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

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Principal Investigators
Amitava Ghosh
Michael Enright

Inclusive Dates:  07/01/07 – Current

Background - Current trends in geotechnical engineering increasingly call for reliability quantification analysis that includes probabilistic considerations in design codes and standards. In particular, applications involving an excavation in a rock mass must deal with extremely complex materials, because natural rock cannot be constructed to project requirements. In addition, properties of the rock are determined by site investigations, which are generally limited to a small set of samples from a few locations, leading to considerable uncertainties in estimation. As a result of this significant inherent randomness, traditional approaches, such as the factor of safety, may not provide sufficient confidence in a design. This study is developing a probabilistic framework for reliability assessment of complex engineering problems with an application in geotechnical engineering. 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 efficient probabilistic techniques as practical alternatives to the current approach.

Approach - This study focuses on rock slope stability problems coupled with system reliability modeling. Rock masses are generally treated as discontinuous media because their characteristics are usually governed by the discontinuities (e.g., joints, bedding planes, faults). If the discontinuities are sparse (i.e., the rock mass has few major discontinuities) the slope stability problem may be defined by simple geometries, such as a plane or a wedge, and solved analytically. If the discontinuities are more numerous or complex, however, a discontinuum modeling approach can be used. In this approach, the rock mass is represented by an assemblage of discrete blocks with fractures modeled as the interfaces between adjacent blocks. Material properties, geometrical information, and constitutive laws specified for blocks and joints control the solution scheme. Traditionally, only single parameter values are considered in slope stability analyses (e.g., the mean or worst-case values). A more complete spectrum of possible rock joint configurations and material property distributions can be achieved 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. Because the computational effort for discontinuum modeling can be extensive, a system reliability approach may be used to allocate an optimal number of Monte Carlo samples to individual failure modes.

Accomplishments - This project investigated variability associated with the parameters describing the geometry and strength of discontinuities in a rock mass. Two broad classes of rock stability problems, namely, plane (two-dimensional) (Figure 1) and wedge (three-dimensional) problems (Figure 2), which can be evaluated analytically, were used to apply the reliability-based techniques. They helped to determine the sensitivity of the parameters involved in assessing the reliability of rock slopes. Additionally, 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. Unlike the factor of safety, however, the reliability index is directly related to the probability of failure and appropriately takes into account the variability associated with the parameters. Factor of safety is completely insensitive to this variability, although a higher variability results in a higher failure probability. Results of the three-dimensional wedge analysis were presented at the 42nd U.S. Rock Mechanics Symposium and 2nd U.S.-Canada Rock Mechanics Symposium. Two-dimensional plane failure analysis will be presented at the International Conference on Rock Joints and Jointed Rock Masses. NESSUS® was used to analyze the plane slope stability problem by the First and Second Order Reliability and Monte Carlo Methods. As expected, the second-order method better estimated reliability because the failure state is nonlinear. Knowledge gained in these analyses will be applied to complex slopes with multiple discontinuity sets using a discontinuum analysis code.

Figure 1. An Idealized Plane Failure Geometry Is Shown. There Is a Tension Crack at the Back of the Rock Slope. The Block, Shown in Red, Can Slide in Reponse to Gravity and Water Pressure in the Tension Crack.

Figure 2. An Idealized Wedge Stability Problem Is Shown, with all Planes Identified. No Tension Crack at the Back of the Slope Is Assumed.

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