Об одном обобщенном подходе в проблеме оценки прочности подземных сооружений, параллельных штолен

Abstract

The work is devoted to studying the characteristics of the stress-strain state of underground structures with multiple partitions, for example, thin deposits exposed by a system of parallel horizontal adits. The structure is modeled by a system of Kirchhoff plates located between a linearly elastic layer located on top and a deformable foundation on the bottom. The latter can be modeled both by the elastic layer and by the Winkler foundation. We consider a method for studying boundary value problems for two deformable layers separated by a plate that has a finite number of strip cavities, based on the application of the block element method using the integral factorization method. The described approach allows us to reduce the boundary-value problem to a system of integral equations. In the work we propose a method of approximate factorization of matrix functions with two complex variables, including polynomial ones, in respect to one of the variables with fixed real values of the other. This method can be used to solve the systems of integral equations to which the problems under consideration are reduced, thus finding contact stresses on supports and sagging of adit roofs.