A localized probabilistic approach for slope stability analysis is presented in this paper, which is also applicable for the risk assessment of slope failure at a specified confidence level. The probabilistic analysis as well as its localization was achieved through the probabilistic characterization of the in-situ strength values, that provide the full statistical distribution of strength variables at every point within the geological formation. An actual case study was made for a surface coal mine to demonstrate its superiority and to show its technical details.
The localized probabilistic analysis of slope failure was formulated into two stages of analysis. In the first stage of analysis, the probabilistic characterization of the in-situ strength parameters was carried out by the geostatistical conditional simulation technique called sequential Gaussian cosimulation method (Almeida 1993). The second stage of analysis involves the probability calculation of slope failures by combining the probability regions of strength values and the deterministic slope analysis methods.
1.1 Probabilistic site characterization The sequential Gaussian co-simulation method generates the local joint probability distribution functions (joint pdf's) of strength parameters, which are conditioned to available experimental samples in the slope area. Therefore, it offers various advantages over other conditional simulation methods, and is ideal for the geotechnical site characterization, where a probabilistic structural analysis and its risk assessments are desirable. Many primary variables can be simulated sequentially with the secondary variables and their covariances are reproduced in the simulation. It includes not only the correlation between the primary strength parameters but also the correlations between the primary hard data and secondary soft data in the estimation of the primary variables, which will improve the quality of primary variable models based on the secondary variable information. The spatial variability of both primary and secondary variables are also quantified and incorporated into the simulation process through covariances and variogram models. In the slope analysis, the primary strength parameters are cohesion values (c) and internal friction angles (4?) of the slope materials. The secondary information could be other soil parameters including pocket penetrometer tests, liquid limits, plastic limits, or geophysical data, and geological interpretations.
Finally the sequential Gaussian co-simulation estimates the full statistical distribution of primary variables at every point in the slope area. The technical details of probabilistic site characterizations are available in other publications (Purejan 1998, Pumjan and Young 1999).
As a simple example, the localized probabilistic model of soil strength parameters is given in Figure 1, where the average strength values (c-values only) are given for every element within the coal mine slope area. It provides the input needed for the local slope analysis in probabilistic terms.