Reliability assessment of rainfall-induced slope stability using Chebyshev–Galerkin–KL expansion and Bayesian approach
Bibliographic record
Abstract
Soil spatial variability has essential influence on the reliability of geotechnical structures. Karhunen–Loève (KL) series expansion is an effective approach to characterize such features of soil properties. Acquiring solution for Fredholm integral equation of the second type is a necessary prerequisite; however, the corresponding analytical expressions are only available for limited circumstances. To overcome this challenge, a newly proposed method called Chebyshev–Galerkin–KL expansion was developed to discretize the random fields of soil parameters, from which the approximated eigenvalues and eigenfunctions can be obtained using the Chebyshev orthogonal polynomials of the second kind combined with Galerkin technique. Application of the proposed approach is illustrated through reliability analysis of an unsaturated slope example under different rainfall patterns, where the uncertainty in selection of a “best” soil-water characteristic curve (SWCC) model and statistical uncertainties in SWCC model parameters are taken into account. Results show that the developed approach is feasible to generate random fields with sufficient accuracy. Under a constant rainfall duration, the Advanced pattern may lead to shallow landslide with the highest probability, followed by Intermediate and Delayed. It should be noted that Bayesian inference and determination of optimal SWCC model should be carried out prior to reliability analysis. Otherwise, the landslide risk level would be exaggerated.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".