System Reliability Analysis of Soil Slopes Using an Advanced Kriging Metamodel and Quasi–Monte Carlo Simulation
Publication: International Journal of Geomechanics
Volume 18, Issue 8
Abstract
Enhancing the efficiency and accuracy of the system reliability analysis of soil slopes is of great importance in engineering design. An advanced kriging metamodel integrated with the quasi–Monte Carlo simulation (AKQMCS) is proposed for such a purpose in this paper. The proposed advanced kriging model is used as a surrogate for the limit state function (LSF) of a slope, and it is established by a sequential design of experiments, which updates the kriging model step by step, with the help of a learning function based on the entropy theory. QMCS simulation is then performed on the advanced kriging metamodel to evaluate the system failure probability of the slope. Finally, three soil slope examples, including a two-layered cohesive slope, a three-layered c-φ slope, and a single-layered sand slope, are examined to verify the capability and validity of the proposed approach. The results indicate that the proposed approach can provide a reasonable and accurate estimation of the system failure probability of slope stability with a significantly reduced number of deterministic stability analyses compared with the ordinary kriging method and the direct Monte Carlo simulation (MCS). The QMCS well outperforms the MCS in efficiency due to the low-discrepancy sequences used in the QMCS. Hence, the proposed AKQMCS provides a new and efficient tool for the system reliability analysis of soil slopes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the Hong Kong Polytechnic University through the account RU3Y and by the GRF project PolyU 5128/13E.
References
Ang, A. H. S., and W. H. Tang. 1984. Probability concepts in engineering planning and design: Design, risk and reliability. Vol. 2. New York: Wiley.
Bichon, B. J., M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. McFarland. 2008. “Efficient global reliability analysis for nonlinear implicit performance functions.” AIAA J. 46 (10): 2459–2468. https://doi.org/10.2514/1.34321.
Ching, J., K. Phoon, and Y. Hu. 2009. “Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling.” J. Geotech. Geoenviron. Eng. 135 (6): 758–768. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000035.
Cho, S. E. 2013. “First-order reliability analysis of slope considering multiple failure modes.” Eng. Geol. 154 (Feb): 98–105. https://doi.org/10.1016/j.enggeo.2012.12.014.
Chowdhury, R. N., and D. W. Xu. 1995. “Geotechnical system reliability of slopes.” Reliab. Eng. Syst. Saf. 47 (3): 141–151. https://doi.org/10.1016/0951-8320(94)00063-T.
Christian, J., C. Ladd, and G. Baecher. 1994. “Reliability applied to slope stability analysis.” J. Geotech. Engrg. 120 (12): 2180–2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180).
Cressie, N. 1993. Statistics for spatial data. New York: Wiley.
Dai, H. Z., and W. Wang. 2009. “Application of low-discrepancy sampling method in structural reliability analysis.” Struct. Saf. 31 (1): 55–64. https://doi.org/10.1016/j.strusafe.2008.03.001.
Ditlevsen, O. 1979. “Narrow Reliability Bounds for Structural Systems.” J. Struct. Mech. 7 (4): 453–472. https://doi.org/10.1080/03601217908905329.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
El-Ramly, H., N. R. Morgenstern, and D. M. Cruden. 2002. “Probabilistic slope stability analysis for practice.” Can. Geotech. J. 39 (3): 665–683. https://doi.org/10.1139/t02-034.
Fang, K. T., and Y. Wang. 1994. Number theoretic methods in statistics. London: Chapman & Hall.
Forrester, A. I. J., A. Sóbester, and A. J. Keane. 2008. Engineering design via surrogate modelling: A practical guide. Hoboken, NJ: Wiley.
Gaspar, B., A. P. Teixeira, and C. G. Soares. 2014. “Assessment of the efficiency of Kriging surrogate models for structural reliability analysis.” Probabilistic Eng. Mech. 37 (Jul): 24–34. https://doi.org/10.1016/j.probengmech.2014.03.011.
GEO (Geotechnical Engineering Office). 2000. Highway slope manual. Hong Kong: Hong Kong SAR Government.
Griffiths, D., and G. Fenton. 2004. “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. Eng., 130 (5): 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507).
Homayouni, S. M., S. H. Tang, and O. Motlagh. 2014. “A genetic algorithm for optimization of integrated scheduling of cranes, vehicles, and storage platforms at automated container terminals.” J. Comput. Appl. Math. 270 (Nov): 545–556. https://doi.org/10.1016/j.cam.2013.11.021.
Huang, X., X. Zhou, W. Ma, Y. Niu, and Y. Wang. 2017. “Two-dimensional stability assessment of rock slopes based on random field.” Int. J. Geomech., 17 (7): 04016155. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000858.
