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

203( ( )) ( ̅) ( ) (5.7)( ) ( ) (5.8)Using these expressions for the four random variables (R EOD , R setup , Q D and Q L ) andsubstituting them into Eq. (5.6), the reliability index can be expressed as follows:. ̅ ̅̅ ̅/ .√ /√ 0. / ( )1(5.9)Replacing the simple mean values with their respective bias factors (λ), a ratio betweenaverage measured and predicted values ( ̅or ̅), and neglecting the terms with themultiplication of two coefficients of variation square (COV 2 COV 2 ) as they would yieldinsignificantly small values, the expression for β is simplified as( ) 0√ . /. / 1√ 0. / ( )1(5.10)Equating the LRFD strength limit state equation (γQ = φR) and replacing the φR withφ EOD R EOD +φ setup R setup , the R setup can be rearranged as(5.11)Substituting Eq. (5.11) into Eq. (5.10) and isolating the φ setup parameter to the left side byrearranging Eq. (5.10), the preliminary form of the resistance factor for pile setup can beexpressed in the following form.