Solution for inverse boundary value problems on the power of a concentrated charge in a mathematical model of subsidence soils compaction

Abstract

The soils of the North Caucasus contain a large share of subsidence loess, which accounts for about 80% of the entire area. Compaction of subsidence soils through deep explosions appears a relevant issue when designing and constructing buildings and other structures. The analysis of the experimental data obtained through explosions shows that it can be a reasonable idea to employ methods of differential calculus to carry out mathematical modeling of this process. Diffusion equations featuring a high degree of reliability can describe a mathematical model of subsidence loess compaction by deep explosions. While describing changes in the compacted soil density, in the case involving a concentrated explosive charge, a function was used, which is a Gaussian function of the compacted soil density distribution. This article offers a look at the equations presented by the boundary value problem with a system of initial and boundary conditions, aiming to solve the inverse applied problem of restoring the power of a concentrated explosive charge. There have been analytical and numerical solutions of the problem obtained. A computational experiment has been held to calculate the power of a concentrated charge relying on a developed program. An analysis of the literature focusing on this issue reveals lack of elaboration of the issue as well as lack of a mathematical description for loess soil compaction problems.