## 5 Results and Discussion
### Strain Distribution  
#### 5.3.1 The Influence of Impact Height  
Figure 16a shows a comparison of the strain--time (\(\varepsilon\)-\(t\)) curves at the mid-span position (B-B)2 between the depicted results from FEA and the measured results from the experiment (EXP) under different impact heights (\(H\)); additionally, a comparison of the peak strains (\(\varepsilon_{\text{max}}\)) at position (B-B)2 among the FEA, EXP, and theoretical (THE) results is also presented in Figure 16b. It can be found from Figure 16 that a generally good agreement was achieved among the FEA, EXP, and THE results, which shows that the developed FEA model has a reasonable precision for predicting the strain of buried pipelines under impact loads. Furthermore, it is shown that \(H\) had a significant influence on the mid-span strain, and the \(\varepsilon_{\text{max}}\) increased with the increase of \(H\). When \(H\) reached 2 m, the predicted \(\varepsilon_{\text{max}}\) from FEA was 763 \(\mu\epsilon\) and the position of \(\varepsilon_{\text{max}}\) was as presented in Figure 17d below.  
The influence of impact height (\(H\)) on the strain distribution of specimens is depicted in Figure 17. It can be found that the maximum strain area occurred at the mid-span and increased with the increase of \(H\), which matches well with the experimental and theoretical results.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multirow{2}{*}{**Specimens**} & \multicolumn{3}{c}{**The Peak Strain in Test**} & \multicolumn{3}{c}{**The Peak Strain in Theory**} & \multicolumn{3}{c}{**The Peak Strain in FEA**} \\ \cline{3-8}  & & \(\varepsilon_{\text{L}}\) (\(\mu\epsilon\)) & \(\varepsilon_{\text{T}}\) (\(\mu\epsilon\)) & \(\varepsilon_{\text{max,EXP}}\) & \(\varepsilon_{\text{max,THE}}\) & **The Relative** & \(\varepsilon_{\text{max,FEA}}\) & **The Relative** \\  & & & **(\(\mu\epsilon\))** & **(\(\mu\epsilon\))** & **(\(\mu\epsilon\))** & **Deviation** & **(\(\mu\epsilon\))** & **Deviation** \\ \hline \multirow{4}{*}{A} & A114 \(\times\) 2.5-d0.6-H0.5 & 354 & 295 & 328 & 348 & 6.09\% & 309 & 5.79\% \\  & A114 \(\times\) 2.5-d0.6-H1.0 & 621 & 424 & 549 & 575 & 4.73\% & 563 & 2.10\% \\ \cline{1-1}  & A114 \(\times\) 2.5-d0.6-H1.5 & 724 & 545 & 645 & 685 & 6.20\% & 658 & 2.02\% \\ \cline{1-1}  & A114 \(\times\) 2.5-d0.6-H2.0 & 816 & 603 & 733 & 792 & 8.18\% & 763 & 4.09\% \\ \cline{1-1}  & B89 \(\times\) 2.5-d0.6-H1.0 & 489 & 321 & 425 & - & - & 386 & 9.17\% \\ \cline{1-1}  & B139 \(\times\) 2.5-d0.6-H1.0 & 774 & 695 & 737 & - & - & 784 & 6.37\% \\ \cline{1-1}  & C114 \(\times\) 3.0-d0.6-H1.0 & 456 & 367 & 418 & - & - & 422 & 1.20\% \\ \cline{1-1}  & C114 \(\times\) 3.5-d0.6-H1.0 & 387 & 204 & 232 & - & - & 215 & 7.32\% \\ \cline{1-1}  & D114 \(\times\) 2.5-d0.3-H1.0 & 1005 & 768 & 955 & 1032 & 8.06\% & 1015 & 7.40\% \\ \cline{1-1}  & D114 \(\times\) 2.5-d0.9-H1.0 & 205 & 165 & 190 & 205 & 7.89\% & 202 & 5.78\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The peak strains of specimens.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**\(H\) (m)**} & \multirow{2}{*}{**Soil Type**} & \begin{tabular}{c} **Quality of Drop** \\ **Hammer (kg)** \\ \end{tabular} & \begin{tabular}{c} **Test Results** \\ **(\(\textbf{{F}}_{\text{max,EXP}}\)) (kN)** \\ \end{tabular} & \
\begin{tabular}{c} **Theoretical Results** \\ **(\(\textbf{{F}}_{\text{max,THE}}\)) (kN)** \\ \end{tabular} &
\begin{tabular}{c} **FEA Results** \\ **(\(\textbf{{F}}_{\text{max,FEA}}\)) (kN)** \\ \end{tabular} \\ \hline
0.5 & Clay & 337 & 67.737 & 61.690 & 65.652 \\
1.0 & Clay & 337 & 126.817 & 115.186 & 117.841 \\
1.5 & Clay & 337 & 150.463 & 136.483 & 140.462 \\
2.0 & Clay & 337 & 181.982 & 163.780 & 173.654 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Peak impact force (\(F_{\text{max}}\)) under different impact heights (\(H\)). FEA—finite element analysis.