Improved Probabilistic Kinematic Analysis Procedure Based on Finite Size Discontinuities and Its Application to a Rock Slope at Open Pit Mine in U.S.
Publication: International Journal of Geomechanics
Volume 17, Issue 2
Abstract
An improved probabilistic kinematic analysis procedure is suggested incorporating the six steps listed in the paper. The variability of the shear strength and discontinuity orientation is taken into account in the probabilistic kinematic analysis. The correlation that exists between the dip angle and dip direction is incorporated in modeling discontinuity orientation by treating it as a bivariate random variable. A part of an open pit mine in the United States was investigated by performing deterministic and probabilistic kinematic analyses. Field and laboratory investigations were conducted to obtain the needed geological and geotechnical data for the analyses. Important differences were obtained between the probabilistic and deterministic kinematic analyses results mainly because of the variability of the discontinuity orientations. The results confirmed that the designed value of the maximum safe slope angle (MSSA) for a particular region in the open pit mine calculated according to the deterministic kinematic analysis can be on the unsafe side. The probabilistic kinematic analysis showed superiority over the deterministic kinematic analysis in providing additional important information regarding designing rock slopes. Based on the previous analyses results available for the same site using block theory, it was found that a 5% instability cumulative probability based on block theory seems to provide a similar level of risk compared with that of 15% based on kinematic analysis results. The calculated MSSA values are in good agreement with the existing quite stable bench face angles reported by the mining company.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work was partially funded by the Centers for Disease Control and Prevention (Contract No. 200-2011-39886), National Basic Research Program of China (973 Program; No. 2015CB057903), the National Natural Science Foundation Projects (Nos. 41502268 and 41202216), the Fundamental Research Funds for the Central Universities (2016QNA4018), and the Research Programs of Transportation Department of Zhejiang Province (Nos. 2014H21 and 2013H46). The support provided by the mining company—providing geological data, rock core, and block samples and allowing access to the mine to perform field investigations—is very much appreciated.
References
Admassu, Y., and Shakoor, A. (2013). “DIPANALYST: A computer program for quantitative kinematic analysis of rock slope failures.” Comput. Geosci., 54, 196–202.
Ang, A. H. S., and Tang, W. H. (1984). Probability concepts in engineering planning and design, Vols. I and II, Wiley, New York.
Baecher, G. B., and Christian, J. T. (2003). Reliability and statistics in geotechnical engineering, John Wiley & Sons, New York.
Carter, B. J., and Lajtai, E. Z. (1992). “Rock slope stability and distributed joint systems.” Can. Geotech. J., 29(1), 53–60.
Gokceoglu, C., Sonmez, H., and Ercanoglu, M. (2000). “Discontinuity controlled probabilistic slope failure risk maps of the Altindag (settlement) region in Turkey.” Eng. Geol., 55(4), 277–296.
Goodman, R. E. (1989). Introduction to rock mechanics, 2nd Ed., Wiley, New York.
Goodman, R. E., and Shi, G. (1985). Block theory and its application to rock engineering, Prentice-Hall, Englewood Cliffs, NJ.
Hoek, E., and Bray, J. W. (1981). Rock slope engineering, 3rd Ed., Institute of Mining and Metallurgy, London.
Kulatilake, P. H. S. W. (1985). “Fitting Fisher distributions to discontinuity orientation data.” J. Geol. Educ., 33, 266–269.
Kulatilake, P. H. S. W. (1988a). “Minimum rock bolt force and minimum static acceleration in tetrahedral wedge stability: A probabilistic study.” Int. J. Surf. Min. Reclam. Environ., 2(1), 19–26.
Kulatilake, P. H. S. W. (1988b). “Stochastic joint geometry modeling: State-of-the-Art.” Proc., Symp. on Reliability-Based Design in Civil Engineering, Swiss Federal Institute of Technology, Lausanne, Switzerland, 2, 67–91.
Kulatilake, P. H. S. W., Chen, J., Teng, J., Shufang, X., and Pan, G. (1996). “Discontinuity geometry characterization in a tunnel close to the proposed permanent shiplock area of the three gorges dam site in China.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33(3), 255–277.
Kulatilake, P. H. S. W., Finley, R. E., and Ghosh, A. (1985). “Effect of variability of joint orientation and strength on factor of safety of wedge stability.” Proc., Int. Symp. on Fundamentals of Rock Joints, CENTEK Publishers, Lulea, Sweden, 25–34.
Kulatilake, P. H. S. W., and Fuenkajorn, K. (1987). “Factor of safety of tetrahedral wedges: A probabilistic study.” Int. J. Surf. Min. Reclam. Environ., 1(2), 147–154.
Kulatilake, P. H. S. W., Um, J., and Morin, B. (2003a). “Investigation of slope stability for a section of Phelps Dodge Sierrita Open Pit Mine.” Trans. Soc. Min. Metall. Explor., 314, 177–182.
Kulatilake, P. H. S. W., Um, J., Wang, M., Escandon, R. F., and Narvaiz, J. (2003b). “Stochastic fracture geometry modeling in 3-D including validations for a part of Arrowhead East Tunnel, California, USA.” Eng. Geol., 70(1), 131–155.
Kulatilake, P. H. S. W., Wang, L., Tang, H., and Liang, Y. (2011). “Evaluation of rock slope stability for Yujian River dam site by kinematic and block theory analyses.” Comput. Geotech., 38(6), 846–860.
