Some Remarks on the Use of Deterministic and Probabilistic Approaches in the Evaluation of Rock Slope Stability

Abstract

The rock slope stability assessment can be performed by means of deterministic and probabilistic approaches. As the deterministic analysis needs only representative values (generally, the mean value) for each physical and geo-mechanical parameter involved, it does not take into account the variability and uncertainty of geo-structural and geo-mechanical properties of joints. This analysis can be usually carried out using different methods, such as the Limit Equilibrium method or numerical modeling techniques sometimes implemented in graphical tests to identify different failure mechanisms (kinematic approach). Probabilistic methods (kinetic approach) aimed to calculate the slope failure probability, consider all orientations, physical characters and shear strength of joints and not only those recognized as kinematically possible. Consequently, the failure probability can be overestimated. It is, therefore, considered more realistic to perform both kinematic and kinetic analyses and to calculate a conditional probability given by the product of the kinematic and kinetic probabilities assuming that they are statistically independent variables. These approaches have been tested on two rock slopes in the Campanian region of Southern Italy affected by possible plane and wedge failures, respectively. Kinematic and kinetic probabilities have been evaluated both by means of the Markland’s test and the Monte Carlo simulation. Using the Eurocode 7, also a deterministic limit equilibrium analysis was performed. The obtained results were compared and commented on.

Estimating the Slope Safety Factor Using Simple Kinematically Admissible Solutions

“…Numerous other computational methods can be found in the literature and engineering practice. In addition to the traditional approaches discussed in [5], such as the Fellenius method, Janbu, or Sarma, more advanced computational approaches can be considered, for example, those based on probabilistic methods [14][15][16][17][18][19]; semi-probabilistic methods [20], including the stochastic finite difference method [21]; and those based on the finite element method [10,11,22].…”

Metamodel-Based Slope Reliability Analysis—Case of Spatially Variable Soils Considering a Rotated Anisotropy

“…Moreover, in the framework of probabilistic analyses, Monte Carlo Simulations (MCSs) have been commonly employed in the existing studies to calculate the failure probability (P f ) [13,14]. This method is widespread due to its simple calculation and robustness.…”