Citation: Tang, X.-S.,Li, D.-Q.,Zhou, C.-B.,Phoon, K.-K. (2012-01). Probabilistic analysis of load-displacement hyperbolic curves of single pile using Copula. Yantu Lixue/Rock and Soil Mechanics 33 (1) : 171-178. ScholarBank@NUS Repository.
Abstract: This paper aims to propose a method for probabilistic analysis of load-displacement hyperbolic curves of single pile using Copula. Firstly, the uncertainties of probabilistic load-displacement hyperbolic model are transformed to the uncertainties of two curve-fitting parameters. Then the Copula theory is adopted to model the joint probability distribution function of the two curve-fitting parameters. The direct integration method is used to carry out the reliability computations for serviceability limit state of single pile. Finally, an example of load-test dataset for Augered Cast-in-Place (ACIP) pile is illustrated to demonstrate the validity and capability of the proposed method. The results indicate that the proposed Copula-based method can provide a more general and flexible way of modeling and simulating the bivariate probability distribution of the two curve-fitting parameters in isolation from their marginal probability distributions, which facilitates the generation of normalized load-displacement hyperbolic curves and thus results in more accurate reliability results for serviceability limit state of single pile. A strong negative correlation between the two parameters underlying the normalized load-displacement hyperbolic model can be observed. Neglecting such negative correlation will overestimate the probability of failure. In addition, the Gaussian Copula, often adopted out of expedience without proper validation, is not the best Copula for modeling the dependence structure underlying the two curve-fitting parameters. If the Gaussian Copula is adopted, the probability of failure of ACIP pile will be underestimated significantly.