Development of Analytical Solution for a Two-Phase Stefan Problem in Artificial Ground Freezing Using Singular Perturbation Theory
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Bibliographic record
Abstract
Abstract Artificial ground freezing (AGF) has historically been used to stabilize underground structure. Numerical methods generally require high computational power to be applicable in practice. Therefore, it is of interest to develop accurate and reliable analytical frameworks for minimizing computational cost. This paper proposes a singular perturbation solution for a two-phase Stefan problem that describes outward solidification in AGF. Specifically, the singular perturbation method separates two distinct temporal scales to capture the subcooling and freezing stages in the ground. The ground was considered as a porous medium with volume-averaged thermophysical properties. Further, Stefan number was assumed to be small, and effects of a few site-dependent parameters were investigated. The analytical solution was verified by numerical results and found to have similar conclusions yet with much lesser computational cost. Keywords: artificial ground freezing, Stefan-like problems, singular perturbation, porous media, outward solidification.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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) | 0.000 | 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 it