## 5 Conclusions  
The current study is a three-dimensional finite-difference analysis on the effect of inserting GECs on the shear behavior of the soil, with a particular emphasis on the use of GECs to improve stability under different scenarios. through changes in various factors  
Figure 14: Failure modes of ordinary granular columns.  
Figure 13: The failure mode in the slope of the embankment before the reinforcement with geogrid encased columns.  
Figure 15: Bending failure mode in the geogrid encased columns.  
such as the area replacement ratio of granular columns, the angle of the embankment slope, and different elastic moduli of geogrid. The analyses were conducted on a clayey sand embankment over a clayey layer. The results indicate that increasing the modulus of elasticity of the geogrid leads to an increase in normalized shear strength and a decrease in lateral displacement in the column. Additionally, the factor of safety increases as the stiffness ratio between the geogrid and the materials increases. However, the factor of safety decreases as the angle of the embankment slope increases. The following points can be concluded:  
* Using geogrid encased granular columns (GECs) can significantly increase the shear strength along the failure plane. The geogrid acts as a reinforcement material that helps to distribute more load and prevent failure.
* The angle of the embankment plays a critical role in determining the failure mode of the slope. As the angle decreases, the failure mode shifts from deep seated, to face failure. This is due to the fact that at lower angles, the soil is less likely to slide.
* The modulus of elasticity of the geogrid can also impact the performance of GECs. At very high modulus of elasticity, the effect of area replacement ratio on the value of factor of safety, is minimal.
* As the angle of the embankment slope decreases, the performance of GECs improves.
* The margin of safety increases as the stability number (m) increases. A higher stability number indicates a more stable slope.
* It is generally not recommended to use GECs for slope protection if the angle of the slope is more than 34 degrees with the horizontal. This is because at steeper angles the soil is more likely to move, and GECs is not effective in preventing failure.
* It was found that the most significant factors affecting the factor of safety are the angle of the slope of the embankment, the modulus of elasticity of the geogrid, the area replacement ratio, and the stability number respectively. These factors were found to have the greatest impact on the overall safety and stability of the embankment.  
Conceptualization, O.H.J. and M.T.; methodology, O.H.J. and M.T.; software, O.H.J.; validation, O.H.J.; formal analysis, O.H.J.; investigation, O.H.J. and M.T.; resources, O.H.J. and M.T.; data curation, O.H.J.; writing--original draft preparation, O.H.J.; writing--review and editing, O.H.J. and M.T.; visualization, O.H.J.; supervision M.T.; project administration, M.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.