A Review of Analytical Methods for Calculating Static Pressures in Bulk Solids Storage Structures
Bibliographic record
Abstract
The Janssen equation is a widely used method for calculating pressures in bulk storage structures. This review explores the historical legacy of Janssen’s equation and its applications in both planar and three-dimensional structures. Our focus is on the limitations of the original formulation of Janssen, extensions made to avoid these deficiencies, and alternative models that have been developed. The motivation behind these modifications is to improve the representation of shear stress within a grain bin in both the horizontal and vertical directions. Modifications to Janssen’s basic assumptions include the vertical-to-horizontal stress ratio (k), the coefficient of friction between the wall and the stored bulk material (μ), internal angle of friction (ϕ), and bulk density (ρ). We also discuss recent developments in pressure theories, which have provided new insights into pressure fields in bulk storage bins. These modern approaches include the continuum elastic theory and microscopic theory. Finally, we discuss recent developments in pressure theories which provide new insights into the storage of bulk solids. Overall, this review provides a comprehensive overview of the Janssen equation and its historical development, limitations, and extensions, as well as recent advancements in pressure theory that offer a more accurate representation of pressure fields in bulk storage structures.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.005 |
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".