Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 151

Table 3.7 Estimated and measured values of Cc/(1 + e) and its coefficient of
variation, for San Francisco Bay mud
Estimated by Estimated Cc / (1 + e) Estimated COV%
Geotechnical Engineer #1 0.30 10
Geotechnical Engineer #2 0.275 5
Geotechnical Engineer #3 0.275 5.5
Geotechnical Engineer #4 0.30 10
Average − #1 through #4 0.29 8
Measured values Cc/(1 + e) = 0.34 COV = 18
Source: Duncan, J.M., 2000, Factors of safety and reliability in geotechnical engineering, Journal
of Geotechnical Engineering , Vol. 126, No. 4, p. 307-316. Used with permission from ASCE.

3.5.4 the “n-sigma rule”
Judgmental estimates of COV or standard deviation can be improved by recognizing that
estimated values of LCV and HCV are unlikely to be sufficiently high and low to encompass
±3σ.
The N-sigma (Foye et al., 2006) rule provides a means of taking into account the fact
that an engineer's experience and available information usually encompass considerably less
than 99.73% of all possible values. The N-sigma rule is expressed as

HCV CV
N

−

σ =

(3.16)

σ

where N σ is a number smaller than 6 that reflects the fact that estimates of LCV and HCV
cannot be expected to span ±3σ. While there is no “one-size-fits-all” value of N σ , a value
of N σ = 4 seems to be appropriate for many conditions. With N σ = 4, the standard deviation
would be calculated using Equation 3.17 :

HCV CV
4

−

σ= (3.17)

N-sigma rule example : The concept of “equivalent fluid pressure” (Terzaghi et al., 1996;
Clough and Duncan, 1991) is often used to estimate earth pressures on walls. The earth
pressure distribution is approximated by a triangular pressure distribution that would be
exerted by a fluid with a unit weight γ eq . Values of γ eq are ascribed to various types of soils
based on experience and judgment, as shown in Figure 3.13 . Because values of γ eq are based
on experience and judgment, the standard deviation of γ eq also has to be based on judgment.
The N-sigma rule is convenient for this purpose.
Using Equation 3.17 , the value of standard deviation of equivalent fluid unit weight (γ eq )
could be estimated as follows:
First, the most likely value of γ eq would be estimated using experience, tables, or charts
of the type found in Terzaghi et al. (1996), Clough and Duncan (1991), or Figure 3.13 . An
example would be γ eq = 7.07 kN/m 3 for a compacted CL backfill, as shown in Figure 3.13 .
Second, the highest and lowest conceivable values of γ eq would be estimated, considering
the ways in which actual conditions might differ from the most likely conditions. These high
and low values would depend on insights regarding the possibilities that the backfill might
be of higher-or-lower quality than expected, that the backfill might contain materials other