Mathematical modelling of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect
Bibliographic record
Abstract
Many geotechnical applications are affected by the melting and formation of ice in soils. Current state of practice involves incorporating the presence of ice within hydrological models for unsaturated soils using the so-called generalised Clapeyron equation [1]. This represents a modification of the conventional Clapeyron equation by allowing for the pressure in ice and liquid to be different at an ice-liquid interface. Such an idea has come about due to the effects of surface tension, which become important within the pores of porous materials such as soil and rock. However, a common assumption when using the generalised Clapeyron equation is that the ice pressure remains constant [2], which leads to unrealistic behaviour in the presence of significant pore-water pressure changes. Here we develop a new mathematical modelling framework to explore the impact of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect. We solve the coupled mass and energy conservation problem using method of lines (e.g., [3]) with pressure and enthalpy as the primary dependent variables. Strong non-linear coupling develops through the chemical potential equation accounting for coexistence of ice and water in the presence of surface tension [5]. We present a sensitivity analysis showing how freezing point depression evolves within a porous block subject to temperature surface boundary cooling and varied capillary pressures.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".