On the role of coating defects in the form of cracks for the destruction of the pre-landslide structure

Abstract

In this paper, the block element method is used to construct a model of the pre-landslide state of a block structure consisting of a water-saturated medium and an elastic coating, taking into account the formation of a crack in the coating. The spatial pre-landslide structure occupies an unlimited cylindrical region, in the cross section of which is the third quadrant. It is filled with a medium described by the anisotropic Helmholtz equation, which is extremely fluid among other water-saturated media. Taking into account the physical and mechanical properties of the pre-landslide structure, it is a vertical deformable containment wall with a deformable horizontal coating, called the sarcophagus of the landslide environment. To construct a model that is adequately formulated, we consider the boundary value problem for the three-dimensional Helmholtz equation in the specified domain, taking into account the presence of deformable walls and coverings. The block element method is used to construct an exact solution of the boundary value problem for the accepted coatings on the membrane boundary. The properties of the crack formed in the sarcophagus membrane and the consequences of its development for the destruction of the pre-landslide structure in the constructed model are investigated. All the results constructed for the Helmholtz equations, thanks to the approach outlined in the authors' latest publication in the Reports of the Russian Academy of Sciences, are transferred to materials of various rheological properties.