Rock mass deformation modeling using the non-Archimedean analysis

The non-Archimedean space is a multi-scale one. The paper shows that this face is applicable to developing mathematical models of rocks exhibiting a hierarchy of structural levels. A closed model, considering anisotropy and weakening of a rock mass, is constructed. The equations in terms of displacements and the resultant internal force vector are derived. The authors have obtained the numerical solution to the problem on deformation of a rock mass around extended galleries, and showed how the areas of weakening and residual strength evolve. The energy flow lines are plotted. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 1, pp. 3–16, January–February, 2008.     

Mathematical Models of Block Media in Problems of Geomechanics. Part IV: Interaction of an Induced Structure and Stress State

A mechanical model of block rock-mass behavior when the block system depends on the existing stress-strain state is developed for the case of plane strain. The blocks are formed by intersecting nonorthogonal planes of weakening in the material, and the mathematical equations include elasticity constants for anisotropic body. The relations obtained for inelastic deformation (plasticity) of rock mass are illustrated by solving some problems of geomechanics. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 11–25, July–August, 2005.     

Devices for Continuous Recording of the Parameters of Deformation — Wave Processes in Rock Mass. Part I: Measurement of Longitudinal Movements of Rocks in a Borehole and Design of the Position Sensor

A sensor for measuring movements in block rock mass through boreholes is presented. Being an organic part of multichannel instrumental set, the sensor ensures revealing of deformation changes in the controlled zones of block geomedia, which is of key importance when stress variations and fatigue failure in rock mass are determined. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 106–115, May–June, 2005.     

Modeling the failure of rock blocks by blasting a cylindrical charge

The calculation model of breaking action exerted by a cylindrical charge blasted in a block rock mass is proposed. The deformation of a block medium in the zones of elasticity and heavy fragmentation is described by a continuum, properties of which are changed as compared with monolithic rocks. It is shown that the accounting of the block rock strength decrease in the massif influences greatly the calculated failure parameters and provides an opportunity to obtain fragmentation zone sizes, close to those observed in actual rock blasting. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 1, pp. 31–38, January–February, 2006.     

Modeling of initial stresses and weakening surfaces by finite-element method

Solutions of geomechanical problems in terms of full and additional displacements are compared for the example of the creation of the mined-out space filled with stowing and the construction of a subway tunnel. An approach to modeling the contact interaction of a block massif is proposed. Data on the stress-strain state of rock mass in forming the mined-out spaces close to extended geological disturbances are presented. Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk. Translated from Fiziko-Tekhnichskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 49–59, March–April, 1999.     

Transient one-dimensional wave processes in a layered medium

Waveguide properties of a block geomedium are studied by using a regular structure composed of elastic layers with elastic inertialess interlayers. The analytical solution of the problem is derived. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 41–54, March–April, 2007.     

Modeling of Deformation of Rocks when Contacting a Rigid Cylinder

The variants of complex loading of rocks in order to fail them are considered in the frames of the Hertz problem. The examples of deformation taking into account indentation, shear, and torsion during interaction of solids are cited. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 25–31, March–April, 2005.     

Math modeling of deformation of a rock mass with an oil-bearing bed

The authors offer the statement of the problem on the deformation of a piecewise-homogenous rock mass with an oil-bearing bed. The derived system of integral equations describes the stress-strain state on the contacts in such rock mass based on the in-situ data. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 5, pp. 3–10, September–October, 2007.     

Mathematical modeling of pressure on the strengthening vertical shaft support in “Mir” mine located in the Charsk saliferous rock series

The problem statement and the solution algorithm are presented for the case of contact between strengthening vertical shaft support and rocks. Hereditary viscoelasticity equations are used as constitutive relations for saliferous rocks. An analysis of the dynamics of the growing pressure on the support is performed versus the shaft cross-section occurrence depth, saliferous rock strength on the contact, and spacing between the rock contour and the support in the shaft. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 18–27, March–April, 2006.     

Investigation into efficiency of the impact energy transfer depending on the head geometry of a pneumodrill

The mathematical models of percussion interaction between the main elements of a pneumodrill are considered with and without a glance on their contact interaction. The basic calculation data are presented, and the numerical value selected for the recoil factor is substantiated for a pneumodrill on forward stroke. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 41–54. May–June, 2008.     

Time-dependent tunnel convergence—I. Formulation of the model

The understanding of the mechanism of tunnel convergence is essential for designing the required support of a tunnel. To take various time effects on the convergence-confinement relation into account, it is possible to correlate different factors with time, then to deal with their collective effects. As a result, the time-dependent tunnel deformation problem can be modelled as a viscoelastic problem. The solutions of various viscoelastic models can be obtained from the corresponding elastic solution based on a standard procedure. In this paper, a hierarchical approach, which considers: (1) the rheological properties of a rock mass; (2) the advancement of the tunnel; and (3) the tunnel-support interaction is proposed to model the excavation/construction process during the tunnelling in a rock mass with rheological properties. The time-dependent factors considered in the proposed model are discussed. Subsequently, the theoretical formulation of this model is developed.     

