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Abstract. Some results of numerical experiments of testing concrete cubes and prisms on unconfined compression, and the comparison of results obtained with experimental and specified data, are presented in the article. When performing calculations of structures in a nonlinear setting, it is very important to choose adequate deformation diagrams or material models. Because of the fact that there are no instructions how to use the diagrams of concrete and armature deformation in collaboration of steel and concrete, the simulation of reinforced concrete structures by finite elements of the same type without any assumptions is impossible. Numerical experiments have been performed in the LS-DYNA software package. This software package allows simulating the collaboration of concrete and steeling with the help of three-dimensional (for concrete) and rod (for the reinforcement) finite elements. As samples, a cube and a prism with dimensions of 150x150x150 mm and 150x150x600 mm, respectively, have been taken. The samples are simulated by solid finite elements. For the simulation of concrete, the non-linear CSCM (Continuous Surface Cap Model) material is used. The tests were carried out with samples of the following classes of concrete as for cylinder compressive strength: C12, C16, C20, C25, C30, C35. This corresponds to the following classes of cube compression strength: B15, B20, B25, B30, B37, B45. The tests have been carried out considering the friction coefficients between the plates of a testing machine, and a sample. The performed researches have shown that the destruction nature of the samples in a numerical experiment corresponds to the failure nature in real tests. The investigated model of CSCM concrete can be used in the calculation of concrete and reinforced concrete structures with acceptable accuracy for main classes of concrete.

This article considers the issues associated with the deep mining of bauxite ores. A need for effective development of Russian aluminum mineral resource base requires companies to reduce the ore losses emerging while moving to the deeper mining, which is characterized by sophisticated geological, technical and geodynamic mining conditions. In this article we have revealed the changing patterns of the inter-chamber pillars’ stress state and stability taking into account the influence of various mining and geological factors. Based on the mine data and the results of numerical experiments performed with the use of PRESS 3D URAL software, this research has revealed that at the depth of more than 700-800 m inter-chamber pillars enter the supercritical mode of deformation and have minimal bearing capacity. Failure to take into account the supercritical mode of deformation leads to the significant losses of ore in pillars reaching 30-50%. At the same time, the ore losses can be reduced to 15-25% by considering the residual strength and supercritical deformation of the pillars while designing their parameters. The economic result would be achieved by improving the design process of mining operations, providing increased safety of mining operations along with losses reduction leading to to increase in production volumes.

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Layered Bragg structures are widely observed in nature and applied in engineering. Permittivity or/and permeability of layers are usually supposed to be periodical functions of space coordinate [1][2][3]. Distortions of periodicity supply additional possibilities for effects of wave scattering [4]. For obtaining desired complex amplitudes of scattered plane waves as function versus incident frequency or angle, spatial distribution of magnitude and phase of quasiperiodic perturbation can be used.In presented work resonance properties of resonators formed by quasiperiodic Bragg reflectors are investigated by solution of some types of eigenvalue problems. In the first eigenvalue problem the values of complex eigenfrequencies are found for the decaying natural oscillations of the "cold" passive resonators. The other eigenvalue problems correspond to undamped oscillations in "hot" structures containing amplifying elements. In the second eigenvalue problem we must find real frequencies and imaginary part of permittivity or permeability (lasing threshold) at fixed value of real part of permittivity and permeability of amplifying layer [3]. In the third case the generation is achieved by introduction of lumped element with negative resistance into structure. In the fourth eigenvalue problem complex eigen permittivities or permeabilities of amplifying layers are found for fixed frequency of oscillations [5].Elements of scattering matrices and equivalent complex impedances used for solving the eigenproblems were found by usage of the formalism of the transmission matrix method [1][2][3]. In this method any layer or lumped element is characterized by the transmission matrix and the matrix of total layered structure can be found as product of matrices of all layers and elements.Eigen modes can be useful or harmful in different engineering application. Proper choice of law of magnitude and phase of quasiperiodic perturbation of parameters allows increasing or decreasing of quality factor of these eigen modes. The exactest method of finding of the eigen parameters is the computation of poles of elements of scattering matrix of structure in two-dimensional domain of parameters.In Fig. 1 complex eigenfrequencies of different type of Bragg resonators are shown. All examined resonators have N=21 layers with "normal" electrical thickness equal to quarter of wavelength on central frequency f 0 and "abnormal" electrical thickness equal to half of wavelength. Permeability is equal to unity for all layers. Complex eigenfrequencies of resonators with single central abnormal layer are shown in Fig.1a. Results for a structure with large values of permittivity of both layers in period (ε 2m-1 =12, ε 2m =9) [3] are presented by the asterisks. Similar structures have much larger Q-factors of unwanted eigenmodes than periodic photonic Bragg structure (ε 2m-1 =2, ε 2m =1) that shown by circles. Different shapes of perturbation magnitude were used. Smoothing of the perturbation magnitude allows decreasing Q-factor (increasing imaginary part of ...