This work is devoted to the modification of the grid-characteristic numerical method. We propose using joint structured regular and curved computational grids to describe the complex geometric shape of objects and save computing resources. In subdomains, where possible, we propose use structured regular computational grids conformal with structured curved grids. Moreover, we use different calculation algorithms in subdomains with structured regular grids and with curved grids. The elastic and acoustic wave equations are also jointly solved in various subdomains of the integration domain for a more accurate description of the simulated model. We use the corresponding contact conditions at the boundaries between subdomains with different types of computational grids, different solved systems of equations, and different elastic and acoustic parameters of the media. We have proved in this paper the equivalence of using the contact condition of complete adhesion with the absence of an interface in the case of the same elastic and acoustic properties. The proposed modification of the grid-characteristic method was tested on the problems of studying the earthquake resistance of a bridge over a river and a bridge over a highway.

Recent researches have shown that the damaged areas, calculated using various failure criteria for materials with complex heterogeneous structure are not always consistent with physical experiments and with each other. In this paper, we compare two failure criteria, i.e. the principal stress criterion and the von Mises yield criterion. Also, we compare two models of destruction formation, i.e. the model of fractures and sand model. Using the wave dynamics analysis, we explain the difference in the calculated zones of destruction. We indicate what differences in elastic wave phenomena cause the difference in the calculated fracture zones. We assume that further study of the connection between wave phenomena and destruction of materials will allow to develop more precise failure criteria. To carry out the research, we applied numerical modeling of spatial dynamic elastic wave processes in a nuclear power plant and enclosing rocks. We use the grid-characteristic method on combined regular and structural hexahedral grids to describe the complex shape of the dome of the nuclear power plant with minimal computational costs. Moreover, in this work, we consider an approach for calculating the contribution of dynamic elastic wave phenomena to seismic stability of facilities. This technique can be especially useful in the development and testing of seismic insulation of buildings. We propose a failure formation model that takes into account the contribution of static loads and dynamic loads separately.