Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Feasible numerical method for analysis of offshore pipeline in installation Pavel A. Trapper Department of Structural Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, P.O.Box 653, Beer-Sheva 84105, Israel ARTICLE INFO Keywords: Finite difference method Energy minimization Nonlinear analysis Pipeline-seabed interaction Elastic seabed Moving boundary conditions ABSTRACT Feasible numerical method for a structural analysis of a pipeline configuration during the installation process is presented. The method considers the whole pipeline, which is partially suspended and partially laid-on a seabed, as a single continuous segment, and is valid for a complete range of laying angles between 0°–90°, i.e., valid for both S-lay and J-lay configurations. The method accounts for a pipeline–seabed interaction and the pipeline is modeled by means of nonlinear large deformation beam theory. The numerical solution is carried out in an incremental-iterative manner by following the actual pipeline installation process, and thus allowing efficient treatment of pipeline-seabed interaction circumventing the further complexities with contact detection. At each increment, the length of the pipeline is increased and new sequential equilibrium configuration is assessed by direct minimization of a total potential energy approximated as a Riemann sum, which yields algebraic system of nonlinear finite difference equations that is further solved by iterations with Newton-Raphson technique. The simplicity, flexibility and robustness of the proposed method allow to enhance the efficiency of engineering calculations and design. Accounting for a bending stiffness in a suspended part allows analyzing variations in laying angle and lay tension independently. The method convergence is validated and compared with Abaqus. The results are in an excellent agreement. Moreover, the comparison with Abaqus shows that for the selected parameters the assumption that the pipeline is inextensible and unshearable is very reasonable. Representative parametric study is conducted to demonstrate the feasibility of the method. Parametric study considers the effects of laying angle (0°–90°), lay tension, laying water depth (up to 3000 m) and seabed stiffness. 1. Introduction A design of offshore pipelines is a laborious process. The purpose of the design is to achieve an optimal pipeline sizes and material grades to satisfy all the possible loadings and configurations during the pipeline life-time. The most severe stage is usually the pipeline installation (Fig. 1), where the pipeline is usually being subjected to the most severe loading due to the lay effects [1,2]. Consequently, the pipeline con- figuration during the installation should be properly addressed. The design is usually carried out in several stages starting from a general conceptual design, which outcome is a rough estimate of as- sociated cost of the project; and down to a detailed design, which outcome is the final detailed specification for the construction [1]. Since the design is an iterative process, during all its stages numerous pipe-lay analyses, which aim at refining the configuration may be re- quired. In general, pipeline installation is a highly nonlinear 3D process, which involves coupled in-plane and out-of-plane phenomena, such as full pipeline-seabed interaction, lateral buckling, lateral stability under hydrodynamic loads, torsion, sideway walking, etc. In order to capture all these phenomena accurately, a complete dynamic 3D analysis should be performed. Such an analysis can be usually carried out by using commercial software, such as OFFPIPE, OrcaFlex, Riflex, etc. In more involved cases or for more refined analyses even heavier general purpose finite element packages such as Abaqus or Ansys, which are able to perform the full 3D Multiphysics analysis, may be required. These codes can yield accurate results, but they are quite time-con- suming, and therefore are usually appropriate to be applied, if required, only for refined analysis at the final stage of the design, where the detailed specification is defined [3]. Taking into consideration that the dominant first order effects, which define a general pipe-lay configuration are usually static and occur in 2D [3], offshore engineers tend to look for more simple and time-saving ways to perform the analyses, especially at the earlier stages of the design, where preliminary calculations are being per- formed to define a general pipeline configuration and estimate a rough cost of the project. Moreover, simple methods can reveal the relevance of further more sophisticated analyses. Over the past decades there was a series of such techniques pro- posed, both analytical (e.g., [3–5]) and numerical (e.g. [6,7],). Those techniques are usually specific to a particular laying method: S-lay or J- lay technique, which mainly differ by a laying angle (Fig. 1.). Moreover, https://doi.org/10.1016/j.apor.2019.04.018 Received 25 January 2019; Received in revised form 4 March 2019; Accepted 17 April 2019 E-mail address: trapper@bgu.ac.il. Applied Ocean Research 88 (2019) 48–62 0141-1187/ © 2019 Elsevier Ltd. All rights reserved. T