Limit of Anisotropic Hydraulic Conductivity Ratio of Homogeneous Granular Materials
Bibliographic record
Abstract
This paper presents a theoretical upper limit for the anisotropic hydraulic conductivity ratio of homogeneous granular materials with internal structure. On the basis of a volume averaging approach, a theoretical analysis is proposed to relate the permeability of granular material to the spatial distribution of pore spaces. For flow in granular materials, both the linear porosity in the flow direction and the areal porosity in the plane perpendicular to the flow direction are required to describe the directional variation of pore space. The permeability tensor is derived by considering the macroscopic momentum balance equation of the fluid in a porous medium. While the permeability is affected by the porosity and the pore space distribution, the permeability anisotropy ratio is dominated by the directional variation of the linear porosity. By accounting for the theoretical maximum and minimum porosity, it is shown that the upper limit of permeability anisotropy for homogeneous granular materials is approximately 2.5, even for very flat (or elongated) particles and pronounced preferential orientations.
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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 | 0.000 | 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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".