Relevant bibliographies by topics / Rock mechanics – Mathematical models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Rock mechanics – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

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

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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Dissertations / Theses on the topic "Rock mechanics – Mathematical models"

1

Liu, Chi-hong, and 廖志航. "Base friction modelling of discontinuous rock masses." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B42577123.

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Li, Lian, and 李煉. "Microscopic study and numerical simulation of the failure process of granite." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242005.

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Choi, Yam-ming Kelvin, and 蔡任明. "Use of block theory in tunnel stability analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B45014358.

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Henderson, Susan Jane. "Analysis of the long-term slope stability of waste-rock dumps /." Title page, table of contents and abstract only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phh4972.pdf.

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Lock, Yick-bun, and 駱亦斌. "An examination of failure criteria for some common rocks in Hong Kong." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31213406.

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Reimnitz, Marc. "Shear-slip induced seismic activity in underground mines : a case study in Western Australia." University of Western Australia. School of Civil and Resource Engineering, 2004. http://theses.library.uwa.edu.au/adt-WU2004.0062.

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Mining induced seismic activity and rockbursting are critical concerns for many underground operations. Seismic activity may arise from the crushing of highly stressed volumes of rock around mine openings or from shear motion on planes of weakness. Shear-slip on major planes of weakness such as faults, shear zones and weak contacts has long been recognized as a dominant mode of failure in underground mines. In certain circumstances, it can generate large seismic events and induce substantial damage to mine openings. The Big Bell Gold mine began experiencing major seismic activity and resultant damage in 1999. Several seismic events were recorded around the second graphitic shear between April 2000 and February 2002. It is likely that the seismic activity occurred as a result of the low strength of the shear structure combined with the high level of mining induced stresses. The stability of the second graphitic shear was examined in order to gain a better understanding of the causes and mechanisms of the seismic activity recorded in the vicinity of the shear structure as mining advanced. The data were derived from the observation of the structure exposures, numerical modelling and seismic monitoring. The numerical modelling predictions and the interpreted seismic monitoring data were subsequently compared in order to identify potential relationships between the two. This thesis proposes the Incremental Work Density (IWD) as a measure to evaluate the relative likelihood of shear-slip induced seismic activity upon major planes of weakness. IWD is readily evaluated using numerical modelling and is calculated as the product of the average driving shear stress and change in inelastic shear deformation during a given mining increment or step. IWD is expected to correlate with shear-slip induced seismic activity in both space and time. In this thesis, IWD was applied to the case study of the second graphitic shear at the Big Bell mine. Exposures of the second graphitic shear yielded information about the physical characteristics of the structure and location within the mine. Numerical modelling was used to examine the influence of mining induced stresses on the overall behaviour of the shear structure. A multi-step model of the mine was created using the three- dimensional boundary element code of Map3D. The shear structure was physically incorporated into the model in order to simulate inelastic shear deformation. An elasto-plastic Mohr-Coulomb material model was used to describe the structure behaviour. The structure plane was divided into several elements in order to allow for the comparison of the numerical modelling predictions and the interpreted seismic data. Stress components, deformation components and IWD values were calculated for each element of the shear structure and each mining step. The seismic activity recorded in the vicinity of the second graphitic shear was back analysed. The seismic data were also gridded and smoothed. Gridding and smoothing of individual seismic moment and seismic energy values resulted in the definition of indicators of seismic activity for each element and mining step. The numerical model predicted inelastic shear deformation upon the second graphitic shear as mining advanced. The distribution of modelled IWD suggested that shear deformation was most likely seismic upon a zone below the stopes and most likely aseismic upon the upper zone of the shear structure. The distribution of seismic activity recorded in the vicinity of the shear structure verified the above predictions. The seismic events predominantly clustered upon the zone below the stopes. The results indicated that the seismic activity recorded in the vicinity of the second graphitic shear was most likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing. Time distribution of the seismic events also indicated that shear deformation and accompanying seismic activity were strongly influenced by mining and were time-dependant. Seismic activity in the vicinity of the second graphitic shear occurred as a result of the overall inelastic shear deformation of the shear structure under mining induced stresses. A satisfactory relationship was found between the spatial distribution of modelled IWD upon the shear structure and the spatial distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy). Seismic activity predominantly clustered around a zone of higher IWD upon the second graphitic shear as mining advanced. However, no significant statistical relationship was found between the modelled IWD and the interpreted seismic activity. The lack of statistical relationship between the modelled and seismic data may be attributed to several factors including the limitations of the techniques employed (e.g. Map3D modelling, seismic monitoring) and the complexity of the process involved.
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Bouteca, Maurice. "Fracturation hydraulique calcul de propagation d'une fracture induite dans un massif rocheux /." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37603363t.

