The slope has an adverse effect on the ultimate bearing capacity of shallow foundations. Due to inherent variability in soil properties and geometric factors of slopes, designing a foundation on slopes is a perplexing and challenging task. The spatial variation in the soil's shear strength property is commonly ignored by the designers to avoid complexity in design. Shear strength property in real scenarios increases along the depth and simultaneously it poses spatial variability. This kind of randomness is modelled using a non-stationary random field. The proposed study aims to evaluate the probabilistic bearing capacity of strip footing on spatially varying slopes. The probabilistic bearing capacity factor is analyzed for different influential factors like geometry and footing placements, correlation distances and coefficient of variation of soil properties. Slopes exhibiting nonstationary characteristics contribute to remarkable differences in the bearing capacity of footing as compared to the stationary condition. The study highlights that the geometry factors, footing placements, soil spatial variability and most importantly the increasing trend of soil strength play a critical role in the bearing capacity and risk of failure of a footing. High variations in the failure probability can be observed even after considering safety factors.

Slope failures are a significant natural geohazard in hilly and mountainous regions, often resulting in loss of life and infrastructure damage. The Muketuri-Alem Ketema road in Ethiopia is particularly vulnerable to landslides due to colluvial deposits on steep slopes from the higher northeastern plots to the lower Jemma River valley. This study investigates the characteristics of colluvial soil and evaluates the stability of slopes prone to landslides. It combines geophysical data, penetrometer tests, laboratory analyses, Google Earth images, and detailed field visits to assess the soil and bedrock composition and structure. Numerical methods, including limit equilibrium (Bishop, Janbu, Spencer, and Morgenstern-Price methods) and finite element methods, were used to analyze slope sections under various saturation conditions and simulate different rainfall patterns. The results indicate that the Bishop, Morgenstern-Price, and Spencer methods produce similar safety factors with minimal differences (<0.3%), while the Janbu method shows more significant variation (1.5%-5.6%). Safety factor differences for sections A-A and B-B range from 5.26% to 9.86% and 3.5%-4.7%, respectively. Simulations reveal that short-term saturation significantly reduces the stability of the upper slope layer by 20%-46.76%, and long-term saturation decreases the entire slope by 26.81%-46.76% compared to dry conditions due to increased pore water pressure and self-weight. Long-term saturation effects, combined with dynamic loads, can further reduce colluvial soil stability by over 50% compared to a dry static state. The finite element method predicts larger failure zones than limit equilibrium methods, emphasizing the need for accurate predictions to characterize slope behavior during failure and inform stabilization decisions. This study provides crucial data for maintaining and planning the Muketuri-Alem Ketema Road, highlighting slope performance over time and the effectiveness of stabilization techniques.