NUMERICAL ESTIMATION OF SOIL DENSITY BY THE METHOD OF FINITE DIFFERENCE GRIDS IN MATHEMATICAL MODELING OF COMPACTION OF SUBSIBLE SOILS BY DEEP EXPLOSIONS

Abstract

In order to ensure the duration of operation and strength of buildings and their expected design and construction on subsiding loess, it is necessary to carry out a numerical grade of the density characteristics of soils. Subsiding loesses are widespread in the world. They can be observed in Russia, China, the countries of Central Asia, etc. On the territory of Russia, their occurrence is noted at least at 17 % of the entire territory of the country. Almost ubiquitous distribution of loess soils occurs on the territory of the North Caucasus region (80–85 % of area). There is a large capacity of them (up to 50 m). This work is devoted to numerical modeling of the grade of density characteristics of subsiding soils using the finite difference grid method in the framework of a mathematical model of loess compaction by deep explosions. The use of the instrument of computational mathematics made it possible to solve the problem of estimating the compacted subsidence soil density depending on the depth of the explosive charge. The main aim of the research is to conduct a numerical assessment of soil density within the framework of mathematical modeling of compaction by the method of deep explosions of subsiding loess soils. Methods: application of the instrument of computational mathematics, differential equations, methods and results of solid state physics, engineering geology, soil mechanics. Experimental technique. Numerical modeling of the assessment of the increase in the compacted soil by deep explosions based on the grid method was carried out. Results. Based on the grid method using an explicit finite-difference scheme, discrete linear dynamic systems were constructed for numerical calculation of compacted subsidence soil density by deep explosions. The paper describs the layer-by-layer approximation to the solution of a differential equation in partial derivatives with given initial and boundary conditions, which mathematically describes the technological process of compaction of subsiding soil for the cases of surface ejection and camouflage compaction. The stability condition for the obtained finite-difference schemes is indicated. A computational experiment was carried out. It demonstrated the adequacy of the proposed method for estimating the compacted soil density to experimental data. Findings. The constructed numerical solutions of problems within the framework of mathematical modeling of the compaction of subsiding soils by deep explosions indicate the possibility of their practical application as calculation methods to reduce the cost of carrying out production work on the compaction of loess. The methods proposed in the work for determining soil density can be implemented in a number of areas of applied research in soil mechanics.