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Shear strength parameters in naturally alluvial deposits bear variation with depth (non-stationarity). Probabilistic analysis of simple slopes with linearly increasing (mean) undrained shear strength with depth and spatial variability is explored using the 2D random limit equilibrium method (RLEM) along with the non-circular failure surface assumption. A deterministic factor of safety design chart method is extended to express margins of safety as probability of failure for soils with random variability and positive correlation between shear strength parameters and unit weight. The effects of isotropic and anisotropic spatial variability and cross-correlation of soil properties on probability of failure are also investigated. Combinations of low correlation length and positive cross-correlation between strength parameters are shown to reduce the probability of failure. This offers the possibility to bring probabilistic …