A semi-analytical solution for laterally loaded non-circular piles in elastic soil
Bibliographic record
Abstract
The traditional method for analysis and design of laterally loaded piles with non-circular cross-sections such as rectangular, H-shaped, and X-shaped piles involves the simplification of converting the non-circular pile to a circular pile with equivalent second moment of inertia. A rigorous semi-analytical method is developed for calculating the response for laterally loaded piles with arbitrary non-circular cross-sections in multi-layered elastic soil without using any simplification regarding the shape of the pile cross-section. The governing differential equations for the pile–soil system are obtained using the principle of virtual work. The soil displacements around the pile are described as products of separable functions that are compatible with horizontal pile movement. As a result, the three-dimensional (3 D) boundary value problem (BVP) is described by a fourth-order linear ordinary differential equation (ODE) governing horizontal pile displacement and second-order partial differential equations (PDEs) governing soil displacements. New solution techniques for the ODE and PDEs are proposed, and the accuracy of the present method is verified by comparing the predicted pile and soil responses with the corresponding results of equivalent 3 D finite element method. The effects of pile cross-section shape and lateral loading direction on the pile and soil responses are highlighted through a series of parametric analyses.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".