Probabilistic Assessment for Slope Using the Generalized Chebyshev Inequalities
Publication: International Journal of Geomechanics
Volume 20, Issue 4
Abstract
This paper aims to estimate the probability of failure () of slope based on Chebyshev inequalities. Traditionally, for a slope reliability analysis, the supposed distribution types of shear strength parameters are employed; this is not accurate because the distribution types of parameters are uncertain. Chebyshev inequalities can estimate the probability even when the distribution types of variables are unknown. The upper bound value of the probability of failure () of a step-shaped slope is derived based on the Chebyshev inequalities. Additionally, the bootstrap method combined with the Akaike information criterion (AIC) are adopted to validate the accuracy and efficiency of the proposed method. It can be concluded from the illustrative example that the of a slope can be estimated by the Chebyshev inequalities. Compared with traditional probabilistic methods, Chebyshev inequalities are a quick and easy way to assess the upper bound value of .
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The work is supported by the National Natural Science Foundation of China (Nos. 51909087, 51679017), Research Fund of Hunan University of Science and Technology (No. E51975), Open Fund of National Engineering Laboratory of Highway Maintenance Technology (Changsha University of Science & Technology, kfj190107), and Scientific Research Projects of Hunan Education Department (18K064).
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©2020 American Society of Civil Engineers.
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Received: May 4, 2019
Accepted: Sep 20, 2019
Published online: Jan 28, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 28, 2020
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