Efficient Bayesian characterization of cohesion and friction angle of soil using parametric bootstrap method
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ORIGINAL PAPER
Efficient Bayesian characterization of cohesion and friction angle of soil using parametric bootstrap method Xiong-Feng Liu 1,2,3 & Xiao-Song Tang 1,2,3 & Dian-Qing Li 1,2,3 Received: 17 March 2020 / Accepted: 26 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study develops an efficient Bayesian approach using the parametric bootstrap method for characterizing the joint probability density function (PDF) of c′ and ϕ′ based on limited site-specific test data and prior knowledge. An example using real data of c′ and ϕ′ obtained from direct shear tests on alluvial fine-grained soils at the Paglia River alluvial plain in Central Italy is presented to illustrate and demonstrate the parametric bootstrap method. A sensitivity study is performed to investigate the impact of the amount of site-specific test data and prior knowledge on the posterior statistics of c′ and ϕ′. The results indicate that the parametric bootstrap method has a good accuracy and efficiency in characterizing the joint PDF of c′ and ϕ′. By reconstructing the likelihood function and rewriting the joint PDF of c′ and ϕ′ based on a large number of parametric bootstrap samples, the parametric bootstrap method significantly improves the efficiency of the conventional Bayesian approach while retaining the same accuracy as the conventional Bayesian approach. The equivalent sample pairs of c′ and ϕ′ generated using the Markov chain Monte Carlo simulation represent the joint PDF of c′ and ϕ′ well. The amount of site-specific test data and prior knowledge have a significant impact on the posterior statistics of c′ and ϕ′. Increasing the amount of the site-specific data and informativeness of the prior knowledge can reduce the statistical uncertainty in the posterior statistics. In addition, the role of prior knowledge decreases as the amount of the site-specific data increases. Keywords Shear strength parameters . Joint probability distribution . Bayesian approach . Markov chain Monte Carlo simulation . Parametric bootstrap method
Introduction It is well known that the effective cohesion (c′) and effective friction angle (ϕ′) of soil are key parameters for evaluating the stability of various geotechnical structures such as slopes (e.g., Young 1985; Griffiths et al. 2011; Tang et al. 2012, 2013, 2015; Wang et al. 2020), retaining walls (e.g., Rowe and * Xiao-Song Tang [email protected] 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 299 Bayi Road, Wuhan 430072, People’s Republic of China
2
Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, 299 Bayi Road, Wuhan 430072, People’s Republic of China
3
Institute of Engineering Risk and Disaster Prevention, Wuhan University, 299 Bayi Road, Wuhan 430072, People’s Republic of China
Skinner 2001; Low 2005), and foundations (e.g., Soubra 1999; Cherubini 2000; Fenton et al. 2008). In a probabilistic analysis of these geotechnical structures, c′ a
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