### Stochastic Analysis  
The focus of this study is on examining the impact of soil spatial variability on the stability and failure mechanisms of geosynthetic-reinforced embankments supporting a strip footing on cohesive soil slopes. The primary aim is to understand how variations in soil properties influence embankment behavior, providing insights into the stability of reinforced embankments under different conditions. This is particularly relevant for designing more reliable and safer geotechnical structures. Previous research has highlighted the significance of geosynthetic reinforcement in improving embankment stability, but the influence of soil spatial variability has not been thoroughly investigated, making this study crucial for advancing geotechnical engineering practices. In the baseline scenario, deterministic values were utilized for various parameters to establish a reference point. These values included unit weight (\(\gamma=20\) kN/m\({}^{3}\)), normalizedslope height (\(H/D=0.5\)), and slope angle (\(\beta=1\):2). By varying one parameter at a time while keeping the others constant, this study provided a clear assessment of the individual impact of each variable on the stability of the embankment. This methodical approach ensured that the effects of soil spatial variability could be accurately measured against a stable baseline, allowing for a comprehensive analysis of how different factors contribute to the overall stability of geosynthetic-reinforced embankments. This study incorporated coefficients of variation to account for the inherent randomness in soil properties and reinforcement strength. The coefficient of variation for cohesion (COV\({}_{\rm c}\)) was set at 0.5, aligning with findings by [PERSON] (2017) and [PERSON] et al. (2023) and typical soil shear strength ranges reported by [PERSON] and [PERSON] (1999) ([PERSON] and [PERSON], 2013; [PERSON] et al., 2023; [PERSON] et al., 2023). Additionally, stationary estimates were used for the coefficient of variation of friction angle (COV\({}_{\rm\phi}=0.2\)) and cohesion (COV\({}_{\rm c}=0.5\)). These values were critical for understanding the variability in soil properties and their impact on embankment stability. Stability criteria for the embankments were established, with a theoretically stable embankment having a factor of safety (\(F_{s}\)) of 1.0, while engineering practice recommends an \(F_{s}\) between 1.3 and 1.5 for safety. By adopting conservative coefficients of variation for reinforcement strength and pullout capacity, this study provided a robust framework for analyzing the reliability of geosynthetic-reinforced embankments. Reported coefficients of variation for reinforcement strength ranged from 0.01 to 0.10 and from 0.20 to 0.27 ([PERSON] et al., 2011; [PERSON] et al., 2011). [PERSON] et al. (2011) found that post-installation variability in geogrid tensile strength could reach COV\({}_{\rm T}=0.2\), and this study adopted a conservative COV\({}_{\rm T}=0.15\). This detailed approach ensured that the probabilistic analyses were grounded in realistic and practical assumptions, enhancing the applicability of the findings. Random variability in reinforcement strength and pullout capacity was considered in this study's probabilistic calculations, recognizing their significant impact on failure probability. Variability in pullout capacity was treated as a function of random variability in \(\phi\) and \(c\). Although pullout rarely governs slope stability, conservative estimates were provided by the pullout model to ensure a comprehensive safety assessment. Mean values for cohesion (\(c\)), friction angle (\(\phi\)), and tensile strength (\(T\)) used in probabilistic calculations were assumed to be nominal values used in deterministic analyses, treating these parameters as random variables with specified coefficients of variation (COV of 0.2 for \(\phi\) and 0.15 for \(T\)).