Accounting for nonuniform correlation structure: Bayesian evidence-based selection of 3D auto-correlation functions for loess properties
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".