Influence of Failure Probability Due to Parameter and Anchor Variance of a Freeway Dip Slope Slide—A Case Study in Taiwan †

Abstract

Abstract:The traditional slope stability analysis used the Factor of Safety (FS) from the Limit Equilibrium Theory as the determinant. If the FS was greater than 1, it was considered as "safe" and variables or parameters of uncertainty in the analysis model were not considered. The objective of research was to analyze the stability of natural slope, in consideration of characteristics of rock layers and the variability of pre-stressing force. By sensitivity and uncertainty analysis, the result showed the sensitivity for pre-stressing force of rock anchor was significantly smaller than the cohesive (c) of rock layer and the varying influence of the friction angle (φ) in rock layers. In addition, the immersion by water at the natural slope would weaken the rock layers, in which the cohesion c was reduced to 6 kPa and the friction angle φ was decreased below 14 • , and it started to show instability and failure in the balance as FS became smaller than 1. The failure rate to the slope could be as high as 50%. By stabilizing with a rock anchor, the failure rate could be reduced below 3%, greatly improving the stability and the reliability of the slope.

Some Remarks on the Use of Deterministic and Probabilistic Approaches in the Evaluation of Rock Slope Stability

“…For this reason, in order to take into account the wide variability of geo-structural and geo-mechanical parameters, methods based on the theory of statistics and probability are increasingly used. A critical review of these approaches and their pros and cons advantages is attributable to [2,3]. The Monte Carlo (MC) simulation is one of the most used methods because it is deemed suitable for considering uncertainties and the most commonly available commercial codes often incorporate it [4].…”

Simplified algorithm for reliability sensitivity analysis of structures: A spreadsheet implementation

“…Because of aleatory and/or epistemic uncertainties associated with loads and capacity of structures alike, deterministic models fail to provide a sufficiently reliable estimation of design variables [1]. In order to consider the uncertainties, probabilistic methods are thus preferred [2–4]. That is, reliability-based design optimization is adopted for structural design process [5].…”