Factor of Safety or Probability of Failure?
Alex Petty - Chartered Geotechnical Professional
I Challenge the Norm to Change the Industry and Help Save my Clients Millions of $$$ | Geotechnical Director | Adjunct Associate Lecturer
Factor of Safety (Deterministic)
How is the acceptability of an engineering design assessed?
The classical approach used is to consider the relationship between the strength or resisting force of the element and the stress or disturbing force. The Factor of Safety of the structure is defined as FoS = strength or resisting force/stress or disturbing force and failure is assumed to occur when FoS is less than 1.
Probability of Failure (Probabilistic)
Rather than using a single calculated FoS , an alternative approach using probabilities can be used. This process begins by completing a series of calculations in which each significant parameter (random variable) is varied systematically over its maximum credible range in order to determine its influence upon the factor of safety.?
Common practice engineering implicitly considers those variabilities (uncertainties) by reducing resistance and increasing loadings to “prudent” values. It then expresses FoS as a single number. Probabilistic methods allow these uncertainties to be considered.
Some random variables for geotechnical applications have standard normal distributions of probabilities (including FoS). Example below.
Some random variables also have a significant effect on FoS. For example, a simple example is drained cohesion c'. In the example below (from https://www.riskope.com/wp-content/uploads/2020/12/Riskope-The-Factor-of-Safety-and-Probability-of-Failure-relationship-1.pdf) a small cohesion variation leads to a significant change in probability of failure.
But why?
Well, the random variables involved in geotechnics (the parameters relating to the ground, generally) can have a significant effect on the factor of safety (as seen in the cohesion above). Just using single values for FoS determination cannot account for the uncertainties. So, the real question becomes whether the FoS determined is sufficient?
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These uncertainties can include:
So - how well can you account for variabilities in each of these aspects to determine a single FoS?
Typically not very well.
The image below is from Silva et al, 2008 and shows the Probability of Failure vs. Factor of Safety for historical dams.
As you can see, a FoS of 1.5 presents an annual probability of failure between 1 x 10-1 and 1 x 10-6 , depending on the dam Category. This is a HUGE difference in probability.
Takeaway
We must consider whether a FoS deterministic approach is appropriate for the geotechnical application. Is the geological and geotechnical model complex, not well investigated or defined? Is the consequence of failure significant? Are the uncertainties well understood?
If there are any concerns with these, it may be beneficial to complete a probabilistic approach.
Specialist Geotechnical Engineer at BHP
5 个月Is a statistical distribution of the effect of a randomised range of inputs to a simplified model of the real world any better than a single calculation of the lowest FoS simplified failure surface in a simplified model? I would think not. Do each have situations in which one is more appropriate than the other? I think so. Is it more important to understand the sensitivities and limitations of the model and technique you’re using? Definitely! For a retaining wall in front of a homogenous soil (or engineered fill) FoS seems most appropriate. For planning a long excavation in a jointed rockmass PoF seems most appropriate. So the best tool or technique is the one that best answers the question(s) you have, with the data you have available.
I Challenge the Norm to Change the Industry and Help Save my Clients Millions of $$$ | Geotechnical Director | Adjunct Associate Lecturer
5 个月Thanks for the reshare Mitterand Kalala Ngoie!