Determination of the mechanical state of tectonic faults

Abstract

The relevance of the work follows from the need to solve the problem of a more accurate prediction of the possibility of a starting earthquake for cases of various mechanical structures of lithospheric plates. The aim of the research was to solve the problem of assessing the strength properties of the shores of the tectonic fault of lithospheric plates when applying new mathematical methods. The destruction of the fault banks near the base is the cause of the initial earthquakes. Methods. The case is studied when the fault is formed as a result of the oncoming approach of the ends of granite fragments of lithospheric plates located on a basalt base at the Conrad boundary, or formed as a result of flexural plate destruction during subduction. In the process of research, a new progressive mathematical apparatus is used – the block element method, which allows analytically obtaining high-precision solutions to boundary value problems that are not available for analysis by other methods. The result of the study was the development of several mathematical approaches specially developed by the authors for the study and solution of the tasks. First of all, the theory of contact problems with deformable stamps began to be developed strictly mathematically for the first time in addition to cases with absolutely rigid stamps. Secondly, a new universal modeling method has been created that allows solutions of vector boundary value problems for systems of partial differential equations describing materials of complex rheologies to be decomposed according to solutions of individual scalar boundary value problems. In the process of constructing the theory of contact problems with deformable stamps, new unknown functionals arise, the definition of which is necessary to solve the problem. With the help of new methods, the possibility of obtaining ratios that allow us to assess the degree of danger of fracture destruction is proved in the work, since it is possible to obtain all the missing parameters for this.