Bayesian model comparison and selection of spatial correlation functions for soil parameters

Abstract

The inherent spatial variability of soils is one of the major sources of uncertainties in soil properties, and it can be characterized explicitly using random field theory. In the context of random fields, the spatial correlation between the values of a soil property concerned at different locations is represented by its correlation structure (i.e., correlation functions). How to select a proper correlation function for a particular site has been a challenging task, particularly when only a limited number of project-specific test results are obtained during geotechnical site characterization. This paper develops a Bayesian model comparison approach for selection of the most probable correlation function among a pool of candidates (e.g., single exponential correlation function, binary noise correlation function, second-order Markov correlation function, and squared exponential correlation function) for a particular site using project-specific test results and site information available prior to the project (i.e., prior knowledge, such as engineering experience and judgments). Equations are derived for the proposed Bayesian model comparison approach, in which the inherent spatial variability is modeled explicitly using random field theory. Then, the proposed method is illustrated and validated through simulated cone penetration test (CPT) data and four sets of real CPT data obtained from the sand site of the US National Geotechnical Experimentation Sites (NGES) at Texas A&M University. In addition, sensitivity studies are performed to explore the effects of prior knowledge, the measurement resolution (i.e., sampling interval), and data quantity (i.e., sampling depth) on selection of the most probable correlation function for soil properties. It is found that the proposed approach properly selects the most probable correlation function and is applicable for general choices of prior knowledge. The performance of the method is improved as the measurement resolution improves and the data quantity increases.