# Incorporating Setup Effects into the Reliability Analysis of Driven Piles
## 5 Validation Example  
In order to verify the accuracy of the formula proposed in this paper, it was compared with the formula proposed by [PERSON] et al. [17]. At the same time, the data in the Case Pile Wave Analysis Program (CAPWAP) were compared; the measured and predicted resistance values of 19 test piles are related in Table 3[17]. For calculating the reliability index, the corresponding load statistical parameters, such as \(\lambda_{\text{R}}\) = 1.335, \(\text{COV}_{\text{R}}\) = 0.325 [21], \(\lambda_{\text{QD}}\) = 1.080, \(\lambda_{\text{QL}}\) = 1.150, \(\text{COV}_{\text{QD}}\) = 0.130, \(\text{COV}_{\text{QL}}\) = 0.180 [29], were considered. Meanwhile, the statistical parameters of setup resistance were calculated at four different intervals of 14 days after EOD (i.e., 30, 45, 60, and 90 days after drive). The values of \(\lambda_{\text{setup}}\) are 1.218, 1.092, 1.059, and 1.033, respectively, and the values of \(\text{COV}_{\text{setup}}\) are 0.641, 0.62, 0.64, and 0.66, respectively. As for the value of the four critical parameters proposed in this study, the conclusion drawn from the \"Reliability Analysis\" in Section 4 shows that the value of FOS is 3.0, and the value of \(\rho\) is 3.69. Referring to the parameter \(A\) model proposed by [PERSON] et al. [17], the value of \(A\) in clay and sand are 0.31 and 0.15, respectively. In this study, the values of \(M_{\text{setup}}\) was calculated using Equation (12) at four different intervals of 14 days after EOD (i.e., 30, 45, 60 and 90 days after driving), which are 0.551, 0.606, 0.645, 0.699 in clay, and 0.267, 0.293, 0.312, 0.338 in sand, respectively. According to the values of \(R_{0}\) and \(R_{\text{setup}}\) shown in Table 3, the value of \(\rho_{\text{R0,Restup}}\) can be calculated as 0.312, 0.387, 0.386, and 0.378 at four different time intervals. The findings of computing the reliability index using the formulas presented by [PERSON] et al. [17] and presented by this study are summarized in Table 4, and the curve of reliability index is drawn together with time interval, as shown in Figure 5. When the correlation between \(R_{0}\) and \(R_{\text{setup}}\) is considered, the reliability index calculated by the formula proposed in this paper is not significantly different from that calculated by the formula proposed in [PERSON] et al. [17], which is usually around 0.3. As a result, this conclusion shows that the formula proposed in this study is feasible. When the correlation  
Figure 4: Reliability indices with \(\rho_{\text{R0,Restup}}\) for driven piles in clay and sand. between \(R_{0}\) and \(R_{\rm setup}\) is not considered, the difference between the results calculated in this study and those calculated by the formula proposed by [PERSON] et al. (1998) is about 0.5. Although the results are slightly higher, the correlation between \(R_{0}\) and \(R_{\rm setup}\) is considered, and more uncertainties in the piling process are investigated, bringing the results closer to engineering application. Compared with [PERSON] et al. (1998), this paper proposes a critical parameter (\(M_{\rm setup}\)), which is suitable for various soil types and takes more uncertainties into account, providing a more comprehensive theoretical basis for future research. Figure 5 further demonstrates that the reliability index for the driven pile considering setup effects in clay is much higher than that of the driven pile in sand, which is consistent with the conclusion of Section 4 \"Reliability Analysis\".