MODELING OF SEISMIC WAVES STRESSES IN A HALF-PLANE WITH A VERTICAL CAVITY FILLED WITH WATER (THE RATIO OF WIDTH TO HEIGHT IS ONE TO TEN)

Abstract

The problem of mathematical modeling of unsteady seismic waves in an elastic half-plane with a ver-tical rectangular cavity filled with water is considered. The problem of modeling problems of the transition peri-od is an actual scientific problem. A quasi-regular approach is proposed to solve a system of linear ordinary dif-ferential equations of the second order in displacements with initial conditions and to approximate the region un-der study. The method is based on the schemes: a point, a line and a plane. An algorithm and a set of programs for solving flat (two-dimensional) problems that allow obtaining a stress-strain state in complex objects have been developed. To assess the reliability of the developed methodology, algorithm and software package, the problem of the effect of a plane longitudinal wave in the form of a Heaviside function on an elastic half-plane was solved. The numerical solution corresponds quantitatively to the analytical solution. The problem of mathe-matical modeling of unsteady elastic stress waves in a half-plane with a cavity filled with water (the ratio of width to height is one to ten) under seismic influence is solved. A system of equations consisting of 8016008 un-knowns is solved. Contour stresses and components of the stress tensor are obtained in the characteristic areas of the problem under study. A cavity filled with water, with a width-to-height ratio of one to ten, reduces the amount of elastic contour stress.

Keywords

• wave theory of seismic safety, wave propagation, elastic half-plane, Heaviside function, vertical rectangular cavity, water medium, contour stresses