# Static and Seismic Responses of Eco-Friendly Buried Concrete Pipes with Various Dosages of Fly Ash
## 6 Static and Seismic Analysis
### The Response of GPC Pipe under Seismic Loadings for Critical State  
The numerical results of the time-history analysis are presented for the induced crown displacement on the upper half of the GPC pipe due to applying the records related to the Tabas earthquake with the peak value of 0.092 m (Figure 10). It is worth noting that the developed model predicts the crown displacement of the GPC pipe with excellent precision. A comprehensive attempt is made at this point to simulate the FE model exactly based on the existing reality in the construction industry considering the valid standards such as ACPA and AASHTO regarding the soil properties and pipe geometry. Based on Figure 25, it can be seen that the maximum value of vertical displacement for the GPC pipe with 0% FA is approximately 0.145 m which is higher than that of GPC pipe with 20% FA with the reduced value of 0.1339 m showing the percentage difference of 8%. Furthermore, the developed FE model enables the prediction of the tendency of the displacement-time relationship as obviously indicated in Figure 25.  
In the case of horizontal displacement, it can be found that there is no remarkable change between two types of the GPC pipe model containing 20% and 0% FA so that the maximum amount of horizontal displacement for the GPC pipe without FA content is around 2.6% higher than that of the GPC pipe model with 20% FA (Figure 26). However, these values belonging to vertical and horizontal displacements of the FE model under seismic loadings are much higher compared to the data corresponding to the static analysis numerically investigated. In addition, node 1 with the coordinates of \(x=0\), \(y=0\), \(z=0\) has been chosen to evaluate the performance of fixed-support at two ends of the GPC pipe under seismic loadings in this study. The implication of these findings is presented in Figure 27. It can be seen that the maximum values subjected to the reaction force in fixed-support of the GPC pipe with 0% and 20% FA are 18,179.3 N and 18,094 N, respectively.  
When comparing the above-mentioned results to those of other earthquakes, for instance, the Friuli earthquake that occurred in Italy (1981), it is useful to point out that a marginal reduction in the case of vertical displacement can be seen with what has previously been found for the Tabas earthquake. As shown in Figure 28, the vertical displacements after applying the records related to the Friuli earthquake are approximately 0.138 m and 0.137 m for underground pipes with the inclusion of 0% and 20% FA, respectively. However, no significant change was observed in the case of horizontal displacement between two types of buried pipe models (0% and 20% FA) under the seismic loading of the Friuli earthquake in Figure 29. Collectively, the results for the underground pipe under the two earthquakes with fully-distinctive data follow from the fact that the efficiency of FA as PC replacement in the decrement of pipe response, especially vertical displacement, under seismic loading with high acceleration is more tangible than that with a lower amount, given that the peak value of acceleration belonging to the Tabas earthquake is around 14 times the value corresponding to the Friuli earthquake.  
Figure 26: Comparison of time-history curves for horizontal displacement of the pipe crown with the inclusion of 20% and 0% FA due to the Tabas earthquake.  
Figure 25: Comparison of time-history curves for vertical displacement of the pipe crown with the inclusion of 20% and 0% FA due to the Tabas earthquake.  
Figure 28: Comparison of time-history curves for vertical displacement of the pipe crown with the inclusion of 20% and 0% FA due to the Friuli earthquake.  
Figure 27: The comparison of the reaction force of fixed-support in the time-history analysis under different FA dosages (**a**) 0% FA, (**b**) 20% FA.