Abstract
Accurate estimation of slope stability based on numerous candidate estimation methods is difficult as different results may be yielded. It becomes even more challenging when only limited data of geotechnical parameters (e.g., shear strength parameters) are available to evaluate slope reliability. Based on the Bayesian sequential updating technology, a hybrid framework for slope reliability was proposed in this study, through which prior knowledge, multiple estimation methods, and corresponding model uncertainties could be integrated to estimate slope reliability using a small amount of geotechnical data. Three slope examples with various stratigraphic configurations and soil properties were used to illustrate the accuracy and efficiency of the proposed framework, during which the Bishop’s simplified method, the upper bound limit analysis method, and the finite element method were adopted. The results showed that with results of direct Monte Carlo simulation based on each method as the benchmark, a compromised mean of the factor of safety (μFS), and conservative standard deviation of the factor of safety (σFS) and failure probability (Pf) were yielded through the proposed framework. When the sample size of geotechnical parameters was greater than a threshold, the estimated μFS was stable, while the σFS and Pf synchronously varied within a small range with the increase in sample size. Demonstrations of the three examples indicated that the proposed hybrid framework can provide reliable and accurate estimations of slope reliability. The proposed framework may serve as a promising vehicle for slope/landslide engineering including failure and preventative mechanisms, movement prediction, and back analysis of geotechnical parameters in a probabilistic context, and big data analysis of geological and geotechnical problems as well.
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References
Aladejare AE, Wang Y (2017) Sources of uncertainty in site characterization and their impact on geotechnical reliability-based design. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part a: Civil Engineering 3(4):04017024. https://doi.org/10.1061/ajrua6.0000922
Aladejare AE, Wang Y (2018) Influence of rock property correlation on reliability analysis of rock slope stability: from property characterization to reliability analysis. Geosci Front 9(6):1639–1648. https://doi.org/10.1016/j.gsf.2017.10.003
Aladejare AE, Wang Y (2019a) Estimation of rock mass deformation modulus using indirect information from multiple sources. Tunn Underg Sp Tech 85:76–83. https://doi.org/10.1016/j.tust.2018.11.047
Aladejare AE, Wang Y (2019b) Probabilistic characterization of Hoek-Brown constant mi of rock using Hoek’s guideline chart, regression model and uniaxial compression test. Geotech Geol Eng 37(6):5045–5060. https://doi.org/10.1007/s10706-019-00961-7
Ang AHS, Tang WH (2007) Probability concepts in engineering planning and design: emphasis on application to civil and environmental engineering. John Wiley & Sons, New York
Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. John Wiley and Sons, New York
Bishop AW (1955) The use of slip circle in the stability analysis of earth slope. Géotechnique 5(1):7–17. https://doi.org/10.1680/geot.1955.5.1.7
Cao ZJ, Wang Y, Li DQ (2016) Site-specific characterization of soil properties using multiple measurements from different test procedures at different locations—a Bayesian sequential updating approach. Eng Geol 211:150–161. https://doi.org/10.1016/j.enggeo.2016.06.021
Cetin KO, Der Kiureghian A, Seed RB (2002) Probabilistic models for the initiation of seismic soil liquefaction. Struct Saf 24(1):67–82. https://doi.org/10.1016/s0167-4730(02)00036-x
Chen WF (1975) Limit analysis and soil plasticity. Developments in Geotechnical Engineering (Vol. 7). Amsterdam: Elsevier Science Press. https://doi.org/10.1016/b978-0-444-41249-2.x5001-x
Cho SE (2010) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron 136(7):975–984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309
Contreras LF, Brown ET, Ruest M (2018) Bayesian data analysis to quantify the uncertainty of intact rock strength. J Rock Mech Geotech Eng 10(1):11–31. https://doi.org/10.1016/j.jrmge.2017.07.008
Contreras LF, Brown ET (2019) Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference. J Rock Mech Geotech Eng 11(3):628–643. https://doi.org/10.1016/j.jrmge.2018.11.008
Coduto DP, Yeung MR, Kitch WA (2011) Geotechnical engineering: principles and practices, 2nd edn. Pearson Education, Upper Saddle River, NJ
Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65. https://doi.org/10.1680/geot.1979.29.1.47
Dadashzadeh N, Duzgun HSB, Yesiloglu-Gultekin N (2017) Reliability-based stability analysis of rock slopes using numerical analysis and response surface method. Rock Mech Rock Eng 50(8):2119–2133. https://doi.org/10.1007/s00603-017-1206-2
Drucker DC, Prager W, Greenberg HJ (1952) Extended limit design theorems for continuous media. Q Appl Math 9(4):381–389. https://doi.org/10.1090/qam/45573
Fellenius W (1936) Calculation of the stability of earth dams. Proceedings of the Second Congress of Large Dams 4:445–463
Feng XD, Jimenez R (2015) Estimation of deformation modulus of rock masses based on Bayesian model selection and Bayesian updating approach. Eng Geol 199:19–27. https://doi.org/10.1016/j.enggeo.2015.10.002
Giam PSK, Donald IB (1989) Example problems for testing soil slope stability programs. Civil Eng Res Rep No. 8/1989, Monash University, Melbourne, Australia.
