UDC 539.3+552.11
М. Lavrenyuk, PhD, Associate Prof. The Faculty of Mechanics and Mathematics Taras Shevchenko National University of Kyiv4-e Аcad. Glushkov Ave., Kyiv, 03127 UkraineE-mail: mykolalav@ukr.net
(Reviewed by the editorial board member V. Shevchuk) The problem of granites holds a special place in geology. Research of the granite formation problem leads to a number of partial problems, among those the question of depth of the granite generation and mechanisms of provision of space for large granitoid solids are distinguished. In the problem of space the geomechanical constituent is of primary importance. The major factors forming the stress-strain state in the system of the granite formation are permanently acting mass gravitation forces, tectonic forces of inter-slabs interaction, pseudo-mass forces, forces of volumetric thermoelastic effects, phase transitions in processes of metamorphism, metasomatism, partial and complete fusion. In existing investigations of stress-strain state of crust systems the geological mediums aresupposed to be quasi-homogeneous. The objective of this work is to develop the general approach to computer modeling of thebehavior of geological and mechanical systems of mega-blocks range, in context of space problem during the granite formation, takinginto account structure anisotropy of the system. While the possibilities of full-size modeling of complex multifactorial magmatogene systems are limited, the possibilities ofmathematical modeling are more appropriate, especially in view of the mechanical systems modeling. Verification of geological hypotheses and empirical data by constructing simple models with its further complication by means of transition to more and more complex combinations of force factors, rheological states, boundary conditions, and other factors is the most optimal. In the article the problem of stress-strain assessment of geological and mechanical system of mega-blocks range is analyzed. Assuming that thetemperature of medium is known, there were obtained governing relations describing the behavior of geological and mechanical systemat combined action of the gravity, non-homogeneous temperature field and power and kinematic influences imposed on the boundariesof considered system. The algorithm for solving of elastic problem is developed by means of the modified boundary element method. The governing relations of the considered problem are obtained as well as the numerical and analytical algorithm of stress-
strain assessment of the considered geological and mechanical system is developed. Mathematical model and corresponding algorithm of the numerical calculation of stress-strain state of the considered system
allow analyzing the stress-strain state of geological and mechanical system at combined action of gravity, non-homogeneous
temperature field and imposed on the boundaries of considered system power and kinematic influences, taking into account structure anisotropy of the system.
Thus the method proposed herein allows investigating the nature of stresses fields, and hence to forecast geometry of potential
zones of relative decompression and tension, which are the most auspicious for granite formation.