The reliability-based design and assessment (RBDA) methodology has gained increasing acceptance in the pipeline industry, largely due to a multi-year PRCI program aimed at establishing RBDA as a viable alternative for the design and assessment of onshore natural gas pipelines. A key limit state of buried pipelines that operate at elevated temperatures is upheaval buckling. The elevated temperatures generate large compressive axial forces that can cause Euler buckling susceptibility. The tendency to buckle is increased at vertical imperfections (i.e. a series of cold formed bends) that primarily occur due to topography. Upheaval buckling in itself is not an ultimate limit state but can lead to high strains, local buckling, high cycle fatigue, expensive remediation measures, and even loss of pressure integrity. The critical forces at which upheaval buckling occurs for typical hill-crest type imperfections present in onshore pipelines cannot be readily predicted using analytical methods. A parametric study is therefore undertaken using non-linear finite element analyses to generate a matrix of upheaval buckling responses. The critical force for the onset of upheaval buckling is then developed using a series of empirical relationships to capture the influences of all key parameters. An upheaval buckling limit state function is subsequently developed by comparing the critical buckling force with applied compressive force, which is a function of operating pressure and temperature differential between the operating and tie-in conditions. The limit state function can be readily implemented in a reliability analysis framework to calculate the pipeline failure probability due to upheaval buckling.

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