Nonlinear subgrade reaction solution for circular tunnel lining design based on mobilized strength of undrained clay
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Bibliographic record
Abstract
This paper presents a nonlinear solution of a radial subgrade reaction–displacement (p k –u r ) curve for circular tunnel lining design in undrained clay. With the concept of soil shear strength nonlinearly mobilized with shear strain, an analytical solution of p k is obtained using the mobilized strength design method. Two typical deformation modes are considered, namely oval and uniform. A total of 197 orthogonally designed cases are used to calibrate the proposed nonlinear solution of p k using the finite element method with the hardening soil model. The calibration results are summarized using a correction factor, η, which is defined as the ratio of p k_FEM to p k_MSD . It is shown that η is correlated to some input parameters. If this correlation is removed by a regression equation, f, the modified solution f(p k_MSD ) agrees very well with p k_FEM . Although in reality the mobilized soil strength varies with principal stress direction, it is found that a simple average of plane strain compression and extension results is sufficient to produce the above agreement. The proposed nonlinear p k –u r curve is applied to an actual tunnel lining design example. The predicted tunnel deformations agree very well with the measured data. In contrast, a linear p k model would produce an underestimation of tunnel convergence and internal forces by 2–4 times due to the overestimation of p k at a large strain level.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it