Increasing temperatures and extreme weather events driven by climate change have heightened the risk of rockfall hazards. Reliable estimates of rockfall hazards have a significant impact on the design of roadways, slopes, open pits, and underground excavations. The reliability of these estimates relies on numerical models calibrated using rockfall catalogs. Recent advancements in radar technology enable high-resolution monitoring of rockfall events, providing valuable data on their propagation. However, there are few methods to back-analyze numerical model parameters from radar data. Hence, we propose a Bayesian Optimization Framework to address this gap and demonstrate the framework through a Doppler-radar-tracked rockfall catalog comprising 21 events and 19,356 rock positions. Specifically, we use Gaussian Process Regression (GPR) as a surrogate model to minimize the number of simulations required to determine the best-fitting coefficients of restitution (CORs). The framework supports event-based and site-wise analysis. The former can readily identify unmatchable low-quality events, and the latter excels in fitting CORs generalizable across multiple events. Our framework achieves comparable resolution using five times fewer simulations compared to a benchmark grid-search method. Trajectories simulated using the mean and covariance of the best-fit CORs exhibit reasonable agreement with the measured data. This framework accelerates data inspection and parameter searching when back-analyzing numerical model parameters using a catalog of multiple rockfall events. (Up to 20x faster!)

Accurate estimation of rockfall trajectories is essential for mitigation of rockfall hazards. Nowadays, Doppler radar technologies can measure rockfall trajectories with centimeter resolution. Calibrating a numerical model to fit these measured trajectories, i.e. back analysis, often involves manual trial-and-error processes and subjective goodness-of-fit criteria. Here, we propose a framework that uses the chi-square statistic to quantify the misfit between modeled and measured rockfall trajectories. The framework can also quantify the uncertainty bounds on the best-fit model parameters. The approach is validated using field data from an Australian copper mine under two scenarios. (1) We perform an unconstrained back-analysis where the initial position and velocity of the rock, in addition to the coefficients of restitution (COR), are free variables. This scenario yields a normal COR R_n = 0.866 ± 0.109 and tangential COR R_t = 0.29 ± 0.151 with 68% confidence. (2) We perform a constrained back-analysis using predetermined initial position and velocity of the rock, which further constrains R_n to 0.8 ± 0.014 and R_t to 0.39 ± 0.065. Both scenarios show a higher uncertainty in R_t than in R_n. We also demonstrate the adaptability of the back-analysis framework to two-dimensional (2D) rockfall modeling using the same data. To the best of our knowledge, this is the first quantitative goodness-of-fit metric for trajectory-based rockfall back analysis that supports the estimation of inherent uncertainty. The simplicity of the metric lends itself to robust model optimization of rockfall back-analysis and can be adapted to other model assumptions (e.g. rigid-body mechanics) and metrics (e.g. velocity or energy).

Transferrable to Enhanced Geothermal System(EGS), Underground Hydrogen Storage (UHS), Carbon capture and sequenstration (CSS), nuclear waste water disposit, and dam leakage monitoring, essentially anywhere rock fracture opening and closing matters!

Journal Paper: https://doi.org/10.1016/j.undsp.2022.01.007