Kulatilake, P. H. S. W., Wathugala, D. N., and Stephansson, O. (1993). “Joint network modelling with a validation exercise in Stripa mine, Sweden.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(5), 503–552.
Kulatilake, P. H. S. W., and Wu, T. H. (1984). “Estimation of mean trace length of discontinuities.” Rock Mech. Rock Eng., 17(4), 215–232.
Kulatilake, P. H. S. W., and Wu, T. H. (1986). “Relation between discontinuity size and trace length.” Proc., 27th U.S. Symp. on Rock Mechanics, American Rock Mechanics Association, Alexandria, VA, 130–133.
Kulatilake, P. H. S. W., Wu, T. H., and Wathugala, D. N. (1990). “Probabilistic modelling of joint orientation.” Int. J. Numer. Anal. Methods, 14(5), 325–350.
Nilsen, B. (2000). “New trend in rock slope stability analyses.” Bull. Eng. Geol. Environ., 58(3), 173–178.
Park, H. J., Um, J., Woo, I., and Kim, J. W. (2012a). “Application of fuzzy set theory to evaluate the probability of failure in rock slopes.” Eng. Geol., 125, 92–101.
Park, H. J., Um, J., Woo, I., and Kim, J. W. (2012b). “The evaluation of the probability of rock wedge failure using the point estimate method.” Environ. Earth Sci., 65(1), 353–361.
Park, H. J., and West, T. R. (2001). “Development of a probabilistic approach for rock wedge failure.” Eng. Geol., 59(3–4), 233–251.
Park, H. J., West, T. R., and Woo, I. (2005). “Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA.” Eng. Geol., 79(3–4), 230–250.
Pathak, S., and Nilsen, B. (2004). “Probabilistic rock slope stability analysis for Himalayan condition.” Bull. Eng. Geol. Environ., 63(1), 25–32.
Priest, S. D., and Hudson, J. A. (1981). “Estimation of discontinuity spacing and trace length using scanline surveys.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 18(3), 183–197.
RockWare. (2013). “RockPack III.” ⟨http://www.rockware.com/product/overview.php?id=119⟩ (Nov. 21, 2013).
Rocscience. (2013). “DIPS 7.0.” ⟨http://www.rocscience.com/products/1/Dips⟩ (Nov. 21, 2013).
Scavia, C., Barla, G., and Bernaudo, V. (1990). “Probabilistic stability analysis of block toppling failure in rock slopes.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 27(6), 465–478.
Sonmez, H., and Gokceoglu, C. (1998). “A computer program for the kinematic analysis of rock slopes and its application.” Earthsciences (Bull. Earthsci. Application Res. Center Hacettepe Univ.), 20, 75–89.
Um, J., and Kulatilake, P. H. S. W. (2001). “Kinematic and block theory analyses for shiplock slopes of the three gorges dam site in China.” Geotech. Geol. Eng., 19, 21–42.
Um, J., Kulatilake, P. H. S. W., Chen, J., and Teng, T. (1996). “Maximum safe slope angles for shiplock slopes of three gorges dam site in China based on kinematic analysis performed on major discontinuities.” Proc., 13th Annual Meeting of ASSMR, Knoxville, TN, 267–281.
Wang, L., Hwang, J. H., Juang, C. H., and Atamturktur, S. (2013a). “Reliability based design of rock slopes—A new perspective on design robustness.” Eng. Geol., 154, 56–63.
Wang, L., Hwang, J. H., Luo, Z., Juang, C. H., and Xiao, J. (2013b). “Probabilistic back analysis of slope failure—A case study in Taiwan.” Comp. Geotech., 51, 12–23.
Wu, Q., and Kulatilake, P. H. S. W. (2012). “REV and its properties on fracture system and mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a dam site in China.” Comput. Geotech., 43, 124–142.
Xu, C., Wang, L., Tien, Y. M., Chen, J., and Juang, C. H. (2014). “Robust design of rock slopes with multiple failure modes: Modeling uncertainty of estimated parameter statistics with fuzzy number.” Environ. Earth Sci., 72(8), 2957–2969.
Zheng, J., Deng, J., Yang, X., Wei, J., Zheng, H., and Cui, Y. (2014a). “An improved Monte Carlo simulation method for discontinuity orientations based on Fisher distribution and its program implementation.” Comput. Geotech., 61, 266–276.
Zheng, J., Deng, J., Zhang, G., and Yang, X. (2015a). “Validation of Monte Carlo simulation for discontinuity locations in space.” Comput. Geotech., 67, 103–109.
Zheng, J., Kulatilake, P. H. S. W., Deng, J., and Wei, J. (2015b). “Development of an improved probabilistic kinematic wedge sliding analysis procedure for rock slope.” Bull. Eng. Geol. Environ.,
Zheng, J., Kulatilake, P. H. S. W., Deng, J., and Wei, J. (2015c). “A Monte Carlo simulation for discontinuity orientations using bivariate empirical distribution.” Chin. J. Rock Mech. Eng., 34(S2), 3922–3929 (in Chinese).
Zheng, J., Kulatilake, P. H. S. W., Shu, B., Sherizadeh, T., and Deng, J. (2014b). “Probabilistic block theory analysis for a rock slope at an open pit mine in USA.” Comput. Geotech., 61, 254–265.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 20, 2015
Accepted: Apr 12, 2016
Published online: May 23, 2016
Discussion open until: Oct 23, 2016
Published in print: Feb 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.