# Reliability-Based Design of Driven Piles Considering Setup Effects
###### Abstract  
The total ultimate resistance (or bearing capacity) of driven piles considering setup effects is composed of initial ultimate resistance and setup resistance, and the setup effects of driven piles are mainly reflected by the setup resistance. In literature, a logarithmic empirical formula is generally used to quantify the setup effects of driven piles. This paper proposes an increase factor (\(M_{\text{setup}}\)) to modify the resistance factor and factor of safety calculation formula in accordance with the load and resistance factor design (LFRD) principle; here, the increase factor is defined as the ratio of the setup resistance (\(R_{\text{setup}}\)) to the initial ultimate resistance (\(R_{0}\)) of driven piles. Meanwhile, the correlation between \(R_{0}\) and \(R_{\text{setup}}\) is fully considered in the resistance factor and factor of safety calculation. Finally, the influence of four key parameters (ratio of dead load to live load \(\rho=Q_{\text{O}}/Q_{\text{L}}\), target reliability index \(\beta_{\text{T}}\), \(M_{\text{setup}}\), correlation coefficient between \(R_{0}\) and \(R_{\text{setup}}\), \(\rho_{\text{R0,Rsetup}}\)) on the resistance factor and factor of safety are analyzed. Parametric research shows that \(\rho\) has basically no effect on the resistance factor, which can be taken as a constant in further research, and \(\rho\) has a significant influence on the factor of safety. The value of \(M_{\text{setup}}\) has almost no effect on the resistance factor and factor of safety. However, \(\beta_{\text{T}}\) and \(\rho_{\text{R0,Rsetup}}\) have a significant influence on the resistance factor and factor of safety, so the value selection of \(\beta_{\text{T}}\) and \(\rho_{\text{R0,Rsetup}}\) are crucial for reliability-based design of  
Many studies are available in the literature to evaluate the capacity of piles on the basis of static and dynamic load tests. [PERSON] et al. [9] suggested installing the hydraulic jack as close to the caliche layers as possible. [PERSON] et al. [10] proposed a new CPT method, which can be expected to lead to more reliable estimates of pile capacity. [PERSON] et al. [11] presented a method in which the risk of soil liquefaction is reduced by using jet-grouted micropiles in sand. [PERSON] et al. [12] put forward the importance of understanding the unique aspects of the site geology. [PERSON] and [PERSON] [13] presented three different pipe pile test methods, which provided the possibility to evaluate the pile base and shaft bearing capacities. However, it is not convenient to evaluate the setup effect of piles. With the accumulation of experience and understanding of the pile setup phenomenon, some researchers [14; 15; 16] recommended that the pile setup phenomenon should be incorporated into the total ultimate resistance by the load and resistance factor design (LRFD) method. LRFD is a more advanced design method than the existing allowable stress design (ASD) [17], and many countries and regions, such as the United States, Canada, China mainland, Japan, Korea, Singapore, Europe, and Hong Kong, have replaced ASD with LRFD. Against this background, many researchers calculated the resistance factor and factor of safety for driven piles considering the setup effects based on the LRFD method. [PERSON] et al. [18] used the factor of safety to estimate setup effects in the driven pile resistance. [PERSON] and [PERSON] [19] proposed to incorporate the setup resistance into LRFD of driven piles based on the first-order reliability method (FORM). A framework for calculating the resistance factor of LRFD for driven piles in clay was proposed, which can fully consider all necessary reliability-related parameters [20]. [PERSON] and [PERSON] [21] presented a method to incorporate the economic advantages of a pile setup into LRFD recommendations to further improve the efficiency of bridge foundations. [PERSON] et al. [22] used reliability theory and the LRFD principle to establish an iterative algorithm of estimation of separate resistance factors.