System reliability evaluation of long railway subgrade slopes considering discrete instability

Abstract

This paper develops a dual-indicator discrete method (DDM) for evaluating the system reliability performance of long soil subgrade slopes. First, they are segmented into many slope sections using the random finite element method, to ensure each section statistically contains one potential local instability. Then, the k-out-of-n system model is used to describe the relationship between the total number of sections n, the acceptable number of failure sections m, the reliability of sections R_{{{text{sec}}}}, and the system reliability R_{{{text{sys}}}}. Finally, m and R_{{{text{sys}}}} are jointly used to assess the system reliability performance. For cases lacking spatial data of soil properties, a simplified DDM is provided in which long subgrade slopes are segmented by the empirical value of section length and R_{{{text{sec}}}} is substituted by that of cross-sections taken from them. The results show that (1) DDM can provide the probability that the actual number of local instabilities does not exceed a desired threshold. (2) R_{{{text{sys}}}} decreases with increasing n or decreasing R_{{{text{sec}}}}; that is, it is likely to encounter more local instabilities for longer or weaker subgrade slopes. n is negatively related to the horizontal scale of fluctuation of soil properties and positively related to the total length of subgrade slopes L. (3) When L is sufficiently large, there is a considerable opportunity to meet local instabilities even if R_{{{text{sec}}}} is large enough.