Constructing multivariate distributions for soil parameters - Risk and Reliability in Geotechnical Engineering - page 2

Constructing multivariate
distributions for soil parameters
Jianye Ching and Kok-Kwang Phoon
1.1 IntroDuCtIon
Reliability-based design (RBD) is known to provide a rational basis for incorporating uncer-
tainties in the design environment explicitly into the geotechnical design (e.g., pile length).
However, one recurring criticism of RBD is that there is no particular reason to use it
because it seems to produce designs comparable to the existing practice. In particular, the
link between potential reduction of uncertainties resulting from collection of more infor-
mation and how this reduction could translate to actual savings in design dimensions has
remained a vague theoretical possibility so far. More information can be collected using
two approaches. One approach is to take field measurements/samples at more locations,
that is, increase the amount of data for a given test type. The second approach is to conduct
more test types, for example, supplement standard penetration test (SPT) with cone penetra-
tion test (CPT). The former approach increases information quantitatively, while the lat-
ter approach increases information qualitatively. This distinction is important, particularly
pertaining to reduction of bias in the estimation of design parameters such as the undrained
shear strength. The first approach may be effective in improving precision, but is usually not
effective in reducing estimation bias. Both approaches are typically carried out simultane-
ously in practice to varying degrees, depending on the needs of the project and economics.
While it is theoretically correct that reduction in uncertainties will translate to design sav-
ings, critical questions of paramount importance to practice such as “how much reduction
in pile length?” and “is it worth my time/money to collect more site information?” cannot
be answered theoretically. These critical questions can be answered only by applying RBD
to actual design problems where the amount of site information can be varied systemati-
cally. In reality, site investigation information always appears in a multivariate form. For
instance, when borehole samples are drawn, SPT-N values are usually available; moreover,
the information regarding unit weight, plasticity index (PI), liquid limit (LL), and water
content can quickly be obtained through laboratory tests. Many of these test indices may
be simultaneously correlated to a design parameter such as the undrained shear strength
s u . With the bivariate correlations at hand, it seems straightforward to update the first two
moments [mean and coefficient of variation (COV)] of s u conditioning on a single-test index
(e.g., SPT-N); however, it is not obvious as how to conduct the same analysis conditioning
on multivariate test indices [e.g., SPT-N and overconsolidation ratio (OCR) simultaneously].
An option is to discard all test indices but retain the most relevant and/or most accurate test
index. However, it is uneconomical to eliminate costly information in the updating process
because the abandoned test indices may further reduce the uncertainties. Even test indices
that are weakly correlated to the design parameter may reduce uncertainties substantially if
a number of test indices are available and their effects can be combined. Another common
approach is to simply take the average of s u estimates from different tests. This approach is
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