJRM is derived according to the Quadrangular prism, the Pentagonal prism and the Hexagonal prism model; combined with Singh’s research results on intermittent joint stress concentration, considering column deflection angles, the joint constitutive model of CJRM in three-dimensional space is established. For the CJRM in the Baihetan dam site area, the Quadrangular prism, the Pentagonal prism and the Hexagonal prism constitutive models were used to calculate the permeability coefficients of CJRM under different deflection angles. The permeability anisotropy characteristics of the three models were compared and verified by numerical simulation results. The results show that the calculation results of the Pentagonal prism model are in good agreement with the numerical simulation results. The variation of permeability coefficient under different confining pressures is compared, and the relationship between permeability coefficient and confining pressure is obtained, which accords with the negative exponential function and conforms to the general rule of joint seepage.
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Skakal's'ka, L. "Physical and reservoir properties prediction for reservoir rocksin unconventional gas-bearing geological structures." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 1 (64) (2014): 35–40. http://dx.doi.org/10.17721/1728-2713.64.07.35-40.
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Research into the behavior of elastic waves in thin-layered gas-bearing geological structures depends on the choice of geophysical and mathematical models of natural geological media and the numerical methods of problem solving. Hence the efficiency of a quasi-homogeneous, isotropic fractured-porous two-phase medium with given physical and mechanical properties. We have suggested a method of calculating empirical relationships between volumetric compression, porosity and pressure in porous rocks of an arbitrary geological region. Data on Zaluzhany wells were used to calculate the correlation and empirical relationships between reservoir properties and parameters of elastic waves and to distinguish dry and oil-gas saturated rocks. The least square technique made it possible to determine the correlation between the compressibility factor of fluid-saturated rocks and their porosity and pressure. Discrimination between oil and water was based on the density parameter. An algorithm has been suggested to do the corresponding calculations. The theoretical and practical implications of this study are as follows: – developing a numerical analytical predictive model for interpreting acoustic data on thin-layered rocks which is based on the correlations between their dynamic physical (effective wave propagation velocities, amplitude attenuation coefficients and their energy absorption) and reservoir (porosity, fracturing, compressibility) properties; – applying the proposed model and software products in geophysical exploration to interpret the geological and geophysical data on the structure and physical characteristics of sections and the physical properties of gas-bearing basins. In seismic acoustic exploration, the numerical model has to include experimental geological and geophysical data on the peculiarities of rock occurrence in the investigated area, with the physical and mechanical properties of different territories showing considerable variation. Such input data, as well as structural features and scattering properties of rocks (density, bedding, microporosity), ensure a significant increase in the accuracy of the numerical analysis. Preliminary testing was based on the data on the elastic moduli and S-wave velocities for dry and fluid-saturated rocks. Calculations were made of the elastic moduli and P-wave velocities for dry and fluid-saturated rocks of the Western oil and gas region of Ukraine (Zaluzhany-18 and Zaluzhany-19 wells). The aim of this work was to demonstrate the efficiency of the predictive method by examining the reservoir rock properties of the wells and to evaluate their gas saturation using the acoustic logging, geophysical and petrophysical data.
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Cerruti, Benedetta, Alberto Puliafito, Annette M. Shewan, Wei Yu, Alexander N. Combes, Melissa H. Little, Federica Chianale, et al. "Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures." Journal of Cell Biology 203, no. 2 (October 21, 2013): 359–72. http://dx.doi.org/10.1083/jcb.201305044.
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The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell–cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell–cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis.
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Kolesnikov, Gennady, and Vitali Shekov. "Energy Criterion for Fracture of Rocks and Rock-like Materials on the Descending Branch of the Load–Displacement Curve." Materials 15, no. 22 (November 9, 2022): 7907. http://dx.doi.org/10.3390/ma15227907.
