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

204, -( )√ [( ). /]. /√( )(5.12)Normalizing the above expression by the total load (Q D + Q L ) and further expressing Eq.(5.12) in terms of the ratio of dead load to live load (Q D /Q L ) and the ratio of initial pileresistance at EOD to total load using ./, the final equation of the resistancefactor for pile setup at a target reliability index (β T ) yields to[( )( )].( )( )/√ [( ). /](5.13). /√( )5.6. Resistance Factors For SetupThe aforementioned derivation resulted in Eq. (5.13) reveals that the φ setup value isdependent on various parameters. Considering only the AASHTO (2010) strength I loadcombination, the probabilistic characteristics (γ, λ and COV) of the random variables Q D andQ L are defined in Eq. (5.2) as documented by Nowak (1999). The probabilisticcharacteristics (λ and COV) of the random variables R EOD and R setup were selected from Cases4 and 5 of Table 5.2, respectively. Therefore, the following analyses focus on the influenceof the remaining random variables (β T , α, φ EOD and Q D /Q L ) on the φ setup value.Since the uncertainty for the pile resistance at EOD is lower than that for setup(COV EOD of 0.157 versus COV setup of 0.317) and both resistance mean biases are closer tounity (λ EOD = 1.111 and λ setup = 0.950), the calculated φ EOD values will likely higher than the