# Analytical Model for the Structural Behavior of Pipelines During Lowering-In
## 5 Discussion  
The load and boundary conditions applied to the pipeline which depend on the construction conditions during lowering-in are continuously changing. Therefore, to analyze the structural behavior of a pipeline, these characteristics should be considered. The previous analytical models are well established but they are limited with respect to formalized conditions such as the geometric, load and boundary conditions. The aims of the segmental pipeline model are to properly consider the formalized conditions, especially for the lowering-in conditions of a pipeline and to obtain numerical accuracy, applicability and convenience in the structural analysis. The segmental pipeline model was verified through FE analysis. In addition, assessment of the applicability and convenience was performed with 5 examples, including Models 1 and 2. The segmental model provides a good accuracy and can accommodate the construction features of lowering-in.  
Torsions as well as bending moments are parameters that effect on the three-dimensional behavior of the pipeline. The proposed model and FE model, which based on the beam elements, are ignored the torsional effect on the structural behavior of pipeline. The pipeline-soil interaction of the FE model is implemented by the tangential and normal direction parameters in the surface between the pipeline and the soil as well as the material properties of the soil. Thus, the interaction between the pipeline and the soil, such as the lateral traction force, is considered in FE model. On the other hand, the pipeline-soil interaction of the segmental pipeline model is simplified to a vertical spring and shear layer with Vlasov and Leont'ev formulas. In addition, the proposed model was modeled without pipeline-soil interaction in the lateral plane. The pipeline of proposed model contacted with both the soil and skid in the lateral plane was assumed as a rigid beam. These rigid beams were not modeled in proposed model but the pipeline except for these rigid beams was modeled as Euler-Bernoulli beams. And then, the adjacent boundaries between the rigid beam and the Euler-Bernoulli beam (TDP and SSP in Figure 3) were pin-supported. In addition, the proposed model was assumed to have constant axial force in all cross sections. Such a simplification of the pipeline-soil interaction and lateral plane model lead to main difference from FE model.  
The segmental pipeline model consists of PCS, PSS and PSP elements and each element can be combined to simulate various construction sequences in lowering-in. With these elements, the requirement of continuity in the geometry and sectional forces should be satisfied in the boundaries between each element. In the TDP and SSP positions, the segmental model has a small error in the sectional forces, compared to the FE analysis results. The error of the sectional forces is larger in the lateral plane than in the vertical plane. The boundary conditions suitable for the segmental model are limited to the translation and rotational displacements only. Also, the pipeline-soil interaction in the segmental model is simply considered with vertical springs and shear layers. If the limitation and simplification are implemented strictly into the model, the analysis results become more accurate. However, a rigorous model will be very complicated.