An analytical analysis method for spanning pipelines with vertical imperfections under different loading conditions is presented. Analytical solutions for the pipe configuration, stress distributions, and contact reaction load to the crossed object are obtained under tensile or compressive axial loads by solving the governing differential equations. A comparison of this analytical method with the finite element method is carried out to evaluate the accuracy and consistency of the solutions. This analytical approach may be very helpful for obtaining preliminary results in a limited time without using the more time-consuming and expensive finite element method.

The analytical model accounts for the vertical pipe-soil interaction and drives the solution for the mechanical response of pipeline at the touchdown points of the spanning pipeline. Parametric analyses of the spanning pipeline are carried out to investigate the influences of the span length, vertical imperfection magnitude, and soil stiffness on the mechanical response of the pipeline.

A simplified analytical method for the span segment only is given to compare with finite element analysis. A correlation of dimensionless span length and dimensionless effective axial force is obtained based on the simplified analytical method for different vertical offsets and axial force (tensile or compressive load). The comparison results show that the simplified analytical method may be used as for a quick engineering calculation when the pipe soil-interaction is not clear.

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