Reliability Assessment of the Capacity of Single Pile Subjected to Vertical Loading

"This paper performs the reliability evaluation of pile foundation under vertical loading condition using the concept of fuzzy set theory. The uncertain parameters are expressed as fuzzy numbers. Monte Carlo simulation technique in conjunction with fuzzy set theory and fuzzy reliability index approach are implemented in evaluation of the probability of failure of pile foundations. The results are validated through some well established methods such as, First Order Reliability Method (FORM), Second Order Reliability Method (SORM), and direct Monte Carlo Simulation (MCS). Response surface method (RSM) is used to approximate the original limit state equation through second order polynomial. The effect of the position of the water table is also highlighted. Finally, the effect of the variation of applied load is examined and it is observed that the fuzzy reliability analysis gives more conservative estimate of failure probability than the other methods.INTRODUCTIONCivil engineering structures, such as high rise buildings, bridges, offshore platforms etc. are always subjected to vertical as well as horizontal loads. To support these structures, pile foundations are generally the solution in most of the situation. It transmits load from the superstructure to soil at a reasonably great depth. This transfer may be by vertical distribution of the load along the pile shaft or a direct application of load to a lower stratum through the pile tip. Different methods are available to estimate the capacity of piles embedded in different types of soil and under the application of vertical and horizontal loading. To consider the variability in soil and other unforeseen able situation, generally a reasonable value of factor of safety is used to estimate the designed capacity of the pile. Recent developments have shown a trend to place the treatment of uncertainty on a more formal basis, in particular by applying the results of reliability theory to geotechnical engineering. Keeping in mind the importance of pile foundation in the engineering structures it is essential to maintain a high structural safety which result in increase in reliability. The probability theory has been proved to be a powerful tool for representing variability in mathematical models. The variability associated with soil parameters and the modeling uncertainties are needed to be considered for the reliability assessment purpose.Recent development (Zhang et al. 2005; Misra and Roberts 2006; Haldar and Babu 2008; Basu and Salgado 2012; Teixeira et al. 2012; Pula and Rozanski 2012; and Chan and Low 2012) showed that the reliability analysis of pile foundations subjected to axial as well as lateral load has been one of the important current research topic in geotechnical field. Probabilistic based performance criteria were quantified for a single pile and pile groups in cohesionless soil by Eloseily et al. (2002). A p-multiplier approach was incorporated into the analysis to modify the p-y curve for a single pile to obtain the p-y curve for individual piles in a pile group. A statistical analysis of set up capacity of pile was carried out from the database of a large number of pile testing data in clay by Yang and Liang (2006). Load and resistance factor design (LRFD) using FORM was used for examining the different load and resistance factor for different target reliability index. Limit state analysis of drilled shaft was performed by Misra and Roberts (2006) in probabilistic framework. The fuzzy based reliability analysis (Dodagoudar and Venkatachalam 2000; and Park et al. 2012) of the earth slope was reported in the literature. Dodagoudar and Venkatachalam (2000) presented a new approach, called fuzzy point estimate method (FPEM) for reliability evaluation of earth slope. Park et al. (2012) reported a hybrid approach, fuzzy set theory in conjunction with Monte Carlo simulation technique, to determine the failure probability of earth slope. Second Order Reliability Method"