Physical Interpretations of the Instabilities Encountered in the Deflection Equations of the Unconstrained Pipeline

Abstract

For a pipeline modeled as having constant rigidity, horizontal tension, and submerged weight per unit length, there is a maximum value that the maximum sag-bend moment attains as the distance from the pin-supported end of the pipe to the sea floor increases. This paper presents the results of a parametric study analyzing a pipeline displaced from the sea floor to some pipeline construction configuration. The pipeline is modeled as a continuous beam having constant submerged weight per unit length and a constant horizontal tension or force with one end supported vertically by the sea floor. The governing differential equations are solved in terms of dimensionless combinations of the three characteristic variables—the submerged weight per unit length, the flexural rigidity, and the constant horizontal tension. This allows any possible pipeline configuration meeting stated constraints to be analyzed. The analysis performed specifies the maximum sag-bend moment. This maximum sag-bend moment is changed by varying the sea floor vertical force until a further change in sea floor reaction does not give a pipeline configuration. This maximum attainable maximum sag-bend moment is then computed and graphed as a function of the three characteristic pipeline values, the horizontal tension, the flexural rigidity, and the submerged weight per unit length.