Rock Mechanics and Rock Engineering

, Volume 52, Issue 10, pp 3791–3808 | Cite as

Stability Analysis of Slopes with Spatially Variable Strength Properties

  • Hossein Rafiei RenaniEmail author
  • C. Derek Martin
  • Pedro Varona
  • Loren Lorig
Original Paper


Natural variability of rock properties can significantly affect the strength of rock masses and factor of safety of slopes. The results of a comprehensive point load testing program showed that coefficient of variation of intact rock strength can reach unity in highly heterogeneous formations. Probabilistic numerical analysis was carried out to explore the effect of strength variability on uniaxial compressive strength of large heterogeneous samples. It was shown that mean large-scale strength decreases with increasing small-scale variability. The effect of spatial variability of strength properties on slope stability was examined using limit equilibrium and shear strength reduction methods. Both approaches gave similar results indicating that for stable slopes, increasing strength variability leads to a reduction in mean factor of safety and increase in the probability of failure. In addition, ignoring spatial variability in probabilistic slope analysis can lead to erroneous estimates of the probability of failure. Based on the results of probabilistic analyses on large heterogeneous samples and slopes, an equivalent uniaxial compressive strength can be obtained by reducing the mean strength by one-third of its standard deviation. This relationship was validated using a dataset of back-analyzed strength values in heterogeneous open pit slopes.


Probabilistic analysis Strength variability Heterogeneous sample Equivalent strength Limit equilibrium Strength reduction 



This work was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC: RES0014117).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  2. 2.GeoControl LtdSantiagoChile
  3. 3.Itasca Consulting Group IncSantiagoChile

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