۱٫ Introduction

۲٫ Mathematical Formulation of the Problem

۳٫ Grid-Characteristic Method

۴٫ Sequence of Nested Hierarchical Grids

۵٫ Dependence of Destructions on the Hypocenter Depth

۶٫ Conclusions

Acknowledgements

References

The purpose of this work was the numerical simulation of dynamic wave processes in heterogeneous media with the subsequent evaluation of their influence on various structures. The effect of earthquakes on ground buildings and underground structures was studied. In the work, we used the grid-characteristic method, which allows taking into account the physics of arising wave processes. The use of hierarchical grid systems allows the calculation of seismic waves directly from the earthquake source to ground-based buildings and underground structures. The work investigated the destruction of high-rise buildings under the influence of seismic loads. The emerging areas of fractures in various structures were studied. The effect of the earthquake on the underground structure was considered. The influence of the depth of the earthquake source was analyzed. Images of wave processes in structures and places of destruction were obtained. Note that we do not calculate the damage caused by falling of some collapsed parts of the building to others, but we calculate only damage caused directly by seismic activity. This type of damage is of the greatest interest, since it is necessary to avoid precisely this primary destruction. Also we investigate the nature of this type of damage, e.g, internal, near the surface, causing collapse, asymmetric. The novelty of the approach used also lies in the fact that we solve a linear elastic wave equation with constant coefficients in various subdomains of the integration domain, between which contact conditions are established. And the size and shape of these subdomains vary over time and depend on the solution. That is, the complete boundary problem of the elastic wave equation is nonlinear.

Introduction

The earthquake is shocks of the ground and earth surface oscillations. Earthquakes reflect the process of geological transformation of the planet. The main cause of earthquakes are global geological and tectonic forces, at present their nature is not entirely clear. Temperature inhomogeneity in bowels of the earth causes the appearance of geological and tectonic forces. Most earthquakes occur on contacts of tectonic plates.