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Warren, Paul A. "Mathematical models of 3-D ocular mechanics and control." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312221.

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Lee, M. E. M. "Mathematical models of the carding process." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249543.

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Carding is an essential pre-spinning process whereby masses of dirty tufted fibres are cleaned, disentangled and refined into a smooth coherent web. Research and development in this `low-technology' industry have hitherto depended on empirical evidence. In collaboration with the School of Textile Industries at the University of Leeds, a mathematical theory has been developed that describes the passage of fibres through the carding machine. The fibre dynamics in the carding machine are posed, modelled and simulated by three distinct physical problems: the journey of a single fibre, the extraction of fibres from a tuft or tufts and many interconnecting, entangled fibres. A description of the life of a single fibre is given as it is transported through the carding machine. Many fibres are sparsely distributed across machine surfaces, therefore interactions with other neighbouring fibres, either hydrodynamically or by frictional contact points, can be neglected. The aerodynamic forces overwhelm the fibre's ability to retain its crimp or natural curvature, and so the fibre is treated as an inextensible string. Two machine topologies are studied in detail, thin annular regions with hooked surfaces and the nip region between two rotating drums. The theoretical simulations suggest that fibres do not transfer between carding surfaces in annular machine geometries. In contrast to current carding theories, which are speculative, a novel explanation is developed for fibre transfer between the rotating drums. The mathematical simulations describe two distinct mechanisms: strong transferral forces between the taker-in and cylinder and a weaker mechanism between cylinder and doffer. Most fibres enter the carding machine connected to and entangled with other fibres. Fibres are teased from their neighbours and in the case where their neighbours form a tuft, which is a cohesive and resistive fibre structure, a model has been developed to understand how a tuft is opened and broken down during the carding process. Hook-fibre-tuft competitions are modelled in detail: a single fibre extracted from a tuft by a hook and diverging hook-entrained tufts with many interconnecting fibres. Consequently, for each scenario once fibres have been completely or partially extracted, estimates can be made as to the degree to which a tuft has been opened-up. Finally, a continuum approach is used to simulate many interconnected, entangled fibre-tuft populations, focusing in particular on their deformations. A novel approach describes this medium by density, velocity, directionality, alignment and entanglement. The materials responds to stress as an isotropic or transversely isotropic medium dependent on the degree of alignment. Additionally, the material's response to stress is a function of the degree of entanglement which we describe by using braid theory. Analytical solutions are found for elongational and shearing flows, and these compare very well with experiments for certain parameter regimes.
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Moore, Matthew Richard. "New mathematical models for splash dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c94ff7f2-296a-4f13-b04b-e9696eda9047.

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In this thesis, we derive, extend and generalise various aspects of impact theory and splash dynamics. Our methods throughout will involve isolating small parameters in our models, which we can utilise using the language of matched asymptotics. In Chapter 1 we briefly motivate the field of impact theory and outline the structure of the thesis. In Chapter 2, we give a detailed review of classical small-deadrise water entry, Wagner theory, in both two and three dimensions, highlighting the key results that we will use in our extensions of the theory. We study oblique water entry in Chapter 3, in which we use a novel transformation to relate an oblique impact with its normal-impact counterpart. This allows us to derive a wide range of solutions to both two- and three-dimensional oblique impacts, as well as discuss the limitations and breakdown of Wagner theory. We return to vertical water-entry in Chapter 4, but introduce the air layer trapped between the impacting body and the liquid it is entering. We extend the classical theory to include this air layer and in the limit in which the density ratio between the air and liquid is sufficiently small, we derive the first-order correction to the Wagner solution due to the presence of the surrounding air. The model is presented in both two dimensions and axisymmetric geometries. In Chapter 5 we move away from Wagner theory and systematically derive a series of splash jet models in order to find possible mechanisms for phenomena seen in droplet impact and droplet spreading experiments. Our canonical model is a thin jet of liquid shot over a substrate with a thin air layer trapped between the jet and the substrate. We consider a variety of parameter regimes and investigate the stability of the jet in each regime. We then use this model as part of a growing-jet problem, in which we attempt to include effects due to the jet tip. In the final chapter we summarise the main results of the thesis and outline directions for future work.
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Books on the topic "Rock mechanics – Mathematical models"

