Underground pipeline strength under non-one-dimensional motion

This paper is devoted to the development of a method for determining longitudinal stresses in underground pipelines under periodic dynamic load, taking into account the complex process of pipe-soil interaction. The method is based on the solution of a two-dimensional axisymmetric unsteady wave problem for the "underground pipeline-soil" system. In this case, the pipeline and soil are taken as linearly deformable bodies. On the surface of their contact, the force of interaction (the friction) is determined from a two-stage (pre-limit and limit) law. The problem is solved numerically - by the finite difference method according to the Wilkins scheme. The changes in longitudinal stresses, velocities, and displacements over time were obtained for various sections of the pipeline and soil. An analysis of the results of numerical calculations showed that when a plane wave propagates along a pipeline with external friction, the hypothesis of flat sections is practically met, which justifies the regularity of considering similar problems in a one-dimensional statement. A multiple increase in the values of longitudinal stresses in the pipeline as compared to the same stresses in soil has been established. The maximum possible value of the stress growth is determined depending on the physic mechanical properties of the pipe material and soil. The role of the interaction force (the friction force) in the multiple increase in longitudinal dynamic stresses in underground pipelines under the effect of dynamic loads was determined.