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices R Astronom Soc 181(3):375–389. https://doi.org/10.1093/mnras/181.3.375
Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron 130(5):507–518. https://doi.org/10.1061/41144(391)9
Huang ML, Sun DA, Wang CH, Keleta Y (2021) Reliability analysis of unsaturated soil slope stability using spatial random field-based Bayesian method. Landslides 18:1177–1189. https://doi.org/10.1007/s10346-020-01525-0
Huang XH, Guo F, Deng ML, Yi W, Huang HF (2020) Understanding the deformation mechanism and threshold reservoir level of the floating weight-reducing landslide in the Three Gorges Reservoir Area, China. Landslides 17:2879–2894. https://doi.org/10.1007/s10346-020-01435-1
Janbu N (1954) Application of composite slide circles for stability analysis. Proceedings of European Conference on stability of Earth Slope. Stockholm, 3:43–9.
Janbu N (1973) Slope stability computations. Publication of. Wiley (John) and Sons, Inc, 47–86.
Ji J, Low BK (2012) Stratified response surfaces for system probabilistic evaluation of slopes. J Geotech Geoenviron 138(11):1398–1406. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000711
Ji J, Zhang CS, Gao YF, Kodikara J (2018) Effect of 2D spatial variability on slope reliability: a simplified FORM analysis. Geosci Front 9(6):1631–1638. https://doi.org/10.1016/j.gsf.2017.08.004
Jiang SH, Li DQ, Cao ZJ, Zhou CB, Phoon KK (2015) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. J Geotech Geoenviron 141(2):04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227
Juang CH, Zhang J (2017) Bayesian methods for geotechnical applications—a practical guide. In: Proceedings of georisk 2017 on geotechnical risk from theory to practice. American Society of Civil Engineers (ASCE) 215–246. https://doi.org/10.1061/9780784480731.019
Kilburn CR, Petley DN (2003) Forecasting giant, catastrophic slope collapse: lessons from Vajont. Northern Italy Geomorphology 54(1–2):21–32. https://doi.org/10.1016/s0169-555x(03)00052-7
Kruschke J (2015) Doing Bayesian data analysis: a tutorial with R, JAGS, and Stan, 2nd edn. Academic Press, Amsterdam, New York. https://doi.org/10.1016/B978-0-12-405888-0.00001-5
Leshchinsky B, Ambauen S (2015) Limit equilibrium and limit analysis: comparison of benchmark slope stability problems. J Geotech Geoenviron 141(10):04015043. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001347
Li LC, Tang CA, Zhu WC (2009) Numerical analysis of slope stability based on the gravity increase method. Comput Geotech 36(7):1246–1258. https://doi.org/10.1016/j.compgeo.2009.06.004
Li DQ, Zheng D, Cao ZJ, Tang XS, Phoon KK (2016) Response surface methods for slope reliability analysis: review and comparison. Eng Geol 203:3–14. https://doi.org/10.1016/j.enggeo.2015.09.003
Li DQ, Zhang FP, Cao ZJ, Tang XS, Au SK (2018) Reliability sensitivity analysis of geotechnical monitoring variables using Bayesian updating. Eng Geol 245:130–140. https://doi.org/10.1016/j.enggeo.2018.07.026
Li CD, Fu ZY, Wang Y, Tang HM, Yan JF, Gong WP, Yao WM, Criss R (2019a) Susceptibility of reservoir-induced landslides and strategies for increasing the slope stability in the Three Gorges Reservoir Area: Zigui Basin as an example. Eng Geol 261:105279. https://doi.org/10.1016/j.enggeo.2019.105279
