Mathematical Modeling of Explosive and Seismic Impacts on an Underground Structure

The article provides information about mathematical (computer) modeling of unsteady waves in an underground structure under explosive (internal and external) and seismic impacts. The issue of mathematical (numerical and analytical) and physical (model and full-scale experiments) modeling of transient period problems is a relevant, fundamental scientific objective, as well as an applied problem and a production target. A technique, algorithm, and a software system were developed to obtain the components of the stress tensor, displacements, and their derivatives in deformable bodies of various shapes under unsteady wave actions. An explicit two-layer scheme was obtained. To evaluate the reliability of the developed technique, algorithm, and software system, the problem of the impact of an impulse in the form of a sinusoidal wave (three half-periods) was solved. The following problems were solved: internal explosive action in an underground structure and its effect on the environment; external explosive action on an underground structure; seismic impact on an underground structure. New results about contour stresses on a free surface under diverse actions were obtained taking into account an underground structure.