Coupled lateral and axial soil-pipe interaction and lateral buckling Part I: Formulation

A general formulation for the two dimensional lateral buckling problem is developed employing classical rod theory. A nonlinear differential system with seven unknowns is derived. Governing equations include a number of previously unaccounted nonlinear terms expressing interaction of various variables representing pipeline geometry and external loads. A rigorous derivation of the transformation of surface loads due to internal and external pressures to line loads revealed some previously unknown limitations on its applicability. Several boundary value problems are formulated corresponding to common pipeline engineering problems. Nonlinear dynamics methods are employed to draw some preliminary results on the behavior of the solutions. It is shown that the trivial solution corresponding to a perfectly straight pipeline experiencing no initial deformation and initial force is unstable.