# Analytical Model for the Structural Behavior of Pipelines During Lowering-In
## 4 Application of the Segmental Pipeline Model  
The number of pipelayers and their locations are key parameters to identifying the structural behavior of the pipeline during lowering-in. Equation (8) represents the vertical displacements of Model 1. Note that Model 1 simulates the pipeline behavior during the lifting construction sequence and it considers only one pipelayer. However, several pipelayers can be added in Model 1 to simulate different construction sequences, which are presented in Table 2. Case 1 considers two pipelayers during lifting construction sequence (Phase 1) and Case 2 considers three pipelayers for the same construction sequence of Case 1. Additionally, Case 3 considers three pipelayers and the construction sequence is the placing the pipeline down into the trench bottom, which is Phase 3 during lowering-in. In Case 3, the lateral behavior of the pipeline should be depicted. In Table 2, LPI to LP3 are the first to third pipelayer and their locations are presented in Table 2. For Case 1, the segmental pipeline model is modeled with three PSP elements due to the presence of one inflection point and one additional lifting point. For Case 2, the segmental pipeline model is modeled with four PSP elements due to the additional lifting point compared to Case 1. For Case 3, the segmental pipeline model is modeled with six PSP elements due to one more inflection point, compared to Case 2. For all cases one PSS element is considered. The analysis results for Case 1 and Case 2 are shown in Figure 10a,b, respectively. The zero-vertical deflection is the initial elevation of the skids. The vertical deflections remain negative up to about a pipeline length of 300 m and the amounts of the vertical deflections are almost identical to the initial deflections caused by the pipeline self-weight. For the range showing positive deflection values, the bending moment increases significantly but becomes zero at the final location of the pipelayers (for instance, LP2 for Case 1 and LP3 for Case 3). The maximum shear force resulting from Case 2 is slightly larger than for Case 1 but the difference is very small. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**LP1**} & \multicolumn{2}{c}{**LP2**} & \multicolumn{2}{c}{**LP3**} \\  & \multicolumn{2}{c}{**(Location of First Pipelayer)**} & \multicolumn{2}{c}{**(Location of Second Pipelayer)**} & \multicolumn{2}{c}{**(Location of Third Pipelayer)**} \\ \cline{2-10}  & \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Displacement**} & \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Displacement**} & \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Displacement**} \\  & & **Vertical** & & & & **Vertical** & & **Lateral** \\ \hline
1 & 380 & 1.5 & - & 400 & 1.8 & - & - & - \\
2 & 365 & 2.4 & - & 385 & 2.5 & - & 400 & 2.4 & - \\
3 & 45 & 0.0 & 0.5 & 65 & 0.5 & 1.5 & 80 & 0.4 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Case examples of the segmental pipeline model. The sectional forces of Case 3 in the vertical plane are larger than those in the lateral plane, as shown in Figure 11. The ratios of the absolute maximum force for Case 1 to Case 2 are about 0.91 for the bending moment and 1.17 for the shear force, respectively. This shows that evaluation of the shear force is needed when the addition of a pipelayer is required for safety. The ratios of absolute maximum force in the lateral direction to the vertical direction are about 0.56 for the bending moment and 0.68 for the shear force, respectively. This indicates that it is necessary to evaluate the sectional forces of pipeline in the lateral direction as well to ensure safety under construction. The case examples show the extension of the segmental pipeline model with increasing pipelayers for both pipeline-lifting and putting construction sequences (lowering-in). In this extension process,  
Figure 11: Analysis results of Case 3: (**a**) vertical plane (x-y plane); (**b**) lateral plane (x-z plane).