Interference of torsion waves in the underground pipeline caused by the movement of the damaged foundation

Abstract

In this article, we study the strength of underground pipelines, which are operated in difficult mining and geological conditions in area full of tectonic faults. In such seismically active areas, in addition to the pressure load of the transportedproduct, the pipe is subjected to additional effects from the movements of the damaged foundation. When the movements are transient,a dynamic analysis of the behavior of structures must be carried out. The aim of the study is to develop a model to describe the non-stationary process of deformation of the pipeline on the damaged foundation, caused by the sudden mutual reversal of several fragments of the base around the axis of the pipe. The dynamics of the pipeline was investigated in a linear setting, modeling it with an infinite tubular rod. We consider blocks of a basis to be absolutely rigid; the behavior of a thin layer of soil backfill is described with the help of Winkler's hypothesis. The kinematics of mutual rotations of the base fragments is given by discontinuous functions from the axial coordinate. The strength of the pipeline is assessed by summing the standard and non-standard stresses, while the pipe is considered a torque-free shell. This approach makes it possible to assess the strength of the underground pipeline not by the external load from the soil, which is usually unknown, but by the kinematic parameters of the movements of the fault banks. An initial-boundary value problem for the differential equation of torsion with a discontinuous right-hand side has been formulated. Based on the analytical solution of the problem, the influence of the interference of torsion waves excited by sudden reversals of the foundation fragments around the axis of the pipe on the stress state of the pipeline under pressure has been studied. It has been established that the dynamic effects significantly depend on the structure of the breaking movements of the foundation and on the distance between the faults.