Analytical solution of pipeline upheaval buckling considering bi-linear axial pipe-soil interaction model

Under thermal loading, upheaval buckling of subsea pipelines occurs when the axial compressive force exceeds the critical buckling load. In order to accurately predict the upheaval buckling behaviour of subsea pipelines, the axial pipe-soil resistance should be considered more precisely, rather than traditionally treated as rigid-plastic in prior analytical researches on pipeline upheaval buckling. Consequently, this study integrates a bi-linear axial pipe-soil resistance model into the mathematical framework of upheaval buckling. This mathematical model incorporates the von-Kármán type of geometrical nonlinearity and the Euler-Bernoulli beam theory. The research examines typical upheaval buckling behaviour and investigates the influence of axial mobilization distance and ultimate resistance on pipeline upheaval buckling behaviour. The results reveal that incorporating bi-linear axial pipe-soil resistance, in contrast to rigid-plastic resistance, leads the pipeline more susceptible to buckling. Displacement amplitudes increase with the axial mobilization distance during the post-buckling stage. Notably, a larger axial mobilization distance exerts a stronger influence on pipeline buckling. Moreover, the critical buckling temperature exhibits an almost linear negative correlation with axial mobilization distance and a positive correlation with axial ultimate resistance. Additionally, greater axial ultimate resistance magnifies the impact of axial mobilization distance. Therefore, in pipeline buckling design, it is advisable to consider a more sophisticated axial pipe-soil model to accurately account for these complexities.