The probabilistic key-group method

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 28, Issue 9, 2004, Pages 899-917

  Yarahmadi Bafghi, A R ^a   Verdel, T ^b  

^a YAZD UNIVERSITY   (Iran)

^b CRPG CNRS   (France)

Author keywords

Key blocks; Key groups; Probabilistic analysis; Reliability; Rock slope stability

Indexed keywords

COMPUTER SIMULATION; MONTE CARLO METHODS; PROBLEM SOLVING; ROCK MECHANICS;

ADVANCED SECOND-MOMENT METHOD (ASMM); PROBABILISTIC KEY-GROUP METHOD (PKGM); ROCK SAMPLES;

PROBABILITY;

GEOMECHANICS; PROBABILITY; ROCK BLOCK; ROCK MECHANICS; SLOPE STABILITY;

EID: 4644248799     PISSN: 03639061     EISSN: None     Source Type: Journal    
DOI: 10.1002/nag.339     Document Type: Article

References (54)

1. Warburton PM. Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces. International Journal of Rock Mechanics and Mining Sciences 1981; 18:415-427.
2. Goodman RE, Shi GH. Block Theory and its Application to Rock Engineering. Wiley: New York, 1985.
3. Lin D, Fairhurst C. Static analysis of the stability of three-dimensional blocky systems around excavations in rock. International Journal of Rock Mechanics and Mining Sciences 1988; 25(3):139-147.
4. Mauldon M, Goodman RE. Vector analysis of key-block rotations. Journal of Geotechnical Engineering (ASCE) 1996; 122(12):976 987.
5. Hoek E, Bray JW. Rock Slope Engineering. The Institution of Mining and Metallurgy: Cambridge, 1981.
6. Giani GP. Rock Slope Stability Analysis. Balkema: Rotterdam-Brookfield, 1992.
7. Mauldon M, Ureta J. Stability analysis of rock wedges with multiple sliding surfaces. International Journal of Rock Mechanics and Mining Sciences 1996; 33(7):51 66.
8. Mauldon M, Chou KC, Wu Y. Limit analysis of 2-D tunnel key blocks. International Journal of Rock Mechanics and Mining Sciences 1997; 34(3 4):379 397.
9. Fulvio-Tonon PE. Generalization of Mauldon's and Goodman's vector analysis of key block rotations. Journal of Geotechnical and Geoenvironmental Engineering 1998: 124(10):913 922.
10. Sagaseta C, Sanchez JM. Canizal JA. General analytical solution for the required anchor force in rock slopes with toppling failure. International Journal of Rock Mechanics and Mining Sciences 2001; 38(3):379 397.
11. Wibowo JL. Consideration of secondary blocks in key-block analysis. International Journal of Rock Mechanics and Mining Sciences 1997; 34(3 4):508.
12. Yarahmadi Bafghi AR, Verdel T. The key-group method. International Journal for Numerical and Analytical Methods in Geomechanics 2003; 27(6):495 511.
13. Conrad F, Jacquine C. Représentation d'un Réseau Bi-dimensionnel de fractures par un modèle probabiliste. Revue de I'Institut Francais du Pétrole 1973; 18(6):843 890.
14. Billaux D, Chiles JP. Hestir K, Long J. Three-dimensional statistical modeling of a fractured rock mass an example from the Fanay-Augéres mine. International Journal of Rock Mechanics and Mining Sciences 1989: 26(3 4):281 299.
15. Kulatilake PHSW, Wathugala DN. Probabilistic joint network modeling in three dimensions including a verification. In Computer Methods and Advances in Geomechanics, Beer G. Booker JR, Karter JP (eds). Balkema: Rotterdam-Brookfield, 1991: 359 364.
16. Villaeseusa E. Statistical modeling of rock jointing. In Probabilistic Methods in Geotechnical Engineering. Li KS, Lo SC (eds). Balkema: Rotterdam-Brookfield, 1993: 221 231.
17. Einstein HH. Risk and risk analysis in rock engineering. Tunnelling and Underground Space Technology 1996: 1(20):141 155.
18. Kulatilake PHSW, Fiedler R, Panda BB. Box fractal dimension as a measure of statistical homogeneity of jointed rock masses. Engineering Geology 1997: 48:217 229.
19. Mauldon M. Estimating mean fracture trace length and density from observation in convex windows. Rock Mechanics and Rock Engineering 1998; 31(4):201 216.
20. Song JJ, Lee CI. Estimation of joint length distribution using window sampling. International Journal of Rock Mechanics and Mining Sciences 2001; 38:519 528.
21. Wu TH, Kraft LM. Safety analysis of slopes. Journal of Soil Mechanic and Foundation (ASCE) 1970: 96(2):609 630.
22. Tang WH, Yucement MS, Ang AHS. Probability-based short term design of slope. Canadian Geotechnical Journal 1976; 13(3):201 215.
23. Vanmarcke EH. Reliability of earth slopes. Journal of Geotechnical Engineering (ASCE) 1977; 103(11):1227 1246.
24. Li KS. Lumb P. Probabilistic design of slopes. Canadian Geotechnical Journal 1987; 24:520 535.
