S - Kam Ng PhD Dissertation Final.pdf - Digital Repository of CCEE ...

2002.33 or 0.57 when β T of 3.00 to both R EOD and R setup having different probabilisticcharacteristics violates the LRFD philosophy.5.4. Statistical EvaluationsTo consider the pile setup resistance estimated using Eq. (5.1a) in pile designs thatconform with the reliability theory in accordance with LRFD framework, the principle ofstrength limit state function (g) corresponding to a safety of margin is expanded as in Eq.(5.3), which is valid only if the initial pile resistance at EOD (R EOD ), pile setup resistance(R setup ) and both dead (Q D ) and live (Q L ) loads have lognormal distribution.g = ln(R EOD ) + ln(R setup ) – ln(Q D ) – ln(Q L ) (5.3)To verify the pile resistances given in Table 5.1 follow the lognormal distributions, ahypothesis test based on Anderson-Darling (1952) normality method was used to assess theGoodness of Fitting of the assumed lognormal distributions. The reason for selecting theAnderson-Darling method is because it is one of the best normality tests for a database withrelative small sample size (Romeu, 2010). Figure 5.1 shows that the Anderson-Darling (AD)values of 0.255 and 0.374 are smaller than the critical P-values of 0.620 and 0.392 within the95% confident interval (CI) for EOD and setup conditions, respectively. Hence, thehypothesis test confirms the assumed lognormal distributions for both resistances. Sinceboth resistances and loads (as assumed by Nowak (1999)) follow lognormal distributions,natural logarithm of resistances and loads follow normal distributions and the safety margin(g) follows a normal distribution such that the relationship between probability of failure (P f )and reliability index (β) is validly given by Eq. (5.4)( ) (5.4)where,β = ratio of E(g) and σ g ,Ф () = cumulative distribution function,