Stability of layered soil slope with tension crack: a closed-form solution
Bibliographic record
Abstract
Evaluating the stability of layered slopes, a common type of terrain in nature and engineering practice, poses a fundamental challenge in the field of geotechnique. The emergence and extension of tension cracks play a crucial role in the failure process of layered slopes, but accurately predicting the location of layered slope cracking and assessing its impact on layered slopes remains a challenge using conventional analytical methods. Herein, we present a closed-form solution for evaluating the layered slope stability with tension cracks without any priori assumptions. The presented closed-form solution enables the location and depth of tension crack, the critical failure surface in different soil layers, and the corresponding normal stress distribution to be determined for all single/layered slopes. Effects of tension cracks on layered slopes are investigated, considering slope inclination, soil properties, layer thickness, and dominant failure mechanism. Note that, the results show that the dominant failure mode of layered slopes could change from toe failure (without cracks) to face/base failure (with tension cracks), which has not been previously reported. Multiple cracks are possible to develop in layered slopes. The proposed closed-form solution can be applied to improve the stability assessment and engineering design of layered slopes considering tension crack.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".