The article discusses the issues of forecasting the strength of underground pipelines laid in seismically active areas through sections composed of relatively rigid moving blocks. In such dangerous areas, in addition to the normal pressure load of the transported product, the pipe is subjected to additional effects from the movements of the fragments of the block foundation. As the literature data show, the problems of the influence of the interaction of faults on the stress state of the pipeline have not yet been studied. The aim of the study is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged foundation caused by static or time-harmonic reciprocal turns of the blocks around the axis of the pipe on both sides of several faults. Static equilibrium and harmonic oscillations of the pipeline are investigated in a linear setting, modelling it with a rod with an annular cross section. The inertia of the transported product is not taken into account. To consider the issues of the ultimate equilibrium of the pipe, the momentless theory of shells and the energy theory of strength are used. The soil backfill is considered as Winkler’s elastic layer. Multiple damages to the solid foundation are presented in the form of several faults on which there is a rupture of the angle of rotation around the axis of the pipe. We formulated boundary value problems for differential equations of static torsion and torsional harmonic oscillations with discontinuous right-hand sides. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetrical reversal of the foundation blocks, the distributions of the torsion angle and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations of the system, are investigated.
Steady time-harmonic oscillations in a linear thermoelastic plate model
