Evolution of geotechnical risk analysis in North American practice - Risk and Reliability in Geotechnical Engineering - page 466

mineral deposit statistics had made this observation earlier, and his work mainly influenced
the emerging field of soil reliability (Matheron 1965). Using empirically observed vari-
ances among test specimens grossly exaggerates the variability of the soil properties within
the mobilized zones that control field performance. The second implication is that spatial
variability leads to size effects, seen most clearly in long, linear structures such as levees
(Vanmarcke 1983). Size effects are important manifestations of spatial variation and, even
today, they are often ignored.
12.3.5 aleatory versus epistemic uncertainty
Another significant realization during this period was the duality of uncertainty between
aleatory and epistemic types and the corresponding centrality of subjective (degree-of-
belief) probability in geotechnical risk (Vick 2002). This realization led to the understand-
ing that much or maybe most of the uncertainty geotechnical engineers face has to do with
information and knowledge rather than randomness in time and space. This opened the
door to Bayesian methods, which have come to dominate geotechnical reliability analysis.
A frequent joke among workers in the field is that hydrologists are invariably frequentist
statisticians, geotechnical engineers are invariably Bayesians, and structural engineers do
not care as long as things align with building codes.
12.4 MInIng engIneerIng (1969-1980)
Mining engineering, especially surface mining, was an early venue for reliability and deci-
sion-theoretic methods. The nominal starting date for this period, 1969, was the year of the
11th U.S. National Symposium on Rock Mechanics in Berkeley, at which early probabilistic
work in rock mechanics began to make its appearance. The closing date, 1980, brackets the
period during which much of the similar work had appeared.
The issues in mining, especially surface mines, were unique in geotechnical reliability
in that they were strongly driven by financial considerations of optimal slope angles and
amounts of excavation, and were highly dependent on the pervasive fracturing of natural
rock masses, that is, the so-called jointing systems. As the later decades of the century rolled
out, these applications of geotechnical risk were quickly extended to underground works,
but these are ignored in this chapter.
Joints are pervasive natural fracturing systems of rock masses induced by geological
forces. They are semiparallel, usually finite-size separations, often organized into subor-
thogonal sets. They introduce planes of weakness and high transmissivity in a rock mass.
As a result, they are important determinants of rock mass strength, permeability, and other
physical properties.
An issue with rock mass jointing is that it is characterized based on statistical samples.
The engineer or geologist goes into the field and observes the surface manifestation of joint-
ing as a population of fracture traces upon the outcrop or excavation wall. These are lines
of intersection of the joint sets with various semiplanar sampling windows. From measure-
ments of these lines of intersection, the three-dimensional (3D) stochastic geometry of the
joints needs to be inferred. This raises interesting questions of geometric probability.
Among the early contributors to this geometric sampling problem were Snow (1970),
Barton (1975), Priest and Hudson (1976), Cruden (1977), and Baecher et al. (1977). The
early work on this statistical problem addressed joint spacing or intensity as separate from
orientation and trace length. Later, modeling attempted to integrate the 3D geometry of
jointing (Dershowitz and Einstein 1988).