Fracture mechanics of rate-and-state faults and fluid injection induced slip
Bibliographic record
Abstract
Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy G c , dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity v r . This opens a possibility to model slip transients on rate-and-state faults as singular cracks characterized by approximately steady-state frictional resistance in the fracture bulk, and by a stress singularity with the intensity defined in terms of G c ( v r ) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1-D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force Δ T . In the context of fluid injection, Δ T is a proxy for the injection volume V inj . We then show that, for ongoing fluid injection, the propagation speed of a transient induced on a frictionally stable fault is bounded by a large-time limiting value proportional to the injection rate dV inj /d t , while, for stopped injection, the maximum slip run-out distance is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">inj</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">total</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.
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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 | 0.000 | 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 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".