OPTIMAL EXCAVATION PROFILE FOR A PIPELINE FREELY RESTING ON THE SEA-FLOOR

A submarine pipeline resting on a rigid, frictionless sea bed assumes an equilibrium configuration which can be determined by solving a unilateral contact problem, i.e. a quadratic program or a variational inequality. Since the sea bed profile is usually irregularly hilly, its regularization is often carried out, in present offshore technology, by costly trench excavations, both in order to avoid excessive bending moments in the pipe and to bury it for protection. Thus, the problem arises of determining profile changes of minimum cost under the condition that an assigned curvature be nowhere exceeded. This optimal design problem is tackled in the paper with reference to a discrete model of the mechanical system, as the minimization of a linear cost function under linear constraints and a single, nonlinear and non-convex, complementarity constraint. A theory is developed which reduces this nonlinear programming problem to a sequence of linear programs, the optimal solutions of which are shown to converge to the original NLP solution. Upper and lower bounds on the absolute minimum cost and optimality conditions are established, on the basis of duality theory in linear programming. An algorithm suitable for solving the problem in a finite number of steps is proposed. Generalizations obtained by relaxing some of the simplifying hypotheses are considered. © 1979.