Modeling the Relationship Between SPT-N Value and Compression Index (Cc) Using Copula Theory for Thi-Qar Clay Soil
Bibliographic record
Abstract
Accurate estimation of the coefficient of compressibility (Cc) is essential for predicting foundation settlement, yet odometer tests on undisturbed samples are often limited in most site investigations.In contrast, standard penetration test (SPT) data are more widely available.Existing SPT-Cc correlations are extremely limited and often inconsistent across soil types, and previous studies relied mainly on linear regression, which cannot capture nonlinear or asymmetric dependence.This study addresses these gaps by developing a probabilistic framework to model the dependency structure between SPT-N₆₀ and Cc for clay soils in Thi-Qar, southern Iraq, using copula theory.Several copula candidates were evaluated using AIC and BIC criteria, and their performance was compared with the classical Nataf model.In addition, the Bootstrap method was adopted as a robust resampling tool to quantify uncertainty in dependence modeling under limited data conditions.The measured data exhibited a moderate negative dependence (ρ = -0.56,τ = -0.43),confirming that denser soils (higher N₆₀) tend to have lower compressibility.Among the tested models, the Gaussian copula provided the best statistical representation of the joint behavior of N₆₀ and Cc.Results also showed that Pearson's correlation (ρ) is not invariant under monotonic transformations, whereas the Nataf model behaves similarly to the Gaussian copula when dependence is approximately linear.The proposed framework enhances reliability-based characterization of local soils and reduces reliance on extensive laboratory testing by enabling accurate simulation of soil parameters.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".