Verification of geotechnical reliability using load tests and integrity tests - Risk and Reliability in Geotechnical Engineering - page 532

FOS is the factor of safety in the traditional ASD. Najjar and Gilbert (2009) show that a
more realistic quantification of reliability can be achieved by incorporating a lower bound
in the distribution of foundation capacity.
If the load statistics are prescribed, Equations 14.24 and 14.25 indicate that the reliability
of a pile foundation designed with an FOS is a function of λ R and COV R . As will be shown
later, if a few pile tests are conducted at a site, the values of λ R and COV R associated with
the design analysis can be updated using the test results. If the test results are favorable,
then the updated COV R will decrease but the updated λ R will increase. The reliability level
or the β value will therefore increase. Conversely, if a target reliability, β T , is specified, the
FOS required to achieve the β T can be calculated using Equations 14.24 through 14.26 and
the costs of construction can be reduced if the pile test results are favorable.
14.5.2 example: Design based on SPt and
verified by proof load tests
For illustration purposes, a standard penetration test (SPT) method proposed by Meyerhof
(1976) for pile design is considered. This method uses the average corrected SPT blow
count near the pile toe to estimate the toe resistance and the average uncorrected blow
count along the pile shaft to estimate the shaft resistance. According to statistical studies
conducted by Orchant et al. (1988), the bias factor and COV of the pile capacity from the
SPT method are λ R = 1.30 and COV R = 0.50, respectively. The within-site variability of the
pile capacity is assumed to be COV = 0.20 (Zhang 2004), which is smaller than the COV R
of the design analysis. This is because the COV R of the prediction includes more sources of
errors such as model errors and differences in construction effects between the site where
the model is applied and the sites from which the information was extracted to formulate
the model.
Calculations for updating the probability distribution can be conducted using an Excel
spreadsheet. Figure 14.2 shows the empirical distribution of the bearing capacity ratio, x ,
based on the given λ R and COV R values and the updated distributions after verification by
proof tests. The translated mean η and standard deviation ξ of ln( x ), calculated based on
the given λ R and COV R , are used to define the empirical log-normal distribution. In Figure
14.2a , all proof tests are positive (i.e., the test piles do not fail at twice the design load);
the mean value of the updated pile capacity after verification by the proof tests increases
with the number of tests while the COV value decreases. Specifically, the updated mean
increases from 1.30 for the empirical distribution to 1.74 after the design has been verified
by three positive tests. In Figure 14.2b , the cases in which no test, one test, two tests, and
all three tests are positive are considered. As expected, the updated mean decreases signifi-
cantly when the number of positive tests decreases. The updated mean and COV values
with different outcomes from the proof tests are summarized in Table 14.3 . The updated
distributions in Figure 14.2 may be approximated by the log-normal distribution for the
convenience of reliability calculations using Equation 14.15 . Because of the differences in
the distributions updated by proof tests of different outcomes, the COV values in Table
14.3 do not change in a descending or ascending manner as the number of positive tests
decreases.
The following typical load statistics in the LRFD Bridge Design Specifications (AASHTO
1997) are adopted for illustrative reliability analyses: λ QD = 1.08, λ QL = 1.15, COV QD = 0.13,
and COV QL = 0.18. The dead-to-live load ratio, Q D / Q L , is structure-specific. Investigations
by Barker et al. (1991) and McVay et al. (2000) show that β is relatively insensitive to this
ratio. For the SPT method considered, the calculated β values are 1.92 and 1.90 for distinct
Q D / Q L values of 3.69 (75 m span length) and 1.58 (27 m span length), respectively, if an