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

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The paper evaluates the reliability of a single pile under vertical loading, accounting for uncertainty in soil properties and applied load. It compares fuzzy-set-based methods with conventional probabilistic approaches.<br /><br />Soil friction angles, unit weights, and pile load are represented as trapezoidal fuzzy numbers. Failure probability is estimated using fuzzy Monte Carlo simulation (FMCS) and a fuzzy reliability index method. Results are compared with First- and Second-Order Reliability Methods (FORM and SORM), direct Monte Carlo simulation, and a response surface method (RSM).<br /><br />The fuzzy methods show that estimated failure probability depends on the parameters defining the fuzzy-number ranges; larger ranges generally produce higher failure probabilities. For the conventional probabilistic analysis, FORM gives a failure probability of 0.0149, while direct Monte Carlo simulation and SORM both give approximately 0.0133. RSM produces reliability indices very close to those from the original limit-state analysis.<br /><br />The study also examines water-table depth and variation in applied load. A deeper water table reduces failure probability across the methods. Increasing the load’s coefficient of variation raises failure probability, with the fuzzy reliability approach giving more conservative estimates at higher variability.<br /><br />Overall, the findings demonstrate that fuzzy reliability analysis can represent vagueness and ambiguity that conventional probabilistic methods do not explicitly capture. The authors recommend considering uncertainty in both geotechnical parameters and loading when assessing pile safety.

Keywords

pile reliability

vertical loading

fuzzy reliability

fuzzy Monte Carlo simulation

failure probability

soil uncertainty

trapezoidal fuzzy numbers

FORM

SORM

response surface method