Dynamic Analysis of Laterally Loaded End-Bearing Piles in Homogeneous Viscoelastic Soil Using Timoshenko Beam Theory
Bibliographic record
Abstract
An approximate semi-analytical method is developed to obtain the dynamic response of laterally loaded end-bearing piles embedded in a homogeneous soil. In the analysis, the soil is modeled as a three-dimensional viscoelastic continuum, and the pile as an elastic Timoshenko beam with solid circular cross-section. The Timoshenko beam theory is used to include the effects of shear deformation and rotatory inertia of the pile cross-section that might be important for short stubby piles and for piles subjected to high frequency loading. In the analysis, the horizontal soil displacements are expressed as products of separable functions, and the extended Hamilton’s principle in conjunction with the calculus of variations is used to obtain two sets of coupled differential equations governing pile and soil motions, along with the relevant boundary conditions. The coupled equations are solved analytically and numerically following an iterative algorithm. The pile differential equations and boundary conditions can be simplified to obtain the Euler-Bernoulli beam theory representing the pile behavior. Complex dynamic pile-head impedances are obtained from the present analysis using the two beam theories.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".