Wave Theory of Seismic Resistance of Underground Pipelines

Abstract

The object of the research is an underground straight horizontal pipeline subjected to seismic impact. The research method was analytical. The results were compared with the experimental results of other authors and computer calculations. It was shown that the main disadvantage of the dynamic theory of seismic resistance of underground pipelines is the neglect of the dynamic stress state in soil under seismic wave propagation. The next drawback of the dynamic theory is an inaccurate, approximate accounting for the displacement of the soil medium to which the underground pipeline is embedded. The complete interaction process includes the stages of nonlinear changes in the interaction force (the friction force) by manifesting its peak value and the Coulomb friction. The contact layer of soil undergoes shear deformations until complete structural destruction of the soil contact layer. The interaction force is the friction force, and its peak value does not appear. The seismic resistance of underground pipelines should be considered based on the theory of propagating seismic waves in a soil medium and the interaction of seismic waves with underground pipelines, i.e., based on the wave theory of seismic resistance of underground pipelines. A one-dimensional coupled problem of seismic resistance of underground pipelines under seismic impacts was posed based on the wave theory. An algorithm and a program for the numerical solution of the stated wave problems were developed using the method of characteristics and the method of finite differences. An analysis of the laws of interaction of underground pipelines with soil under seismic influences shows that it is necessary to use in the calculations the laws of interaction that account for the complete interaction processes observed in experiments. The analysis of the obtained numerical solutions and the posed coupled problems of the wave theory of seismic resistance of underground pipelines show the occurrence mechanisms of longitudinal stresses in underground pipelines under seismic influences. The results of calculations stated that an account for the dynamic stress normal to the underground pipeline’s outer surface leads to multiple increases in longitudinal stress in the underground pipeline. This multiple increase is due to the transformation of the interaction force into an active frictional force, resulting from a greater strain in soil than the one in the underground pipeline. Based on the analysis results, a theory of the seismic wave propagation process in an underground pipeline and surrounding soil was proposed.

Inertia force effect on longitudinal vibrations of underground pipelines

“…In the works [7][8], the use of different mechanical mathematical models was analyzed, and several urgent problems of underground and ground structures were solved.…”

Transverse Vibrations of Underground Pipelines with Different Interaction Laws of Pipe with Surrounding Soils

“…To date, in domestic and foreign science, there are theoretical and experimental studies for determining the stress-strain state [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and stability [17][18][19][20][21][22][23][24] of underground pipelines interacting with the surrounding soil under seismic effects. A theory of propagating seismic waves in an underground pipeline and surrounding soil called the wave theory of seismic resistance of underground pipelines is proposed in [12]. According to linear and nonlinear laws, this theory is used to analyze only longitudinal vibrations of a pipeline interacting with homogeneous soil.…”

“…This is especially important for long pipelines buried in the ground and stretched over large areas, where soil conditions change significantly. In this case, the behavior of the pipeline mainly depends on the choice of the law of its interaction with the surrounding soil, which in the simplest cases is characterized by the interaction coefficients determined from experiments [5,7,11,12].…”

Quasistatic elastic-plastic loading and unloading of rods with coulomb dry friction

“…In works [1][2][3][4][5][6][7][8][9][10][11], the problem of quasistatic loading of structural elements in the form of an elastic rod interacting with its environment according to the Coulomb dry friction law was formulated and solved. It is known that in the problems of longitudinal vibrations of rods interacting with soil media, attention is drawn to the fact that in certain situations, it is possible to neglect the inertial terms in the equations of motion (works [12,16,20,21], etc.)…”