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Dynamic torsion of underground pipeline due to sudden rotation of foundation fragment

In the paper, we study the strength of underground pipelines, which are laid through tectonic faults, and, as a consequence, are operated in difficult mining and geological conditions. In such dangerous areas, in addition to the standard pressure load of the transported product, the pipe is subjected to additional effects from the movements of the inhomogeneous, often damaged, foundation. Predictably, the most dangerous situation is when such movements are transient. The paper aims at developing a model to describe the non-stationary process of pipeline deformation on a damaged foundation caused by sudden mutual rotations of rock blocks around the pipe axis. The dynamics of the pipeline was studied in a linear formulation, modeling it with a rod with a tubular cross-section. The momentless theory of cylindrical shells and the energy concept of strength were used while considering the issues of ultimate equilibrium. The soil backfill was considered as Winkler's elastic layer. Local continuity disturbances of the foundation are described by a sudden rupture of the angle of rotation of its fragment. This approach, developed on the problems of statics, makes it possible to dynamically assess the strength of the underground pipeline not by external load from the soil, which is usually unknown, but by the observed or predicted parameters of the fault edges. We formulated an initial-boundary value problem for a hyperbolic differential equation of torsion with a discontinuous right-hand side. Based on the analytical solution of the problem, constructed in the form of squares from Bessel functions, the influence of the sudden rotation of the foundation fragment around the pipe axis on the stress-strain state of the pipeline is studied. Plots of the space-time distribution of the angle of rotation, angular velocity, torsion deformation and equivalent stresses of von Mises in the prefrontal and postfrontal areas are constructed. It is established that considering dynamic effects leads to an increase in the torsion deformation maxima and the equivalent stress in the pipe wall in comparison with the case of static perturbation.