Verification of geotechnical reliability using load tests and integrity tests - Risk and Reliability in Geotechnical Engineering - page 531

made. Let us assume the detected amount of toe debris is tolerable so that no repair actions
are necessary. In this case, on-site information on both the occurrence probability and the
toe debris thickness can be obtained from the tests. Accordingly, the distributions of occur-
rence probability and toe debris thickness can both be updated. Thus, the p f of the pile can
be updated. In particular, if the observed occurrence probability is smaller than the prior
occurrence probability, and the observed toe debris thickness is less than the prior thickness,
then the updated p f after the tests will be smaller than that before the tests. The reliability of
the piles will then be changed even though no remedial actions are taken.
If some toe debris is found in a random sampling at a site as in case 2 and the detected
toe debris is deemed intolerable, then the toe debris needs to be repaired (e.g., by pressure
grouting) or the defective piles need to be replaced. Upon detecting serious toe debris in the
sampled piles, further inspection on other piles at this site may be carried out. If it is further
assumed that all toe debris present will be detected and repaired, the occurrence probability
of toe debris becomes zero. Obviously, the updated p f will be significantly smaller than that
before the tests and repair.

14.5 relIabIlItY oF PIleS VerIFIeD bY ProoF loaD teStS

14.5.1 Calculation of reliability index
In an RBD, the safety of a pile can be described by a reliability index β. To be consis-
tent with current efforts in code development, such as AASHTO's LRFD Bridge Design
Specifications or the National Building Code of Canada (Barker et al. 1991; NRC 1995;
Becker 1996; AASHTO 1997; Withiam et al. 2001; Phoon et al. 2003), the first-order
reliability method is used for calculating the reliability index. If both resistance and load
effects are log-normal variates, then the reliability index for a linear performance function
can be written as

( )

ln (/ )( RQ 1 + COVCOV

2

)/( 1 +

2

)

Q R

(14.24)

β=

ln [( 1 + COV

2

)( 1 + OV

2

)]

R Q

where Q and R are the mean values of load effect and resistance, respectively, and COV Q
and COV R are the COV for the load effect and resistance, respectively. If the only load
effects to be considered are dead and live loads, Barker et al. (1991), Becker (1996), and
Withiam et al. (2001) have shown that

R
Q

λ
λ

FOS QQ

QQ

(( / ) + 1 )

R D L

= (14.25)

( / ) + λ

QD DL QL

and

2 2 2

COV = OV + COV (14.26)

Q QD QL

where Q D and Q L are the nominal values of dead and live loads, respectively; λ R , λ QD ,
and λ QL are the bias factors for the resistance, dead load, and live load, respectively, with
the bias factor referring to the ratio of the mean value to the nominal value; COV QD , and
COV QL are the coefficients of variation for the dead load and live load, respectively; and