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This article deals with the problem of predicting the brittle fracture of rocks and similar materials, which can also include frozen sandy soils. Such materials, due to the diversity of their conditions of origin, are characterized by natural heterogeneity at the micro-, meso-, and macro-levels, which makes it difficult to develop sufficiently universal criteria for their strength. Despite a number of known models and criteria of strength and fracture, the search for such criteria remains an urgent problem. In this paper, using the energy approach to the mathematical modeling of mechanical systems, the fracture criterion is justified, which differs from the known criteria that do not require integration to calculate the strain energy We and dissipation energy Wd. The well-known relation for the input energy W=We+Wd is used. The object of the study was the ratio of dW=dWe+dWd. The main research question concerned what the ratio of dWe and dWd would be at the point of brittle failure. The search for an answer to the question led to the justification of a differential energy criterion for the failure of brittle materials on the descending branch of the full stress–strain curve. It was found that the point of predicted fracture is determined by the equality σ=0.5 εEtangential (if there is an inflection point on the ascending branch) or σ=0.5 εEsecant_secant. The main result of the work was ascertaining the differential strength and fracture criteria of brittle materials in the form of inequalities and equations, which were oriented for application in engineering calculations. Examples of application of the developed criteria are given; their consistency with the experimental data known from the literature confirmed.
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Bout, Gabriel, Diego Brito, René Gómez, Gonzalo Carvajal, and Guillermo Ramírez. "Physics-Based Observers for Measurement-While-Drilling System in Down-the-Hole Drills." Mathematics 10, no. 24 (December 18, 2022): 4814. http://dx.doi.org/10.3390/math10244814.
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Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this context must be designed and conditioned for operating in harsh conditions, imposing trade-offs between the complexity, cost, and reliability of the measurement system. This paper presents a methodology for integrating physics-based observers into an MWD system as an alternative to complement or replace traditional physical sensors. The proposed observers leverage mathematical models of the drill’s electrical motor and its interaction with dynamic loads to estimate the bit speed and torque in a Down-the-Hole rig using current and voltage measurements taken from the motor power line. Experiments using data collected from four test samples with different rock strengths show a consistent correlation between the rate of penetration and specific energy derived from the observed drilling variables with the ones obtained from standardized tests of uniaxial compressive strength. The simplicity of the setup and results validate the feasibility of the proposed approach to be evaluated as an alternative to reduce the complexity and increase the reliability of MWD systems.
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Germay, C., T. Richard, E. Mappanyompa, C. Lindsay, D. Kitching, and A. Khaksar. "The Continuous-Scratch Profile: A High-Resolution Strength Log for Geomechanical and Petrophysical Characterization of Rocks." SPE Reservoir Evaluation & Engineering 18, no. 03 (July 17, 2015): 432–40. http://dx.doi.org/10.2118/174086-pa.
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Summary Knowledge of rock properties is essential to predict and optimize the performance of oil and gas reservoirs by means of the reduction of the uncertainty pertaining to standard subsurface issues such as the mechanical integrity of the borehole (Tiab and Donaldson 1996; Moos et al. 2003), the risk of sanding (Tronvoll et al. 2004), and the geometry and efficiency of hydraulic fractures. These properties are evaluated by combining different field-measurement techniques (wireline logs, results of well tests, seismic surveys) and laboratory-test results (Archie 1942, 1950; Serra 1986; Bassiouni 1994). When cores are available, empirical models are built from correlations derived between well logs and laboratory measurements to estimate rock properties in noncored wells. The validity of these empirical models is often limited to specific litho-facies (see reviews by Chang et al. 2006; Blasingame 2008; Khaksar et al. 2009), which makes the identification of lithofacies a necessity before applying the model for predictions in uncored wells (Massonnat 1999). Because of the heterogeneity of rocks (Haldorsen 1996), with characteristic length scales commonly smaller than the resolution of wireline logs or even the core-plug size, the robustness of correlations is determined by how plug samples capture the dispersion in rock properties over the lithofacies under consideration. The correlation between a very localized core-plug measurement and a low-resolution wireline log with inherent low-pass filtering properties raises issues related to the upscaling of a property from one length scale (few centimeters for core plugs) to another (up to 1 m for wireline log). As an illustration, consider the high-resolution, continuous profile X, where the variations of the measured property are quantified for length scales smaller than typical plug sizes. We filter this data to produce the profiles X5 and X50 (the subscript stands for the length scale in centimeters at which the signal is averaged out) with lower spatial resolutions similar to the plug and the well-log resolutions, respectively (Fig. 1). The resulting crossplot, shown in Fig. 2, of X5 vs. X50 exhibits a cloud of points in which the dispersion is governed by the properties of the signal (the degree of heterogeneity or the frequency content) and the difference between the two resolution length scales. Two linear-fit optimizations were carried out with the low-resolution-data X50 and the high-resolution-data X5 as the dependent variables, respectively. It is interesting to note that these linear fits yield different results, with a slope of 0.96 in the first case and 0.69 in the second case. This is a mathematical artifact caused by the minimization process inherent in the search for the best linear fit, which is most commonly a minimization of the vertical distance between the representative data points and the best-fit line. On the basis of this result, it should always be advisable to select the high-resolution data (plug) as the dependent variable. Discrete sampling (i.e., plugging) and the dispersion caused by the difference in resolution scales of two measurements are two important root causes of the errors often seen in correlations between two variables. The examples shown in Fig. 2 illustrate how the correlations derived from several sampling schemes can deviate from the expected one-to-one relation between the two variables. To circumvent these issues, petrophysicists usually select large quantities of plugs to build representative statistical data sets, with the hope that they are large enough to attenuate the effects listed previously. However, extensive plugging strategies imply longer lead times and higher costs, and are therefore not always viable (e.g., in the cases of rock-mechanics testing or special-core-analysis programs). As an illustration, consider the modeling of the variations of rock strength, one of the key geomechanical properties along a well trajectory. Such an exercise relies heavily on correlations derived between well logs and laboratory tests (uniaxial or triaxial compressive tests), because there is no wireline log providing a direct measure of a mechanical property related to strength. In their comprehensive review of existing literature, Khaksar et al. (2009) listed approximately 40 models designed to derive strength properties from wireline logs. The authors showed that the relevance of these as empirical is limited to specific rock types. A broader application of these models would require the considerations of additional complexity such as the coexistence of several facies within the same data set or the impact of diagenesis on petrophysical variability within one facies. The elements of reflection introduced previously all suggest that a continuous measure of a physical property such as the strength profiles generated from the scratch test, which provides some useful elements for the mapping of rock heterogeneity, could partially fill the gap between measurements on plugs and well logs and help with the optimization of the selection of plug samples. In the main sections of this paper, we first describe briefly the scratch test and outline the key intrinsic benefits of the test. We then discuss how standard and special core analysis could benefit most from all the features of the scratch test when introduced at a very early stage of the work flows. In particular, we illustrate with some examples how rock-strength profiles averaged to the relevant length scale can be correlated with other petrophysical properties either measured on core plugs or inferred from well logs.
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Kolegov, Grigoriy A., and Aleksey Yu Krainov. "Simulation of the coal mine ventilation with account for gob areas." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 79 (2022): 78–88. http://dx.doi.org/10.17223/19988621/79/7.
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Mine ventilation network models are widely used in underground coal mining in Russia. The models cover a variety of practical problems ranging from simple air distribution in active mine workings to changes in the static air pressure gradient associated with complex technological or hazardous processes occurring in mines. Isolated gob areas are integral parts of ventilation networks in coal mines. The most commonly used underground coal extraction technology in Russia is the longwall mining. A gob forms when a coal seam is extracted, and the upper layers of the rock cave in. Gobs are isolated from active mine entries with seals, but there is always air leakages from active faces inducing the air circulation in isolated areas. Gobs join different coal seams and often become the sources of underground fires. Therefore, the inclusion of gobs in mine ventilation network models would help contain accidents and eliminate the caused damage. The study uses the method of representative elementary volumes to incorporate a porous medium into mine ventilation network models. Quadratic resistances are assigned to the edges of the model, where Kirchhoffs laws are valid. The aerodynamic resistances of the gob edges are calculated using the Ergun equation. The proposed method has been used to evaluate pressure gradients in the gob area of the Raspadskaya mine. Several scenarios of the aerodynamic resistance variation in the active mine workings surrounding the gob area, such as partial flooding and drilling of boreholes from the surface, have been simulated, and the corresponding changes in pressure gradients have been analyzed.
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Wei, Jianping, Junzhao Zhang, Zhihui Wen, Libo Zhang, Yongjie Ren, and Leilei Si. "Natural Frequency of Coal: Mathematical Model, Test, and Analysis on Influencing Factors." Geofluids 2022 (May 31, 2022): 1–13. http://dx.doi.org/10.1155/2022/7891894.
