Analytical Slope Stability Analysis Based on Statistical Characterization of Soil Primary Properties
Publication: International Journal of Geomechanics
Volume 15, Issue 2
Abstract
The role of statistical tools in the modeling of slope stability has been increasingly studied in the last decades. Mainly, this growth can be related to the availability of fast computational routines that enable massive-repetition numerical algorithms such as Monte Carlo simulations. On the other hand, analytical approaches to this problem, in the majority of cases, rely on considering the random variables of interest being normally distributed. This latter assumption tends to provide incorrect results when dealing with skewed data because normal distribution is symmetric about its mean value. To address this issue, a complete statistical study of a set of porosities data is undertaken. A total of seven well-known statistical distributions are adjusted to such data, showing that normal distribution is the worst possible fit for the considered data set. By means of an empirical correlation between strength properties and porosity, the probability-density function of the factor of safety of a hypothetical slope is analytically derived based on a Mohr-Coulomb failure criterion. This way, it is shown that the probability of failure can be explicitly obtained by means of solely the distribution of a primary property of the material in study, namely, its porosity. Also, the results obtained by considering the porosity data normally distributed are compared with the ones hereby developed, showing considerable differences.
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Acknowledgments
The authors acknowledge the Coordination for the Improvement of Higher Level Personnel (CAPES), the Brazilian Research Council (CNPQ), and University of Brasilia (UNB) for funding this research. The authors also thank the reviewers and associate editor for useful comments that improved the paper.
References
Anderson, T. W., and Darling, D. A. (1954). “A test of goodness-of-fit.” J. Am. Stat. Assoc., 49(268), 765–769.
Bishop, A. W. (1966). “The strength of soils as engineering materials.” Geotechnique, 16(2), 91–128.
Bishop, A. W., and Green, G. E. (1965). “The influence of end restraint on the compression strength of a cohesionless soil.” Geotechnique, 15(3), 243–266.
Bjerrum, L., Kringstad, S., and Kummeneje, O. (1961). “The shear strength of a fine sand.” Proc., 5th Int. Conf. on Soil Mechanics and Foundation Engineering, Vol. 1, Dunod, Paris, 29–37.
Bolton, M. D. (1986). “The strength and dilatancy of sands.” Geotechnique, 36(1), 65–78.
Cai, F., and Ugai, K. (2004). “Numerical analysis of rainfall effects on slope stability.” Int. J. Geomech., 69–78.
Chalermyanont, T., and Benson, C. (2005). “Reliability-based design for external stability of mechanically stabilized earth walls.” Int. J. Geomech., 196–205.
Cornforth, D. H. (1964). “Some experiments on the influence of strain conditions on the strength of sand.” Geotechnique, 14(2), 143–167.
Cornforth, D. H. (1973). “Prediction of drained strength of sands from relative density measurements.” STP-523, ASTM, West Conshocken, PA, 281–303.
D’Agostino, R. B., and Stephens, M. A. (1986). Goodness-of-fit techniques, Marcel Dekker, New York.
Duncan, J. M. (2000). “Factors of safety and reliability in geotechnical engineering.” J. Geotech. Geoenviron. Eng., 307–316.
Espósito, T. J. (2000). “Metodologia probabilística e observacional aplicada à barragens de rejeito construídas por aterro hidráulico.” Ph.D. thesis, Publicação G.TD-004A/00, Dept. de Engenharia Civil e Ambiental, Univ. de Brasília, Brazil (in Portuguese).
Genevois, R., and Romeo, R. W. (2003). “Probability of failure occurrence and recurrence in rock slopes stability analysis.” Int. J. Geomech., 34–42.
Holický, M. (2013). “Functions of random variables.” Chapter 7, Introduction to probability and statistics for engineers, Springer, New York, 79–93.
Kleiber, C. (2008). “A guide to the Dagum distributions.” Chapter 6, Modeling income distributions and Lorenz curves (economic studies in inequality, social exclusion and well-being), D. Chotikapanich, ed., Springer, New York.
Lambe, W. T., and Whitman, R. V. (1979). Soil mechanicas, SI version, Wiley, New York.
Liu, D.-S., and Zheng, Y. (1997). “A probabilistic yield criterion of geomaterials [C].” Proc., Int. Symp. on Rock Mechanics and Environmental Geotechnology, J. Sun, ed., Chongqing University Press, Chongqing, China, 377–382.
Mathematica 9 [Computer software]. Champaign, IL, Wolfram Research.
Nomikos, P. P., and Sofianos, A. I. (2011). “An analytical probability distribution for the factor of safety in underground rock mechanics.” Int. J. Rock Mech. Min. Sci., 48(4), 597–605.
Silva, F., Lambe, T. W., and Marr, W. A. (2008). “Probability and risk of slope failure.” J. Geotech. Geoenviron. Eng., 1691–1699.
Sivakumar Babu, G. L., and Singh, V. P. (2011). “Reliability-based load and resistance factors for soil-nail walls.” Can. Geotech. J., 48(6), 915–930.
Wang, Y., Au, S., and Kulhawy, F. (2011). “Expanded reliability-based design approach for drilled shafts.” J. Geotech. Geoenviron. Eng., 140–149.
Whitman, R. V. (1984). “Evaluating calculated risk in geotechnical engineering.” J. Geotech. Engrg., 110(6), 143–188.
Zhang, L., Liu, D.-S., Song, Q.-H., and Liu, S.-W. (2008). “An analytical expression of reliability solution for Druker-Prager criterion.” Appl. Math. Mech. (Engl. Ed.), 29(1), 121–128.
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Published In
International Journal of Geomechanics
Volume 15 • Issue 2 • April 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 18, 2013
Accepted: Dec 23, 2013
Published online: Dec 27, 2013
Published in print: Apr 1, 2015
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