Quasi-monte carlo simulation with low-discrepancy sequence for reinforced soil slopes

Journal of Geotechnical and Geoenvironmental Engineering

Volumn 133, Issue 4, 2007, Pages 393-404

  Shinoda, M ^a  

^a Integrated Geotechnology Institute   (Japan)

Author keywords

Monte Carlo method; Simulation; Slope stability; Structural reliability

Indexed keywords

COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; FOUNDATIONS; MONTE CARLO METHODS; RANDOM VARIABLES; SLOPE STABILITY; STRUCTURAL INTEGRITY;

GEOSYNTHETIC REINFORCED SOIL; LOW DISCREPANCY SEQUENCE MONTE CARLO (LDSMC);

GEOSYNTHETIC MATERIALS;

BACKFILL; FOUNDATION; GEOSYNTHETICS; MONTE CARLO ANALYSIS; NUMERICAL METHOD; PROBABILITY; SIMULATION; SLOPE STABILITY; SOIL REINFORCEMENT;

COMPUTER SIMULATION; GEOSYNTHETICS; SOIL REINFORCEMENT; STABILITY; STATISTICAL ANALYSIS;

EID: 34249054961     PISSN: 10900241     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)1090-0241(2007)133:4(393)     Document Type: Article

References (44)

1. Alonso, E. E. (1976). "Risk analysis of slope and its application to slopes in Canadian sensitive clays." GeotechniqueGTNQA80016-8505, 26(3), 453-472.
2. Braaten, E., and Weller, G. (1979). "An improved low-discrepancy sequence for multidimensional quasi-Monte Carlo integration." J. Comput. Phys.JCTPAH0021-9991, 33, 249-258.
3. Bratley, P., and Fox, B. L. (1988). "Implementing Sobol's quasirandom sequence generator." ACM Trans. Math. Softw.ACMSCU0098-350010.1145/42288.214372, 14(1), 88-100.
4. Bratley, P., Fox, B. L., and Niederreiter, H. (1992). "Implementation and tests of low-discrepancy sequences." ACM Trans. Math. Softw.ACMSCU0098-3500, 2(3), 195-213.
5. Chalermyanont, T., and Benson, C. H. (2004). "Reliability-based design for internal stability of mechanically stabilized earth walls." J. Geotech. Geoenviron. Eng.JGGEFK1090-024110.1061/ (ASCE)1090-0241(2004)130:2(163), 130(2), 163-173.
6. Christian, J. T., Ladd, C. C., and Baecher, G. B. (1994). "Reliability applied to slope stability analysis." J. Geotech. Engrg.JGENDZ0733-941010.1061/(ASCE)0733-9410(1994)120:12(2180), 120(12), 2180-2207.
7. Duncan, J. M., Navin, M., and Wolff, T. F. (2003). "Discussion of 'Probabilistic slope stability analysis for practice.'" Can. Geotech. J.CGJOAH0008-367410.1139/t03-030, 40, 848-850.
8. El-Ramly, H., Morgenstern, N. R., and Cruden, D. M. (2002). "Probabilistic slope stability analysis for practice." Can. Geotech. J.CGJOAH0008-367410.1139/t02-034, 39, 665-683.
9. El-Ramly, H., Morgenstern, N. R., and Cruden, D. M. (2003). "Reply to the 'Discussion by J.M. Duncan, M. Navin, and T.F. Wolff on Probabilistic slope stability analysis for practice.'" Can. Geotech. J.CGJOAH0008-367410.1139/t03-031, 40, 851-855.
10. Engelund, S., and Rackwitz, R. (1993). "A benchmark study on importance sampling techniques in structural reliability." Struct. SafetyZZZZZZ0167-4730, 12, 255-276.
11. Faure, H. (1982). "Discrepancy of sequences associated with a number system (in dimension s)." Acta Arith.AARIA90065-1036, 41(4), 337-351.
12. Fox, B. L. (1986). "Implementation and relative efficiency of quasirandom sequence generators." ACM Trans. Math. Softw.ACMSCU0098-3500, 12(4), 362-376.
13. Halton, J. H. (1960). "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals." Numer. Math.NUMMA70029-599X10.1007/BF01386213, 2, 84-90.
14. Hara, K., and Masuo, T. (2005). "Dispersion of tensile strength of geogrid using ISO geotextile testing protocol." Geosynthetic Engineering Journal, 20, 287-294 (in Japanese).
15. Harbitz, A. (1986). "An efficient sampling method for probability of failure calculation." Struct. SafetyZZZZZZ0167-4730, 3, 109-116.
16. Hasofer, A. M., and Lind, N. C. (1974). "Exact and invariant second-moment code format." J. Engrg. Mech. Div.JMCEA30044-7951, 100(1), 111-121.
17. Hassan, A., and Wolff, T. (1999). "Search algorithm for minimum reliability index of earth slope." J. Geotech. Geoenviron. Eng.JGGEFK1090-024110.1061/(ASCE)1090-0241(1999)125:4(301), 125(4), 301-308.
18. Ibrahim, Y. (1991). "Observations of applications of importance sampling in structural reliability analysis." Struct. SafetyZZZZZZ0167-4730, 9, 269-281.
