The aim of this study is mathematical modelling of the southern part of the Siberian craton using the finite element method. The task of the study is to carry out mathematical modelling of the stress-strain state of the visco-elastic-plastic medium of the Yakutsk-Vilyui large eruptive province on the basis of the boundary value problem. Hypothesis of the study: the possibility of using the results of numerical study to determine the zones of mineral dislocations. In the southern part of the craton, on the territory of the Republic of Sakha-Yakutia, there are the richest oil and gas fields, the largest of which is the Ust-Vilyuyskoye field located in the southern part of the craton. Research method: numerical experiment carried out by the method of mathematical modelling. Results achieved: finite element studies were carried out, the possibility of using numerical methods was determined, the stress-strain state of the plate was analysed, and the locations of anomalies of dislocations of craton rocks were determined to identify potential oil and gas bearing fields.

Keywords: craton, mathematical modeling, stress-strain state, geophysics, geotectonics, stretching, igneous province, material models, Hardening Soil model, finite element method, mineral dislocation

This study is a pilot one. The purpose of the study is to identify the nature of the relationship between Poisson's ratio and cohesion, on the example of a soil mass. The main objective of the study is to identify the dependence of Poisson's ratio and cohesion coefficient to obtain the fracture limit of the material (in this study of soil massif) - plastic flows in the material. The study is conducted by methods of mathematical modeling. In order to achieve the objective, it is necessary to justify the possibility of performing this experiment by means of boundary value problem, and to perform the ranking of the number of numerical experiments by experiment planning method to obtain the extrema. Next, it is necessary to perform the numerical experiment itself to reveal the relationship between Poisson's ratio and cohesion. The obtained data will be used to compose the inverse problem when testing a new Russian software product in the field of geotechnical and geomechanical modeling.

Keywords: Poisson's ratio, cohesion, soil massif, numerical experiment, finite element method, mathematical modelling, plastic flow, deformation, stress