1

Fractals in rock mechanics. Rotterdam: A. A. Balkema, 1993.

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U, Hunsche, ed. Time effects in rock mechanics. Chichester: Wiley, 1998.

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V, Egorov P., Murashev V. I, and Grit͡s︡ko Gennadiĭ Ignatʹevich, eds. Strukturnye modeli gornogo massiva v mekhanizme geomekhanicheskikh prot͡s︡essov. Novosibirsk: "Nauka," Sibirskoe otd-nie, 1990.

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A, Mironov V. Vvedenie v distortnostʹ. Tverʹ: Tverskoĭ gos. tekhn. universitet, 1994.

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E, Mirenkov V., and Oparin V. N, eds. Metody matematicheskogo modelirovanii͡a podzemnykh sooruzheniĭ. Novosibirsk: VO "Nauka", 1994.

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International Symposium on Numerical Models in Geomechanics. (2nd 1986 Ghent, Belgium). Numerical models in geomechanics: Proceedings of the International Symposium on Numerical Models in Geomechanics, Ghent, 31st March-4th April, 1986. Redruth, England: Jackson, 1986.

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International Symposium on Numerical Models in Geomechanics. (10th 2007 Rhodes, Greece). Numerical models in geomechanics: Proceedings of the 10th International Symposium on Numerical Models in Geomechanics (NUMOG X), Rhodes, Greece, 25-27 April 2007. Edited by Pande G. N and Pietruszczak S. London: Taylor & Francis, 2007.

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Łydżba, Dariusz. Zastosowania metody asymptotycznej homogenizacji w mechanice gruntów i skał. Wrocław: Oficyna Wydawnicza Politechniki Wrocławskiej, 2002.

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Sharma, V. M. Distinct element modelling in geomechanics. Edited by Saxena K. R and Woods Richard D. Rotterdam: A.A. Balkema, 1999.

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Discontinuity analysis for rock engineering. London: Chapman & Hall, 1993.

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Book chapters on the topic "Rock mechanics – Mathematical models"

1

Wittke, Walter. "Models of the Grain and Rock Mass Fabrics." In Rock Mechanics, 7–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-88109-1_2.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 95–134. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16408-8_4.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 81–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05229-7_4.

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Kolymbas, Dimitrios. "Similarity in soil and rock mechanics." In Advanced Mathematical and Computational Geomechanics, 141–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45079-5_6.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53605-6_138-1.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1514–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_138.

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Zin, W. A., and R. F. M. Gomes. "Mathematical Models in Respiratory Mechanics." In Anaesthesia, Pain, Intensive Care and Emergency Medicine — A.P.I.C.E., 391–400. Milano: Springer Milan, 1996. http://dx.doi.org/10.1007/978-88-470-2203-4_34.

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Serovajsky, Simon. "Mathematical models of fluid and gas mechanics." In Mathematical Modelling, 261–78. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-14.

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Surana, Karan S. "Thermodynamic Relations and Complete Mathematical Models." In Classical Continuum Mechanics, 441–56. 2nd ed. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003105336-15.

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Bellomo, Nicola, Luigi Preziosi, and Antonio Romano. "Models and Mathematical Problems." In Mechanics and Dynamical Systems with Mathematica®, 19–55. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1338-3_2.

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Conference papers on the topic "Rock mechanics – Mathematical models"

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Zhu, Zhaopeng, Xianzhi Song, Liang Han, Rui Zhang, Wei Liu, Jiasheng Fu, Xiaoli Hu, Dayu Li, Furong Qin, and Donghan Yang. "Prediction Method of Cutting Settling Velocity in Gas-Liquid Two-Phase Flow Based on Multi-Gene Genetic Programming." In 56th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2022. http://dx.doi.org/10.56952/arma-2022-0977.

