# Static and Seismic Responses of Eco-Friendly Buried Concrete Pipes with Various Dosages of Fly Ash
## 7 Summary and Conclusions  
In this study, the William-Warnke failure criterion and the modified Popovics model were presented for the nonlinear behavior of underground GPC pipes to illustrate the response of stress-strain for underground GPC pipes with diverse values of FA. To objectively evaluate the nonlinear performance of an underground GPC pipe exposed to static loading, the displacement of node no. 20 in element 1126 located in the region of the pipe crown is taken into account as the critical zone in the middle of the GPC pipe. The value of this displacement varies based on the material properties of the concrete with the variety of FA content defined in the FE model.  
The following conclusions are drawn:  
* The numerical results of the static analysis demonstrate that the highest value of displacement occurs in the middle of the GPC in which traffic load and fault displacement were utilized as the two types of static loads in this study. The output of numerical results indicated that the dosage of FA in the range of 10-30% has a key role in the improvement of the optimal displacement in static analysis.
* As regards the time-history analysis, based on the displacement records from two distinctive actual earthquakes (Tabas, Iran in 1979; Friuli, Italy in 1981), it was proved that the inclusion of FA in the GPC pipe has a significant role in the improvement of the vertical displacement in the underground model compared to horizontal displacement as it was observed in the static analysis as well.
* In conclusion, it would appear that the role of FA on the improvement of the vertical response of the GPC pipe under seismic loading with high acceleration is more visible compared to the other earthquakes with low acceleration.  
In addition, the assumptions and limitations used in this study are given as follows:  
* The concrete properties of the GPC pipe for linear and nonlinear behavior of the GPC pipe are based on the findings experimentally obtained in this study, such as compressive strength, density, and other parameters numerically validated in this field.
* The trench simulated in the ANSYS platform is composed of stiff clay for bedding and sidefill soil along with silty clay for backfill soil.  
Despite the fact that this study can distinguish the initial assessment regarding the response of a GPC pipe with various percentages of FA under static loading, further  
Figure 29: Comparison of time-history curves for horizontal displacement of the pipe crown with the inclusion of 20% and 0% FA due to the Friuli earthquake.  
explorations including more details on significant factors and parameters as a key role in the development of GPC pipe response are needed.  
As regards time-history analysis for seismic loading, the numerical results are widely accepted in case of the response of GPC pipe under seismic loading which can be considered as the great breakthroughs in this field; nevertheless, there are several limitations over the implementation of each step of the FE analysis. The major source of limitation is due to the lack of previous studies related to GPC pipes under seismic loading so that we are unable to compare the current findings with those in preliminary studies to reach the yield answer about the performance of this concrete pipe type against applied static and seismic loadings. Therefore, the necessity of utilizing a parametric study to identify the main factors playing a key role in the improvement of GPC pipe response as well as the quantitative evaluation of these parameters needs to be centralized in upcoming studies.  
Both authors ([PERSON] and [PERSON]) equally contributed to the present work. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data reported in this study can be found in the sources cited in the reference list.  
The authors declare no conflict of interest.