Mechanism of deformation of a granular material under high shear

Ревуженко, А. Ф.; Stazhevskii, S. B.; Shemyakin, E. I.

doi:10.1007/bf02509483

Cited by 32 publications

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“…После появления этой работы часть исследо-вателей стала отождествлять именно слои локали-зации с зарождающимися макроскопическими на-рушениями в сплошной среде. Появлению такой интерпретации способствовало и то, что в 70-х го-дах прошлого столетия возможность зарождения систем слоев локализации была продемонстриро-вана как экспериментально [Revuzhenko et al, 1974;Stoyanov, 1977], так и (с учетом стеснения деформа-ции массива) теоретически [Nikitin, Ryzhak, 1977].…”

Section: представления о приобретенной дискретностиunclassified

On Discrete Structure of Geologic Medium and Continual Approach to Modeling Its Movements

Мухамедиев

2016

Geodin. tektonofiz.

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This paper discusses the structure of a geologic medium represented by accessible lithified rocks and provides an overview of methods used to describe its movements. Two basic opinions are considered in the framework of the discussion: (1) an initially homogeneous and continuous geologic medium acquires the structure composed of blocks in the process of the geologic medium's deformation/destruction/degradation, and (2) a geologic medium is composed of blocks (and often has hierarchic, active, energy-saturated features), and the continuity model is thus not valid for describing the geologic medium's deformation. Proponents of the first point of view actively apply the standard or modified continuum model of a solid deformed body (SDB) in estimations of the stress-strain state, but the input parameters of this model do not contain any information on discreteness in principle. Authors who support the second opinion, either explicitly or implicitly assume that the block structure of the geologic medium, which is detectable by geological methods, makes a direct and unambiguous impact on all other mechanical properties of the geologic medium and, above all, on the nature of its movements.Based on results obtained by interpreting the data collected in our long-term field studies of rock fracturing, mathematical processing of GPS-measurements, and theoretical models, we agree with the concept of the geologic medium's block structure, but argue that the geologic block-structure property is not acquired but congenital. Regarding sedimentary rocks, it means that the discrete structure has been already embodied in the rock before sediment lithification, regardless of the intensity of macroscopic deformations. A discrete structure is the form of the geologic medium existence and a cause of the congenital anisotropy of the geologic medium's strength characteristics. Due to subsequent deformation of the geologic medium, some elements of the structure can be manifested more clearly, and the structure itself can become more complex due to secondary effects. At the same time, the structure of geologic blocks is not directly manifested in the spatial and temporal features of the recent movements in the geologic medium. However, it is not an obstacle to developing continuum models of such movements in the same way as, for instance, the adequacy of the continuum general theory of relativity is not denied in view of the discrete-hierarchical structure of the Universe.The key requirements to a model include its applicability, testability, confirmability/deniability of its predictions in the investigated space-time scale, and compliance with conservation laws. This paper briefly discusses the most important aspects of the continuum approach based on the concept of an effective continuous medium and, above all, the Cauchy continuum model, envisaging that the dynamic response of the medium in spatial descriptions is given only by the Cauchy symmetric stress tensor (T). In more general continuum models of the medium (such as mom...

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Section: представления о приобретенной дискретностиunclassified

On Discrete Structure of Geologic Medium and Continual Approach to Modeling Its Movements

Мухамедиев

2016

Geodin. tektonofiz.

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“…Let us now analyze the conditions on the line of possible discontinuity. can be written in the form Relation (4) E~6R,,+E,,,6Rm=6K. (9) Apart from notation, (9) is the same as (3).…”

Section: (4)mentioning

confidence: 99%

“…Further generalization to the class of hardening or weakening plastic materials reveals that the measure of shear on the slip area must have the dimensions of a length [2]. Thus, we must introduce parameters with the dimensions of a length, characterizing the discreteness of the network of sllp lines.Some of the equations of state take the form of relations between the stresses and the slips, with the dimensions of length; these are expressed in terms of the gradients of the displacements, a new kinematic variable, and the discreteness parameters of the network of sllp lines.Thus the continuous model [2] allows for the discreteness of the slip lines, and consequently occupies an intermediate position between the classical models of plasticity assuming infinitely close sllp lines and the fracture models in which the behavior of one or several essentially discrete cracks is considered (including shear cracks).If the stress--slip diagram has a descending branch, then the solution in terms of the equations in [2] can lead to the result that the sllp lines, along which load relief does not occur and the sllp increases, become essentially discrete.It is evident that such a transition to discrete lines is observed experimentally and is the cause of qualitatively new deformation effects [3,4].Thus, the equations of plasticity [2] lead to a model of the material with essentially discrete fracture surfaces on which tangential, and possibly normal, displacement discontinuities are associated with the stresses.This model borders on the class of models which are developed directly for cracks and in which account is taken of the interaction between their flanks [5][6][7][8].Let us consider some variational formulations of the boundary-value problems. (One of the possible variational approaches to problems of fracture was discussed in [9].)…”