Ji, J., and B. Low. 2012. “Stratified response surfaces for system probabilistic evaluation of slopes.” J. Geotech. Geoenviron. Eng., 138 (11): 1398–1406. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000711.
Jiang, S., D. Li, Z. Cao, C. Zhou, and K. Phoon. 2015. “Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.” J. Geotech. Geoenviron. Eng., 141 (2): 04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227.
Jiang, S. H., D. Q. Li, C. B. Zhou, and L. M. Zhang. 2014a. “Capabilities of stochastic response surface method and response surface method in reliability analysis.” Struct. Eng. Mech. 49 (1): 111–128. https://doi.org/10.12989/sem.2014.49.1.111.
Jiang, S. H., D. Q. Li, L. M. Zhang, and C. B. Zhou. 2014b. “Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method.” Eng. Geol. 168 (Jan): 120–128. https://doi.org/10.1016/j.enggeo.2013.11.006.
Jiang, S. H., and J. S. Huang. 2016. “Efficient slope reliability analysis at low-probability levels in spatially variable soils.” Comput. Geotech. 75 (May): 18–27. https://doi.org/10.1016/j.compgeo.2016.01.016.
Johnson, M. E., L. M. Moore, and D. Ylvisaker. 1990. “Minimax and maximin distance designs.” J. Stat. Plann. Inference 26 (2): 131–148. https://doi.org/10.1016/0378-3758(90)90122-B.
Kang, F., S. Han, R. Salgado, and J. Li. 2015. “System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling.” Comput. Geotech. 63 (Jan): 13–25. https://doi.org/10.1016/j.compgeo.2014.08.010.
Kaymaz, I. 2005. “Application of kriging method to structural reliability problems.” Struct. Saf. 27 (2): 133–151. https://doi.org/10.1016/j.strusafe.2004.09.001.
Kostić, S., N. Vasović, and D. Sunarić. 2016. “Slope stability analysis based on experimental design.” Int. J. Geomech., 16 (5): 04016009. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000551.
Krige, D. G. 1951. “A statistical approach to some basic mine valuation problems on the Witwatersrand.” J. Chem. Metall. Min. Soc. South Afr., 52, 19–139.
Li, D. Q., D. Zheng, Z. J. Cao, X. S. Tang, and K. K. Phoon. 2016. “Response surface methods for slope reliability analysis: Review and comparison.” Eng. Geol. 203 (Mar): 3–14.https://doi.org/10.1016/j.enggeo.2015.09.003.
Li, D. Q., S. H. Jiang, Z. J. Cao, W. Zhou, C. B. Zhou, and L. M. Zhang. 2015. “A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties.” Eng. Geol. 187 (Mar): 60–72. https://doi.org/10.1016/j.enggeo.2014.12.003.
Li, D., Y. Chen, W. Lu, and C. Zhou. 2011. “Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.” Comput. Geotech. 38 (1): 58–68. https://doi.org/10.1016/j.compgeo.2010.10.006.
Li, L., and X. S. Chu. 2015. “Multiple response surfaces for slope reliability analysis.” Int. J. Numer. Anal. Methods Geomech. 39 (2): 175–192. https://doi.org/10.1002/nag.2304.
Lim, K., M. Cassidy, A. Li, and A. Lyamin. 2017. “Mean parametric Monte Carlo study of fill slopes.” Int. J. Geomech., 17 (4): 04016105. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000812.
Liu, L. L., and Y. M. Cheng. 2016. “Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation.” Comput. Geotech. 79 (Oct): 41–54. https://doi.org/10.1016/j.compgeo.2016.05.001.
Liu, L., Y. Cheng, and X. Wang. 2017. “Genetic algorithm optimized Taylor Kriging surrogate model for system reliability analysis of soil slopes.” Landslides 14 (2): 535–546. https://doi.org/10.1007/s10346-016-0736-0.
Lophaven, S. N., H. B. Nielsen, and J. Søndergaard, 2002. DACE: A MATLAB Kriging toolbox, version 2.0. Technical Rep. IMM-TR-2002-12. Copenhagen, Denmark: Technical University of Denmark.
Low, B. K., and W. H. Tang. 2007. “Efficient spreadsheet algorithm for first-order reliability method.” J. Eng. Mech., 133 (12): 1378–1387. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378).
Low, B. K., J. Zhang, and W. H. Tang. 2011. “Efficient system reliability analysis illustrated for a retaining wall and a soil slope.” Comput. Geotech. 38 (2): 196–204. https://doi.org/10.1016/j.compgeo.2010.11.005.
