Probability Characteristics of a Crack Hitting Spherical Healing Agent Particles: Application to a Self-Healing Cementitious System
Bibliographic record
Abstract
A geometric model is developed to statistically study the probability characteristics of crack intersecting self-healing capsules with a structured random distribution in a cement paste mix. To evaluate the probability of a crack intersecting encapsulated particles, the fill ratio of the crack, and the depth of the first-hit capsule, Monte Carlo simulations are performed. The variables are the crack geometry, i.e., width, length, depth, orientation, skewness, and so on; the size and mass fraction of healing capsules; and the agglomeration of capsules. Models based on statistical analyses for hit probability Ph, crack fill ratio Rf-95 at 95% confidence level, and first hit depth h0-95 at 95% confidence level are expressed as functions of capsule size and mass fraction, as well as crack geometry. The model assumptions and results are evaluated using data reported in the literature. The data include results from experimental and theoretical studies.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".