Strain demand of elastic pipes subjected to permanent ground displacements using the finite difference method

Abstract

Long-distance pipelines are one of the primary means of oil and gas transportation. During the construction process, long-distance pipelines are inevitably buried across geohazard zones, which potentially generate permanent ground displacements. These ground displacements can potentially induce excessive strains in the pipe posing a great threat to the pipe’s safety and integrity. In this study, a new numerical methodology for the response analysis of pipes subjected to ground displacements is proposed based on the finite difference method. Simulating the pipeline as a large deformation Euler Bernoulli beam, the finite difference method is used to solve the two interacting nonlinear differential equations of equilibrium in the longitudinal and lateral directions considering the nonlinear pipe-soil interaction induced by the ground displacement. Implemented using the nonlinear equation solver of FindRoot by Mathematica for solving nonlinear equations, the longitudinal strain along the pipeline can be subsequently derived, and the tensile and compressive strain demands can be therefore determined for engineering reference. Finally, the applicability of this method is validated based on two hypothetical study cases involving symmetric and non-symmetric soil resistance on the lateral direction of the pipe. Comparing the results with the finite element analysis solver Abaqus, we demonstrate that this present methodology has excellent predictive capabilities. Our study is carried out for elastic response calculation, but the proposed method shows a great promise for further development involving material nonlinearity, which is appropriate for the preliminary safety evaluation for the design of new pipelines or for risk prescreening of existing pipelines.

Keywords

• Strain demand
• Buried pipes
• Permanent ground displacement
• Finite difference method
• Elastic response