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/ B. G. Tarasov, V. M. Sadovskii // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964990 . -
Аннотация: Mathematical model of the equilibrium fan-structure formation between two elastic half-planes is constructed, simulating a shear rupture at stress conditions of seismogenic depths. The stress-strain state far from the fan-structure is analyzed with the help of solution of the problem on the Volterra edge dislocation resulted in estimation of the fan length. The model of formation of two differently directed fans due to the localized action of tangential stress, which pushes two edge dislocations with the antiparallel Burgers vectors, is proposed and analysed. © 2016 Author(s).

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Держатели документа:
University of Western Australia, Stirling Highway 35, Perth, WA, Australia
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.

[Текст] : статья / Борис Григорьевич Тарасов, Владимир Михайлович Садовский, Оксана Викторовна Садовская // Физическая мезомеханика. - 2016. - Т. 19, № 4. - С. 28-37 . - ISSN 1683-805X
   Перевод заглавия: Modeling of fan formation in the shear rupture head on the basis of equations of plane elasticity

УДК

539.374

Аннотация: В приближении плоской деформации строится математическая модель равновесного веера в прослойке между двумя упругими полуплоскостями, имитирующей головную зону растущей трещины сдвига в прочной горной породе в условиях сильного гидростатического сжатия. Напряженно-деформированное состояние вдали от веера анализируется с помощью решения задачи о краевой дислокации. В полной постановке задача решается на основе оригинального метода суперпозиции дислокаций, приводящего к двум нелинейным интегральным уравнениям в зоне веера, для численного исследования которых применяется метод последовательных приближений.
The mathematical model of an equilibrium fan formation in the interlayer between two elastic half-planes which simulates the shear rupture head in a hard rock under high hydrostatic pressure has been constructed in the plane strain approximation. The stress-strain state far from the fan is analyzed by solving the problem of edge dislocation. This problem in a complete formulation is solved on the basis of an original method of superposition of dislocations that yields two nonlinear integral equations in the fan zone. The integral equations are solved numerically using the method of successive approximations.

РИНЦ

Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.; Садовская, Оксана Викторовна; Sadovskaya O.V.; Tarasov B.G.

/ B. G. Tarasov, V. M. Sadovskii // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P648-656, DOI 10.1007/978-3-319-57099-0_74 . -
Аннотация: The main goal of this paper is to analyze the fan-mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating growth of shear ruptures in super brittle rocks. A physical model recently designed demonstrates that the fan-structure formation can be stable at the absence of distributed shear stress applied. The action of distributed shear stress causes the fan propagation as a wave representing the rupture head. The developed mathematical model of a fan-structure as a continuous system establishes the relation between the fan velocity and the fan length. It is shown that in the absence of friction the fan velocity may be arbitrary, but not greater than the limit velocity which is determined by the moment of inertia of slabs, the initial angle of their orientation and the elastic coefficient of bonds. In a system with friction the velocity of traveling fan is solely determined by the opening angle. The action of distributed shear stress leads to the instability start before the fan-structure completion. The fan length decreases with increasing velocity. © Springer International Publishing AG 2017.

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Держатели документа:
University of Western Australia, Stirling Highway 35, Perth, WA, Australia
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович

/ B. G. Tarasov, V. M. Sadovskii, O. V. Sadovskaya // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P657-664, DOI 10.1007/978-3-319-57099-0_75 . -
Аннотация: The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface is studied. This mechanism governs the propagation of shear ruptures in super brittle rocks at stress conditions of seismogenic depths. The current paper analyzes a built laboratory physical model, which demonstrates the process of fan waves propagation. Equations of the dynamics of the fan-structure as a mechanical system with a finite number of degrees of freedom are obtained. Computational algorithm, taking into account contact interaction of slabs, is worked out. The computations, showing the incomplete disclosure of fans with different opening angles due to fast or slow change in the velocity of rotation of the first slab, are performed. Comparison of the results of computations of length and velocity of a fan by means of a discrete model with laboratory measurements and observations shows good correspondence between the results. © Springer International Publishing AG 2017.

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Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia, Stirling Highway 35, Perth, WA, Australia
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович; Sadovskaya, O.V.; Садовская, Оксана Викторовна

/ B. G. Tarasov [et al.] // Appl. Math. Model. - 2018. - Vol. 57. - P268-279, DOI 10.1016/j.apm.2018.01.020 . - ISSN 0307-904X
Аннотация: The mathematical model of an equilibrium fan-structure in the interface between two elastic blocks, simulating the shear rupture head in a hard rock under high confining pressure, is constructed. The stress–strain state far from the fan-structure is analyzed with the help of a solution of the problem on edge dislocation. The fan length is estimated using this solution. The model of formation of two oppositely directed fans due to the localized action of tangential stress, which pushes two edge dislocations with antiparallel Burgers vectors, is proposed. In complete formulation, the problem on an equilibrium fan-structure in the interface between infinite elastic half-planes is analyzed by means of original method of superposition of dislocations, leading to two nonlinear integral equations in the fan zone. To solve them numerically, the method of successive approximations is applied. Based on this method, fields of stresses and displacements around the equilibrium fan modelling of a deep-seated shear rupture in the seismogenic zone of the Earth's crust are computed. Such fields can be used, when setting the initial data in the analysis of dynamics of the fan-shaped mechanism. © 2018 Elsevier Inc.

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Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia, Perth, WA, Australia
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.; Cassidy, M. J.; Randolph, M. F.

/ B. G. Tarasov, V. M. Sadovskii, O. V. Sadovskaya // J. Appl. Mech. Tech. Phys. - 2017. - Vol. 58, Is. 7. - P1139-1152, DOI 10.1134/S0021894417070100. - Cited References:23. - This research was partially supported by the Centre for Offshore Foundation Systems (the University of Western Australia) and the Complex Fundamental Research Program no. II.2P "Integration and Development" of Siberian Branch of the Russian Academy of Sciences (grant no. 0356-2016-0728). . - ISSN 0021-8944. - ISSN 1573-8620РУБ Mechanics + Physics, Applied

Аннотация: The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth's crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

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Держатели документа:
Univ Western Australia, Ctr Offshore Fdn Syst, Perth, WA 6009, Australia.
Inst Computat Modeling SB RAS, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.; Centre for Offshore Foundation Systems (the University of Western Australia); Complex Fundamental Research Program [II.2P, 0356-2016-0728]

/ V. M. Sadovskii, O. V. Sadovskaya, B. G. Tarasov // AIP Conference Proceedings : American Institute of Physics Inc., 2018. - Vol. 2025: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2018 (20 June 2018 through 25 June 2018, ) Conference code: 141497, DOI 10.1063/1.5064918 . -
Аннотация: In our research, we analyze the laboratory physical model of the system of rotating bonded slabs on inclined plane, which was created to imitate the process of fan waves formation and propagation in hard rocks at the depths of seismic activity in the Earth's crust. Mathematical model of the dynamics of this system as a mechanical system with a finite number of degrees of freedom is realized by means of the Merson method for numerical solution of ordinary differential equations. We consider two approaches describing the resistance to separation of slabs in a fan-structure. In the first of them, a nonlinear tension diagram for the bonds between the slabs with a characteristic tooth simulating the initial strength of the bonds is determined. In the second one, the value of limiting force is assumed to be given. Comparison of the computational results by these two approaches shows a good qualitative and quantitative correspondence. The influence of dry friction on the process of motion of a fan as well as the dependence of the speed of a fan on the geometrical and mechanical parameters of a system are analyzed. © 2018 Author(s).

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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia

Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.; Tarasov, B. G.