NAVFAC DM 7.2: Probability and Reliability in Geotechnical Engineering

The last chapter (the example problems, which we plan to discuss in our last post of the series, are in an appendix) of NAVFAC DM 7.2 is on probability and reliability in engineering. Generally speaking engineers associate this with LRFD, and there have been objections to this being applied to certain geotechnical problems, as Mark Svinkin noted in his Letter Concerning Dynamic Methods. However, these methods are here to stay, and this chapter provides a comprehensive overview of the topic that goes past LRFD, which will be useful to many of the “old heads” unfamiliar with statistical methods. (Statistical methods, like linear algebra, are just about de rigeur in engineering curricula these days, not the case in the past.)

In some ways this is the best written part of the book, probably (pun partially intended) because it was written from the “ground down” (this is a geotech book, after all.) In previous chapters the authors had to wrestle with material which they felt engineers expected and whether to keep certain items or to pitch them. In this case the presentation was free of those conflicts, although the subject matter introduces complexity which can glaze the eyes.

A Basic Declaration

One thing that the chapter sets forth, in common with many presentations on the subject, is that engineers in the past have used “deterministic” methods while now we used “probabilistic” methods. This is simply not true. The factors of safety, as they lumped the uncertainties of loads and resistances into one number, may have been crude in their way of incorporating uncertainty, were in fact a recognition of uncertainty. Attempts to sort out the sources of uncertainty have been ongoing since Isaacs’ famous “factor of ignorance” statement in 1931. Beyond that, geotechs in general have been very aware of the uncertainties of designing structures in and next to the earth, which is why “engineering judgement,” not a well quantified thing in itself, has been critical in the way things get designed and built.

There are three basic problems with statistical methods.

The first is that, while the way the physics are quantified in this profession hasn’t changed (at least not enough, as I’ve noted in this series more than once) the way we deal with uncertainties has made the design process considerably more complicated. That’s why, when teaching Foundation Design and Analysis, I waited until the end to introduce Foundation Design and Analysis: AASHTO LRFD Method. It was hard enough to get the students proficient in the basic physics without adding the complexity of LRFD.

Second, NAVFAC DM 7.2 mentions the fact that some LRFD factors were based on ASD safety factors. This was very much in vogue in Geotechnical LRFD’s early years, as you can see in this document. When this fact was stated during an ASCE national convention in the late 1990’s, Jean-Louis Briaud asked the obvious question: if we’re basing load and resistance factors on ASD, what’s the point of LRFD? That question has been answered in the intervening quarter century to a large extent, but given the variations in geotechnical data (and age; I recently performed a drivability study using boring data from the 1940’s) I don’t think we’re quite there.

Third, the inevitable temptation with the computing power we have at our disposal is to use statistical methods in place of analysing the physics of the problem. This is something that must be stoutly resisted. I am not alone in being concerned about this, as I noted in My Response to Rodrigo Salgado’s “Forks in the road: decisions that have shaped and will shape the teaching and practice of geotechnical engineering” and an announcement.

One thing that statistical methods are much better in doing than ASD is including the effects of “black swan” events such as earthquakes, hurricanes, and ship impacts.

Outline of the Chapter

The chapter has four main sections:

• An Introduction to the topic.
• Principles of Statistics and Probability, a nice overview of the basic concepts.
• Uncertainty in Geotechnical Engineering, outlining the sources, effects of and designing for uncertainty.
• Applications, including an overview of LRFD. The last doesn’t include a tabulation of load and resistance factors. This is doubtless a wise decision because a) there is more than one system of these, and b) they, like the tax code, have all the stability of Burnham Wood, and are subject to change by their promulgators.

One interesting inclusion of statistical methods are Monte Carlo methods, which are notoriously computationally expensive.

Overall this is an excellent section on a topic which is developing in several ways and will grow in importance in geotechnical analysis and design.