One of the major difficulties encountered by geotechnical engineers is dealing with the uncertainty present in every aspect of the slope design process. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters and models. Probabilistic methods are traditionally used to account for the uncertainty in engineering design. However, the probabilistic approach as it is currently used in slope design has drawbacks. The lack of a formal framework to incorporate subjective information, such as engineering judgment and the inability to provide a proper measure of the confidence of parameters inferred from data, are examples of these limitations.
The Bayesian approach is an alternate route to the conventional probabilistic methods used in slope design. The approach is based on a particular interpretation of probability and provides an adequate framework to treat uncertainty in the geotechnical model for slope design. Methods of Bayesian statistics have been applied in many scientific fields, such us physics, astronomy, biology and social sciences, and in areas of engineering, such as the oil and gas industries and in the dam and foundation design disciplines. However, these methods are not used in geotechnical analysis for mine design where they would be of great benefit.
Probabilistic data analysis using the Bayesian approach involves numerical procedures to estimate parameters from posterior probability distributions. These distributions are the result of combining prior information with available data through the Bayes equation. The posterior distributions are often complex, multidimensional functions whose analysis requires the use of a class of methods called Markov Chain Monte Carlo (MCMC). These methods are used to draw representative samples of the parameters investigated, providing information on their best estimate values, variability and correlations. See the 2 figures to the above. Understanding the concepts behind the various algorithms used to perform MCMC analysis is important to properly assess the quality of results; however, the analyst does not have to develop the software to use the method. Open source packages in various programming languages, already developed by computer scientists and related specialists, have been tested extensively by these communities. These packages can be easily incorporated into ad hoc code for different model applications.
The author is working on a research project aimed at developing a system to quantify the uncertainty in the geotechnical model for slope design using methods of Bayesian statistics.
Luis Fernando: lfcontreras@srk.co.za