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The difficulty in enhancing the low permeability of deep coal seams is the key problem restricting gas extraction. The technology of coal rock resonance and permeability enhancement excited by vibration wave is hailed as a new technology to enhance coal seam permeability. In particular, the effect of resonance and permeability enhancement is remarkable when the excitation frequency is exactly the same as the natural frequency of coal. In order to promote the application of the technology, the first step is to explore the variation characteristics of coal natural frequency and its influencing factors. In this study, two mathematical models of coal natural frequency were established, and the variations and influencing factors of coal natural frequency were discussed through an experiment on the natural frequency of coal. The results show that coal vibration has multiorder natural frequency which grows with the increase of the order. In addition, the natural frequency of coal is closely related to its elastic modulus, density, size, mass, stiffness, and other physical and mechanical parameters. The larger the coal size and mass are, the lower the natural frequency would be. The natural frequency parallel to the bedding plane is higher than that perpendicular to the bedding plane. For the saturated coal sample, moisture changes its density and reduces its elastic modulus. Consequently, its natural frequency is lower than that of the dried coal sample. The difference of organic matter and mineral content coal of different rank affects the physical and mechanical properties of coal, which leads to the difference in natural frequency of different-rank coals. The natural frequencies of different-rank coal show bituminous > anthracite > lignite. The natural frequencies of coal samples under different influencing factors are all tens of Hz. Thus, the vibration excitation of coal under the low-frequency condition is the focus of future research. The study can provide a theoretical basis for the technology of coal resonance and permeability enhancement excited by vibration wave.
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Nabiullin, Rustem, Irina Teliman, and Sergey Khoroshavin. "The interaction of the main actuators of hydraulic excavators." E3S Web of Conferences 177 (2020): 03013. http://dx.doi.org/10.1051/e3sconf/202017703013.
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The operation modes of the main actuators of hydraulic excavators during their joint operation in the process of rock excavation are considered. It is shown that the main mechanisms for turning the boom of the handle and the bucket are part of hydromechanical units consisting of an engine (hydraulic cylinder) and a main mechanism in which the engine (the cylinder and the rod itself) and elements of the working equipment (boom, handle or bucket) are the links of the mechanism. It has been established that the relationship between the parameters of the mechanical energy of the engines and the power parameters implemented on the driven (output) links of the mechanisms depend on the magnitude of the extension of the hydraulic cylinder rod. Mathematical models of the main mechanisms are developed. A computational experiment was carried out to determine the actual values of energy-power parameters implemented on the cutting edge of the bucket (teeth) during excavation of rocks at characteristic points of the excavator's working area, as well as reactive loads in the rota-tion mechanisms of the boom and stick. The proposed methodology for determining the operational parameters of the main mechanisms will allow us to estimate the range of changes in the power parameters implemented on the cutting edge of the bucket in the working area and to identify the relationship between active and reactive loads in the mechanisms due to the serial connection of hydromechanical units.
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Sas, Ivan E., and Elena B. Cherepetskaya. "Features of Numerical Modeling In Situ Stress State Massive of Rocky and Issues of Verification of the Data." Applied Mechanics and Materials 843 (July 2016): 36–44. http://dx.doi.org/10.4028/www.scientific.net/amm.843.36.
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Modern buildings erected on bedrock or is to be equipped directly in an array (in particular hydroelectric power stations, underground storage facilities and soon), are technically complex, often unique objects construction. At the same time, the cost of design and construction of such facilities is very high. In this context, particular relevance is the question of stable and safe operation of facilities. Now, generally recognized that the study of the functioning of large technical systems (such as the base - structure) with a randomly varying characteristics most adequately carried out was done by different types of complex modeling, particularly mathematical, simulation, and in some cases - physical modeling [3]. However, before moving to a system of «building/foundation» is necessary to examine the massif in situ. Modern software systems (such as Plaxis, ZSoil, Comsol, Abaqus, and soon) have are significant opportunities that allow to make calculations with high accuracy. In particular, implemented a specialized model of soils, such as models of Hoek-Brown, Jointed Rock and others [5]. They allow you to get a more objective picture of the state stress of the array according to the degree of fracturing and anisotropy properties. They allow you to get a more objective picture of the state stress of the array according to the degree of fracturing and anisotropy properties. In addition, is possible a reflection of the detailed features of the geological structure in the 3D calculation that gives an idea of the influence of the field to an array of building/foundation. But, it is necessary to understand that the simulation is based on idealization and averaging the physical and mechanical properties of the medium under study. The inevitable errors and inaccuracies in the calculations. As a real rock massif is a complex system, in the work showed of drawing up an analysis of structural models and their implementation using conventional concepts and a more detailed study. The isolation of the structural elements and boundaries in an array of rocky soils should be approached with special attention. This is due, primarily, with the features of the geological structure of the study area: for example, improperly allocate lithological boundaries as in the case of consideration arrays dispersed soils, because rocky soils is a monolithic solid. Select elements should be performed in accordance with the characteristic feature, such as a fracture, blocking and so on. Besides the issue of numerical modeling of rock masses, in the issues of verification data obtained by numerical method. With the increasing complexity of the technical constructions, increasingly there is a need to verify the results of numerical simulations with actual operating voltage value in the array. Since the field of stress research methods is very expensive and labor-intensive, trade-off seems logical to use in the verification of the results of numerical modeling of acoustic emission (AE) [6]. This method may be used in combination of laboratory tests. With this approach, it is possible to achieve significant improvements in the quality of the received information.
