Mathematical Modeling of Charge Power Assessment with Exclusion of Loess Subsidence by Deep Hydraulic Blasts

Introduction. Subsidence loess soils, widespread in Russia, China and Central Asia, are a challenge in modern construction due to their tendency to subsidence and low strength under external loads. Insufficient attention to their mechanical-and-physical properties can cause deformation of structures, which creates a safety hazard and financial losses. Scientific research in this area is fragmentary and does not provide sufficient understanding of compaction methods and their impact on the durability of structures. Moreover, there are no developed optimized mathematical models to predict the efficiency of engineering and technology processes of compaction. Thus, the objective of this study is to develop a mathematical model that determines the explosive charge capacity for compaction of loess. This model is aimed at eliminating the experimental stage, which improves the quality of compaction and contributes to saving financial resources in construction. Materials and Methods. Mathematical modeling was carried out by including the solution to the inverse applied problem of assessing the power of an explosive charge when eliminating loess subsidence. Initial-boundary value problems with a semiempirical partial differential equation describing the compaction of loess with and without the ejection of soil onto the construction site’s surface were considered by analyzing specific models and mathematical approaches. Based on the solution to these problems using the analytical method, a mathematical model for assessing the power of an explosive charge was developed. The power was determined numerically using two methods: calculations in a program developed in the Python language, and modeling a computational experiment with an assessment of the error of the result. In this case, the effect of the mechanical-and-physical properties of soils, their isotropy and anisotropy were taken into account. Results. A mathematical model of the explosive charge power during compaction of subsiding loess using deep hydraulic blasts was constructed. The density of dry soil before and after compaction, the vertical diffusion coefficient, dispersion coordinate changes of gas in the compacted soil, and the depth of the explosive charge were taken into account. With an average density of dry compacted soil, the absolute error of the calculated values of the charge power was 3.28 g for compaction of loess without ejection, and 21.13 g for the situation with soil ejection onto the surface. The adequacy of the proposed mathematical solution to the experimental data of a full-scale construction site was shown. Discussion. The proposed model allows for the assessment of the explosive charge power for isotropic and anisotropic geological systems. The resulting analytical representations demonstrate the degree and nature of the influence of mechanical-and-physical properties of soils on the magnitude of the charge power. Numerical comparison with both experimental data on natural soil compaction and recommendations for compaction of subsidence soils of high power by the hydraulic blasting method has shown that the proposed mathematical model is consistent with empirical data. Conclusion. The main result of the study is a mathematical model of the explosive charge power when eliminating loess subsidence using deep hydraulic blasts. Analytical representations of the charge power are constructed taking into account the mechanical-and-physical properties of soils. A numerical estimate of the power consistent with the values of empirical data is obtained. The practical significance of the study involves the possibility of using the mathematical model as a calculation method and implementing it in research and design organizations. Further study will be aimed at constructing solutions using mathematical modeling and other inverse problems within the framework of the engineering and technology process of soil compaction.