Generalized Response of Marine Pipelines
Authors: Lambroakos K.F. , Remseth S. , Verley R.L.P. 
Published: October 2008

ABSTRACT
The lateral dynamic displacement and strain response of offshore pipelines in storms has been generalized on the basis of scaling considerations. The predicted response has been expressed as a function of four non-dimensional parameters for sand and clay soils. These parameters represent groups of physical quantities that describe the pipeline and the environment. Simulations have been performed to develop generalized response curves for ranges of these parameters. The curves can be used to calculate the response of a pipeline for relatively arbitrary soil and storm conditions. The generalized pipeline response could be used in the development of a sound design methodology.

INTRODUCTION
The computer program PONDUS developed within the PIPESTAB project [1] can be used to calculate the dynamic response, movement and strain, for pipelines during storms. The program includes state-of-the-art models for the fluid-pipe and pipe-soil interaction. Although the program is efficient for this application, repeated simulations with PONDUS are in general costly, time consuming and require a level of expertise to interpret the results. For these reasons it was decided to attempt to scale the pipeline response in order to generalize results.
Successful scaling of this physical problem has several benefits. The pipeline response is expressed in terms of a few non-dimensional parameters that represent combinations of a larger number of physical quantities describing the pipeline and the ocean environment. Thus, the response for pipeline cases of varying size and weight in different storms and soil conditions can easily be calculated from the generalized response. Also, successful scaling can aid the development of pipeline on-bottom stability design procedures.
Scaling of the pipeline response has been achieved on the basis of dimensional analysis and numerical simulations with PONDUS. The simulations were used to verify the non-dimensional parameters and to derive generalized response curves for parameter ranges of pipeline design interest.
The non-dimensional parameters governing the pipeline response are derived in this paper. The paper also gives examples of generalized response curves for selected ranges of these parameters, and addresses the uncertainties associated with these curves. An example of their use is also presented.

2. SCALING OF THE PIPELINE RESPONSE
The scaling of the response is performed on the basis of the equation of motion for the pipeline, assuming first free ends and then ends with constraints that generate stresses in the pipeline. The initial development is performed with the Coulomb soil friction model and a two-dimensional sea (no short-crestedness). The scaling is then extended to the history dependent soil resistance model of the PIPESTAB project [2] and to shortcrested seas.

Pipeline with Free Ends
The equation of motion for pipeline sections far from end constraints or with free ends (Fig. 1) is:(Mathematical equation available in full paper) where m is the mass of the pipeline per unit length, y and t are the pipeline displacement and time, respectively; FD and F1 are the drag and inertia hydrodynamic forces per unit length, respectively, and Fs is the soil resistance force per unit length.
The external forces (FD,F1,Fs) for the moving pipe are defined as follows: (Mathematical equation available in full paper