A paper entitled “Probability and Risk of Slope Failure” (Silva et al. 2008) proposed using quantification of expert judgement, a subjective/semi-empirical probability evaluation, as a practical alternative for determining probability of slope failure. We call this approach SLM, using the initials of the authors Silva, Lambe and Marr. SLM culminates with semi-empirical relationships between Factor of Safety (FoS) and probability of failure (pf). That relationship allows estimating the probability of slope failures with relatively modest effort.
Not a New Approach
SLM was not the first attempt to generate a relationship between FoS and pf. This approach goes back 35 years. One example by Oboni & Martinenghi (1984) showed that with equal FoS, a slope in clay has a significantly higher pf than a slope in granular soil due to higher variability of clay’s geomechanical parameters. A 1985 paper from Caldwell Moss, “Design of Non-Impounding Waste Dumps,” (M K McCarterP47–P61, NY: AIME, 1985) also showed how to generate FoS-pf relationships. It used relatively simple probabilistic approaches: pf=function of FoS, including mechanical parameters variability.
What is the Advantage?
The advantage of using SLM vs. the “1980s approach” is that SLM introduced “expert judgement” on testing, monitoring and other human factors. To do that, they created four main categories to express a judgement on the quality of the structure. The idea is that the better the structure, the lower the pf is under constant FoS. Thus, after selecting the category of the structure, the FoS-pf functions generate the estimate of the pf. In the end, SLM yields estimates of pf=function (FoS) including mechanical parameters variability, geotechnical investigations, design, monitoring, construction and more.
SLM looked at the stability of a given, individual earthen embankment slope; it did not look specifically at dams. Thus, it is informative, but does not represent a general approach to evaluation of the probability of failure of a hydro or tailings dam. The probability of failure of a dam is far more complex than the SLM slope pf,FoS chart representation can capture. For example, the dam may have:
- tailings distribution pipeline (that can rupture) at its crest
- a combination of various types of ancillary surface water management structures (weirs, spillways, diversion ditches) that may be insufficient or damaged
- seepage and erosion controls, drainages that may be insufficient or old
Building the Knowledge Base
Given the age or expected life of a dam, its knowledge base is spread over many different documents, many authors/sources and over years, if not decades. Building the knowledge base is a daunting task faced by anyone willing to perform a risk assessment.
Furthermore, strategic decisions/choices and other human factors may contribute to the potential for triggering of tailings liquefaction. See, for example, Martin & McRoberts (1999) “Some considerations in the stability analysis of upstream tailings dams” (Proceedings of the Sixth International Conference on Tailings and Mine Waste 99, pp. 287−302, Rotterdam, Netherlands: AA Balkema). This and other aspects go obviously beyond what a simple slope stability calculation may capture.
Conclusion of SLM and the Probability of Failure of a Tailings Dam
The SLM is a great tool for its intended purpose. However, if you try to apply it to something else, it can become extremely hazardous and should be handled with care.
ORE2_Tailings is built for dams and is a repeatable, organized and swift way of evaluating the probability of failure of a slope (dam). Like any other approach, the first step is to build the knowledge base for each dam.
