One-Dimensional Problems Involving Thermo-Poroelastic Processes
Bibliographic record
Abstract
This chapter examines the thermo-hydro-mechanical problems related to the one-dimensional case of deformation. One-dimensional deformation occurs, for example, in a semi-infinite half-space subjected to uniform stress, fluid pressure and temperature change on its free surface, or in the problem of a uniformly heated fluid layer bounded by two parallel planes which is inserted into an infinitely large poroelastic body. If a poroelastic body has the shape of a cylinder or a column, one-dimensional deformation in such a body can be achieved, for example, by applying uniform stress, fluid pressure and temperature change to its top surface, and setting the displacement, fluid velocity and heat flux normal to the lateral surface of the cylinder to zero. The problem described in this chapter analyses a cylinder that has a finite height or depth. The lateral surface of this column is restrained from lateral motion, heat and fluid flow, and thus only the axial displacement, axial heat and fluid flow are allowed in this one-dimensional column. The column may be subjected to axial load, fluid pressure and heating applied to its upper surface, and, in addition, the initial fluid pressure and temperature can be applied to the volume of the cylinder. We first solve the thermoelastic problem or thermo-mechanical (TM) problem, where the effect of the fluid pressure is neglected. Then we analyze a hydro-mechanical (HM) problem in which the effect of the temperature change is ignored. Finally, we consider the thermo-hydro-mechanical (THM) problem in which mechanical, hydraulic and thermal effects are taken into account. An analytical solution will be obtained by separation of variables and expanding the unknown fields in Fourier series. The influence of the fluid and solid-phase compressibility on the magnitude of the fluid pressure for the HM and THM problems is underlined. The analytical solution will be compared with the numerical results – a finite element solution obtained using the COMSOL™ finite element program.
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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 | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".