## 1 Introduction  
The stability of slopes is a crucial topic in the field of engineering because a failure in a slope can result in severe consequences for adjacent structures and infrastructure, therefore, in the current study, protection of slopes of an embankment was studied. The failure of the slope is mainly related to the amount of shear strength along the slip surface in the soil. Failure happens once the shear stress exceeds the shear strength of the soil. Some solutions, such as passive piles, retaining walls, soil nailing, deep mixing columns etc., have been proposed by different researchers to increase the dragging forces at the slip surface [1; 2; 3; 4; 5; 6; 7]. However, the bearing capacity and the stability of the soft soil under the embankment can also be improved by using rigid inclusions. Using geosynthetic-encased granular columns to oppose the path of the slip surface and reduce the potential failure of the slope has recently attracted the attention of some researchers. Granular columns that stabilize slopes behave similarly to passive piles [8]. Their stiffness is the main difference between them [8]. There is a piece of good evidence that granular columns have been used to increase the bearing capacity and the safety against sliding [9; 10; 11; 12; 13; 14]. [PERSON] et al. [15] used a small-scale model to examine the effect of granular column inserted vertically in the clay and it was concluded that the factor of safety was increased by 1.18-1.62 times, also using granular columns increased the bearing capacity and decreased the settlement. [PERSON] et al. [8] conducted an experimental and numerical analysis to study the impact of slope-stabilizing granular columns on the bearing capacity of a rigid strip footing installedon a sand slope in which concrete piles and ordinary and encased granular columns were investigated. According to the outcomes of the study, the bearing capacity of the soil under the footing was reported to be increased as the stiffness and granular column spacing decreased. The use of geotextile-encased granular columns (GECs) as a reinforcement method for sandy slopes is a promising approach for improving slope stability. Geotextile-encased granular columns are similar to ordinary granular columns, but they are wrapped in a layer of geotextile material, which can help to improve the performance of the columns and increase their effectiveness as a reinforcement method. According to [PERSON] et al. [16], the use of GECs was found to significantly increase the factor of safety of a sandy slope, with an increase of up to 37%. The GECs were also found to increase the bearing capacity of the slope foundation by 1.66 times compared to using ordinary granular columns (OGCs) without a geotextile wrap. These results suggest that GECs can be an effective way to reinforce sandy slopes and improve their stability and performance. [PERSON] et al. [17; 18] carried out a research project that compared the effectiveness of ordinary and rigid granular columns in improving the stability of sandy slopes. The findings indicated that placing the granular columns in the middle of the slope was most effective, as this is where the greatest displacements occur. The use of rigid granular columns resulted in a significant increase in the factor of safety and provided a 1.41 times greater shear strength than ordinary granular columns. Additionally, the use of rigid granular columns improved the stability of the slope by 40.6% in comparison to using only ordinary granular columns. [PERSON] et al. [19] reported that the use of GECs was found to increase the lateral load-carrying capacity of granular columns in both model and prototype scale. Furthermore, [PERSON] et al. utilized numerical modeling techniques, including three dimensional simulations with the FLAC(tm) software [19], and the behavior of geosynthetic encased granular columns (GECs) was examined under various conditions.