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ABSTRACT: The cuttings settling process becomes erratic in the complex gas-liquid mixture under gas kick, it is very difficult to accurately describe the migration process of cuttings. Meanwhile, the traditional empirical formula based on fitting experimental data is difficult to accurately predict the complex cuttings settlement. Neural network and other intelligent models with high prediction accuracy are difficult to be popularized and applied due to their black box properties. Multi-gene genetic programming can accurately describe complex nonlinear problems and automatically optimize the structure and parameters of the mathematical model, so as to effectively reduce the complexity of the model. Based on the multi-gene genetic programming algorithm, this study used a variety of input parameters to predict the settling velocity, explored the relationship between the input variables and the result, and established an explicit mathematical model of settling velocity with RMSE of 0.0896 in test set and R2 of 0.9292, which breaks the accuracy limits of traditional empirical model and the inexplicability of neural network model. This new method for predicting cuttings settling velocity in gas-liquid mixture can provide theoretical guidance for efficient cuttings migration in wellbore during gas kick. 1. INTRODUCTION The migration of bottom-hole cuttings during oil and gas well drilling and the migration of solid proppant in cracks during fracturing are examples of particle settling in the field of petroleum engineering (Xu et al, 2017). When the particles settle freely in the fluid, they will be affected by their own gravity, buoyancy and resistance (Nouri et al, 2014). When these three forces reach an equilibrium state, the particles will reach a stable settling velocity, which is called the particle terminal settling velocity (McCabe et al, 2004). Understanding the settling law and properties of solid particles in their fluid environment, such as rock cuttings and fracturing proppant, is critical for enhancing drill cleaning efficiency and fracturing design. Until now, Many industry specialists and academics have devoted a significant amount of time and effort to the study of particle settling velocity.
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Gravanis, E., E. Sarris, and S. Patruno. "A Simplified Hydro-Mechanical Model for Sanding from Hollow Cylinder Tests." In 56th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2022. http://dx.doi.org/10.56952/arma-2022-0854.

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ABSTRACT: Particles produced by the hydro-mechanical processes during sanding in hydrocarbon wells is a highly complex physical process. Sanding onset is influenced by a number of factors which include mechanical failure and hydrodynamic erosion. Over the years a number of mathematical and numerical models have been developed to describe the sand production process, involving sanding criteria or constitutive laws of mechanical or hydro-dynamical nature. In this work we propose a new simplified model working along the lines of the hydro-dynamical constitutive law of previous research works. The model amounts to a set of two ordinary differential equations coupling the mechanical process of plastic yielding with hydro-dynamic erosion, including degradation of the material. The model is constructed for hollow cylinder tests which allows cylindrical symmetry which is particularly useful for determining the sand production coefficient λ from such tests. The sand production coefficient as a function of the externally applied stress is estimated from previously published experimental data via a single parameter best fit. It is shown that the sand production coefficient is nearly constant for the range of values of the external stress considered. Additionally, the mathematical sand production curves capture fairly well the experimental data. 1. INTRODUCTION The production of sand particles from oil and gas wells is a phenomenon by which detached rock solids, due to erosion, migrate from the exposed surface of the well along with reservoir fluids during production. Predicting sand production is highly important in hydrocarbons recovery because they can cause a number of operational problems like: local formation failure, blocking of perforation channels, inability of sand control measures, which may lead eventually to local well collapse or in extreme cases cause catastrophic failures (Wilson et al., 2002; Rahmati et al., 2013; Volonté et al., 2013; Wang and Sharma, 2016; Li et al., 2018; Eshiet et al., 2019). The majority of rocks that are prone to sand production are sandstones, mainly poorly consolidated or even consolidated, but also hydrocarbons provinces. For these reasons, petroleum companies are seeking collaborations with academia in search for solutions via advance modelling to help in the understanding of the physics and the mechanics of this phenomenon because it costs to the entire industry 2 billion per annum (Gravanis et al., 2015; Gravanis et al., 2016; Sarris et al., 2021).
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Manzhirov, Alexander V. "Mechanics of Growing Solids: New Track in Mechanical Engineering." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36712.

