Bayesian identification of random field model using indirect test data

• Published in: Engineering geology 2016-08, Vol.210, p.197-211
• Main Authors: Tian, Mi, Li, Dian-Qing, Cao, Zi-Jun, Phoon, Kok-Kwang, Wang, Yu
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Bayesian approaches; Cone penetration test; Correlation; Design analysis; Design engineering; Effective friction angle; Fields (mathematics); Gaussian copula; Inherent spatial variability; Markov Chain Monte Carlo Simulation; Mathematical models; Soil (material); Transformations
• ISSN: 0013-7952; 1872-6917
• DOI: 10.1016/j.enggeo.2016.05.013

Inherent spatial variability (ISV) of design soil properties (e.g., effective friction angle φ′) can be incorporated into probability-based geotechnical analyses and designs using random field models. Defining a random field model includes determination of random field parameters (i.e., mean μ, standard deviation σ, and scale of fluctuation λ) and the correlation function that specifies the spatial correlation of the concerned design soil property (e.g., φ′) at different locations. This is, however, a challenging task at a given site due to a lack of direct test data of design soil properties and various uncertainties (e.g., transformation uncertainty) arising during site investigation. This paper develops Bayesian approaches for probabilistic characterization of the ISV of φ′ using indirect test data (i.e., cone penetration test (CPT) data) and prior knowledge, which identify random field parameters of φ′ through Markov Chain Monte Carlo Simulation (MCMCS) and, simultaneously, make use of Gaussian copula to select the most probable correlation function M⁎ among a pool of candidate correlation functions based on MCMCS samples. The proposed Bayesian approaches account, rationally and transparently, for the transformation uncertainty associated with the transformation model between φ′ and CPT data. The proposed approaches are illustrated and validated using real-life and simulated CPT data. Results show that the proposed approaches properly identify the random field model (including μ, σ, λ, and M⁎) of φ′ using project-specific CPT data, and the random field parameters of φ′ depend on the correlation function used to interpret CPT data. In addition, the suitability of MCMCS in Bayesian probabilistic characterization of soil properties is highlighted, particularly for the cases with a limited number of test data. •Bayesian approaches are proposed to identify random field model using CPT data.•Markov Chain Monte Carlo simulation (MCMCS) is used to solve the Bayesian equation.•Gaussian copula is applied to evaluating the evidence based on MCMCS samples.•The proposed approaches are validated using real and simulated CPT data.•Determination of random field parameters relies on choice of correlation function.