Summary
We present a system reliability approach to rock wedge stability analysis. Different failure modes are considered, and a disjoint cut-set formulation is employed – with each cut-set corresponding to a different failure mode – to explore the system aspects of the problem, so that the reliability of the system is assessed by computing the probability of failure of the slope under each failure mode. An example case is used to demonstrate different approaches to compute the reliability of the slope design. Our results show that an approximation to the “exact” probability of failure – given by Monte Carlo simulation results – may be obtained using a first order approximation to the failure domain, and that linear programming techniques may be used to obtain bounds of the probability of failure. Furthermore, we identify the most likely failure mode, and we explore the sensitivity of the computed probabilities to changes in the random variables considered. The results indicate that the reliability results are quite sensitive to the geometry of the wedge. Changes in water conditions are also found to have a significant impact on the computed probabilities, while changes in unit weight of the rock have a considerably smaller effect on the reliability.
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R. Ambartzumian A. Der Kiureghian V. Ohanian H. Sukiasian (1998) ArticleTitleMultinormal probability by sequential conditioned importance sampling: theory and application Probabil. Engng. Mech. 13 IssueID4 299–308 Occurrence Handle10.1016/S0266-8920(98)00003-4
P. Bjerager (1990) ArticleTitleOn computation methods for structural reliability analysis Struct. Saf. 9 79–96 Occurrence Handle10.1016/0167-4730(90)90001-6
O. Ditlevsen P. Bjerager (1989) ArticleTitlePlastic reliability analysis by directional simulation J. Engng. Mech. 115 IssueID6 1347–1362 Occurrence Handle10.1061/(ASCE)0733-9399(1989)115:6(1347)
O. Ditlevsen H. Madsen (1996) Structural reliability methods Wiley Chichester
H. S. B. Duzgun M. S. Yucemen C. Karpuz (2003) ArticleTitleA methodology for reliability-based design of rock slopes Rock Mech. Rock Engng. 36 IssueID2 95–120 Occurrence Handle10.1007/s00603-002-0034-0
Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M., Rossi, F. (2003): GNU Scientific Library Reference Manual, 2nd edn. Network Theory Ltd.
R. E. Goodman (1989) Introduction to rock mechanics EditionNumber2 Wiley New York
R. E. Goodman D. S. Kieffer (2000) ArticleTitleBehavior of rock in slopes J. Geotech. Geoenviron. Engng. ASCE 126 IssueID8 675–684 Occurrence Handle10.1061/(ASCE)1090-0241(2000)126:8(675)
R. E. Goodman G. Shi (1985) Block theory and its application to rock engineering SeriesTitlePrentice-Hall international series in civil engineering and engineering mechanics Prentice-Hall Englewood Cliffs, N.J
Hoek, E. (2000): Practical rock engineering. http://www.rocscience.com/hoek/PracticalRockEngineering.asp, World Wide Web edn.
E. Hoek J. Bray (1981) Rock slope engineering, rev. EditionNumber3 Institution of Mining and Metallurgy London
J. A. Hudson (1992) Rock engineering systems: Theory and practice SeriesTitleSeries in Civil Engineering, Geotechnics Ellis Horwood New York
R. Jimenez-Rodriguez N. Sitar J. Chacón (2006) ArticleTitleSystem reliability approach to rock slope stability Int. J. Rock Mech. Min. Sci. 43 IssueID6 847–859 Occurrence Handle10.1016/j.ijrmms.2005.11.011
Liu, P.-L., Lin, H.-Z., Der Kiureghian, A. (1989): CALREL user manual. Structural engineering, mechanics and materials. Department of Civil Engineering. University of California at Berkeley.
B. K. Low (1997) ArticleTitleReliability analysis of rock wedges J. Geotech. Geoenviron. Engng. 123 IssueID6 498–505 Occurrence Handle10.1061/(ASCE)1090-0241(1997)123:6(498)
C. Nathanail (1996) ArticleTitleKinematic analysis of active/passive wedge failure using stereographic projection Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 IssueID4 405–407 Occurrence Handle10.1016/0148-9062(95)00079-8
J. Song A. Der Kiureghian (2003) ArticleTitleBounds on system reliability by linear programming J. Engng. Mech. 129 IssueID6 627–636 Occurrence Handle10.1061/(ASCE)0733-9399(2003)129:6(627)
S. Tamimi B. Amadei D. M. Frangopol (1989) ArticleTitleMonte Carlo simulation of rock slope stability Comput. Struct. 33 IssueID6 1495–1505 Occurrence Handle10.1016/0045-7949(89)90489-6
Y. J. Wang J. H. Yin (2002) ArticleTitleWedge stability analysis considering dilatancy of discontinuities Rock Mech. Rock Engng. 35 IssueID2 127–137 Occurrence Handle10.1007/s006030200016
P. M. Warburton (1981) ArticleTitleVector stability analysis of an arbitrary polyhedral rock block with any number of free faces Int. J. Rock Mech. Min. Sci. 18 IssueID5 415–427 Occurrence Handle10.1016/0148-9062(81)90005-X
W. Wittke (1990) Rock mechanics: theory and applications with case histories Springer Berlin Heidelberg New York Tokyo
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Jimenez-Rodriguez, R., Sitar, N. Rock Wedge Stability Analysis Using System Reliability Methods. Rock Mech. Rock Engng. 40, 419–427 (2007). https://doi.org/10.1007/s00603-005-0088-x
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DOI: https://doi.org/10.1007/s00603-005-0088-x