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confidence: 99%

Variational formulation of some problems concerning fracture

Kramarenko¹,

Ревуженко²

1978

Soviet Mining Science

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i. Problems concerning fracture are of great practical importance in mining and other branches of technology.The problem of fracture is closely associated with the general problem of plastic deformation of a continuous medium.We will consider an approach to fracture problems which follows from a successive development of one class of models of plasticity. We will limit ourselves to the case of plane deformation.In soil mechanics and rock mechanics we are faced with the problem of generalizing plasticity models for materials with internal friction.It is known that in plastic conditions, depending on the first invarlant of the stress tensor, the characteristics of the stress field are nonorthogonal.The construction of kinematic equations for such media leads to the necessity of introducing a new kinematic variable which represents the possible difference between the shears on the sllp areas from different families [i]. Further generalization to the class of hardening or weakening plastic materials reveals that the measure of shear on the slip area must have the dimensions of a length [2]. Thus, we must introduce parameters with the dimensions of a length, characterizing the discreteness of the network of sllp lines.Some of the equations of state take the form of relations between the stresses and the slips, with the dimensions of length; these are expressed in terms of the gradients of the displacements, a new kinematic variable, and the discreteness parameters of the network of sllp lines.Thus the continuous model [2] allows for the discreteness of the slip lines, and consequently occupies an intermediate position between the classical models of plasticity assuming infinitely close sllp lines and the fracture models in which the behavior of one or several essentially discrete cracks is considered (including shear cracks).If the stress--slip diagram has a descending branch, then the solution in terms of the equations in [2] can lead to the result that the sllp lines, along which load relief does not occur and the sllp increases, become essentially discrete.It is evident that such a transition to discrete lines is observed experimentally and is the cause of qualitatively new deformation effects [3,4].Thus, the equations of plasticity [2] lead to a model of the material with essentially discrete fracture surfaces on which tangential, and possibly normal, displacement discontinuities are associated with the stresses.This model borders on the class of models which are developed directly for cracks and in which account is taken of the interaction between their flanks [5][6][7][8].Let us consider some variational formulations of the boundary-value problems. (One of the possible variational approaches to problems of fracture was discussed in [9].) Let S denote the deformed region, bounded by the perimeter P. Let the region be divided by a line of possible discontinuity of the displacements L. Let us introduce Cartesian coordinates Ox~xa.The indices + and -will denote symbols pertaining to the regions to the right and left...

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“…These blocks arise at critical loads and characterize the anisotropic shear resistance: within the blocks the material possess its initial cohesion and friction; along the Jo!ntlng surfaces the cohesion and friction are less than those for the initial state (Fig. i) [13].…”

Section: I)mentioning

confidence: 99%

Two problems in rock mechanics arising out of the working of deep ore or coal deposits

Shemyakin¹

1975

Soviet Mining Science

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Research of the stress-strain state of extensive rock masses, including that in the neighborhood of systems of underground workings, is becoming important as deep coal and ore deposits are being opened up, deep mines being planned and constructed, and systems for mining at great depths being created.This research is being done by geophysicists, mechanical engineers, and mining engineers, both in order to refine our basic ideas on the state of stress of the earth's crust and for practical purposes associated with mining at great depths. Depths have already been reached at which the stresses in the undisturbed rock are comparable with its strength (we arbitrarily call such depths "great").At these depths such dangerous phenomena as shock bumps are more frequent and more hazardous; here we must reexamine the question of the "optimim" technology (e.g., work with continuous stowing).We can distinguish two main groups of problems in rock mechanics, the first of which involves assessing the initial state of the rock (before disturbance by human agency), estimating its stresses and principal displacements; the second involves strength calculations on the structural elements of systems of workings (development and main workings and the influence of extraction operations).

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Mechanism of deformation of a granular material under high shear

Cited by 32 publications

References 0 publications

On Discrete Structure of Geologic Medium and Continual Approach to Modeling Its Movements

On Discrete Structure of Geologic Medium and Continual Approach to Modeling Its Movements

Variational formulation of some problems concerning fracture

Two problems in rock mechanics arising out of the working of deep ore or coal deposits

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