# Analytical Model for the Structural Behavior of Pipelines During Lowering-In
## 1 Introduction  
A pipeline experiences large deformation and high stress during the construction process, especially during lowering-in. API STANDARD 1104-Appendix A limits the maximum stress during the construction sequence to 75% of the yield stress and defines it as the Specified Minimum Yield Strength (SMYS). In addition, this standard encourages a pipeline stress level check accompanied by construction procedure analysis, defined as an Engineering Critical Assessment (ECA) [1]. The finite element (FE) model, which has a strictly implemented boundary condition, can provide accurate analysis results but it requires large model preparation and computational times. On the other hand, the analytical model can offer a considerably shortened analysis time while providing appropriate response results, even though the analytical model has somewhat less accuracy than the FE model. An elastic beam model partitioned or segmented according to the geometric deformation and loading condition was proposed by [PERSON] et al. [2] and [PERSON] et al. [3]. However, the proposed model has a limitation since the factors adopted for the analysis are determined by experience. Furthermore, the demand for continuity of the rotational angle at the boundary between each beam element is not satisfied since the boundaries are simplified into free or fixed ends. The proposed models are inconvenient as the factors adopted for the analysis were determined by construction conditions based on experience. Therefore, these models are unable to simulate various states of lowering-in. Most analytical models for the structural behavior of buried pipelines mainly deal with the soil-pipeline interaction and stresses on pipeline. The simplest analytical modeling of a buried pipeline was proposed by [PERSON] and [PERSON] [4] and [PERSON] and [PERSON] [5]. In this model, the pipeline is assumed to be dominated by the deformation of the ground, so soil pipeline interactions cannotbe considered. [PERSON] et al. [6] and [PERSON] and [PERSON] [7] have proposed an analytical model for a quasi-static analysis considering the soil-pipeline interaction. This model is based on a spring supported beam to simulate buried pipelines. Although the analytical model can be estimated the axial deformation but the cross-section response of a pipeline may not be expressed in the model. To overcome this drawback, a shell models for pipelines have been developed [8; 9; 10]. Subsequently, [PERSON] et al. [11], [PERSON] et al. [12] and [PERSON] and [PERSON] [13] have proposed the soil-pipeline interaction using a plane strain model for the 3-D analysis of a pipeline. The cross sectional buckling and radial displacement can be evaluated using these models. However, in this shell modeling approach, it is difficult to consider the complete soil-pipeline interaction. Also the analysis procedures involve a series of equations, which in turn require intensive computational effort [14]. Another analytical model for the structural performance assessment of a pipeline buried in a fault zone was proposed by [PERSON] et al. [15]. This model is assembled with both the beam on an elastic foundation (BOEF) and a cable element. However, this model does not correctly assume the maximum bending stress in an actual fault zone. [PERSON] and [PERSON] [16], [PERSON] et al. [17] and [PERSON] and [PERSON] [18] tried to overcome this shortcoming by modeling the pipeline partitioned with BOEF and a Euler-Bernoulli beam, as shown in Figure 1. In these models, the axial force of the pipeline due to fault displacement is appropriately considered but the axial forces are absent in the BOEF zone. Also, in the fault zone, the pipeline is modeled with the specified deformation and partitioning points. Due to its features, it is difficult to apply these models for the analysis of the lowering-in phase. [PERSON] and [PERSON] [19] developed natural catenary theory, forming the stiffened catenary theory to solve the pipeline laying problem.