Mathematical modeling in the problems of the geodesic control of the stressed-formated state of the gas pipelines at above-ground parts

Abstract

Geodetic methods of monitoring the stress-strain state of gas pipelines in the areas of overhead pipeline crossing involve obtaining discrete data on the deformation of its axis in the form of a set of three coordinates (x, y, z). For their elaboration a mathematical model of the experimental-theoretical method of geodetic control of gas pipelines’ SSS is proposed. The simulation process was performed on the basis of geodetic discrete data, based on which, using the Lagrange interpolation polynomial, the equation of the line of bending of the axis of the gas pipeline was obtained, which allowed to pass further to the bending moments along the entire span. The accuracy of the proposed method has been estimated, which showed that the obtained bending moment diagrams reflect the SSS of gas pipelines with an accuracy of 1.5% in the central part of its span, and with the approach to the peripheral sections the error increases to 6%. It is shown that the obtained expression of the maximum bending moment allows us to form the required number of additional equations for the disclosure of a statically indeterminate system of "gas pipeline-support", taking into account the possibility of fastening on stretch marks. The mathematical model is presented aimed at decomposition of overburden gas pipeline structures, which allows to model the SSS at each of the spans separately within the integral structure.. It is established that additional stretch marks reduce the maximum bending stress by 22%, and in case of loss of one of the stretches of the bearing capacity of the gas pipeline SSS increases by 11.1-14.8% depending on the previous stretch tension. The proposed mathematical model for the processing of discrete data forms the basis of the experimental-theoretical method of geodetic control of the gas pipelines’ SSS, taking into account their structural and technological factors.