Jackknifing for modeling sampling properties of soil statistics for geotechnical reliability analysis

Abstract

This study introduces the jackknife method to model the statistical uncertainty in the joint distribution of geotechnical parameters derived from a small sample and its effect on geotechnical reliability. A numerical example using simulated data is adopted to validate the accuracy of the jackknife method. The following three real examples are studied to illustrate and demonstrate the jackknife method: (1) the reliability analysis of an infinite slope, (2) the serviceability limit state (SLS) reliability analysis of piles, and (3) the reliability analysis of a single-layered slope. The results indicate that sample statistics and resulting reliability index estimated from a small sample show visible statistical uncertainty. The jackknife method has a good accuracy and efficiency in modeling the sampling properties of sample statistics and resulting reliability index. The jackknife method overcomes the drawback of inefficiency associated with the bootstrap method, and can be applied to both the simple and complex geotechnical problems. By applying the jackknife method, an interval estimate of reliability index at a specified confidence level instead of a point estimate of reliability index is derived. The interval estimate of reliability index not only includes the point estimate of reliability index, but also quantifies the upper and lower bounds within which the point estimate of reliability index may vary. A larger sample size produces smaller statistical uncertainty in sample statistics and resulting reliability index, which provides an incentive for geotechnical engineers to draw more data of geotechnical parameters in a typical site investigation.