Luo, X. F., X. Li, J. Zhou, and T. Cheng. 2012. “A Kriging-based hybrid optimization algorithm for slope reliability analysis.” Struct. Saf. 34 (1): 401–406. https://doi.org/10.1016/j.strusafe.2011.09.004.
Lv, Z. Y., Z. Z. Lu, and P. Wang. 2015. “A new learning function for Kriging and its applications to solve reliability problems in engineering.” Comput. Math. Appl. 70 (5): 1182–1197. https://doi.org/10.1016/j.camwa.2015.07.004.
Metya, S., and G. Bhattacharya. 2014. “Probabilistic critical slip surface for earth slopes based on the first order reliability method.” Indian Geotech. J. 44 (3): 329–340. https://doi.org/10.1007/s40098-013-0089-8.
Metya, S., T. Mukhopadhyay, S. Adhikari, and G. Bhattacharya. 2017a. “Efficient system reliability analysis of earth slopes based on support vector machine regression model.” In Handbook of neural computation, edited by P. Samui, S. S. Roy, and V. Balas, 127–143. London: Academic Press.
Metya, S., T. Mukhopadhyay, S. Adhikari, and G. Bhattacharya. 2017b. “System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines.” Comput. Geotech. 87 (Jul): 212–228. https://doi.org/10.1016/j.compgeo.2017.02.017.
Nie, J., and B. R. Ellingwood. 2004. “A new directional simulation method for system reliability. Part I: Application of deterministic points sets.” Probab. Eng. Mech. 19 (4): 425–436. https://doi.org/10.1016/j.probengmech.2004.03.004.
Niederreiter, H. 1992. Random number generation and quasi-Monte Carlo methods. Philadelphia: SIAM.
Shannon, C. E. 1948. “A mathematical theory of communication.” Bell Syst. Tech. J. 27 (3): 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.
Silvestrini, R. T., D. C. Montgomery, and B. Jones. 2013. “Comparing computer experiments for the Gaussian process model using integrated prediction variance.” Qual. Eng. 25 (2): 164–174. https://doi.org/10.1080/08982112.2012.758284.
Wang, Y., Z. J. Cao, and S. K. Au. 2011. “Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet.” Can. Geotech. J. 48 (1): 162–172. https://doi.org/10.1139/T10-044.
Xia, Y., M. Mahmoodian, C. Li, and A. Zhou. 2017. “Stochastic method for predicting risk of slope failure subjected to unsaturated infiltration flow.” Int. J. Geomech., 17 (8): 04017037. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000908.
Xu, B., and B. Low. 2006. “Probabilistic stability analyses of embankments based on finite-element method.” J. Geotech. Geoenviron. Eng., 132 (11): 1444–1454. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:11(1444).
Yi, P., K. Wei, X. Kong, and Z. Zhu. 2015. “Cumulative PSO-Kriging model for slope reliability analysis.” Probab. Eng. Mech. 39 (Jan): 39–45. https://doi.org/10.1016/j.probengmech.2014.12.001.
Yuan, X., Z. Lu, C. Zhou, and Z. Yue. 2013. “A novel adaptive importance sampling algorithm based on Markov chain and low-discrepancy sequence.” Aerosp. Sci. Technol. 29 (1): 253–261. https://doi.org/10.1016/j.ast.2013.03.008.
Zhang, J., H. W. Huang, C. H. Juang, and D. Q. Li. 2013a. “Extension of Hassan and Wolff method for system reliability analysis of soil slopes.” Eng. Geol. 160 (Jun): 81–88. https://doi.org/10.1016/j.enggeo.2013.03.029.
Zhang, J., H. Huang, and K. Phoon. 2013b. “Application of the Kriging-based response surface method to the system reliability of soil slopes.” J. Geotech. Geoenviron. Eng., 139 (4): 651–655. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000801.
Zhang, L., Z. Lu, and P. Wang. 2015. “Efficient structural reliability analysis method based on advanced Kriging model.” Appl. Math. Modell. 39 (2): 781–793. https://doi.org/10.1016/j.apm.2014.07.008.
Zhang, J., L. M. Zhang, and W. H. Tang. 2011a. “Kriging numerical models for geotechnical reliability analysis.” Soils Found. 51 (6): 1169–1177. https://doi.org/10.3208/sandf.51.1169.
Zhang, J., L. M. Zhang, and W. H. Tang. 2011b. “New methods for system reliability analysis of soil slopes.” Can. Geotech. J. 48 (7): 1138–1148. https://doi.org/10.1139/t11-009.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jun 22, 2017
Accepted: Feb 6, 2018
Published online: May 24, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 24, 2018
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.