Reliability of heterogeneous slopes with cross-correlated shear strength parameters

Spatial variabilities of the soil shear strength parameters (friction angle and cohesion coefficient) have long been recognised as an important factor influencing the reliability of geo-structures including slopes. However, these two parameters are frequently considered separately in research studies even though, in natural soils, both parameters are likely to vary simultaneously with existence of cross-correlation between them. This study stochastically investigates the reliability of a slope constructed in soil having spatially varying both friction angle and cohesion coefficient, and compares that with the scenarios where each soil parameter varies individually. The finite element method is merged with the random field theory to probabilistically evaluate the factor of safety and probability of failure of the slope via Monte Carlo simulations. A simple procedure to create perfect cross-correlation is discussed. The results show that the variabilities of both friction angle and cohesion coefficient even without cross-correlation can elevate the probability of failure relative to the cases where each of them varies individually. If a perfectly positive cross-correlation exists, the probability of failure increases significantly due to increasing occurrences of local failures.