# Development of Rock Embedded Drilled Shaft Resistance Factors in Korea based on Field Tests
## 3 Determination of Resistance Factors
### Determination of Target Reliability Index  
To consider the transition from ASD to LRFD, a reliability analysis was performed and the reliability indices of shafts designed using the current design practice (ASD) were estimated. The Korean design standard for foundation structures requires a safety factor of 3.0 for pile bearing capacity design; therefore, the reliability analysis was performed for safety factors of 2.0-5.0 using the advanced first-order second moment (AFOSM) method.  
The AFOSM method, named so because it is based on a first-order Taylor series approximation of the limit state function and because it uses only the second-moment statistics (mean and COV) of the variables, was proposed by [PERSON] and [PERSON] [29] and is known as one of the most accurate methods of reliability analysis. When the AFOSM method is used, the limit state function is linearized at the design point on the nonlinear failure surface, so the full distribution of information can be used rather than simply the mean value of the random variables. The results of the AFOSM reliability analysis are summarized in Table 10.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Reliability index (\(\beta_{\text{T}}\))**} \\ \cline{2-5}
**Bearing capacity equation** & **FS = 2.0** & **FS = 3.0** & **FS = 4.0** & **FS = 5.0** \\ \hline [PERSON] \& [PERSON] (1988) & 1.73 & 2.40 & 2.88 & 3.25 \\ \hline [PERSON] \& [PERSON] (1979) & 1.62 & 2.30 & 2.78 & 3.15 \\ \hline FHWA (1999) & 1.71 & 2.39 & 2.87 & 3.24 \\ \hline [PERSON] \& [PERSON] (1987) & 0.34 & 1.01 & 1.49 & 1.86 \\ \hline \multicolumn{5}{c}{**(b) Base resistance.**} \\ \cline{2-5}
**Bearing capacity equation** & \multicolumn{4}{c}{**Reliability index (\(\beta_{\text{T}}\))**} \\ \cline{2-5}
**Eearing capacity equation** & **FS = 2.0** & **FS = 3.0** & **FS = 4.0** & **FS = 5.0** \\ \hline [PERSON] \& [PERSON] (1988) & 1.20 & 1.89 & 2.37 & 2.75 \\ \hline FHWA (1999) & 0.89 & 1.41 & 2.02 & 2.38 \\ \hline [PERSON] \& [PERSON] (1998) & 1.08 & 1.97 & 2.60 & 3.08 \\ \hline \multicolumn{5}{c}{**(c) Total resistance.**} \\ \cline{2-5}
**Bearing capacity equation** & \multicolumn{4}{c}{**Reliability index (\(\beta_{\text{T}}\))**} \\ \cline{2-5}
**Eearing capacity equation** & **FS = 2.0** & **FS = 3.0** & **FS = 4.0** & **FS = 5.0** \\ \hline [PERSON] \& [PERSON] (1988) & 2.12 & 2.80 & 3.26 & 3.65 \\ \hline FHWA (1999) & 1.61 & 2.24 & 2.68 & 3.03 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Reliability analysis results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(b) Base resistance.**} \\ \hline
**Design method** & **Pile no.** & **Mean (\(\lambda_{\text{R}}\))** & **Standard deviation** & **Coefficient of variation** \\ \hline [PERSON] \& [PERSON] (1988) & 9 & 1.30 & 0.83 & 0.64 \\ \hline FHWA (1999) & 10 & 1.12 & 0.75 & 0.67 \\ \hline [PERSON] \& [PERSON] (1998) & 10 & 0.97 & 0.45 & 0.47 \\ \hline \multicolumn{5}{c}{**(c) Total resistance.**} \\ \hline
**Design method** & **Pile no.** & **Mean (\(\lambda_{\text{R}}\))** & **Standard deviation** & **Coefficient of variation** \\ \hline [PERSON] \& [PERSON] (1988) & 6 & 2.29 & 1.48 & 0.65 \\ \hline FHWA (1999) & 6 & 1.88 & 1.34 & 0.71 \\ \hline \hline \end{tabular}
\end{table}
Table 9: _Cont._Recently, AASHTO LRFD [1] selected a target reliability index of 3.0 for a typical drilled shaft. Moreover, KICT [5] suggested a target reliability index between 3.0-3.5 for drilled shafts. Based on the reliability analysis results and previous research [1; 5], target reliability indices (\(\beta_{\text{T}}\)) of 2.5, 3.0, and 3.5 were selected for the calibration of the resistance factors in this study.