Discontinuum rocking of rigid masonry macro-blocks using physics engines: analytical, numerical and experimental benchmarking
Bibliographic record
Abstract
Rigid block rocking, significant across disciplines from structural to mechanical engineering, remains challenging to predict accurately using continuum-based numerical solutions. Traditional discontinuum simulation methods, although widely employed for modelling particle separation, re-contact, and collision with multiple contact points, often involve prohibitive computational cost. Analytical solutions, while computationally simpler, are limited primarily to straightforward planar cases with regular geometries. Physics engines - simulation platforms initially developed for digital animations and videogames - present an underexplored yet promising alternative for rigorously modelling multi-body rocking mechanics. These engines utilize discontinuum analysis principles comparable to established discrete models like the Distinct Element Method (DEM), but differ notably in contact detection and modelling strategies, typically providing faster, albeit less precise, predictions. This paper explores and enhances the capabilities of two physics engines - Bullet (integrated within Blender) and Vortex (within Vortex Studio) - to numerically simulate free and forced rocking of isolated and stacked rigid blocks, particularly from an earthquake engineering perspective. Rocking during seismic events frequently impacts blocky structural systems, such as unreinforced masonry (URM), posing assessment challenges for complex constructions. Initially, calibrated Bullet and Vortex simulations are compared with results from Housner’s analytical equations for free rocking blocks with various aspect ratios. Subsequently, forced rocking responses to sine-pulse and sinusoidal base motions are examined, employing analytical solutions and referencing experimental and DEM-derived data across different frequencies and acceleration amplitudes. Lastly, the study replicates the rocking response of stacked blocks observed in shake-table tests using DEM, Bullet, and Vortex. Comparative analysis demonstrates that calibrated Bullet and Vortex models yield satisfactory accuracy while significantly reducing computational demands compared to conventional DEM approaches. Consequently, physics engines emerge as viable, efficient alternatives for simulating rocking mechanics, relevant both within structural engineering and beyond.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".