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27 the midpoint AR of the interval. For example, for the 139 piles than the load multiplied by the load factors. When fitting with AR between 175 and 350, the mean KSW, 1.656, and the LRFD to ASD, the issue is less significant because, in prac- standard deviation, 1.425, are plotted at the center of the tice, the factors are established to conform (often conserva- interval (i.e., AR 262.5). Figure 12a suggests that piles with tively) to existing factors of safety. When calibrating for a an AR smaller than 350 present less accurate predictions and database, however, the establishment of an acceptable proba- larger scatters compared to the mean and the scatter of all bility of failure is cardinal, including the question of a new cases. Above an AR of 350, the mean and standard deviation design versus the existing state of practice. An approximate of the individual intervals fall within the range of all cases. relationship between probability of failure and target reliabil- Because driving resistance may affect the data, in Figure ity for a lognormal distribution was presented by Rosenbleuth 12a the influence of the area ratio was further examined for and Esteva (1972) and is commonly in use (e.g., Withiam piles with a driving resistance greater than 16 BP10cm at et al., 1998): EOD. Figure 12b presents the relationship between AR and KSW for 71 case histories answering to this criterion. These pf = 460 e-4.3 (31) data suggest even when excluding the easy driving resistance effects, the accuracy of the dynamic predictions are still Baecher (2001) shows, however, that this approximation is lower and have a larger scatter for piles with AR smaller than not very accurate below of about 2.5; and Table 12 provides 350. The boundary of AR = 350 between small and large dis- a comparison between the approximation and the "exact" placement piles was therefore confirmed, based on database numbers for different values of that suggests significant PD/LT2000. errors, especially in the zone of interest for foundation design, ( = 2 to 3). 2.6 DRILLED SHAFTS-- STATIC ANALYSIS METHODS 2.7.2 Concepts for Establishing Based on the established state of practice in design Target Reliability (reviewed in section 2.1 and presented in Appendix A), the following analysis methods and correlations have been used General Methods of Approach for the static capacity evaluation of the drilled shaft database: Three accepted methods exist to determine probabilities of an event occurring: (1) historical data providing the results 1. FHWA Method (Reese and O'Neill, 1988)-- method of frequent observations, (2) mathematical modeling derived and method were used for sand and clay respectively. from probability theory, and (3) quantification of expert sys- For the undrained shear strength, Su, the SPT correlation given by Terzaghi and Peck (1967) was used. tems (Benjamin and Cornell, 1970). Combination of the three, 2. R&W Method (Reese and Wright, 1977)--for sands when possible, can lead to a practical tool in design (e.g., Zhang while for sand and clay mix layers the method was et al., 2002, for dam slope failure). Such knowledge does not used for the clay. exist for foundations, and the selection of target reliability lev- 3. C&K Method (Carter and Kulhawy, 1988)--for rock. els is a difficult task as these values are not readily available 4. IGM Method (Intermediate Geomaterials) (O'Neill et al., 1996; O'Neill and Reese, 1999). The design TABLE 12 Comparison between Rosenbleuth assumed a smooth rock socket for skin friction and and Esteva approximation and series expansion closed joints for end bearing. labeled "Exact" of the probability of failure (pf) for different values of reliability index () Details of the analysis methods, the analyzed case histo- (Baecher, 2001) ries, and the obtained results are summarized in Appendix C. Rosenbleuth Exact pf Percent Error and Estevas' pf 2.0 8.4689E- 2 2.2750E-2 272.3% 2.7 LEVEL OF TARGET RELIABILITY 2.5 9.8649E- 3 6.2097E-3 58.9% 2.7.1 Target Reliability 3.0 1.1491E- 3 1.3500E-3 -14.9% and Probability of Failure 3.5 1.3385E- 4 2.3267E-4 -42.5% The utilization of LRFD requires the selection of a set of 4.0 1.5592E- 5 3.1686E-5 -50.8% target reliability levels, which determine the probability of 4.5 1.8162E- 6 3.4008E-6 -46.6% failure and, hence, the magnitude of the load and resistance 5.0 2.1156E- 7 2.8711E-7 -26.3% factors (see section 1.3.1 and Figure 2). The probability of 5.5 2.4643E- 8 1.9036E-8 29.5% failure represents the probability for the condition at which 6.0 2.8705E- 9 9.9012E-10 189.9% the resistance multiplied by the resistance factors will be less