On the theory of global factor influence on the strength of a set of parallel connections of layers

Abstract

We consider the problem of estimating the strength of facilities such as underground structures placed in materials with armature cavities, fixtures such as diaphragm wall interlayers arranged in parallel in multilayer structures and forming some sets. Traditionally, studies are carried out for an individual fixture and then the parameters found are accepted for all other facilities. At the same time a plurality of such facilities may lead to the occurrence of another factor badly affecting the strength. This factor is associated with the capability to localize the state of strain in one of the structure zones, which results in exceeding the planned strength parameters. In the present work, as a practical example of the theory for calculation of the strength properties of these objects, underground structures are investigated. The block element method having its origin in factorization approaches forms the basis of our research. The problem is reduced to the system of Fredholm integral equations of the second kind. We have succeeded to reduce the system of integral equations to that of algebraic equations, which are accessible to the analytical analysis allowing finding the localization of strain and shift during the calculation of integrals describing the kernels of these equations by the theory of residue. An algorithm realizing this investigation is presented. The applicability of factorization methods for such problems is discussed.