Method of strain analysis of pipelines under landslides: An improved semi-analytical method for softening bending moment-curvature

•Establish a concise landslide thrust mechanical model considering pipe-soil interaction.•Considering the softening bending moment-curvature relationship of pipe section during the plastic stage.•Established a complete strain SAM that considers the interaction between axial and bending deformation of pipelines.•The accuracy of the improved SAM is improved by 20% through FEM and tests data verification. The accurate description of the elastic‒plastic stress‒strain of a pipeline is used to evaluate the risk that the pipeline will undergo failure during a landslide. This paper proposes a complete set of refined semi-analytical methods (SAMs) for pipeline elastic-plastic strain to accurately evaluate the safety of pipelines. First, a concise model for the calculation of landslide thrust is established based on the pipe-soil interaction mechanism as load boundaries of the SAMs. Secondly, the plastic softening bending moment-curvature relationship (BMCR) is derived to establish a difference equation for the deformation of the pipeline during the plastic stage based on the principle of internal force balance of the pipe section, and then the bending plastic strain is calculated accurately. Finally, the axial strain is fully calculated considering the interaction between axial force and bending of the pipeline. The comparison of the results of small-scale landslide tests, large-scale landslide tests, and SAM calculations shows that the improved SAM has good applicability, with 20% better accuracy than traditional methods. In conclusion, the SAM proposed in this paper can effectively guide the design and evaluation of the strain-based design pipeline.