Determination of Sealines Elastic Curves and Stresses to be Expected During Laying Operations
Authors: Brando P. , Sebastiani G. 
Published: October 2008

Abstract
The article describes a finite elements calculation procedure to determine sealines elastic curves and stresses expected during laying operations both in presence and in abusence of barge applied tension. The present method overcomes the difficulties encountered by other authors in determining complete curves which tend asymptotically to the stiffened caternary contour when deep water high tension and sealines with low specific gravity are to be considered. This method can also be used for small tension cases in shallow waters where the stiffened catenary formula would provide very high values for the maximum bending moment near the sea bottom. Actually - even in case of zero tension on the bottom - 90° deformation angles can be registered with the bending moments never reaching any critical values. Dimensionless diagrams with tension data, deformation angle and bending moment figures illustrate the complete elastic curve and span the entire range of significance of the considered parameters (pipe weight, stiffness and bottom tension). Problems connected with pipe laying on sloping bottoms and in presence of side currents (requiring a three-dimensional approach) too can be tackled with success.

Introduction
One of the most important aspects of sealines stress analysis is the determination - out of all possible curves - of that particular deflection curve which minimizes pipe stresses during laying operations. This problem - as it is well known - is non-linear hence its solutions besides being very difficult is hard to represents graphically. These difficulties can be overcome in part or totally by the adoption of dimensionless parameters which allow an analytical solution of such problems and may be used for plotting dimensionless curves. The greatest advantage of those dimensionless curves is the overall picture which they provide of the pipe behavior during laying operations. It is then easy to obtain with few elementary calculations the required solutions for the actual cases. While the analysis procedure is valid for any pipe loading conditions we describe here for simplicity sake, the procedure used for the analysis of the plane curve representing the pipe deflection under its own submerged weight. Partial solutions are already available in the literature for such problem and they can be used for comparison. Our analysis procedure consists of a numerical integration similar to %quot;Finite Beam Element, Initial Value Approach" paper submitted by Power and Finn (Ref 2) during this same conference in 1969 suitably modified in order to assure convergence also for high values of pipe axial tension and water depth, which limit the application of the above mentioned method. Besides our method solves the problems resulting from low pipe axial tension and water depth conditions, which limit the validity of other calculation procedures such as the "Stiffened Catenary" methof applied by Dixon and Rutdlege (Ref 3).

Definition of the problem
We consider the deflection of a sealine with one end supported by the sea bottom and the other end clamped on the lay barge. We assume the sea bottom horizontal and non-compressible. Therefore the reactions applied in the point of contact of the pipe on the sea bottom consists of a shear force (To) with zero values of the bending moment (Mo).