A Study of the Stress State of Underground Gas Pipelines in Mine Working Zones Using the Method of Internal Response Function

Abstract

The stress state of pipelines in mine working zones, where the main loading factor is longitudinal soil displacements caused by the gradual filling of mine voids, has been calculated. Differential equations of pipe deformation have been formulated, for the solution of which the method of internal response function is proposed, which takes into account the mutual displacement of the pipe and soil in each iteration using a classical three-part nonlinear model of pipe–soil interaction. The type of interaction is determined on the basis of the concept of the basic displacement of the pipe, which is refined using displacements calculated in the previous iteration. The procedure of refining the basic solution is an important component of the method, where the basic solution in the next iteration is found as the sum of the previous solution and the difference between the calculated and previous solutions, multiplied by the convergence-control factor of the iterative procedure. To check the convergence accuracy and rate of the proposed iterative procedure, a comparative analysis with other existing procedures and results, obtained with the aid of commercial finite element programs, has been performed. To diagnose the stress state of pipelines during the working of longwall faces, a system for their continuous monitoring has been created. The correctness of the results of the performed numerical modeling of the stress state of a gas pipeline and the effectiveness of the measures that are developed to reduce the high stress level in its individual zones have been confirmed by relevant monitoring data, which are important both for refining the physical characteristics of pipe–soil interaction and for further taking into account the relaxation of these relations in time.