A stochastic approach to slope stability analysis in bimrocks

Bimrocks (block-in-matrix rocks) are defined as heterogeneous mixtures of hard rocks surrounded by a matrix of finer texture. A common practice when planning engineering works in these challenging materials is to take into account only the strength and deformation properties of the weaker matrix. However, as proved by many case histories recorded in the literature, such a simplified assumption can lead to incorrect results and, consequently, to unexpected difficulties and instability problems during construction works. The aim of this paper was to investigate slope stability in bimrocks using both finite element (FEM) and limit equilibrium (LEM) methods. More than 90 2D stability analyses were performed on slope models with the same geometry and with block proportions varying between 0% (matrix-only) and 70%. A stochastic approach was introduced in order to consider the inherent spatial and dimensional variability of rock inclusions. To this aim, a specific Matlab routine, performing numerical Monte Carlo simulations, was implemented. The code generates populations of 2D blocks with random sizes and positions within the slope models, according to specific statistical rules and given block contents. To achieve a statistical validity of the results, ten extractions and, hence, ten stability analyses were performed for each block proportion considered. Two empirical strength criteria available in the literature were also applied to the bimrock slope models by way of comparison. These criteria assume bimrocks to be homogeneous and isotropic masses with strength parameters that depend on their block contents and matrix strength. The effects of block proportions on safety factors, volumes involved and failure surfaces tortuosity provided by the different methods are discussed in detail. The findings of this study strongly suggest that bimrocks should be treated as heterogeneous materials, in order to avoid potential inaccuracies caused by neglecting the presence of blocks at the design stage. Furthermore, the benefits of using a stochastic rather than a deterministic approach to perform slope stability analyses in these heterogeneous materials is highlighted.