Bibliographic record
Abstract
This thesis investigates the class of problems that are of interest to geomechanics, earth sciences and resource geomechanics within the frameworks of Biot’s poroelasticity. This study aims to provide analytical solutions that can be used as benchmarks to validate computational approaches for examining problems pertaining to consolidation, crack nucleation and extension in poroelastic media. The problems considered in this thesis are restricted to plausible axisymmetric ones that are mathematically well-posed and analytically manageable. The formulation of these mixed boundary value problems uses the stress function approach applicable to semi-infinite domains. Laplace and Hankel integral transforms are used to reduce the mixed boundary value problems to sets of coupled Fredholm integral equations of the second-kind. These integral equations are solved using numerical approaches in order to examine the transient behavior of the fluid-saturated medium.The first problem examined in this thesis re-examines the indentation of a halfspace region with poroelastic properties by considering the displacement boundary conditions that are consistent with adhesive contact. The pore fluid pressure boundary conditions employ either: (i) completely pervious conditions, (ii) completely impervious boundary conditions or (iii) impervious boundary conditions within the contact zone and free drainage conditions exterior to the contact zone. The analytical estimates for the axial displacement of the rigid indenter are used to develop numerical results for the Degree of Consolidation of the rigid indenter, which indicates the relative consolidation settlement of the indenter over time. The accuracy of the numerical schemes used in the solution of these poroelastic contact problems is also discussed.The thesis then examines the problem of the indentationmof a poroelastic halfspace that is reinforced with an inextensible permeable/impermeable membrane located at a finite depth. The developments address (i) frictionless/adhesive constraints at the contact between the poroelastic halfspace and the rigid indenter, (ii) the pore fluid pressure boundary conditions at the base of the indenter, and (iii) pore fluid pressure boundary conditions at the plane of the inextensible membrane. The boundary condition (iii) is indicative of geosynthetic reinforcing elements that provide only tensile resistance or provide a combined reinforcement and barrier/drainage arrangement by imposing impervious/zero-pore fluid pressure boundary conditions at the reinforcement level. The analytical estimates for the time-dependent displacements of the rigid indenter are compared with results obtained using a finite element approach. It is recognized that the inextensibility constraint is a highly idealized approximation to reinforcing elements that have finite flexibility; nonetheless it provides a useful benchmark problem for examining the validity of computational approaches for reinforced geomaterials.This thesis also considers certain canonical problems that can be of assistance to the calibration of computational approaches in modelling the mechanics of stable fractures in poroelastic media. The study first examines the problem of fluid injection over a circular area within a poroelastic halfspace domain that would create the skeletal stress state necessary to initiate fracture. The triggering of the fracture is assumed to create an axisymmetric penny-shaped crack whose surfaces will be subjected to fluid pressure. The mechanics of the penny-shaped crack in terms of its potential to extend in an axisymmetric fashion is examined. The analysis of the poroelasticity problem of fluid-injection into the crack gives rise to time-dependent skeletal stress intensity factors (SIFs) at the crack tip; these are combined with a mixed-mode brittle skeletal fracture criterion to establish the injection pressures
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".