Novel Numerical Approach to Analysis of Axial Stress Accumulation in Pipelines Subjected to Mine Subsidence

Mine subsidence can pose a considerable threat to pipeline integrity. Three constituents quantitatively determine the distribution of strains along the pipeline: the function of ground displacements along the pipeline axis; the physical law of soil–pipe interaction due to their relative displacements; and the metal deformation response to axial stress in the pipe. All three are usually well understood, but there is still a small number of successful examples of prediction of stresses in such pipelines. In our opinion, the reasons are the following. First, the law of pipe–soil interaction with a large number of required pipeline elements is highly nonlinear; second, usually the history of ground displacement development is not taken into account even though it may be highly significant. Therefore, in this paper we develop an effective algorithm for axial strain and displacement calculation based on notions of basic and correction solutions. The basic solution is algebraically corrected after each iteration step for the correction solution, which is obtained by a numerically efficient transfer matrix method. The role of the basic solution is rather limited here: first, it determines the choice of the particular type of law of soil–pipe interaction; and second, the resulting solution is considered to be accurate when the basic and correction solutions coincide. The effectiveness of the algorithm is shown with a number of examples. The algorithm is updated to account for the effect of the history of ground displacements on the resulting stress-strain state. Two examples of significant influence of history are given: the first for two consecutive perpendicular mine seam developments; and the second for parallel mine seam development.