Is Complexity the Answer to the Continuum vs. Discontinuum Question in Rock Engineering?
Bibliographic record
Abstract
Abstract The question for which rock masses discontinuum modeling must be used and which can be abstracted as a continuum concerned rock engineering for decades. This paper proposes that the answer to the continuum versus discontinuum question lies in the relative structural complexity of the rock mass and its discontinuities. Complexity in this case refers to discretely computed parameters that put a number on the perceived complexity of a rock mass and quantify its emergent properties. Parameters like the multiscale structural complexity, the Shannon entropy, the compression complexity or the Euler characteristic are implemented in a computational framework. It is shown that there are two scale-dependent low complexity end members: on the one hand, massive rock masses with very few discontinuities or very small rock samples, and on the other, rock masses with a very high discontinuity density approaching soil-like material or mountain-range scale samples. In between, however, lies a spectrum where rock mass complexity increases rapidly with increasing discontinuity density and then decreases again. Based on this observation, we assert that the discontinuum approach should be used for the majority of rock masses, but the continuum approach can be justified in cases of low complexity. Two case studies show how these theoretical insights support conceptual approaches in real rock engineering cases. The full code and data for the executed simulations are provided to facilitate further studies on this topic.
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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 | 0.002 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".