Abstract
The railway embankment slope is a complex open system including uncertainty of soil parameters. Considering the influencing factors with randomness, ambiguity and uncertainty, the reliability analysis of slope stability is often accompanied by an implicit state equation, subtle changes of the input variables may result in drastic changes to the slope stability. In this work, a coupled Markov chain model is used to describe the staggering occurrence of different geotechnical types. To further describe the inherent variability of soil parameters, a response surface method (RMS) based Monte Carlo simulation (MCS) is conducted to perform the reliability analysis. One case study is carried out using borehole data collected from Masao District in Yunnan, China. The results indicate the proposed RMS-based MCS approach could be utilized as a practical and efficient tool for the slope reliability analysis to address the system reliability analysis for complex slopes.
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References
Cao Z, Wang Y, Li D (2010) Efficient Monte Carlo simulation of parameter sensitivity in probabilistic slope stability analysis. Comput Geotech 37(7):1015–1022
Cheung RWM, Tang WH (2005) Realistic assessment of slope reliability for effective landslide hazard management. Geotechnique 55(1):85–94
Cho SE (2009) Probabilistic stability analyses of slopes using the ANN-based response surface. Comput Geotech 36(5):787–797
Chowdhury R, Rao BN (2010) Probabilistic stability assessment of slopes using high dimensional model representation. Comput Geotech 37(7–8):876–884
Elfek AM (2006) Reducing concentratian uncertainty using the coupled Markov chain approach. J Hydrol 317(1):1–16
Elfeki AMM (1996) Stochastic characterization of geological heterogeneity and its impact on groundwater contaminant transport. Balkema, Lisse
Elfeki AMM, Dekking M (2006) A Markov chain model for subsurface characterization: theory and applications. Math Geol 38(4):503–505
Fang G, Hao Y, Lei H (2011) Stochastic analog circuit behavior modeling by point estimation method. In: Proceedings of the 2011 international symposium on physical design 2011. ACM Press the 2011 international symposium, Santa Barbara, CA, USA
Figueiredo B et al (2015) Coupled hydro-mechanical processes and fault reactivation induced by CO2 Injection in a three-layer storage formation. Int J Greenhouse Gas Control 39:432–448
Gates P, Tong H (1976) On Markov Chain modeling to some weather data. J Appl Meteorol 15(15):1145–1151
Geng M, Wang D, Li P (2018) Undrained dynamic behavior of reinforced subgrade under long-term cyclic loading. Adv Mater Sci Eng 2018(2):1–9
Ghosh S et al (2010) Rock slope instability assessment using spatially distributed structural orientation data in Darjeeling Himalaya (India). Earth Surf Proc Landf 35(15):1773–1792
Gong Y et al (2019) Stability analysis of soil embankment slope reinforced with polypropylene fiber under freeze-thaw cycles. Adv Mater Sci Eng 2019(3):1–10
Griffiths DV et al (1999) Slope stability analysis by finite elements. Geotechnique 49(7):653–654
Hassan AM, Wolff TF (1999) Search algorithm for minimum reliability index of earth slopes. J Geotech Geoenviron Eng 125(4):301–308
Hong HP, Roh G (2008) Reliability evaluation of earth slopes. J Geotech Geoenviron Eng 134(12):1700–1705
Ishii K, Suzuki M (1986) Stochastic finite element method for slope stability analysis. Struct Saf 4(2):111–129
Jha SK (2014) Effect of spatial variability of soil properties on slope reliability using random finite element and first order second moment methods. Indian Geotech J 45(2):1–11
Ji J, Low BK (2012) Stratified response surfaces for system probabilistic evaluation of slopes. J Geotech Geoenviron Eng 138(11):1398–1406
Jiang SH et al (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168:120–128
Jiang SH et al (2015) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. J Geotech Geoenviron Eng 141(2):04014096
Kang F, Li J (2016) Artificial bee colony algorithm optimized support vector regression for system reliability analysis of slopes. J Comput Civ Eng 30(3):04015040
Kang F et al (2015) System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling. Comput Geotech 63:13–25
Kaymaz I, Mcmahon C (2005) A response surface method based on weighted regression for structural reliability analysis. Probab Eng Mech 20(1):11–17
Li KS, Lumb P (1987) Probabilistic design of slopes. Can Geotech J 24(4):520–535
Li D et al (2011) Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables. Comput Geotech 38(1):58–68
Li D-Q et al (2014) A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Eng Geol 187:60–72
Liu L et al (2019) Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines. Geosci Front 10(2):671–682
Myers RH, Montgomery DC (2008) Response surface methodology: process and product in optimization using designed experiments. Technometrics 38(3):284–286
Phoon KK, Kulhawy FH (1999) Evaluation of geotechnical property variability. Can Geotech J 36(4):625–639
Piliounis G, Lagaros ND (2014) Reliability analysis of geostructures based on metaheuristic optimization. Appl Soft Comput 22:544–565
Samui P, Lansivaara T, Bhatt MR (2013) Least square support vector machine applied to slope reliability analysis. Geotech Geol Eng 31(4):1329–1334
Shui-hua J et al (2015) System reliability analysis of slope with stochastic response surface method. Rock Soil Mech 36(3):809–818
Tan XH et al (2011) Reliability analysis using radial basis function networks and support vector machines. Comput Geotech 38(2):178–186
Tan XH et al (2013) Response surface method of reliability analysis and its application in slope stability analysis. Geotech Geol Eng 31(4):1011–1025
Tang XS et al (2015) Copula-based approaches for evaluating slope reliability under incomplete probability information. Struct Saf 52:90–99
Vanmarcke EH (1980) Probabilistic stability analysis of earth slopes. Eng Geol 16(1–2):29–50
Wong FS (1985) Slope reliability and response surface method. J Geotech Eng 111(1):32–53
Xu B, Low BK (2006) Probabilistic stability analyses of embankments based on finite-element method. J Geotech Geoenviron Eng 132(11):1444–1454
Yan Z et al (2019) Dynamic response law of loess slope with different shapes. Adv Mater Sci Eng 2019(2):1–7
Yu W et al (2011) Reliability evaluation of slopes based on vector projection response surface and its application. Chin J Geotech Eng 33(9):1434–1439
Yücemen MS, Al-Homoud AS (1990) Probabilistic three-dimensional stability analysis of slopes. Struct Saf 9(1):1–20
Zhang LM, Murty D (2012) Spatial variability of in situ weathered soil. Geotechnique 62(5):375–384
Zhang J, Zhang LM, Tang WH (2011) New methods for system reliability analysis of soil slopes. Can Geotech J 48(7):1138–1148
Zhang J, Huang HW, Phoon K-K (2013) Application of the Kriging-based response surface method to the system reliability of soil slopes. J Geotech Geoenviron Eng 139(4):651–655
Zhao HB (2008) Slope reliability analysis using a support vector machine. Comput Geotech 35(3):459–467
Zhu B, Pei H, Yang Q (2019) Reliability analysis of submarine slope considering the spatial variability of the sediment strength using random fields. Appl Ocean Res 86:340–350
Acknowledgements
This study was supported by the National Natural Science Foundation of China under Grant No. 51878560.
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National Natural Science Foundation of China under Grant No. 51878560.
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Kong, D., Luo, Q., Zhang, W. et al. Reliability analysis approach for railway embankment slopes using response surface method based Monte Carlo simulation. Geotech Geol Eng 40, 4529–4538 (2022). https://doi.org/10.1007/s10706-022-02168-9
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DOI: https://doi.org/10.1007/s10706-022-02168-9