19. Kocis, L., and Whiten, W. J. (1997). "Computational investigations of low-discrepancy sequences." ACM Trans. Math. Softw.ACMSCU0098-3500, 23(2), 266-294.
20. Li, K. S., and Lumb, P. (1987). "Probabilistic design of slopes." Can. Geotech. J.CGJOAH0008-3674, 24(4), 520-535.
21. Low, B. K., and Tang, W. H. (1997). "Reliability analysis of reinforced embankment on soft ground." Can. Geotech. J.CGJOAH0008-367410.1139/cgj-34-5-672, 34(5), 672-685.
22. Low, B. K., Gilbert, R. B., and Wright, S. G. (1998). "Slope reliability analysis using generalized method of slices." J. Geotech. Geoenviron. Eng.JGGEFK1090-024110.1061/ (ASCE)1090-0241(1998)124:4(350), 124(4), 350-362.
23. Matsumoto, M., and Nishimura, T. (1998). "A 623-dimensionally equidistributed uniform pseudorandom number generator." ACM Trans. Model. Comput. Simul.ATMCEZ1049-330110.1145/272991.272995, 8(1), 3-30.
24. Matsuo, M., and Kuroda, K. (1974). "Probability approach to design of embankments." Soils Found.SOIFBE0038-0806, 14(2), 1-17.
25. Melchers, R. E. (1989). "Importance sampling in structural systems." Struct. SafetyZZZZZZ0167-4730, 6, 3-10.
26. Melchers, R. E. (1999). Structural reliability analysis and prediction, Wiley, Chichester, U.K., 73-83.
27. Niederreiter, H. (1978). "Quasi-Monte Carlo methods and pseudo-random numbers." Bull. Am. Math. Soc.BAMOAD0002-9904, 84(6), 957-1041.
28. Niederreiter, H. (1988). "Low-discrepancy and low-dispersion sequences." J. Number TheoryJNUTA90022-314X10.1016/ 0022-314X(88)90025-X, 30, 51-70.
29. Niederreiter, H. (1992). "Random number generation and quasi-Monte Carlo methods." CBMS-NSF Regional Conference Series in Applied Mathematics No. 63, SIAM, Philadelphia.
30. Niederreiter, H., and McCurley, K. (1979). "Optimization of functions by quasi-random search methods." ComputingCMPTA20010-485X, 22, 119-123.
31. Oka, Y., and Wu, T. H. (1990). "System reliability of slope stability." J. Geotech. Engrg.JGENDZ0733-9410, 116(8), 1185-1189.
32. Phoon, K. K., Kulhawy, F. H., and Grigoriu, M. D. (1999). "Characterization of geotechnical variability." Can. Geotech. J.CGJOAH0008-367410.1139/cgj-36-4-612, 36(4), 612-624.
33. Robinson, D. G., and Atcitty, C. (1999). "Comparison of quasi-Monte Carlo sampling for reliability and uncertainty analysis." Proc., AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Vol. 4, 2942-2949.
34. Schueller, G. I., and Stix, R. (1987). "A critical appraisal of methods to determine failure probabilities." Struct. SafetyZZZZZZ0167-4730, 4, 293-309.
35. Shinoda, M., Horii, K., Yonezawa, T., Tateyama, M., and Koseki, J. (2006). "Reliability-based seismic deformation analysis of reinforced soil slopes." Soils Found.SOIFBE0038-0806, 46(4), 477-490.
36. Shinozuka, M. (1983). "Basic analysis of structural safety." J. Struct. Eng.JSENDH0733-9445, 109(3), 721-740.
37. Sobol', I. M. (1967). "The distribution of points in a cube and the approximate evaluation of integrals." USSR Comput. Math. Math. Phys.CMMPA90965-5425, 7, 86-112.
38. Sobol', I. M. (1982). "On an estimate of the accuracy of a simple multidimensional search." Sov. Math. Dokl.ZZZZZZ0197-6788, 26, 398-401.
39. Tamura, T., and Shirakawa, H. (1999). "Quasi random number by the generalized Faure sequence and its application to the option evaluation." JAFEE J., 95-111 (in Japanese).
40. Tang, W. H., Yucemen, M. S., and Ang, A. H.-S. (1976). "Probability-based short term design of soil slopes." Can. Geotech. J.CGJOAH0008-3674, 13, 201-215.
41. Tezuka, S. (1995). Uniform random numbers: Theory and practice, Kluwer Academic, Boston, 161-185.
42. Vanmarcke, E. H. (1977). "Reliability of earth slopes." J. Geotech. Engrg. Div.AJGEB60093-6405, 103(11), 1247-1265.
43. Whitman, R. V. (1984). "Evaluating calculated risk in geotechnical engineering." J. Geotech. Engrg.JGENDZ0733-9410, 110(2), 145-188.
44. Whitman, R. V. (2000). "Organizing and evaluating uncertainty in geotechnical engineering." J. Geotech. Geoenviron. Eng.JGGEFK1090-024110.1061/(ASCE)1090-0241(2000)126:7(583), 126(7), 583-593.