Efficient Probabilistic Stability Analysis of Geosynthetic Reinforced Slopes Using Collocation-Based Stochastic Response Surface
Publication: International Journal of Geomechanics
Volume 21, Issue 10
Abstract
This paper presents an efficient and robust probabilistic approach to analyze the geosynthetic reinforced slopes (GRSs). The deterministic analysis will be performed that employs the rigorous (5N−1) formulation of the horizontal slice method (HSM), which is made efficient using the nonlinear constrained optimization (N = number of slices). The probabilistic analysis will be performed using a surrogated assisted Monte Carlo simulation (MCS). Collocation based stochastic response surface (SRS) will be employed to build the surrogate model using a third-order multidimensional polynomial chaos expansion (PCE). The random variables include the internal friction angle of soil (ϕ), soil unit weight (γ), and tensile strength of the reinforcement (Tu). Dependence between the random variables will be established using the Gaussian copula. A comparative analysis of the results with the First-Order Reliability Method (FORM) will be presented. The performance function will be evaluated 125 times using the SRS method in contrast to the direct MCS where it will be evaluated ≥50,000 times. This will reduce the computation time from approximately 2 days to approximately 20 min. In addition, the influence of correlation between the random variables will be highlighted comprehensively by adopting a wide range of correlation coefficients. This study concludes that the SRS method that incorporates an accurate deterministic model is a highly efficient and powerful approach to analyze GRSs probabilistically.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research has been supported by the mission mode program of CSIR-Central Building Research Institute (CSIR-CBRI), Roorkee, India “Safety of Vital Infrastructures against Landslides (SOVIAL)” (HCP - 017). The authors acknowledge the financial support from CSIR-CBRI, Roorkee, India during this work. The authors are thankful to the anonymous reviewers for giving their precious time, constructive suggestions, and comments to enhance the quality of the manuscript.
References
Au, S. K. 2001. “On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment.” Doctoral dissertation, Dept. of Mechanical and Civil Engineering, California Institute of Technology, CA, US.
Ausilio, E., E. Conte, and G. Dente. 2000. “Seismic stability analysis of reinforced slopes.” Soil Dyn. Earthquake Eng. 19 (3): 159–172. https://doi.org/10.1016/S0267-7261(00)00005-1.
Avramidis, A. N. 2014. “Constructing discrete unbounded distributions with Gaussian-copula dependence and given rank correlation.” INFORMS J. Comput. 26 (2): 269–279. https://doi.org/10.1287/ijoc.2013.0563.
Avramidis, A. N., N. Channouf, and P. L’Ecuyer. 2009. “Efficient correlation matching for fitting discrete multivariate distributions with arbitrary marginals and normal-copula dependence.” INFORMS J. Comput. 21 (1): 88–106. https://doi.org/10.1287/ijoc.1080.0281.
Babu, G. S., and V. P. Singh. 2009. “Reliability analysis of soil nail walls.” Georisk 3 (1): 44–54. https://doi.org/10.1080/17499510802541425.
Babu, G. S., and A. Srivastava. 2007. “Reliability analysis of allowable pressure on shallow foundation using response surface method.” Comput. Geotech. 34 (3): 187–194. https://doi.org/10.1016/j.compgeo.2006.11.002.
Basha, B. M., and G. S. Babu. 2012. “Target reliability-based optimisation for internal seismic stability of reinforced soil structures.” Géotechnique 62 (1): 55–68. https://doi.org/10.1680/geot.8.P.076.
Bathurst, R. J., T. M. Allen, P. Lin, and N. Bozorgzadeh. 2019. “LRFD calibration of internal limit states for geogrid MSE walls.” J. Geotech. Geoenviron. Eng. 145 (11): 04019087. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002124.
Bhattacharya, G., D. Jana, S. Ojha, and S. Chakraborty. 2003. “Direct search for minimum reliability index of earth slopes.” Comput. Geotech. 30 (6): 455–462. https://doi.org/10.1016/S0266-352X(03)00059-4.
Chalermyanont, T., and C. H. Benson. 2005. “Method to estimate the system probability of failure of mechanically stabilized earth (MSE) walls.” In Slopes and Retaining Structures under Seismic and Static Conditions, Geotechnical Special Publication 140, edited by M. A. Gabr, J. J. Bowders, D. Elton, and J. G. Zornberg, 1–15. Reston, VA, US: ASCE.
Chowdhury, R. N., and D. W. Xu. 1992. “Reliability index for slope stability assessment—two methods compared.” Reliab. Eng. Syst. Safety 37 (2): 99–108. https://doi.org/10.1016/0951-8320(92)90002-3.
Duncan, J. M. 2000. “Factors of safety and reliability in geotechnical engineering.” J. Geotech. Geoenviron. Eng. 126 (4): 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307).
