Elastic Buckling of Thin-Walled Liners Encased in Partially Grouted Pipelines under External Pressure

In this study, the pressure-displacement equilibrium path and the elastic buckling pressure were formulated analytically for a thin-walled circular liner encased in a partially grouted pipeline–liner system. Numerical verification was conducted in the plane strain condition assuming a frictionless interface between the pipeline and the liner. Nonlinear equilibrium equations were developed to obtain the theoretical solutions by employing the principle of minimum potential energy and admissible displacement functions of the liner selected for different pipeline–liner contact conditions. The external pressure increases proportionally with displacement to an initial limit when the liner is not restrained by the pipeline, varies slightly to a lower bound due to geometrical nonlinearity, suddenly increases again to the critical buckling due to pipeline confinement, and finally decreases rapidly in the postbuckling stage. The confinement effect on the buckling pressure of the liner, defined by a ratio of the critical and initial pressures, decreases with an increase of void thickness between the liner and the pipeline. The analytical solution in critical buckling pressure differed from the numerical result by less than 6%. Both the analytical and numerical predictions were consistent with other available closed-form solutions in special cases.