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A vast majority of objects around us arise from some growth processes. Many natural phenomena such as growth of biological tissues, glaciers, blocks of sedimentary and volcanic rocks, and space objects may serve as examples. Similar processes determine specific features of many industrial processes which include crystal growth, laser deposition, melt solidification, electrolytic formation, pyrolytic deposition, polymerization and concreting technologies. Recent researches indicates that growing solids exhibit properties dramatically different from those of conventional solids, and the classical solid mechanics cannot be used to model their behavior. The old approaches should be replaced by new ideas and methods of modern mechanics, mathematics, physics, and engineering sciences. Thus, there is a new track in solid mechanic that deals with the construction of adequate models for solid growth processes. The fundamentals of the mathematical theory of growing solids are under consideration. We focus on the surface growth when deposition of a new material occurs at the boundary of a growing solid. Two approaches are discussed. The first one deals with the direct formulation of the mathematical theory of continuous growth in the case of small deformations. The second one is designed for the solution of nonlinear problems in the case of finite deformations. It is based on the ideas of the theory of inhomogeneous solids and regards continuous growth as the limit case of discrete growth. The constitutive equations and boundary conditions for growing solids are presented. Non-classical boundary value problems are formulated. Methods for solving these problems are proposed.
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Reckmann, Hanno, Pushkar Jogi, and Christian Herbig. "Using Dynamics Measurements While Drilling to Detect Lithology Changes and to Model Drilling Dynamics." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29710.

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As a result of bit-rock interaction, downhole weight-on-bit, downhole torque, instantaneous downhole rotational speed and bit motion (acceleration and rate of penetration) are directly affected by the formations being drilled. Since these measurements react differently to different lithologies, and assuming that drilling problems do not effect these measurements, any changes in the measurements in some way will reflect changes in the properties of the lithology. If, based on these measurements, the lithology is assumed to have certain properties, then it is possible to derive models for the interaction between bit, formation and drillstring. With these models it is possible to simulate the dynamic behavior of the system including phenomena like stick-slip. Rate of penetration has long been used as a lithology indicator, and drilling models have been developed using surface measured drilling parameters to infer changes in lithology. With the advent of MWD measurements, significant improvements were made in the mathematical models by involving downhole torque. The model derived parameters were shown to be related to rock strength (drilling and shear strength) and proved to be good indicators of formation changes. Similar expressions in the form of simple bit models can be used in combination with a finite element model of the drillstring to simulate the dynamic behavior of the complete system. A significant improvement in this analysis can be affected by introducing measurements from the dynamics tool, such as instantaneous torque, weight and rotation rate, as well as the bit acceleration. These measurements provide not only static but also dynamic data which can be used to validate simulations and the underlying models. The present analysis explores the use of the dynamic measurements and the application of some drilling models in analyzing formation changes while drilling, and the use of these data and models in simulating drilling dynamics.
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Adeyemi, Bamikole, Prashant Jadhawar, and Lateef Akanji. "Surface Complexation Modelling of Potential Determining Ions Sorption on Oil/Brine and Brine/Rock Interfaces." In SPE Nigeria Annual International Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/207128-ms.

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Abstract Previous studies on smart water effects have suggested wettability alteration as the most significant mechanism for additional oil recovery during smart water injection. Though many other mechanisms have been observed and proposed in several other studies, much more attention is paid to the detachment of oil films from rock surfaces. It is, however, clear from prevailing understanding that the activities at oil/brine interfaces might require as much attention as given to the brine/rock interfaces. This paper presents diffuse double layer surface complexation modelling of the adsorption of potential determining (Ca2+, Mg2+ and SO42-) ions on oil carboxylic and carbonate surfaces. Surface complexation models are developed by defining the adsorption sites, surface area and mass of the oil and carbonate surfaces. The chemical reactions involving the surface sites and five different brine solutions are also defined. The brine solutions include formation water, sea water, sea water diluted 20 and 50 times, and sea water with four times SO42- concentration. The amount of the divalent ions adsorbed at pH range of 5 to 8 are determined after the reactions had reached equilibrium. Adsorption of the ions on oil carboxylic and carbonate surfaces at elevated temperature for the sea water is also investigated. Results show that significant number of divalent ions are collected at the oil/brine interfaces just as adsorbed at the brine/rock interfaces. The results suggest that the equilibrium reactions and the dynamics at the two mathematical interfaces in any oil/brine/rock systems are equally important to reach a full understanding of the main mechanisms behind smart water effects. Therefore, the dynamics of ionic reactions at the oil/brine interface can play critical roles in defining smart water effects on residual oil mobilization.
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Cayeux, Eric, and Hans Joakim Skadsem. "Modelling of the Dynamic Behavior of the Power Transmission of an Automatic Small Scale Drilling Rig." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62523.

