Based on existing data of experimental studies of underground structure-soil interaction, a condition for boundary interaction between the underground pipeline and soil was developed. The proposed condition (a model) of interaction at the contact boundary takes into account the structural destruction of the contact soil layer and the cyclical nature of interaction process. The authors have shown by parametric analysis of the interaction model, that under cyclic interaction of the underground pipeline with soil, the structural disturbance of the soil contact layer does not reach the peak shear stress; the applicability of the problems of underground structure-soil interaction is also shown. The model of interaction on the contact structure-soil surface in particular cases passes into the existing conditions of interaction, including Coulomb friction.

A method of numerical solution of one-dimensional problem of cylindrical shear wave propagation in an elastic and elastic-plastic soil is developed in the article using the finite difference method. The numerical results obtained are presented in the form of graphs. From the results obtained, the attenuation of the parameters (shear stress, shear strain, and angular velocity) of cylindrical wave propagation with distance in an elastic and elastic-plastic soil was determined. The attenuation of waves with distance is justified by the dissipation of strain energy on the expanding cylindrical soil layer. In the case of load exceeding the elastic limit, plastic strains occur in soil near the point of load application. The boundaries of elastic-plastic strain of soil are determined.

The unsteady-state axisymmetric problem of longitudinal interaction of a cylindrical body with external elastic medium is considered in the paper. The condition of Coulomb friction is accepted at the contact boundary. The solution is implemented by the finite difference method. The results are shown in graphs and analyzed. The changes in stress, velocity, and displacement of particles at some points of a cylindrical body and external medium are presented. An increase in longitudinal stresses and particle velocities in the cylinder was determined when compared to a given load due to the outflow of strain energy from the external medium. The mechanism of strain energy redistribution and friction forces formation is shown, the changes in the direction of contact forces action are revealed. A significant violation of the uniform deformability of the medium, and possible maximum value that occurs in a cylindrical body, is determined. The established dependences of tangential stresses on relative displacements qualitatively coincide with experimental data obtained during the interaction of fragments of underground pipelines with soil.

Solution of the problems of longitudinal interaction of underground pipelines with soil in a one-dimensional statement requires precise measurements of the thickness of the soil layer contacting with the pipeline. In order to determine the dimensions of the contact layer of soil, the behavior of soil medium under shear interaction of a rigid body with soil is studied. Under straining in soil medium, structural changes denoted by the coefficient of structural destruction are taken into account; the condition of complete adhesion is taken in the contact rigid body – soil boundary. The interaction process under consideration is investigated numerically by the finite difference method. The results of the calculations are presented in the form of graphs and are analyzed. From the obtained results, the maximum values of the thickness of soil contact layer are determined as well as the layers with the corresponding degree of structural destruction depending on the geometric dimensions of the rigid body.

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.