Evolution of geotechnical risk analysis in North American practice - Risk and Reliability in Geotechnical Engineering - page 463

aleatory from epistemic uncertainties, and other subtleties that prominently figure in the
later epochs.
The focus was on lumped-parameter models in which spatial variation and the taxonomy
of sources of uncertainty was more or less ignored. As the period evolved, the texture of con-
sideration in geotechnical reliability became even more complex. As the period progressed,
the principal contributors to the literature transformed from researchers who had primarily
matriculated as old-fashioned engineering mechanics types to people who had fundamental
training in stochastic theory.
Typical work of the period looked at the probability of bearing capacity failures of shal-
low foundations or the probability of slope failures of embankments when soil properties
or empirical factors were described by probability distributions. In the early years of this
period, rock mechanics and mining applications of reliability were as common, maybe more
common, as those to soil mechanics (Einstein et al. 1976; Priest and Hudson 1976). Among
the important contributors in these early years—in addition to those referenced earlier—
were (alphabetically) Harr, Schultze, Tang, Vanmarke, and Veneziano, among many others.
The early textbook by Cornell (Benjamin and Cornell 1970) as well as later topics by Tang
(Ang and Tang 1975) and Harr (1987) also contributed to the rising interests in reliability
analysis for geotechnical problems.

12.3.2 Variability of soil-engineering properties
In retrospect, this was a period in which many naïve assumptions were made in geotechnical
modeling that now in hindsight we recognize as simplistic. The multiattributed sources of
uncertainty in geotechnical data were widely ignored ( Figure 12.2 ) , as was the distributed
nature of soil properties (i.e., soil properties are spatially variable). This sometimes led to
wild overestimates of the probabilities of adverse performance, since measurement noise,
spatial variation, model uncertainty, and other sources of uncertainty were undifferentiated
from one another.
This period saw growing interest among senior names in traditional soil mechanics in
probabilistic approaches and formal methods of uncertainty analysis. Casagrande's Terzaghi
Lecture, while ignoring formal probability analysis, caught the attention of mainline prac-
tice in grappling with uncertainty (Casagrande 1965). Notable contributions to this stra-
tegic level of thinking about uncertainty followed from Whitman (1984, 1996), Duncan
(2000), Kulhawy and Phoon (1996), and others.
Much of the work of this period began with lumped-parameter analysis of traditional
geotechnical models. Soil-engineering parameters were modeled as uncertain but uniform
within strata. A good deal of attention was invested in empirical data and the variation of
soil properties that those data suggested. Many early applications made the (retrospectively)
innocent assumption that the variability observed in empirical data was representative of
the uncertainty that should be imputed to engineering parameters in the design. This some-
times led to significant overestimates of uncertainty and therefore of probability of failure

Soil property uncertainty
Natural variation (aleatory)

Bias error (epistemic)

Spatial
variation

Temporal
variation

Parameter
error

Model bias

Figure 12.2 Sources of error in soil-engineering properties. (Adapted from Baecher, G., and J. Christian.
2003. Reliability and Statistics in Geotechnical Engineering . 1st ed. Wiley.)