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

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Abstract

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.

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Acknowledgments

Funding for this study was provided by the Railway Ground Hazard Research Program (RGHRP) and the Canadian Railway Research Laboratory (CaRRL). The authors acknowledge the Canadian National Railway Company (CN) for providing the information needed for the study and Dr. T. Keegan from Klohn Crippen Berger Ltd. for his insights about the rockfall hazards along the study area.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Alberta, 1-035 Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta, T6G 2W2, Canada

    Renato Macciotta

  2. Canadian Rail Research Laboratory, Department of Civil and Environmental Engineering, University of Alberta, 3-071 Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta, T6G 2W2, Canada

    C. Derek Martin

  3. Department of Civil and Environmental Engineering, University of Alberta, 3-064 Markin/CNRL Natural Resources Engineering Facility, Edmonton, AB, T6G 2W2, Canada

    David M. Cruden

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  1. Renato Macciotta
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  2. C. Derek Martin
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Correspondence to Renato Macciotta.

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Macciotta, R., Martin, C.D. & Cruden, D.M. Probabilistic estimation of rockfall height and kinetic energy based on a three-dimensional trajectory model and Monte Carlo simulation. Landslides 12, 757–772 (2015). https://doi.org/10.1007/s10346-014-0503-z

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  • DOI: https://doi.org/10.1007/s10346-014-0503-z

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