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The automatization of the drilling process opens the opportunity to faster reactions in case of unexpected drilling conditions, therefore reducing the risk that a drilling incident escalates to a serious situation. It also allows to push the drilling performance to be as close as possible to the limits of drillability as a function of the varying drilling conditions. But to achieve high level of drilling process automation, it is necessary to have access to accurate mathematical models of the complex physical system that is composed of the drilling rig, the drill-string, the drilling fluid and the borehole itself. As the development of accurate heat transfer, mechanical and hydraulic models and their utilization in full scale drilling applications is a huge and complex task, it is tempting to recreate drilling automatization problems in a laboratory scale setup. Because of sudden variations of the downhole drilling conditions, like when transitioning from soft to hard rock or when the bit is subject to large torque variations induced by interbedded rock layers, the boundary conditions at the bit change suddenly and require quick response from the automatic top-drive and hoisting system controllers. At a small laboratory scale, the necessary reaction times are of the order of milliseconds and therefore exclude any manual intervention. It is therefore crucial that the automatic control methods utilize precise mathematical models of the physical system to accurately estimate the limits by which the drilling process can be managed under safe conditions. For that reason, a general purpose mathematical model of small-scale drilling rigs has been developed. First, the Rayleigh-Ritz method is used to determine the deflection of the drill-string and to estimate the side forces at the contact points along the drill-string and BHA (Bottom Hole Assembly). Then the dynamic response of the power transmission system is modelled for both variable frequency drive controlled tri-phase motors and for stepper motors, including friction effects at the contact points. Friction is modelled using Stribeck theory rather than the classical Coulomb laws of friction. Finally, the expected response of 3D accelerometers, that could be placed on the outside of a BHA component, is modelled to retrieve possible inclination variations and potential vibration modes such as torsional oscillations, forward or backward whirl. The generality of the model is such that it can be used for many small-scale drilling rig designs.
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Khramchenkov, M. G., E. M. Khramchenkov, and A. N. Garaeva. "MATHEMATICAL MODEL OF DEPOSITION/EROSION MECHANISM OF UNDERGROUND MIGRATION." In The Geological Evolution of the Water-Rock Interaction. Buryat Scientific Center of SB RAS Press, 2018. http://dx.doi.org/10.31554/978-5-7925-0536-0-2018-235-238.

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Chemmakh, Abderraouf. "Machine Learning Predictive Models to Estimate the UCS and Tensile Strength of Rocks in Bakken Field." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/208623-stu.

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Abstract Uniaxial Compressive Strength (UCS) and Tensile Strength (TS) are among the essential rock parameters required and determined for rock mechanical studies in Petroleum Engineering. However, the determination of such parameters requires some laboratory experiments, which may be time-consuming and costly at the same time. In order to estimate these parameters efficiently and in a short period, some mathematical tools have been used by different researchers. When regression tools proved to give good results only in the limited range of data used, machine learning methods proved to be very accurate in generating models that can cover a wide range of data. In this study, two machine learning models were used to predict the UCS and TS, Support Vector Regression optimized by Genetic Algorithm (GA-SVR) and Artificial Neural Networks (ANNs). The results were discussed for both uniaxial compressive strength and tensile strength in terms of coefficient of determination R2, root mean squared error (RMSE) and mean average error (MAE). First, for the case of UCS, values of 0.99 and 0.99, values of 3.41 and 2.9 and values of 2.43 and 1.9 were obtained for R2, RMSE and MAE for the ANN and GA-SVR, respectively. Second, for the TS, the same analogy was followed, a coefficient R2 of 0.99 and 0.99, RMSE values of 0.41 and 0.45 and MAE values of 0.30 and 0.39 were obtained for ANNs and GA-SVR, respectively. The next step was to assess these models on a different dataset consisting of data obtained from Bakken Field in Williston Basin, North Dakota, United States. The models showed excellent results comparing to the correlations they were compared with, outperforming them in terms of R2, RMSE and MAE, giving the following results for ANN and SVR respectively, R2 of 0.93, 0.92, RMSE of 9.54, 11.22 and MAE of 7.28, 9.24. The resultant conclusion of this work is that the use of machine learning algorithms can generate universal models which reduce the time and effort to estimate some complex parameters such as UCS and Tensile Strength.
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Papamichos, E., I. Vardoulakis, and J. Sulem. "Generalized continuum models for borehole stability analysis." In Rock Mechanics in Petroleum Engineering. Society of Petroleum Engineers, 1994. http://dx.doi.org/10.2118/28025-ms.

