Reliability Analysis of Vertically Loaded Piles Using Conditional Random Fields

Soil has spatial variability, which means that soil properties at two spatial points are correlated but different. Reliability analysis and risk evaluation of vertically loaded pile in spatially variable soils is important for both the safety evaluation and optimal design of the pile. In this study, the conditional random field theory is adopted to simulate the random fields of soil parameters, and the Karhunen–Loève (KL) expansion method is employed to discrete the random fields. Based on the formulas of unconditional Karhunen–Loève (UKL) expansion method, calculation process and formulas of two conditional KL expansion methods (CKL1 and CKL2) are derived. A hybrid method, FORM-CKL-LTM, is proposed to carry out reliability analysis for pile’s stability. In FORM-CKL-LTM, the first-order reliability method (FORM) is used to calculate the reliability index of the pile, the conditional Karhunen–Loève (CKL) is adopted to discrete random fields of soil parameters, and the load transfer method (LTM) is employed to calculate the ultimate bearing capacity of the pile. By applying FORM-CKL-LTM to a case study of a vertically loaded pile, features of the CKL1, CKL2, and FORM-CKL-LTM are illustrated. The two CKLs can make full use of the measured soil properties at different observation points near the pile. CKL1 and CKL2 are superior to UKL because the first two methods can constrain the fluctuation of the discrete values of random field near each observation point, and CKL1 is better than CKL2 because CKL1 can force the fluctuation of random field to be zero at the observation points. The reliability index of the pile depends on the locations and number of observation points. Optimal design of geotechnical investigation points is necessary for the safe evaluation and economical design of piles in spatially variable soils.