Accounting for nonuniform correlation structure: Bayesian evidence-based selection of 3D auto-correlation functions for loess properties

Loess deposits are often considered as regionally homogeneous, but their geotechnical properties exhibit pronounced site-specific spatial variability due to depositional heterogeneity. Accurately capturing this variability is essential for reliable geotechnical design and risk assessment in loess regions. This study proposes a Bayesian selection framework to address two important yet frequently overlooked aspects of three-dimensional (3D) random field modeling for loess deposits: (1) selecting the most appropriate auto-correlation function (ACF) among competing candidates, and (2) evaluating the common assumption that different geotechnical parameters can be modeled using identical ACF structures. Model evidence serves as a quantitative metric for comparing the plausibility of three widely used ACF types: single exponential function, squared exponential function, and second-order Markov models. The proposed framework is demonstrated using both numerical and field data from a 3D site investigation in Taiyuan, China. Results indicate that conventional assumptions of shared ACF structures across different soil properties may not hold for loess. Specifically, a transverse isotropic single exponential ACFs better represents the spatial variability of self-weight collapsibility coefficient and water content, whereas a transversely isotropic squared exponential model more accurately characterizes the natural void ratio and dry density. These findings offer practical, evidence-based guidance for selecting spatially consistent and property-specific random field models in loess, thereby improving reliability in geotechnical characterization and engineering design.