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Tolovkhan, Bauyrzhan, Vladimir Demin, Zhursyn Amanzholov, Assemgul Smagulova, Gaukhar Tanekeyeva, Sherzod Zairov, Oleksandr Krukovskyi, and Edgar Cabana. "Substantiating the rock mass control parameters based on the geomechanical model of the Severny Katpar deposit, Kazakhstan." Mining of Mineral Deposits 16, no. 3 (September 30, 2022): 123–33. http://dx.doi.org/10.33271/mining16.03.123.
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Purpose. The research purpose is to develop a geomechanical model for ensuring the safety of mining operations by determining the optimal slope angles and probabilistic assessment of the stability of the open-pit walls. Methods. Three-dimensional geomechanical models for surface mining of deposits have been developed based on calculations of the stability factor (safety factor SF) of the open-pit walls in the Rocscience program to determine the rock mass stress-strain state at the end of mining using the finite element method. The geological wireframe model (GWM) has been built on the basis of the available geological sections, horizon plans and the results of the engineering-geological surveys using the Surpac geoinformation system. Findings. Strength reduction factor (SRF) has been determined taking into account the physical-mechanical properties of rocks that constitute the near-wall mass. An assessment of the stability of walls according to the selected geological sections is given, taking into account the projected contour of the Severny Katpar open-pit walls. The calculation of the projected contour stability of the open-pit walls by several different methods has revealed that the open-pit walls are generally stable. The open-pit parameters at the end of mining have been determined. Originality. For the first time, it has been determined that in the Southern and South-Western area of the Severny Katpar open-pit wall in the horizons +700…+400, there is a decrease in SF from 1.18 to 1.41 due to the predominant occurrence of siltstones and tectonic disturbances of the walls. Practical implications. The mathematical calculation results of the stability of the projected contour walls in the Severny Katpar open pit have been generalized. In addition, a geological and structural wire-frame model of the deposit has been developed, which makes it possible to ensure the safety of mining operations in the open pit.
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KACHURIN, Nikolai, Galina STAS, and Alexander KACHURIN. "DYNAMICS OF GAS EMISSION FROM EXPOSED SURFACE OF GAS-BEARING COAL SEAMS HAVING MEDIUM THICKNESS." Sustainable Development of Mountain Territories 13, no. 3 (September 30, 2021): 441–48. http://dx.doi.org/10.21177/1998-4502-2021-13-3-441-448.
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The goal of the research was to clarify the regularities of the dynamics of gas release from the surface of the outcrop of the developed coal seam. The main research methods were theoretical methods of mathematical physics and non-equilibrium thermodynamics. Gas-bearing coal seams are usually mined underground. When driving development workings, outcropping surfaces of gas-bearing coal seams appear and gases in the seams under excessive pressure are released into the atmosphere of the mine workings. Gas-bearing coal seams are usually mined underground. When driving preparatory workings, surfaces of outcropping of gas-bearing coal seams arise and gases that are in the seams under excessive pressure are released into the atmosphere of the mine workings. The most important gas-dynamic characteristic of this process is the rate of gas release, which represents the volume of gases released from a unit area of exposure of a coal seam per unit of time. A generalized law of resistance for gas filtration in a rock mass is recommended, and a fairly rigorous thermodynamic substantiation is given. It is shown that the densities of gas mass flows in accordance with the postulate of their linear relationship with the driving forces are determined by the Onsager relation. The results obtained and their discussion is presented. Mathematical models are proposed for engineering calculations of the dynamics of methane release from the outcropping surface of medium-thick coal seams. The error of the adopted approximations does not exceed 3%. The intensity of methane release is directly related to the planogram of work in the working face. Analysis of this dependence indicates that during the extraction cycle, methane release increases due to an increase in the area of the gas-release surface. The main conclusions are as follows: mathematical modeling of the processes of gas movement in a porous sorbing medium using approximate mathematical models representing linearized equations of mathematical physics; the regularities of the dynamics of the rate of gas release from the surface of the outcrop of a gas-bearing coal seam is the theoretical basis for the mathematical description of the process of gas release; the use of a linearized hyperbolic filtration equation most accurately describes the processes of methane release from the outcropping surface of mined coal seams.
