Bayesian Hierarchical Spatial Modeling of Soil Properties

In geotechnical engineering, the mechanical properties of the soil at a specific site are usually inferred based on data obtained from in-situ or laboratory measurements. Results of geotechnical design and assessment depend on the proper quantification of the soil properties based on typically sparse site-specific data. We present a comprehensive hierarchical Bayesian model for incorporating measurement information in the probabilistic modeling of soil properties, which accounts for the inherent spatial variability of the properties and the spatial correlation of the measurements. We employ a conjugate prior approach to update the prior random field of the soil property such that closed-form expressions are obtained for the spatial posterior predictive distribution. The model requires specification of the parameters of the prior autocorrelation structure of the random field, which can be done through evaluating their maximum a-posteriori estimates. In this way, the proposed framework represents an efficient yet theoretically thorough approach to probabilistic site characterization. We illustrate the approach using real data from a geotechnical site.

Keywords: Site characterization, random fields, Bayesian analysis, hyperparameters, conjugate prior, predictive distribution