A Framework for Back-Analysis of 3D Rockfall Trajectories
- DOI
- 10.2991/978-94-6463-258-3_75How to use a DOI?
- Keywords
- Rockfall; parametric studies; back-analysis; Monte Carlo
- Abstract
We define a novel normalized loss function to quantitatively evaluate the goodness-of-fit between simulated and measured rockfall trajectories using elapsed time and sampled rock positions. This loss function is optimized to back-analyze the coefficients of restitution Rn and Rt using a Monte-Carlo search of the parameter set θ = [Rn, Rt, v0] where v0 is the initial horizontal velocity. The trajectories are simulated assuming lumped mass rocks with initially horizontal projectiles and zero rotation. While our results are derived using position as the loss term, we note that our framework is entirely compatible with velocity or energy as a loss term as suggested by other researchers. The efficacy of the back-analysis framework is examined using synthetic and measured rockfall trajectories from a copper mine in British Columbia, Canada. The Monte Carlo search reveals significant non-uniqueness in the back-analyzed values of Rn and Rt, which can be mitigated by joint back-analysis that stacks the loss contour of multiple target trajectories. Parametric studies suggest that a minimum of 10,000 Monte Carlo samples should be simulated for an accurate solution, and that the spatial resolution of the topography is linearly correlated to the minimum loss. This measured trajectory was also used to test the viability of scaling Rn by velocity and mass. Our results suggest that velocity scaling performs similarly (12% deviation from measured path) to a static Rn value (9% deviation) while the measured trajectory cannot be satisfactorily reproduced (43% deviation) when scaling Rn by mass.
- Copyright
- © 2023 The Author(s)
- Open Access
- Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
Cite this article
TY - CONF AU - Arnold Y. Xie AU - Zhanyu Huang AU - Thamer Yacoub AU - Bing Q. Li PY - 2023 DA - 2023/11/08 TI - A Framework for Back-Analysis of 3D Rockfall Trajectories BT - Proceedings of the Rocscience International Conference (RIC 2023) PB - Atlantis Press SP - 806 EP - 819 SN - 2589-4943 UR - https://doi.org/10.2991/978-94-6463-258-3_75 DO - 10.2991/978-94-6463-258-3_75 ID - Xie2023 ER -