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Sun, Zhuoyue, Yongzheng Wu, Zhiguo Lu, Youliang Feng, Xiaowei Chu, and Kang Yi. "Stability Analysis and Derived Control Measures for Rock Surrounding a Roadway in a Lower Coal Seam under Concentrated Stress of a Coal Pillar." Shock and Vibration 2020 (December 2, 2020): 1–12. http://dx.doi.org/10.1155/2020/6624983.
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Numerical simulations have often been used in close-distance coal seam studies. However, numerical simulations can contain certain subjective and objective limitations, such as high randomness and excessively simplified models. In this study, close-distance coal seams were mechanically modeled based on the half-plane theory. An analytical solution of the floor stress distribution was derived and visualized using Mathematica software. The principal stress difference was regarded as a stability criterion for the rock surrounding the roadway. Then, the evolution laws of the floor principal stress difference under different factors that influence stability were further examined. Finally, stability control measures for the rock surrounding the roadway in the lower coal seam were proposed. The results indicated the following: (1) The principal stress difference of the floor considers the centerline of the upper coal pillar as a symmetry axis and transmits radially downward. The principal stress difference in the rock surrounding the roadway gradually decreases as the distance from the upper coal pillar increases and can be ranked in the following order: left rib > roof > right rib. (2) The minimum principal stress difference zones are located at the center of the left and right “spirals,” which are obliquely below the edge of the upper coal pillar. This is an ideal position for the lower coal seam roadway. (3) The shallowness of the roadway, a small stress concentration coefficient, high level of coal cohesion, large coal internal friction angle, and appropriate lengthening of the working face of the upper coal seam are conducive to the stability of the lower coal seam roadway. (4) Through bolt (cable) support, borehole pressure relief, and pregrouting measures, the roof-to-floor and rib-to-rib convergence of the 13313 return airway is significantly reduced, and the stability of the rock surrounding the roadway is substantially improved. This research provides a theoretical basis and field experience for stabilizing the lower coal seam roadways in close-distance coal seams.
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Yang, Yongjie, Yang Zhang, and Gang Huang. "Research on Stress Distribution Regularity and Support Optimization of an “Umbrella” Coal Pillar in a Gob-Side Roadway Based on Irregular Gob." Energies 15, no. 11 (May 26, 2022): 3932. http://dx.doi.org/10.3390/en15113932.
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Aiming at the phenomenon of a large amount of roof subsidence and rib caving in the gob-side roadway under the special “umbrella” coal pillar in isolated panel No. 325 of Yangcun Coal Mine, the stress distribution regularity of the gob-side roadway under a “umbrella” coal pillar was studied in detail by establishing mathematical models, theoretical analysis, and numerical simulations. The results show that the following: (1) The stress distribution regularity of the irregular coal pillar is actually the mechanical structure of irregular gob. (2) The abutment pressure of the gob is always distributed vertically along the edge of the gob. When the edge of the gob intersects diagonally with the gob roadway, the stress distribution of the surrounding rock of the roadway cannot be calculated only by the width of the coal pillar—the angle between the edge of the gob and the roadway should also be considered. (3) The abutment pressure at each cusp position in irregular gob extends in the opposite direction of the bisection cusp line, which may lead to peak stress concentration area in gob roadways with solid coal on both sides, and even roof caving and sidewall deviation disasters.
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Bagrii, O. V. "Plane problem of discrete environment mechanics." Problems of Tribology 27, no. 2/104 (June 25, 2022): 104–11. http://dx.doi.org/10.31891/2079-1372-2022-104-2-104-111.
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Many engineering problems related to the design of structures and machines, the mathematical description of technological processes, etc., are reduced to the need to solve a plane problem for materials with a significant effect of internal friction on their deformation. Such materials include a large class of materials in which the compressive strength is greater than tensile. These are composite materials, concretes, rocks, soils, granular, loose, highly fractured materials, as well as structurally heterogeneous materials in which rigid and strong particles are interconnected by weaker layers. The laws of deformation and destruction of such materials differ significantly from elastic ones. A feature of these laws is an increase in resistance to shear deformations and an increase in the strength of materials with an increase in the magnitude of compressive stresses. This is associated with the influence of internal Coulomb friction on the process of their deformation in the limiting and boundary stages.
