SwRI IRD 2010--Development of an Efficient Probabilistic Approach for Risk Assessment of Geotechnical Applications, 20-R9726

Development of an Efficient Probabilistic Approach for Risk Assessment of Geotechnical Applications, 20-R9726

Background - There is an increasing demand in the geotechnical engineering field for reliability quantification to address the current trend to include probabilistic considerations in design codes and standards. In particular, applications involving an excavation in a rock mass have to deal with an extremely complex material, as natural rock cannot be constructed to project requirements. In addition, properties of the rock are determined by site investigations, generally limited to a small set of samples from a few predetermined locations, which leads to considerable uncertainties in estimation. A result from this significant inherent randomness is that traditional approaches, such as the factor of safety, may not provide sufficient confidence in a design at different sites. This study proposes to develop a probabilistic framework for reliability assessment of complex engineering problems with an application to geotechnical engineering. Therefore, by addressing a field where risk is commonly assessed using deterministic analyses and engineering judgment, this research will demonstrate the benefits of both the probabilistic approach and the use of efficient probabilistic techniques as alternatives to the current approach.

Approach - This study focuses on rock slope stability problems coupled with system reliability modeling to develop an estimate of probability of failure of the slope depending on the level of risk tolerance by a particular project. The rock mass is generally treated as a discontinuum medium as the characteristics are generally governed by the discontinuities (e.g., joints, bedding planes, faults). Traditionally, only single values (e.g., the mean or worst-case values) of rock and associated discontinuity parameters are considered in slope stability analysis. As can be seen in Figure 1, this single-value approach results in significant uncertainty of the estimated safety factor. For example, varying only the rock discontinuity geometry-related parameters with constant strength properties, the estimated factor of safety of a rock slope ranged from 1.3 (acceptable as a stable slope in many applications) to 0.8 (failed slope). This analysis illustrates the significant need for probabilistic assessment in geotechnical engineering areas. However, in geotechnical engineering, the term "failure" is not uniquely defined. Not all failures (in this case, rock slope failure) lead to "catastrophic consequences." Some failures can better be described as "tolerable." They certainly disrupt normal operation but can be well tolerated by the project. In this study, a "tolerable risk"-based approach is pursued to develop a methodology to estimate the probability of slope failure associated with a specific consequence (e.g., a given volume of rock slide).

Accomplishments - In this project, a method has been developed to estimate the reliability or probability of failure of rock slopes in terms of volume (actually area as a two-dimensional analysis was conducted) of failed rock or sliding mass considering the uncertainties associated with the geometry and strength of rock joints or discontinuities of the rock mass. For simplicity, in this study, consequence has been equated with the volume of sliding mass; however, it can be any user-defined parameter, such as, economic value of a loss event. A separate analysis to estimate the economic value of loss can be conducted if necessary; however, basic approach to estimate the reliability remains unchanged. Figure 2 shows the probability that the failed area (i.e., consequence) will be larger than a given value, based on Monte Carlo simulation using 1,000 samples. This hypothetical rock slope has two intersecting joint sets. The results obtained in this case study show that as long as the friction angles of both joint surfaces are larger than about 25 to 27°, the slope is not likely to fail. However, if one or both friction angles are below this value, the slope fails and amount of failed area is very sensitive to small changes in friction angle. This means that a small randomness in strength parameters in this range can have significant influence on consequence (i.e., volume of failed rock blocks in this case). Figure 2 also shows that the probability of a major rock slope failure is high for the range of parameters considered in this study.

Figure 1. Scatter of estimated factor of safety with rock joint set friction angles ɸ₁ and ɸ₂ fixed at 30° and cohesion fixed at 0.02 MPa with only randomness in joint geometry parameters. Joint geometry parameters varied within ranges observed in nature.

Figure 2. Exceedance probability associated with failed rock area for the rock slope application example. Approximately 20 percent probability that area of failed rock blocks will be more than 10,000 m²; however, the exceedance probability increases to approximately 45 percent if the project can tolerate only a consequence or failure of 1,000 m².