Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 136

(a)

0.450

0.400

0.350

0.300

Std dev. = 1 kPa

Average s u = 14 kPa

0.250

0.200

0.150

Std dev. = 2 kPa

0.100

Std dev. = 3.5 kPa

0.050

0.000

0 5 10 15 20 20 30

s u (kPa)

Normal distributions for average s u = 14.36 kPa and COV = 5%, 15%, and 25%

(b)

0.600

0.500

0.400

ζ = 0.050 (Std dev. = 1 kPa)

Average s u = 14 kPa

0.300

0.200

ζ = 0.157 (Std dev. = 2 kPa)

0.100

ζ = 0.246 (Std dev. = 3.5 kPa)

0.000

0 5 10 15 20 25 30

s u (kPa)

Lognormal distributions for average s u = 14.36 kPa and COV = 5%, 15%, and 25%

Figure 3.4 Normal and lognormal PDFs.

hypothesis regarding the variability of the data that extends beyond the results of the 25
tests that were performed.
There is some theoretical justification for the normal distribution. The “central limit
theorem” indicates that the sum of a large number of distributions approaches the normal
distribution as the number of distributions approaches infinity. However, use of the normal
or any other theoretical distribution to form generalizations about distributions of data is
really an assumption about the distribution. Such assumptions are made partly because they