Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks
Bibliographic record
Abstract
The generalized mixture rule (GMR) is used to provide a unified framework for describing Young's ( E ), shear ( G ) and bulk ( K ) moduli, Lame parameter ( λ ), and P- and S-wave velocities ( V p and V s ) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E , G , K and λ of each material are systematically different and display consistent correlations with the Poisson's ratio of the nonporous material ( ν 0 ). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson's ratio ( ν ) remains constant is at ν 0 = 0.2, and J ( G ) > J ( E ) > J ( K ) > J ( λ ) and J ( G ) < J ( E ) < J ( K ) < J ( λ ) for materials with ν 0 > 0.2 and ν 0 < 0.2, respectively. J ( V s ) > J ( V p ) and J ( V s ) < J ( V p ) for the materials with ν 0 > 0.2 and ν 0 < 0.2, respectively. The effective ν increases, decreases and remains unchanged with increasing porosity for the materials with ν 0 < 0.2, ν 0 > 0.2 and ν 0 = 0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the ν fixed point decreases nonlinearly with decreasing pore aspect ratio ( α : width/length). With increasing depth or pressure, cracks with smaller α values are progressively closed, making the ν fixed point rise and finally reach to the point at ν 0 = 0.2.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".