A Framework for Analysis of Piles with Rectangular Cross Section
Bibliographic record
Abstract
An analysis framework is presented for piles with rectangular cross section. Existing analysis and design methods are mostly applicable for piles with circular cross section. For piles with cross section other than a circle, an equivalent circle is often assumed and the methods for circular piles are applied. The newly developed framework explicitly takes into account the rectangular cross section and produces the response of piles under axial and lateral loads. A rational soil displacement field surrounding the rectangular cross section of the pile is assumed, and the total potential energy of the loaded pile-soil system is considered. The potential energy is minimized using calculus of variations to obtain the differential equations governing the pile and soil displacements. Closed-form solutions are obtained for pile settlement and axial force in the case of axially loaded piles. For laterally loaded piles, closed-form solutions are obtained for lateral deflection, slope of the deflected curve, pile bending moment, and shear force. The input parameters needed for the analysis are the pile geometry, applied load, and the elastic constants of the soil and pile. The new analysis framework produces results in seconds and has the accuracy of equivalent three-dimensional finite element analysis.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".