Deformation and failure of originally isotropic media under the mises strength condition

A model of an originally isotropic material is constructed from rigid particles — blocks. Any deformation of the model is presented as a sum of simple shears and lengthenings. Simple shears occur due to overcoming of friction forces on contact surfaces. The model does not assume an elastic or a quasi-elastic deformation in the second principal direction. Failure is considered as a decrease in resistance as strains increase. For the plane strain state, under the Mises strength condition, the equation of failure, the characteristics and the relations on the characteristics are determined, as well as the statements of the problem on failure are analyzed. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 17–30, July–August, 2006.     

Breakage of fissured rock by blasting

Conclusions When charges are exploded in a fissured rock mass, the fragmentation is mainly localized in the directions of maximum contact of the medium with the piece which is broken first. The directions of maximum fragmentation correspond to the maximum velocities and distances of flight. According to the linear dimensions of the blocks, the crushed volume varies from cruciform to circular shape, being elliptical in vertical section. The degree of crushing and the relative formation of new surface decrease from block to block with increasing distance from the charge. These experiments indicate that the elements of the fissuring are some of the principal criteria in the choice of rational charge parameters and blasting systems. State Scientific-Research and Planning Institute of Coal, Ore, Petroleum, and Gas Industries of the Ukrainian SSR (UkrNIIProekt), Kiev. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 39–45, May–June, 1969.     

Regularities revealed on cyclic deformation of sand soil on the single-plane direct shear machine

The test data are presented for strength characteristics and weakening of sand soil under shear. It is studied how the weak periodic pulsed stresses affect the contact of sheared rocks and granular materials under selected friction and the shearing-to-pressing load ratio. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 5, pp. 5–19, September–October, 2006.     

Mathematical modeling of slip in a rock along the uneven fracture

A mathematical model is presented for the unstable deformation of rock along an existing fracture in it. It is shown that this process is essentially nonlinear and can be described by the Gordon equation. An analysis is made for the influence of geometric irregularities and friction of the contact surfaces on the evolution of the velocity of solitary slip waves which are caused by local deformation effects and propagate along the fracture. Institute of Tectonics and Geophysics, Far East Branch, Russian Academy of Sciences, Khabarovsk, Russia. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 64–70, May–June, 2000     

Experimental investigation of spatial periodicity of induced deformations in a rock mass

The different-scaled periodicity of the non-uniform spatial distribution of deformations in a rock mass, resulted from its natural hierarchic block structure, is detected by using the Fourier and wavelet analyses. It is established that the block structure of the studied rock mass sections meets the concept on fundamental canonic series of geoblocks in the Earth’s crust. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 21–27, March–April, 2007.     

Formation of an incipient crack in the impact fracture of a brittle body by a wedge

A study is made of the problem of the penetration of a wedge-shaped tool in rock. It follows from the solution of the problem in the elastoplastic formulation that the continuation of the axis of the wedge in the elastic region includes a zone in which the rock is subjected to tension perpendicular to the axis. In accordance with the kinetic thermofluctuation theory of strength, this determines the formation and propagation of microcracks oriented along the wedge axis. A computer model is proposed to describe the process of random accumulation of microdefects in a loaded solid body. The model is used to create an algorithm to calculate the formation and development of an incipient crack before the vertex of the wedge. The length of the crack is determined by the properties of the medium and the parameters of the penetrated tool. Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 1, pp. 52–59, January–February, 1999.     

To the phenomenon of self-organizing deformation of a granular material in a rotating cylindrical reservoir

A model is constructed for describing deformation of upper layer of a granular material in a cylindrical reservoir rotating with a slow velocity. The problem on determining sequences of the free surface inclinations toward the horizon, when separate batches of the medium are flowing, is reduced to studying the dynamics of one-dimensional mappings. A possibility for different deformation modes to arise is demonstrated: cyclic modes with various periods, “noisy” cycles and gradual transfer to chaos. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 48–54, November–December, 2006.     

Modeling elastic behavior of compressed rock samples in the pre-failure zone

The experimental results are presented for deformation of rock samples in the pre-failure zone under compression. Anomalous periodic character of change in strains is established. An elastic solution to the corresponding problem on the anomalous behavior of rock samples is found, and the experimental databased phenomenological parameters of the model are determined. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 3–13, November–December, 2005.     

Rock mass deformation near a crack located on an interface of rocks with different properties

The present paper focuses on considering an elastic problem on stress-strain state in the vicinity of a finite crack located on a boundary between half-planes with different physical properties. The problem is reduced to the Fredholm singular integral equations of second order for the contact conditions. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 10–16, July–August, 2006.