Accounting the links of inclusions hierarchy ranks with the physical and mechanical medium properties

Abstract

Geological environment and artificial material with a multilevel hierarchical structure and strength properties requires regular study of the stability of its state. For this purpose, a new method for modeling acoustic monitoring by longitudinal and transverse waves of a layered-block medium with hierarchical inclusions was developed, the ranks of which differ in physical-mechanical properties. An iterative process of solving a direct problem is developed for the case of an acoustic field penetrating the hierarchical inclusions of l, m, s ranks based on the use of two-dimensional integral- differential equations. For each group of l, m, s ranks (l = 1, …, L, m = 1, …, M, s = 1, …, S) the physical-mechanical model of the inclusions environment changes. Within each group the model of the medium does not change. The degree of filling of inclusions of each rank for all hierarchical inclusions may be different, and it is determined by the values of L, M, S. The simulation results can be used to monitor studies of the stability of geological, mechanical and medical structures of a complex hierarchical structure under various mechanical influences.