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29 failure, and T = 4.25 for shear failures. These values are Zhang et al. (2001) used a first order reliability method to higher than those in Tables 13 and 14 because they reflect dif- evaluate the reliability of axially loaded pile groups designed ferent environmental loading conditions and, possibly, differ- using the traditional concept of group efficiency. Group effects ent design life. The Canadian Standard Association presented and system effects were identified as the major causes of the the following target failure probabilities for developing significantly greater observed reliability of pile foundations design criteria for offshore installation in Canadian waters compared to the calculated reliability of single piles. Group (Mansour et al., 1994): 10-5 per year for failures that would effect relates to the combined action of any number of piles result in great loss of life or have a high potential for envi- vs. a single pile. A system effect is the contribution of the ronmental damage; and 10-3 per year for failures that result superstructure stiffness to the load distribution and resistance. in small risk to life or a low potential for environmental dam- The calculated probability of failure of pile groups was age. (It is important to note that no direct relationship exists found to be 1 to 4 orders of magnitude smaller than that of between general probability of failure and annual probability single piles, depending on the significance of system effects of failure.) (changing the system bias factor s from 1 to 2). Based on Madsen et al. (1986) also discuss target reliability levels their study, Zhang et al. (2001) state that the target reliabil- that were used by the Nordic Committee on Building Regu- ity index, T, for achieving a specified reliability level should lations (1978). Target reliability values were selected differ for an isolated single pile (), an isolated pile group depending on the failure consequences of a building: T = 3.1 (TG), and a pile system (TS). They give the following rec- for less serious failure consequences, T = 5.2 for very seri- ommendations based on their research: ous failure consequences, and T = 4.3 for common cases. 1. A TG value of 3.0 requires a of 2.0 to 2.8 if no sys- tem effects are considered. 2. A TG value of 3.0 requires a of 1.7 to 2.5 if a system 2.7.4 Geotechnical Perspective effect factor of 1.5 is considered. The review provided in section 2.7.3 suggests that typical Additional aspect to the increased reliability of deep foun- target reliability for members and structures relevant to bridge dations can be obtained from the limited data available construction varies between 1.75 and 3.0, with a target relia- regarding the loads, which actually arrive at the piles during bility of 2.5 to 2.7 for relevant bridges. their service. Tang et al. (1994) followed the response of Barker et al. (1991, p. A-51) state the following regarding drilled shafts during construction loading and found that, target reliability index for driven piles: while 44% to 67% of the design load was measured at the pile's top, only 6% to 13% of the design load arrived at the Meyerhof (1970) showed that the probability of failure of tip in the rock socket. In the design of drilled shafts the fric- foundations should be between 10-3 and 10-4, which corre- tion or the end bearing are often being neglected, especially sponds to values of between 3 and 3.6. The reliability index of offshore piles reported by Wu, et al. (1989) is between 2 in rock sockets. This practice and the observed values sug- and 3. They calculated that the reliability index for pile sys- gest that piles are often underutilized (over conservative), a tems is somewhat higher and is approximately 4.0, corre- fact contributing to the reliability of pile foundations, which sponding to a lifetime probability of failure of 0.00005. Tang rarely fail. These facts, while recognized, cannot be consid- et al. (1990) reported that offshore piles have a reliability ered when assigning a target reliability value until more data index ranging from 1.4 to 3.0. are available and relevant load factors can be directly devel- oped for foundations. Reliability indices for driven piles are summarized in Table 5.4 [Table 15 of this report]. Values of between 1.5 and 2.8 are generally obtained for the lognormal procedure. Thus a 2.7.5 Recommended Target Reliability target value of between 2.5 to 3 may be appropriate. How- ever, piles are usually used in groups. Failure of one pile does General Range for Single Piles not necessarily imply that the pile group will fail. Because of this redundancy in pile groups, it is felt that the target relia- and Pile Groups bility index for driven piles can be reduced from 2.5 to 3.0 to a value between 2.0 and 2.5. Based on the above review and the data presented, it seems reasonable to establish the target reliability between 2.0 and 2.5 for pile groups and as high as 3.0 for single piles. TABLE 15 Reliability indices for driven piles It is clear from the review that, while the redundancy of (Barker et al., 1991) pile groups serves as the major reason for the decrease in tar- Dead to Live Reliability Index, get reliability, no logical distinction was made (when choos- Load Ratio Lognormal Advanced ing target reliability) between the target reliability of single 1.00 1.6 2.8 1.6 3.0 piles and pile groups. One can evaluate the performance of 3.69 1.7 3.1 1.8 3.3 the piles on the basis of their "redundancy." A nonredundant