Improved Vanmarcke analytical model for 3D slope reliability analysis

Abstract

This paper presents an improved algorithm for evaluating the reliability of three-dimensional soil slopes based on the Vanmarcke model (VM). In the development of the improved Vanmarcke model (IVM), the sliding mass is assumed to be a portion of a cylinder bounded by two ellipsoidal end sections. The soil spatial variability of both the cylindrical and ellipsoidal sections is considered. A set of equations is derived to determine critical failure surfaces and compute their reliability indices. Numerical studies are performed to examine the IVM. The results indicate that (1) the IVM predicts a similar critical failure length compared with that computed by the VM. However, a lower reliability index is obtained by the former. (2) The relative difference between the reliability indices computed by the two analytical models can reach 20% for practical situations. The horizontal scale of fluctuation (SOF) of soil properties is the main factor affecting the relative difference. (3) Compared to the random finite element method, the IVM still gives unconservative analysis results, especially at low horizontal SOFs. This is due to the prediction of smaller critical failure lengths by the IVM for small horizontal SOFs and some retained assumptions of the VM when developing the IVM.