# Analytical Model for the Structural Behavior of Pipelines During Lowering-In
## 2 Modeling of a Pipeline During Lowering-in  
### Segmental Pipeline Model Elements  
Figure 2 [21] shows the construction procedure of the lowering-in of a pipeline. The pipelayers lift the pipeline from the ground surface and pull it down on the centerline of the trench bottom. The gravity loads from the self-weight of the pipeline activate as a force to lower the pipeline into the trench. After one end of the pipeline is lowered into the trench, all the pipelayers subsequently drive along the pipeline at the same speed in the direction away from the lowered end, such that the remainder of the pipeline is lowered into the trench. This lowering-in subjects the pipeline to large deformations and bending loads, producing significant curvature between two zones of the pipeline, the above ground and the bottom of the trench zone [22]. During this process, the pipeline experiences three-dimensional behavior with variable contact boundary conditions at the trench bottom. Therefore, to analyze the structural behaviors of the pipeline during lowering-in, the characteristics described above should be implemented in the analytical model. However, previous analytical models can consider specific loading points and deformations only, without reflecting variable loading and boundary conditions [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. The 3-D behaviors of the pipeline can be simulated by superposition of the vertical plane (\(x\)-\(y\) plane) and lateral plane (\(x\)-\(z\) plane) behaviors. The pipeline in each plane can be partitioned into three zones: (i) contacting soil, (ii) supported by the skid and (iii) suspended by pipelayers. Herein, the geometry continuity and load transfer mechanism for each adjacent zone should be established. The torsional effects on the structural behavior of the pipeline during lowering-in were ignored. The axial forces applied to the pipeline were considered but the deformation corresponding to that forces was not considered. Also, axial forces are assumed to be consistently distributed over the entire pipeline. For the zone contacting soil, the pipeline may be modeled as a Winkler foundation to simplify the pipeline-soil interaction. However, this model, which consists of independent discrete springs, fails to consider the interactions of adjacent spring elements and traction forces at the contact surface between the pipeline and soil. To clearly consider the pipeline and soil interaction, the pipeline contacted with soil can be modeled with a two-parameter beam on an elastic foundation (BOEF, [23; 24; 25; 26; 27; 28; 29; 30]); in this study, pipeline model contacted with soil is referred to as a PCS (Pipeline Contacted with Soil) element. For the zone supported by the skid placed on the ground along the sideline of the trench--as shown in Figure 2--the spacing of the skids is very small compared to the entire length of the pipeline. Consequently, the effect of the skid on the structural behavior of pipeline is negligible. Therefore, this zone is modeled as a series of springs with a single material property representing the skids. Thus, this model is effectively the same as the PCS element and is named a PSS (Pipeline Supported Skid) element. In the lowering-in phase, the lateral displacement of the pipeline is constrained to prevent the pipeline from leaving the skid and the centerline of the trench bottom. Therefore, the dislocations and deformations of the pipeline in the lateral plane are negligibly small in these zones. On the other hand, at the locations where the pipeline is separated from the skid and touches soil, the pipeline has  
Figure 2: Pipeline during lowering-in [21]. a rotational angle in the lateral direction. Therefore, the pipeline in the lateral plane of both zones can be modeled as a rigid beam. Finally, in the zone where the pipeline is suspended by pipelayers, discontinuity of the shear force is developed due to the pipelayer suspending forces and the inflection point appears due to the double bending moments.