On stress ratio equations in three-dimensional stress space for modelling soil behaviour
Bibliographic record
Abstract
Constitutive models and failure criteria of soils, rocks, and other materials often need to be extended beyond the triaxial state where they are usually defined, for plane strain, axisymmetric, or three-dimensional analyses. This extension is commonly done by making the stress ratio a function of the Lode angle. This process turns two-dimensional yield, plastic potential, bounding, dilatancy and similar surfaces into three-dimensional shapes such as cones and bullets. The equations used have a range of shapes on the octahedral or π-plane between Mohr-Coulomb’s irregular hexagon and Drucker-Prager’s circle. Nine stress ratio generalization equations popular in soil mechanics are evaluated based on numerical stability, agreement with available data, and ease of implementation. The computed limits on their convexity, and the flexibility they offer in the calibration process are discussed. At the end, a new equation that satisfies all these criteria while remaining simple and easy to calibrate is proposed, implemented in a finite element model, and demonstrated to improve numerical stability and efficiency.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".