Environmental Engineering Reference
In-Depth Information
(a)
2.0
One positive test
Two positive tests
ree positive tests
Five positive tests
Empirical distribution
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Bearing capacity ratio x
(b)
2.0
ree positive out of 3 tests
ree out of 3, approx. log-normal
Two positive out of 3 tests
One positive out of 3 tests
None positive out of 3 tests
Empirical distribution
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Bearing capacity ratio x
Figure 14.2
Distributions of the pile capacity ratio after verification by (a) proof tests that pass at twice the
design load and (b) proof tests in which some piles fail.
FOS of 2.5 is used. The difference between the two β values is indeed small. In the follow-
ing analyses, the larger value of Q
D
/Q
L
= 3.69, which corresponds to a structure on which
the dead loads dominate, is adopted. This Q
D
/Q
L
value was used by Barker et al. (1991) and
Zhang (2004) and would lead to FOSs on the conservative side.
Figure 14.3
shows the reliability index β values for single piles designed with an FOS of
2.0 and verified by several proof tests. Each of the curves in this figure represents the reli-
ability of the piles when they have been verified by n proof tests out of which r tests are posi-
tive (see the likelihood function
Equation 14.9
).
The β value corresponding to the empirical
distribution (see
Figure 14.2
)
and an FOS of 2.0 is 1.49. If one conventional proof test is
conducted to verify the design and the test is positive, then the β value will be updated to
2.23. The updated β value will continue to increase if more proof tests are conducted and if
all the tests are positive. In the cases when not all tests are positive, the reliability of the piles
will decrease with the number of tests that are not positive. For instance, the β value of the
piles verified by three positive tests is 2.58. If one, two, or all of the three test piles fail, the
β values decrease to 2.21, 1.70, and 0.67, respectively. If multiple proof tests are conducted,
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