Numerical solution of inverse problems in mathematical modeling of geological systems

Abstract

The relevance of the research. Mathematical modeling of geological systems is relevant both theoretically and practically. Inverse applied problems make it possible to systematize knowledge about the models under study. This article deals with the problem of assessing the depth of an explosive charge in collapsible soils in order to compact them and, as a consequence, reduce subsidence. This method of compaction is widely used at civil construction sites, relief features of the territories, etc. It should be noted as well that Russian territories are presented by loesses in about 17 % of cases. The main aim of the research is analytical and numerical modeling of the solution of inverse problems in geological systems when compacting loesses by deep explosions. Methods: iterative methods for solving problems, methods of computer modeling in the study of geological systems, conclusion statistics. Results. Analytical and numerical solutions of the considered inverse applied problem of the geological system are proposed. Solutions are described under the conditions of complete absorption of the gas formed as a result of the explosion of a concentrated charge by the surrounding collapsing soil (the loess is compacted) and the complete reflection of the gas from the soil (the release to the surface occurs). Various states of subsidence loess with characteristic properties of isotropy and anisotropy of the geological system have been studied in detail mathematically. A computational experiment was carried out to find an approximate iterative solution to the inverse problem for determining the depth of explosions in order to compact loess. The calculations were carried out taking into account the available experimental data on the example of a civil construction object in the North Caucasus. Conclusions. The studies carried out indicate the adequacy of the proposed approach for assessing the depth of the charge. The numerical solution of the problem is found with high accuracy and with minimal computational costs.