# Static and Seismic Responses of Eco-Friendly Buried Concrete Pipes with Various Dosages of Fly Ash
## 6 Static and Seismic Analysis
### Static Analysis of GPC Underground Pipe
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mix**} & \multirow{2}{*}{**\% FA**} & \multicolumn{2}{c}{**NoOH**} & \multicolumn{2}{c}{**Na\({}_{2}\)SiO\({}_{3}\)**} & \multicolumn{2}{c}{**Water**} & \multicolumn{2}{c}{**Na\({}_{2}\)SiO\({}_{3}\)**} & \multicolumn{2}{c}{**NaOH Molarity**} \\  & & **(gr)** & **(gr)** & **(mL)** & **NaOH** & **(M)** & **AS/FA** \\ \hline PF7030A & 30 & 250 & 625 & 1500 & 2.5 & 4.16 & 0.25 \\ \hline PF7030B & 30 & 250 & 625 & 1500 & 2.5 & 4.16 & 0.25 \\ \hline PF5050B & 50 & 428 & 1070 & 1500 & 2.5 & 7.13 & 0.25 \\ \hline PF3070B & 70 & 600 & 1500 & 1500 & 2.5 & 10 & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The details of concrete mixtures with different ratios of AS for dosages of 30%, 50%, 70% FA. The movement of the GPC underground pipe is in coordination with soil under static loadings. It is possible to assess that the magnitude of the vertical displacement for the GPC pipe with diverse dosages of FA is commonly less than that of the horizontal displacement when comparing the force-displacement graphs which are shown in Figures 18-23. Indeed, Figures 18-23 demonstrate the comparison of the GPC pipe response for both vertical and horizontal displacements with the values of 0% to 70% FA as a raw material of the GPC pipe in which the compressive strength of this concrete type is experimentally examined in this study (Tables 11-13) and other equivalent parameters are also defined in the model (Table 14). These graphs demonstrate that the vertical displacement of GPC pipes subjected to static loading is much higher in comparison with the horizontal displacement of underground GPC pipes. Figure 18 shows that the variation of the vertical displacement for the GPC pipe with 0% FA as benchmark case is 0.035842 m which is roughly 3.56 times the amount of the horizontal displacement. In addition, Figure 23 shows a significantly higher vertical displacement in the FE analysis under static loadings for the GPC pipe with 70% FA, so that, the vertical displacement is 5.67 times the horizontal displacement. The values of vertical and horizontal displacements for this GPC pipe model are 0.055327 m and 0.009748 m, respectively. For numerical simulations of GPC pipes with 10%, 20%, 30%, and 50% FA, based on Figures 19-22, it is found that the values of the vertical displacement for 10% and 20% are 1.92 times compared to horizontal displacements showing no change with adding the FA content by 10%, whereas the GPC pipe model including 30% FA has a vertical displacement which is 3.61 times the horizontal displacement. This trend is dramatically enhanced for the GPC pipe involving 50% FA so that the values subjected to a vertical displacement are approximately 5.7 times those of the horizontal displacement. Figure 17: The typical vertical displacement of the GPC pipe. Figure 19: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 10% FA. Figure 18: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 0% FA. Figure 21: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 30% FA. Figure 20: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 20% FA. Figure 23: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 70% FA. Figure 22: Horizontal and vertical displacements at node 20, element 1126 with coordinate details: (\(x=0\), \(y=0.25\), \(z=-4\)) and 50% FA. Eventually, the optimal performance of the underground GPC pipe, as the lowest vertical and horizontal displacements under static loadings, is numerically achieved for the FE model with the inclusion of 20% FA among all the GPC mix designs investigated in this study (Figure 24).