This paper explores application of the Finite Element Method (FEM) and Shear Strength Reduction (SSR) analysis to compute probabilities of failure for slopes. It does so using two probabilistic approaches: the Point Estimate Method (PEM) and limited numbers of Monte Carlo simulations. The paper explains why probabilistic analysis with numerical methods such as the FEM is challenging, and how the PEM and Monte Carlo simulations can be used to calculate the statistical moments of output variables and to estimate slope probability of failure. One of the paper’s two examples describes application of probabilistic FEM analysis to determine slope probability of failure due to the random distribution of joints (joint networks).
Keywords: Rock Slopes; Probabilistic Analysis; Risk Analysis; Probability of Failure; Joint Networks; Discrete Fracture Networks; Jointed Rock Masses, Finite Element Method; Shear Strength Reduction Analysis
Due to rock masses being formed over large time periods under wide-ranging, complex physical conditions, their properties can vary significantly from place to place, even over short distances. As well the measurement of rock mass properties, especially in situ, is a very challenging undertaking. Except at exposed surfaces (which are generally limited compared to the volume of rock impacting design and which may not be representative of a volume of geologic material), rock mass features such as networks of joints are not directly observable. Even when properties can be readily determined, inaccuracies in measurement and differences between laboratory- and field-scale behaviour introduce significant error. As a result the engineering of excavations in rock involves large uncertainties.
In such an environment, predictions based on single evaluations (typically average values) have practically zero probability of ever being realized, and design decisions based on them are therefore open to question. It is better to evaluate and manage risks (the probability of unpleasant circumstances).
Statistical simulation offers a means for dealing with uncertainty. It can quantify uncertainty and estimate the likelihoods of occurrence of different outcomes. It can thus help engineers to develop more robust and economic designs and solutions.
Numerical methods such as the Finite Element Method (FEM) and the Discrete Element Method (DEM) have been successfully applied to slope stability analysis [1-4]. This is achieved through the Shear Strength Reduction (SSR) approach [5-11] for calculating factor of safety.
A primary advantage of numerical methods is their versatility. They can model a broad range of continuous and discontinuous rock mass behaviours without a priori assumptions.
The capabilities of numerical methods have helped soften the boundaries between the classification of rock slope stability problems into categories such as wedge-type failures controlled discontinuities, step-path failures that combine slip along joints with shearing through intact material, and rotational-type failures in which rock masses essentially behave as continua.
Application of numerical methods to probabilistic analysis in rock engineering has challenges however. Because numerical methods are more computationally intensive than limit-equilibrium approaches and thus relatively slower to compute, their application in probabilistic rock engineering requires careful thought and implementation.
