<p>The aim of the research is to construct a mathematical model of the formation of a fracture system in magma intrusion in the permeable zones of the lithosphere and on this basis to study the formation of magmatic channels in the lithosphere and crust. The lithosphere substrate is modeled by a saturated porous medium in which the processes of small-scale destruction in the mantle magma intrusion lead to the formation of faults and, consequently, to a magmatic channel. Destruction and occurrence of micro-fracture fields can be associated with both magma flow and external seismic effect leading to the rock breaking. The process of small-scale destruction is described within the framework of the dynamics of the elastoplastic fracture-porous medium and causes variations in the rheological properties of the lithosphere substrate. A feature of this process is the destruction substrate in the compression zone represented by a narrow area with a sharply changing concentration of micro-fractures. The micro-fracture accumulation provides the conversion of the broken area into a macro-fissure. The elastoplastic porous matrix in the destruction zone contains both broken and intact substrate, the relative content of which is determined by relaxation of deformations, the speed of which depends on stress and yield stress point according to the power law. The obtained mathematical model provides investigation of currents in fractured-porous media and their effect on the small-scale destruction. Based on the TVD-Runge Kutta method numerical simulation of the compressible fluid infiltration into the fracture-porous permeable channel has shown that stresses in the compression domain can reach stress limits of breaking and result in fracture formation. Change in relaxation time does not result in a marked change in stress fields. The concentration of maximum stresses is observed in the channel center leading to an increase in its fracture porosity. The computational results show the appearance of high stress values in the compression domain in the process of a liquid phase injection, for instance, magma, into a low-permeable fracture-porous layer. The introduction of the destruction criterion will help to associate the occurrence of such regions to the local breaking of the porous matrix. Thus, the proposed micro-fracture generation mechanism can be used to describe the formation of fracture or channels in micro-fracture porous media. Work is done on state assignment of IGM SB RAS with partial support from the Russian Foundation for Basic Research, grants No. 16-29-15131, 19-05-00788.</p>
Kinetics of filtration consolidation of water-saturated clay soils