25. Halim IS, Tang WH. Reliability of undrained clay slope considering geologic anomaly. Proceedings of the 6th International Conference on Applications of Statistics and Probability in Soil and Structure Engineering. Mexico City, Mexico, 1991; 776 783.
26. Mostyn GR, Li KS. Probabilistic slope analysis-state of play. In Probabilistic Methods in Geotechnical Engineering. Li KS, Lo SC (eds). A.A. Balkema: Rotterdam-Brookfield, 1993.
27. e trimestre 1994; 69:3 10.
28. Quek ST, Leung CF. Reliability-based stability analysis of rock excavations. International Journal of Rock Mechanics and Mining Sciences 1995; 32(6):617 620.
29. Feng P, Lajtai EZ. Probabilistic treatment of the sliding wedge with EzSlide. Engineering Geology 1998: 50(1 2): 153 163.
30. Moarefvand P. Méthode des éléments distincts stochastique. Thèse de Doctorat, LAEGO-Ecole des Mines de Nancy, INPL. 1998.
31. Xu D, Chowdhury R. Probabilistic analysis of structured rock soil slope-several methods compared. In Slope Stability Engineering. Proceedings of the International Symposium on Slope Stability Engineering-IS-Shikoku 99. Yagi N. Yamagami T, Jiang JC (eds). Balkema: Rotterdam-Brookfield, 1999.
32. Tono F, Bernardini A, Mammino A. Reliability analysis of rock mass response by means of random set theory. Reliability Engineering and System Safety 2000; 70(3):263 282.
33. Park H, West TR. Development of a probabilistic approach for rock wedge failure. Engineering Geology 2001: 59(3 4):233 251.
34. Goodman RE. Introduction to Rock Mechanics. Wiley: New York. 1989.
35. Baecher GB. Geotechnical reliability. Electronic Course. www.glue.umd.edu gbaecher. December 2000.
36. Hasofer AM, Lind NC. Exact and invariance second moment code format. Journal of Engineering Mechanics (ASCE) 1974; 100:111 121.
37. Rackwitz R, Fiessler B. Structural reliability under combined random load sequences. Computers and Structures 1978; 9:489 494.
38. Kamien DJ. Introduction to probability and reliability in geotechnical engineering. (APPENDIX B), U.S. Army Corps of Engineering. Technical Letter 30 September 1997; 1110-2-547.
39. Kreyszing. Advanced Engineering Mathematics (6th edn). Wiley: New York, 1988.
40. Ayyub BM, Halder A. Practical structural reliability techniques. Journal of Structural Engineering (ASCE) 1984: 110(8):1707 1727.
41. Baecher GB. Parameters and approximations in geotechnical reliability. In Uncertainty Modeling in Civil Engineering, Bilal M, Ayyub (eds). CRC Press LLC: Boca Raton, FL, 1998.
42. Christian JT, Baecher GB. Statistical and reliability for geotechnical engineering. Short course presented at Winnipeg, Manitoba, April 2001.
43. Rackwitz R. Practical probability approach to design. Comité Européen du Béton, Bulletin 112, Paris, 1976.
44. Low BK, Tang WH. Reliability analysis of reinforced embankments on soft ground. Canadian Geotechnical Journal 1997; 34:672 685.
45. Christian JT, Baecher GB. Probabilistic slope analysis using Jamb's generalized procedure of slices. Computers and Geotechnics 1997; 22(2):121 142.
46. CRMRMGE. Committee on Reliability Methods for Risk Mitigation in Geotechnical Engineering. Probabilistic Methods in Geotechnical Engineering. Appendix C. National Research Council, Washington, DC, 1995.
47. Zhao YG, Ono T. A general procedure for first second-order reliability method (FORM SORM). Structural Safety 1999: 21:95 112.
48. Wang J, Tan W, Feng S, Zhou R. Reliability analysis of an open pit coal mine slope. International Journal of Rock Mechanics and Mining Sciences 2000: 37(4):715 721.
49. Karpuz D. A probabilistic design approach for rock slope. Planning and Equipment Selection. A.A. Balkema: Rotterdam, 1998: 84 179.
50. Chowdhury R, Flentje P. Role of slope reliability analysis in landslide risk management. Bulletin of Engineering Geology and the Environment 2003; 62:41 46.
51. Priest SD, Brown ET. Probabilistic stability analysis of variable rock slopes. Transactions of the Institution of Mining and Metallurgy (Section A: Mining industry) 1983; 99:A1 A12.
52. Wolfram S. The Mathematica Book (4th edn). Wolfram Media Cambridge University Press: Cambridge, MA. 1999.
53. Malkawi AHI, Hassan WF, Abdulla FA. Uncertainty and reliability analysis applied to slope stability. Structural Safety 2000; 22:161 187.
54. Duncan JM. Factor of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering (ASCE) 2000; 126(6):307 316.