the undrained shear strength (Su) of a clayey site soil. Alternatively, the information
contained in research findings such as in Figure 3.18 can be utilized in planning
subsurface investigations. Intuitively, one also realizes that the standard deviation
estimates obtained from a given evaluation method correlate well with reliability of
the evaluation method, i.e., a relatively higher standard deviation indicates a less reliable
evaluation method.
The typical variability associated with soil index tests and strength tests as reported by
Phoon et al. (1995) are shown in Table 3.10 and Table 3.11, respectively. For analytical
purposes, one can completely describe a random variable using an appropriate probability
density function (in the case of a continuous random variable) or probability mass
function (in the case of a discrete random variable) that satisfies the statistics of that
particular random variable. The distribution that satisfies all the statistical properties of
the random variable would obviously be its own histogram. However, what is assumed in
many instances is a mathematical function that would closely ‘‘model’’ the statistical
properties of the considered random variable. When selecting an appropriate mathematical
distribution for a given variable, it is most common to match only the mean and the
standard deviation of that variable with the corresponding quantities that are computed
using the mathematical equation of the considered distribution as follows: