Determination of ground reaction curve for hyperbolic soil model using the hodograph method
Bibliographic record
Abstract
This paper reintroduces an efficient method for analyzing the problem of a deep circular tunnel and for determining the ground reaction curve (GRC). It is assumed that the tunnel is excavated in soilrock mass subjected to a hydrostatic in situ stress field under a plane strain condition. The constitutive law for the surrounding material is assumed to follow DuncanChang's hyperbolic stressstrain relation. The technique for analysis is known as Biot's hodograph method, which relies on expressing principal strains as functions of principal stresses. The problem is reduced to solving a first order differential equation for the hoop stress σ θ as a function of the radial stress σ r . The GRCs are graphically presented in dimensionless form. It is shown that the hodograph method is straightforward and can be easily applied in engineering practice.Key words: circular tunnel, ground reaction curve, hyperbolic soil model, hodograph method.
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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 | 0.000 |
| 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".