Finite difference method for estimating the density of loess compacted by explosion

Abstract

The need for preliminary numerical modeling of the density assessment of loess compacted by deep blasts in order to reduce economic costs during production work. Soil subsidence was eliminated at the stages of design and construction of buildings and structures to ensure their safe, long-term operation. Loess subsidence soils are widespread throughout the world, often in Europe and Asia. Loess is characterized by low density of the soil skeleton, high dust content, and macroporosity. Aim. To numerically estimate the density of soil after compaction by deep blasting using the finite difference method. Methods. Finite difference method; computational experiment; numerical modeling. Results and conclusions. To solve initial boundary problems within the framework of mathematical modeling of loess compaction by deep explosions, the finite difference method was used. The model is based on a parabolic differential equation. A six-point symmetrical Crank–Nicholson circuit was used. The constructed linear systems of equations take into account the initial and boundary conditions, the input effects of the soil diffusion coefficient, the power of the explosive charge, and the vector of horizontal gas distribution. The result of solving the systems are the values of soil density at the nodes of the grid function. The estimate of soil density found by the finite difference method has second order accuracy in spatial coordinates and time. The constructed six-point circuits are absolutely stable. A computational experiment was implemented using the proposed method for assessing soil density, which showed adequacy to the experimental data of a natural construction site.