Fakher, A., H. Nouri, and M. Shahgholi. 2002. “Limit equilibrium in reinforced soil walls subjected to seismic loads.” In Vol. 3 of Proc., 3rd Iranian Int. Conf. on Geotechnical Engineering and Soil Mechanics, 281–286. Tehran, Iran: Iranian Geotechnical Society.
Faravelli, L. 1989. “Response-surface approach for reliability analysis.” J. Eng. Mech. 115 (12): 2763–2781. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2763).
Farshidfar, N., A. Keshavarz, and S. M. Mirhosseini. 2020. “Yield acceleration of reinforced soil slopes using the modified pseudo-dynamic method.” SN Appl. Sci. 2 (5): 897. https://doi.org/10.1007/s42452-020-2655-x.
Gavin, H. P., and S. C. Yau. 2008. “High-order limit state functions in the response surface method for structural reliability analysis.” Struct. Saf. 30 (2): 162–179. https://doi.org/10.1016/j.strusafe.2006.10.003.
Ghanem, R. G., and P. D. Spanos. 1991. “Spectral stochastic finite-element formulation for reliability analysis.” J. Eng. Mech. 117 (10): 2351–2372. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:10(2351).
Ghanem, R. G., and P. D. Spanos. 2003. Stochastic finite elements: A spectral approach. Mineola, NY, US: Dover Publication.
Isukapalli, S. S., A. Roy, and P. G. Georgopoulos. 1998. “Stochastic response surface methods (SRSMs) for uncertainty propagation: Application to environmental and biological systems.” Risk Anal. 18 (3): 351–363. https://doi.org/10.1111/j.1539-6924.1998.tb01301.x.
Javankhoshdel, S., and R. J. Bathurst. 2017. “Deterministic and probabilistic failure analysis of simple geosynthetic reinforced soil slopes.” Geosynth. Int. 24 (1): 14–29. https://doi.org/10.1680/jgein.16.00012.
Ji, J., and B. K. 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.
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: 13–25. https://doi.org/10.1016/j.compgeo.2014.08.010.
Khosravizadeh, M., M. Dehestani, and F. Kalantary. 2016. “On the seismic stability and critical slip surface of reinforced slopes.” Soil Dyn. Earthquake Eng. 85: 179–190. https://doi.org/10.1016/j.soildyn.2016.03.018.
Lebrun, R., and A. Dutfoy. 2009. “A generalization of the Nataf transformation to distributions with elliptical copula.” Probab. Eng. Mech. 24 (2): 172–178. https://doi.org/10.1016/j.probengmech.2008.05.001.
Leshchinsky, D., H. Ling, and G. Hanks. 1995. “Unified design approach to geosynthetic reinforced slopes and segmental walls.” Geosynth. Int. 2 (5): 845–881. https://doi.org/10.1680/gein.2.0039.
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, D. Q., S. H. Jiang, Y. G. Cheng, and C. B. Zhou. 2013. “A comparative study of three collocation point methods for odd order stochastic response surface method.” Struct. Eng. Mech. 45 (5): 595–611. https://doi.org/10.12989/sem.2013.45.5.595.
Li, K. S., and P. Lumb. 1987. “Probabilistic design of slopes.” Can. Geotech. J. 24 (4): 520–535. https://doi.org/10.1139/t87-068.
Ling, H. I., and D. Leshchinsky. 1998. “Effects of vertical acceleration on seismic design of geosynthetic-reinforced soil structures.” Géotechnique 48 (3): 347–373. https://doi.org/10.1680/geot.1998.48.3.347.
Ling, H. I., D. Leshchinsky, and E. B. Perry. 1997. “Seismic design and performance of geosynthetic-reinforced soil structures.” Géotechnique 47 (5): 933–952. https://doi.org/10.1680/geot.1997.47.5.933.
Liu, L. L., and Y. M. Cheng. 2018. “System reliability analysis of soil slopes using an advanced kriging metamodel and quasi–Monte Carlo simulation.” Int. J. Geomech. 18 (8): 06018019. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001209.
Lo, S. R., and D. W. Xu. 1992. “A strain-based design method for the collapse limit state of reinforced soil walls or slopes.” Can. Geotech. J. 29 (5): 832–842. https://doi.org/10.1139/t92-090.
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).
Lü, Q., and B. K. Low. 2011. “Probabilistic analysis of underground rock excavations using response surface method and SORM.” Comput. Geotech. 38 (8): 1008–1021. https://doi.org/10.1016/j.compgeo.2011.07.003.
Luo, N., and R. J. Bathurst. 2018. “Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction.” Georisk 12 (2): 87–108. https://doi.org/10.1080/17499518.2017.1362443.
Luo, N., R. J. Bathurst, and S. Javankhoshdel. 2016. “Probabilistic stability analysis of simple reinforced slopes by finite element method.” Comput. Geotech. 77: 45–55. https://doi.org/10.1016/j.compgeo.2016.04.001.
