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

Principal Investigators
Amitava Ghosh
Michael Enright

Inclusive Dates:  07/01/09 – Current

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 practical alternatives to the current approach.

Approach - This study focuses on rock slope stability problems coupled with system reliability modeling. 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). If the discontinuities are sparse (i.e., the rock mass has a few major discontinuities), the slope stability problem may be defined by simple geometries, such as a plane or a wedge, and solved analytically. However, if the discontinuity characteristics make the slope stability problem a complex one, a discontinuum modeling approach can be used in which the rock mass is represented by an assembly of discrete blocks with fractures as the interfaces between adjacent blocks. Traditionally, only single values (e.g., the mean or worst-case values) of these parameters are considered in the slope stability analysis. However, a more complete spectrum of possible rock joint configurations and material property distributions can be accounted for using uncertainty analysis. In this research, both approaches are used to gain critical insights regarding the most risk-significant parameters, sensitivity of multiple failure modes, and quantified risk values. Traditional slope stability analysis gives equal importance to failure of any slope, regardless of the amount of rock and soil that becomes detached from it (Figure 1). In this study, a risk-based approach is pursued to develop a methodology to estimate the probability of slope failure associated with a specific consequence (e.g., for a given volume of rock slide, as in Figure 1).

Accomplishments - This project investigated method(s) to efficiently estimate the probability of failure of rock slopes considering the uncertainties associated with the geometry and strength of discontinuities in rock mass. Two broad classes of stability problems — namely, plane and wedge, which can be evaluated analytically — were used to apply the reliability-based techniques. These analyses helped to determine the sensitivity of the parameters involved in assessing the reliability of rock slopes. This information can be extended to complex slope stability problems. A relatively new concept of characterizing the stability of a rock slope (and other structures) using the "reliability index" has been used. As the reliability index increases, the slope becomes more stable, similar to the factor of safety approach. Moreover, the reliability index appropriately takes into account the variability associated with the parameters; a higher variability results in a higher failure probability unlike the factor of safety. Results of these analyses were presented at the 42^nd U.S. Rock Mechanics Symposium and the International Conference on Rock Joints and Jointed Rock Masses. A two-block sliding model of a slope, formed as result of a tension crack either on the slope surface or at the top surface, has been used to demonstrate the usefulness of optimal sampling to estimate the failure probability (Figure 2). Optimal sampling has reduced the number of Monte Carlo realizations by about 30 percent for this two-block case. Systems with larger numbers of members (i.e., blocks in this case) would require significantly smaller numbers of realizations; a reduction of up to 98 percent was achieved over uniform sampling. These results were presented at the 10^th International Conference on Structural Safety and Reliability, Japan. Knowledge gained in these analyses is used to study complex slopes with multiple discontinuity sets using a discontinuum analysis code coupled with the NESSUS® code.

Figure 1. Different Sizes of Potential Failure of a Slope With Different Consequences: (A) Relatively Small Failed Rock Volume and (B) Relatively Large Failed Rock Volume.

Figure 2. A Rock Slope Modeled Using Two Elements: (A) Tension Crack at Top of Slope and (B) Tension Crack on Face of Slope.

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