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-N 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 ( = -0.56, = -0.43),confirming that denser soils (higher N) tend to have lower compressibility.Among the tested models, the Gaussian copula provided the best statistical representation of the joint behavior of N and Cc.Results also showed that Pearson's correlation () 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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".