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

222(6.3)where,F o [Z i ] = the cumulative density function of Z at i data = Pr (Z ≤ z i ),Pr ( ) = probability function,Z = standardized normal distribution of expected resistance bias λ R or ln(λ R ),z i = standardized normal distribution of estimated resistance bias λ R or ln(λ R ) =λ RNor( ) ( )( ),= resistance bias, a ratio of estimated and measured pile resistances, and= sample size.The normality test revealed the necessity of categorizing the sites into three soil profiles,because the case with all soil conditions increased the uncertainties and deviated from thetypical characteristic of a lognormal distribution. The hypothesis test generally confirms theassumed lognormal distribution for the resistances. In addition, Nowak (1999) concludedthat load and resistance are mutually independent. Therefore, the resistance factors weredetermined using the FOSM closed-form equation given by. / √[ ( )]( ). / , √ [( )( )]- (6.4)where,λ RCOV R= the resistance bias factor of the resistance ratio,= the coefficient of variation of the resistance ratio,γ D , γ L = the dead load factor (1.25) and live load factor (1.75),λ D , λ L = the dead load bias (1.05) and live load bias (1.15),COV D , COV L = the coefficients of variation of dead load (0.1) and live load (0.2),β T= target reliability index, andQ D /Q L = dead to live load ratio.