An analytical solution for self-weight consolidation based on one-dimensional small-strain consolidation wave theory
Bibliographic record
Abstract
Terzaghi's consolidation theory neglects inertial effects on the consolidation of saturated soils. To quantify the inertial effects, in this paper an original one-dimensional small-strain consolidation wave (C-wave) theory is developed, based upon a proposed modified Darcy's law with relaxation time and the equation of motion for soil ensemble. The one-dimensional governing equations were first formulated for self-weight consolidation, followed by a closed-form solution employing the method of separation of variables. The proposed model was then validated against wave velocity measurements and verified against finite-difference analysis. The half-closed self-weight consolidation behaviour was subsequently investigated, compared with Terzaghi's theory, Fillunger–Heinrich's dynamic theory and the u–p form of Biot's wave theory. This research indicates that: (a) superior to conventional models under comparison, the C-wave model enhances the predictability of the C-wave velocity; (b) the dimensionless C-wave coefficient (Cw) dominates the fundamental consolidation behaviour; (c) a wave-diffusion duality underlying the consolidation mechanism contributes qualitatively to the spatial bottom-up pattern and temporal response delay in consolidation observations; and (d) Terzaghi's theory can afford a practically accurate solution provided the Cwand time factor are below and above approximately 0·01, respectively. The C-wave theory may enrich the understanding of consolidation-related phenomena involving an appreciable Cw.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".