The need to formulate and solve a special boundary value problem for materials with significant internal friction is because the results of solving problems using models of elasticity and plasticity differ significantly from experimental data. The difference increases when approaching the limiting state of discrete materials and depends significantly on the structure of the material and operating conditions.
The boundary value problem of the mechanics of a deformable solid is formulated as a system of equations of three types: static, geometric, and physical. For all linear and physically nonlinear problems, provided the deformations are small, the first two groups of equations remain the same. Thus, these differences can be attributed to the inconsistency of the accepted in the calculations of physical relations "stress - strain" and the real laws of deformation of these materials, which are more complex rheological objects than structurally homogeneous solids, liquids or gases.
The article uses an approach where the material is immediately considered as quasi-continuous, and the physical equations are based on the experimentally obtained relationships between the invariants of the stress and strain tensors, which consider the influence of both molecular connectivity and internal Coulomb friction.
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Carcione, José M., Hans B. Helle, and Anthony F. Gangi. "Theory of borehole stability when drilling through salt formations." GEOPHYSICS 71, no. 3 (May 2006): F31—F47. http://dx.doi.org/10.1190/1.2195447.
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We present a mathematical analysis of borehole stability when drilling through rock salt. First, we consider an elastic transversely isotropic medium and find the optimal mud weight as a function of the vertical overburden and horizontal tectonic stresses. Then, the Zener and Maxwell mechanical models are used to model the effects of transient and steady-state creep flow, respectively, in isotropic media. Under certain conditions such as the absence of dilatational anelasticity, the Burger model can be used to describe the steady-state flow, including transient creep effects. The type of creep is regulated by critical octahedral-stress values that depend on temperature and pressure. A typical drilling results in conditions of plane strain, whose solution is given by Kirsch’s equations. In this case, the borehole is subject to minimum and maximum horizontal stresses, which differ from the vertical stress. The analysis provides expressions for the shape of the borehole-cross section, the borehole-wall closure time, and the optimal mud weight to avoid wall collapse or expansion. It is shown that an anisotropic state of tectonic stress may require mud pressures exceeding the overburden stress and that the calculation should consider the joint optimization of the shape and area of the borehole cross section.
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Drbohlav, K., H. Bůzková, J. Kaigl, and P. Němec. "Rock media mathematical models processing." Mathematical Geology 23, no. 1 (January 1991): 53–69. http://dx.doi.org/10.1007/bf02065966.
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Katarov, Vasily, Vladimir Syunev, and Gennady Kolesnikov. "Analytical Model for the Load-Bearing Capacity Analysis of Winter Forest Roads: Experiment and Estimation." Forests 13, no. 10 (September 21, 2022): 1538. http://dx.doi.org/10.3390/f13101538.
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In northern forests, winter is the preferred time for logging operations, since, when wet soils freeze, their strength increases, which ensures a high load-bearing capacity of winter forest roads and reduces the cost of forestry work by increasing the load on forestry equipment, including when driving through frozen lowlands. The present article analyzes frozen loamy–sandy soil, which, at subzero temperatures, behaves like a brittle material with a sufficiently high, but limited, strength. Well-known models commonly use empirical parameters, correlations, and numerical methods to estimate the strength of such materials. An analytical model of the full load–displacement curve would reduce the number of necessary calculations and increase the ability to predict the bearing capacity of winter forest roads. However, there are few of these models. Such models were developed, as a rule, to study stress–strain in concrete and rocks, meaning that researchers have to recalculate the load into stress and displacement into deformation, which is not always simple. This work aimed at theoretically justifying a new analytical model for quantifying the bearing capacity of winter forest roads and assessing the adequacy of the model by comparing it with experimental data. To achieve this purpose, the concepts of fracture mechanics and methods of mathematical modeling were used. The model was verified using experimental data, and model examples for determining the peak load were provided. Prospects for development of the research topic were also considered, taking into account new developments in forest road monitoring for logging management.
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Huang, Linqi, Shaofeng Wang, Xin Cai, and Zhengyang Song. "Mathematical Problems in Rock Mechanics and Rock Engineering." Mathematics 11, no. 1 (December 25, 2022): 67. http://dx.doi.org/10.3390/math11010067.
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