Slope reliability analysis using length-based representative slip surfaces
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ORIGINAL PAPER
Slope reliability analysis using length-based representative slip surfaces Xuesong Chu 1 & Liang Li 1 & Yujie Wang 2
Received: 23 September 2014 / Accepted: 1 April 2015 # Saudi Society for Geosciences 2015
Abstract This paper develops an empirical approach to slope reliability considering 2D spatial variability of soil properties with length-based representative slip surfaces. The correlation coefficient between factors of safety for two slip surfaces is analogous to that between two slip surfaces which is quantified based on the lengths within different elements of the slip surface. A large number of potential slip surfaces are categorized into separate slip surface groups within each of which the correlation coefficient between any two slip surfaces is higher than the threshold value. A slip surface with the minimum factor of safety is considered to be the representative slip surface for each of slip surface groups. The factor of safety is minimized among all the representative slip surfaces, and the minimum one is regarded as the output for each set of random samples generated by Monte Carlo simulation (MCS). The methodology is validated through comparison with other methods. It is found that slope failure probability, pf, increases as the scale of fluctuation, λy (in vertical direction), and λx (in horizontal direction) increase. The effect of non-circular failure mechanism was studied at different λx and λy values. Significant larger failure probabilities are provided with noncircular failure mechanism than with circular failure
* Liang Li [email protected] Xuesong Chu [email protected] Yujie Wang [email protected] 1
School of Civil Engineering, Qingdao Technological University, Qingdao, China
2
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Institute of Water Resources and Hydropower Research, Beijing, China
mechanism. For 2D spatial variability case, two orders of magnitude larger failure probability is noticed. Keywords Slope reliability analysis . Monte Carlo simulation . Slope stability . Limit equilibrium method . Length-based representative slip surface
Introduction Slope may fail along any individual slip surfaces. Therefore, the slope stability is a system problem, although evaluating the system reliability among all individual slip surfaces is a mathematically formidable task (EI-Ramly et al. 2002). Early works dealt with the system reliability on a number of predefined slip surfaces that were taken to be important failure modes (e.g., Oka and Wu 1990; Chowdhury and Xu 1995; Li et al. 2011; Low et al. 2011; Ji and Low 2012; Zhang et al. 2013). Although these works provided reasonably narrow bounds of system failure probability, the details for determining the predefined slip surfaces were not mentioned. Zhang et al. (2011) developed an iterative approach to dynamically determine the representative slip surface and evaluated the slope system reliability based on the identified representative slip surfaces. However, the most important limitati
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