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Journal articles on the topic 'Rock mechanics – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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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 mo

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2

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 (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

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3

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 Geomechani

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4

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 bl

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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 (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

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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 (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. Inspir

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7

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 ro

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8

Deng, Wubing, and Igor B. Morozov. "Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies." GEOPHYSICS 81, no. 4 (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 di

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9

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 des

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10

Deng, Wubing, and Igor B. Morozov. "Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity." GEOPHYSICS 83, no. 6 (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 f

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11

Xu, Liqi, Xiaoli Xu, Yiming Sun, and Tianci Lu. "Evaluation of Rock Brittleness Based on Complete Stress–Strain Curve." Mathematics 10, no. 23 (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 vari

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12

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 surr

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13

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 (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 Dist

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14

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-cutti

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15

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, whe

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16

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 (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 t

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17

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

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18

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 (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 typ

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19

Xie, Shijie, Hang Lin, Yixian Wang, et al. "A statistical damage constitutive model considering whole joint shear deformation." International Journal of Damage Mechanics 29, no. 6 (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 typi

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20

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 (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, th

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21

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 (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 natur

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22

Khan, Naseer Muhammad, Kewang Cao, Muhammad Zaka Emad, et al. "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 (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

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23

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.

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24

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 (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

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25

Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (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. Curre

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26

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 (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 th

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27

Kolesnikov, Gennady, and Timmo Gavrilov. "Sandstone Modeling under Axial Compression and Axisymmetric Lateral Pressure." Symmetry 14, no. 4 (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 pressur

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28

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 develop

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29

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 (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

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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 (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

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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 (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-dim

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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 (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,

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33

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 a

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Cerruti, Benedetta, Alberto Puliafito, Annette M. Shewan, et al. "Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures." Journal of Cell Biology 203, no. 2 (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

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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 (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 sys

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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 (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 tradi

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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 (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; Bassi

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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

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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 f

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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 po

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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

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Tolovkhan, Bauyrzhan, Vladimir Demin, Zhursyn Amanzholov, et al. "Substantiating the rock mass control parameters based on the geomechanical model of the Severny Katpar deposit, Kazakhstan." Mining of Mineral Deposits 16, no. 3 (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

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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 (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, surfac

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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

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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 (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 distr

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Bagrii, O. V. "Plane problem of discrete environment mechanics." Problems of Tribology 27, no. 2/104 (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

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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 (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

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Drbohlav, K., H. Bůzková, J. Kaigl, and P. Němec. "Rock media mathematical models processing." Mathematical Geology 23, no. 1 (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 (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

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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 (2022): 67. http://dx.doi.org/10.3390/math11010067.

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