CPT-Based Liquefaction Probabilistic Triggering Using a New Adaptive Kernel Density Estimation Method

A probabilistic cone penetration test (CPT) based liquefaction triggering procedure for granular soil is developed utilizing adaptive kernel density estimation (KDE). KDE with a fixed bandwidth has been applied for the computation of conditional probabilities for liquefied and non-liquefied datasets in prior studies; however, liquefaction data inherently have a combination of different distributions, so the use of a fixed bandwidth is a suboptimal solution. In this study, we presented a mathematical framework for the calculation of adaptive bandwidth through an iteration process. We validated the proposed adaptive KDE by comparing the result of conditional probability with the true density function for one-dimensional and two-dimensional problems. Then, the proposed adaptive KDE was applied for two-dimensional probabilistic liquefaction triggering using Bayes theory. The variables of tip resistance and cyclic stress ratio were considered as main predictors for two-dimensional classification. The proposed method's performance was evaluated using receiver operating characteristics (ROC) curves and the area under the curve (AUC) of the ROC. Training and testing data are selected randomly by a ratio of 80% and 20%. Three iterations were found as the best value satisfying the generality of conditional probability for liquefied and nonliquefied data and the performance of the Bayes classifier. An optimum classifier for this CPT database was found to be a threshold of 0.54 for the liquefaction probability. The results indicate that this estimator can effectively predict the liquefaction potential of CPT data, with an AUC above 0.88. The conclusion reached was that the variability in the probability of liquefaction calculated using the proposed method offers a better description of probabilities than the previous methods.