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Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities

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Abstract

Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy–frequency diagram to assess the hazard.

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Abbreviations

d max :

Maximum joint diameter

E :

Kinetic energy

g(x):

Probability density function for joint diameters

k :

Shape factor of the block

h :

Height of highwall

l :

Length of highwall

\( \lambda\) :

Shape parameter for the exponential diameter distribution

\( \lambda_{\rm E}\) :

Global kinetic energy frequency distribution

\( \lambda_{\rm E^i} \) :

Kinetic energy frequency distribution for a given rock mass volume

\( \lambda_{\rm f} \) :

Rock mass mean failure frequency

\( \lambda_{\rm f^i} \) :

Failure frequency of a given rock mass volume

\( \lambda_{\rm fst} \) :

Spatial-temporal rockfall failure frequency

\(\lambda_{\rm P} \left(\rm E, x \right)\) :

Frequency of energy occurence at a given location

\(\mu\) :

Shape parameter for the log-normal diameter distribution

P s :

Probability of propagation

P r :

Probability of reach

\( \sigma \) :

Shape parameter for the log-normal diameter distribution

Tfi :

Return period for a rockfall event of a given rock mass volume

V :

Volume of block

V max :

Maximum volume of block

V min :

Minimum volume of block

w :

Width of block

x :

Horizontal position along slope profile

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Acknowledgments

The financial support of the Australian Coal Association Research Program (ACARP) is greatly acknowledged. The technical support from mine personnel and Marc Elmouttie (CSIRO) were greatly appreciated. The financial support of the Australian Research Council provided to the Newcastle authors is also acknowledged.

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Authors and Affiliations

  1. Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand

    Cédric Lambert

  2. Centre for Geotechnical and Materials Modelling, The University of Newcastle, Newcastle, Australia

    Klaus Thoeni, Anna Giacomini & Scott Sloan

  3. University of Milan, Milan, Italy

    Davide Casagrande

Authors
  1. Cédric Lambert
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  2. Klaus Thoeni
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  3. Anna Giacomini
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  4. Davide Casagrande
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Correspondence to Cédric Lambert.

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Lambert, C., Thoeni, K., Giacomini, A. et al. Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities. Rock Mech Rock Eng 45, 871–884 (2012). https://doi.org/10.1007/s00603-012-0250-1

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  • DOI: https://doi.org/10.1007/s00603-012-0250-1

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