# Incorporating Setup Effects into the Reliability Analysis of Driven Piles
## 1 Introduction  
Piles that are driven into the soil usually show an increase in bearing capacity (ultimate resistance) over time after EOD, which is often referred to as the setup effect of driven piles. This phenomenon is reported by many geotechnical engineers. [PERSON] and [PERSON] [1] first put forward the setup effect of driven piles. [PERSON] and [PERSON] [2] illustrated four cases in which the bearing capacity of piles changed significantly over time. [PERSON] et al. [3] investigated the jacking of piles in clay by finite element method. [PERSON] et al. [4] proposed a large number of references related to the topic of pile setup. [PERSON] et al. [5] developed a method for quantifying pile setup by using recent field tests when the steel H-piles were driven into clay. The soil setup phenomenon is mainly composed of three factors: (1) excess pore water pressure dissipation, (2) thixotropic effect, and (3) aging effect [6]. Driven piles have obvious disturbance and remodeling effects on the soil around the pile, which makes the pore water pressure dissipate. Therefore, the effects of setup on pile resistance depend on the type of soil in which the pile is driven.  
As for the bearing capacity of piles, along with some of the most traditional and commonly used methods among practitioners [7; 8; 9; 10; 11], there are more recent approaches, which are based on, for example, the finite element method [12; 13; 14]. Meanwhile, some researchers [15; 16; 17] indicated that pile setup phenomena should be formally included in the forecast technique of total pile resistance as experience and understanding of thephenomenon grew. For the purpose of predicting the pile's side resistance at a specific time after EOD and incorporating its influence into the pile design, [PERSON] et al. [18] presented a conservative method in which the side shear setup was included in pile resistance design. Due to different uncertainties associated with EOD resistance and setup resistance, [PERSON] et al. [19] proposed an approach to split factors of safety into EOD and setup parts in terms of pile capacity, and this method was especially suitable for load and resistance factor design (LRFD).  
LRFD is the most important and potential class of reliability-based design approaches, which commonly can quantitatively incorporate more uncertainties into the design process, in particular for uncertainties in loads and resistances [20]. Some research studies [21] were conducted to incorporate the setup effects on the LRFD resistance factor into deep foundation design. [PERSON] and [PERSON] [22] added setup resistance into the LRFD of driven piles. [PERSON] et al. [23] suggested a method for a reliability-based design that takes setup effects into account. Despite the fact that full-scale load tests were undertaken for driven piles with setup effects, and a substantial amount of data was acquired [24], the setup resistance of driven piles was rarely used to the maximum extent due to large uncertainties in the driving process. Therefore, the focus of this study is to establish a model for reliability analysis of driven piles considering setup effects.  
First, this paper presents a novel reliability index formula for driven piles by incorporating setup into the reliability evaluation method. Second, the range of relevant parameters is determined by the uncertainty analysis of load and resistance. Next, the influence of four critical parameters (factor of safety FOS; the ratio of dead load to live load \(\rho=Q_{\text{D}}/Q_{\text{L}}\); the ratio of setup resistance to initial ultimate resistance \(M_{\text{setup}}\); the correlation coefficient between \(R_{0}\) and \(R_{\text{setup}}\), \(\rho_{\text{R0,Resup}}\)) on the reliability index are analyzed. Finally, through a validation example analysis, it is verified that the method proposed in this study is reasonable, and it is concluded that the method proposed in this study is more accurate in calculating the reliability index and considers more uncertainties.