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Vaziri, Hans, Yuing Xiao, and Ian Palmer. "Assessment Of Several Sand Prediction Models With Particular Reference To HPHT Wells." In SPE/ISRM Rock Mechanics Conference. Society of Petroleum Engineers, 2002. http://dx.doi.org/10.2118/78235-ms.

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Reports on the topic "Rock mechanics – Mathematical models"

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Modlo, Yevhenii O., Serhiy O. Semerikov, Stanislav L. Bondarevskyi, Stanislav T. Tolmachev, Oksana M. Markova, and Pavlo P. Nechypurenko. Methods of using mobile Internet devices in the formation of the general scientific component of bachelor in electromechanics competency in modeling of technical objects. [б. в.], February 2020. http://dx.doi.org/10.31812/123456789/3677.

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An analysis of the experience of professional training bachelors of electromechanics in Ukraine and abroad made it possible to determine that one of the leading trends in its modernization is the synergistic integration of various engineering branches (mechanical, electrical, electronic engineering and automation) in mechatronics for the purpose of design, manufacture, operation and maintenance electromechanical equipment. Teaching mechatronics provides for the meaningful integration of various disciplines of professional and practical training bachelors of electromechanics based on the concept of modeling and technological integration of various organizational forms and teaching methods based on the concept of mobility. Within this approach, the leading learning tools of bachelors of electromechanics are mobile Internet devices (MID) – a multimedia mobile devices that provide wireless access to information and communication Internet services for collecting, organizing, storing, processing, transmitting, presenting all kinds of messages and data. The authors reveals the main possibilities of using MID in learning to ensure equal access to education, personalized learning, instant feedback and evaluating learning outcomes, mobile learning, productive use of time spent in classrooms, creating mobile learning communities, support situated learning, development of continuous seamless learning, ensuring the gap between formal and informal learning, minimize educational disruption in conflict and disaster areas, assist learners with disabilities, improve the quality of the communication and the management of institution, and maximize the cost-efficiency. Bachelor of electromechanics competency in modeling of technical objects is a personal and vocational ability, which includes a system of knowledge, skills, experience in learning and research activities on modeling mechatronic systems and a positive value attitude towards it; bachelor of electromechanics should be ready and able to use methods and software/hardware modeling tools for processes analyzes, systems synthesis, evaluating their reliability and effectiveness for solving practical problems in professional field. The competency structure of the bachelor of electromechanics in the modeling of technical objects is reflected in three groups of competencies: general scientific, general professional and specialized professional. The implementation of the technique of using MID in learning bachelors of electromechanics in modeling of technical objects is the appropriate methodic of using, the component of which is partial methods for using MID in the formation of the general scientific component of the bachelor of electromechanics competency in modeling of technical objects, are disclosed by example academic disciplines “Higher mathematics”, “Computers and programming”, “Engineering mechanics”, “Electrical machines”. The leading tools of formation of the general scientific component of bachelor in electromechanics competency in modeling of technical objects are augmented reality mobile tools (to visualize the objects’ structure and modeling results), mobile computer mathematical systems (universal tools used at all stages of modeling learning), cloud based spreadsheets (as modeling tools) and text editors (to make the program description of model), mobile computer-aided design systems (to create and view the physical properties of models of technical objects) and mobile communication tools (to organize a joint activity in modeling).
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