Bootstrap method for characterizing statistical uncertainty in bivariate shear strength parameters and its application to reliability‐based design of slopes

Abstract

This study characterizes the statistical uncertainties in the bivariate distribution of friction angle and cohesion of soils using bootstrap method and explores its application to the reliability‐based design of slopes. First, the bivariate distribution of friction angle and cohesion is modelled using the copula approach based on limited test data. Then, the statistical uncertainties in the derived bivariate distribution of friction angle and cohesion are characterized by the bootstrap method. Finally, an infinite slope is employed to investigate the impact of the statistical uncertainties in friction angle and cohesion on slope reliability. The reliability‐based designs of slopes based on the point and interval estimate of reliability index are compared. The results indicate that the bivariate distribution of friction angle and cohesion derived from limited test data exhibits large statistical uncertainties. The reliability index of the infinite slope shows visible variation because of the large statistical uncertainties in friction angle and cohesion. The reliability index of slopes considering the statistical uncertainties in friction angle and cohesion is presented as a confidence interval. The interval estimate of reliability index gives a more comprehensive description of slope reliability than the point estimate of reliability index. Furthermore, the reliability‐based design of slopes based on the interval estimate of reliability index can reflect the effect of the amount of test data on the design and link the site investigation efforts and investments on shear tests to final design savings.