Probabilistic estimation of rockfall height and kinetic energy based on a three-dimensional trajectory model and Monte Carlo simulation

Railways across the Canadian Cordillera have long histories of losses associated with ground hazards. The hazards most frequently reported are rockfalls, which are ubiquitous along the steep rock cuts required to accommodate the railway alignment. Several hazard control measures can be adopted in rockfall areas. However, when rockfall frequencies cannot be controlled, protective structures may be necessary to decrease rockfall-related risks to tolerable levels. Designs of protective structures require knowing rockfall trajectory heights and kinetic energies. This information is difficult to obtain even at locations where comprehensive rockfall records are kept. We present a method to calculate rockfall trajectory heights and velocities based on three-dimensional, lumped mass, rockfall simulations. Rockfall source location, model parameters and model calibration are also discussed. In this regard, the model should be calibrated against observed values of rockfall heights and velocities, and the design parameters should be validated before proceeding with the design of rockfall mitigation measures. The method is illustrated with the analysis of a section of a railway along the Canadian Cordillera. Furthermore, a probabilistic approach is adopted to calculate rockfall trajectory heights and velocities when intersecting the railway alignment. This is consistent with the natural variability of rockfall trajectories and falling block volumes. We illustrate the use of probability distributions of rockfall velocities and volumes to calculate the distribution of kinetic energy at three locations along the study section. The calculated rockfall trajectory heights are also presented in probabilistic terms and discussed. The rockfall kinetic energy distributions are used to assess the type of protective structures that could be required for further reduction of risk levels.