Shear waves around an underground pipeline

Abstract

A two-dimensional axisymmetric problem of shear wave propagation around an underground pipeline under longitudinal motion of the pipeline is solved numerically. Due to the significant difference in pipeline and soil rigidity, the underground pipeline is considered to be a rigid undeformable body and the soil medium around the pipeline is modeled by a viscoelastic law in the form of a generalized Eyring model. To solve the problem, the finite difference method modified by the Wilkins difference scheme was used. On the contact surface of the underground pipeline with soil, the conditions of complete cohesion are fulfilled. Changes over time in shear stress, velocity and soil particles motion in the direction of pipeline axis in fixed sections of soil are obtained. The process of soil displacement around the pipeline at fixed time points is shown. The attenuation of the maximum values of wave parameters in soil in the radial direction with distance from the underground pipeline was detected. The maximum value of shear stress was reduced by three times compared with the value of shear stress at the contact with the pipeline. The effect of the load action time and unloading waves on the wave parameters in soil around the underground pipeline is also obtained. Based on the results of problem solution, the viscoelastic diagram “shear stress - shear strain” is obtained. The results obtained make it possible to determine the mechanism of formation of the stress state and soil reaction to the underground pipeline, which can be used in strength and reliability calculation of the pipelines.