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.
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. 2017. “System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines.” Comput. Geotech. 87: 212–228. https://doi.org/10.1016/j.compgeo.2017.02.017.
Michalowski, R. L. 1998. “Soil reinforcement for seismic design of geotechnical structures.” Comput. Geotech. 23 (1–2): 1–17. https://doi.org/10.1016/S0266-352X(98)00016-0.
Mollon, G., D. Dias, and A. H. Soubra. 2011. “Probabilistic analysis of pressurized tunnels against face stability using collocation-based stochastic response surface method.” J. Geotech. Geoenviron. Eng. 137 (4): 385–397. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000443.
Nouri, H., A. Fakher, and C. J. F. P. Jones. 2006. “Development of horizontal slice method for seismic stability analysis of reinforced slopes and walls.” Geotext. Geomembr. 24 (3): 175–187. https://doi.org/10.1016/j.geotexmem.2005.11.004.
Nouri, H., A. Fakher, and C. J. F. P. Jones. 2008. “Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium horizontal slices method.” Geotext. Geomembr. 26 (3): 263–278. https://doi.org/10.1016/j.geotexmem.2007.09.002.
Phoon, K. K., and S. P. Huang. 2007. “Uncertainty quantification using multi-dimensional Hermite polynomials.” In Probabilistic Applications in Geotechnical Engineering, Geotechnical Special Publication 170, edited by K.-K. Phoon, G. A. Fenton, E. F. Glynn, C. Hsein Juang, D. V. Griffiths, T. F. Wolff, and L. Zhang, 1–10. Reston, VA, US: ASCE.
Phoon, K. K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Rajashekhar, M. R., and B. R. Ellingwood. 1993. “A new look at the response surface approach for reliability analysis.” Struct. Saf. 12 (3): 205–220. https://doi.org/10.1016/0167-4730(93)90003-J.
Shahgholi, M., A. Fakher, and C. J. F. P. Jones. 2001. “Horizontal slice method of analysis.” Géotechnique 51 (10): 881–885. https://doi.org/10.1680/geot.2001.51.10.881.
Sudret, B., and A. Der Kiureghian. 2000. Stochastic finite element methods and reliability: A state-of-the-art report. Berkeley, CA, US: Dept. of Civil and Environmental Engineering, Univ. of California.
Wang, F., and H. Li. 2017. “Stochastic response surface method for reliability problems involving correlated multivariates with non-Gaussian dependence structure: Analysis under incomplete probability information.” Comput. Geotech. 89: 22–32. https://doi.org/10.1016/j.compgeo.2017.02.008.
Wong, F. S. 1985. “Slope reliability and response surface method.” J. Geotech. Eng. 111 (1): 32–53. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:1(32).
Xiao, Q., and S. Zhou. 2019. “Matching a correlation coefficient by a Gaussian copula.” Commun. Stat. - Theory Methods 48 (7): 1728–1747. https://doi.org/10.1080/03610926.2018.1439962.
Yi, P., K. Wei, X. Kong, and Z. Zhu. 2015. “Cumulative PSO-Kriging model for slope reliability analysis.” Probab. Eng. Mech. 39: 39–45. https://doi.org/10.1016/j.probengmech.2014.12.001.
Yuan, J. X., Y. Yang, L. G. Tham, P. K. K. Lee, and Y. Tsui. 2003. “New approach to limit equilibrium and reliability analysis of soil nailed walls.” Int. J. Geomech. 3 (2): 145–151. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:2(145).
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: 81–88. https://doi.org/10.1016/j.enggeo.2013.03.029.
Zhang, J., H. W. 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, J., L. M. Zhang, and W. H. Tang. 2011. “Kriging numerical models for geotechnical reliability analysis.” Soils Found. 51 (6): 1169–1177. https://doi.org/10.3208/sandf.51.1169.
Zornberg, J. G., N. Sitar, and J. K. Mitchell. 1998. “Performance of geosynthetic reinforced slopes at failure.” J. Geotech. Geoenviron. Eng. 124 (8): 670–683. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:8(670).
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 2, 2020
Accepted: May 29, 2021
Published online: Aug 2, 2021
Published in print: Oct 1, 2021
Discussion open until: Jan 2, 2022
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.
Cited by
- Ekansh Agarwal, Anindya Pain, Annan Zhou, Probabilistic Assessment of Reinforced Soil Walls Using Fourth Moment Normal Transformation, Proceedings of the TMIC 2022 Slope Stability Conference (TMIC 2022), 10.2991/978-94-6463-104-3_6, (55-60), (2023).
- E. Agarwal, A. Pain, Reliability assessment of reinforced slopes with unknown probability distribution, Geosynthetics International, 10.1680/jgein.21.00106, (1-13), (2022).