Constitutive Relationships Governing Thermo-Poroelastic Processes
Bibliographic record
Abstract
We consider a poroelastic material consisting of a linear elastic porous skeleton and accessible pore space that is fully saturated with a non-viscous liquid. The solid phase of the porous skeleton is a linear elastic solid material, which can be compressible. The liquid that saturates the pores of the poroelastic material is also assumed to be compressible. The porosity of the porous elastic material is defined as the ratio of the volume of the pores (or the volume of the liquid) to the total volume and is denoted by ϕ. Typical examples of such a porous medium are soil and rock saturated with water. For poroelastic materials, the linear elastic stress–strain relation can be expressed in terms of the elastic constants of the fully drained poroelastic body or the porous skeleton without any pore fluid. Under drained conditions, the fluid is allowed to flow in to and out of the accessible pore space, but in the fully drained state the pressure remains independent of time (Rice and Cleary, 1976). For example, the fully drained conditions can be reached when, in the loaded poroelastic body, the pore fluid pressure dissipates with time and eventually becomes equal to zero. The overall mechanical properties and the overall thermal expansion coefficient of such a “drained” poroelastic medium will be equivalent to those of the elastic skeleton with empty or unoccupied pores. (Note, however, that, even when the pressure is zero, the liquid is technically present in the pore space of the medium since the medium remains fully saturated.) Normally, if drainage in the poroelastic body is allowed, fully drained conditions of the body subjected to various loadings prevail in the long term, i.e., as time goes to infinity. We also define undrained conditions as those that arise when change in the mass of fluid is equal to zero. Typically, the undrained response of the poroelastic material is an instantaneous or initial response of the body to applied mechanical, hydraulic or thermal loadings. It is clear that the linear elastic stress–strain relation for a poroelastic body can also be expressed in terms of the elastic moduli of the undrained poroelastic material.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".