Li CD, Criss RE, Fu ZY, Long JJ, Tan QW (2021a) Evolution characteristics and displacement forecasting model of landslides with stair-step sliding surface along the Xiangxi River, Three Gorges Reservoir region. China Eng Geol 283:105961. https://doi.org/10.1016/j.enggeo.2020.105961
Li SH, Luo XH, Wu LZ (2019b) An improved whale optimization algorithm for locating critical slip surface of slopes. Adv Eng Softw 157–158:103009. https://doi.org/10.1016/j.advengsoft.2021.103009
Li SH, Wu LZ, Chen JJ, Huang RQ (2020) Multiple data-driven approach for predicting landslide deformation. Landslides 17(3):709–718. https://doi.org/10.1007/s10346-019-01320-6
Li SH, Luo XH, Wu LZ (2021b) A new method for calculating failure probability of landslide based on ANN and a convex set model. Landslides 18:2855–2867. https://doi.org/10.1007/s10346-021-01652-2
Li SH, Wu LZ, Huang JS (2021c) A novel mathematical model for predicting landslide displacement. Soft Comput 25:2453–2466. https://doi.org/10.1007/s00500-020-05313-9
Liu LL, Deng ZP, Zhang SH, Cheng YM (2018) Simplified framework for system reliability analysis of slopes in spatially variable soils. Eng Geol 239:330–343. https://doi.org/10.1016/j.enggeo.2018.04.009
Liu LL, Zhang SH, Cheng YM (2019) Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines. Geosci Front 10(2):671–682. https://doi.org/10.1016/j.gsf.2018.03.013
Loukidis D, Bandini P, Salgado R (2003) Stability of seismically loaded slopes using limit analysis. Géotechnique 53(5):463–479
Low BK (2014) FORM, SORM, and spatial modeling in geotechnical engineering. Struct Saf 49:56–64. https://doi.org/10.1016/j.strusafe.2013.08.008
Lucy L (1977) A numerical approach to testing the fission hypothesis. Astronom J 82:1013–1024. https://doi.org/10.1086/112164
Ma JZ, Zhang J, Huang HW, Zhang LL, Huang JJ (2017) Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction. Comput Geotech 85:199–206. https://doi.org/10.1016/j.compgeo.2016.12.033
Matsui T, San KC (1992) Finite element slope stability analysis by shear strength reduction technique. Soils Found 32(1):59–70. https://doi.org/10.3208/sandf1972.32.59
McGuire MP, VandenBerge DR (2017) Interpretation of shear strength uncertainty and reliability analyses of slopes. Landslides 14:2059–2072. https://doi.org/10.1007/s10346-017-0836-5
Mongenstern NR, Price VE (1965) The analysis of stability of general slide surfaces. Géotechnique 15(1):79–93. https://doi.org/10.1680/geot.1965.15.1.79
Naylor DJ, Pande GN (1981) Finite elements in geotechnical engineering. Pineridge Press, Swansea
Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624. https://doi.org/10.1139/t00-089
Robert C, Casella G (2011) A short history of Markov chain Monte Carlo: subjective recollections from incomplete data. Stat Sci 26(1):102–115. https://doi.org/10.1214/10-sts351
Sarma SK (1979) Stability analysis of embankments and slopes. J Geotech Eng Div 23(3):1511–1524. https://doi.org/10.1061/AJGEB6.0000903
Shi GH (1988) Discontinuous deformation analysis: a new numerical model for the static and dynamics of block systems. PhD thesis, University of California, Berkeley.
Sivia D, Skilling J (2006) Data analysis: a Bayesian tutorial. Oxford University Press, New York
Song LF, Yu X, Xu B, Pang R, Zhang ZY (2021) 3D slope reliability analysis based on the intelligent response surface methodology. B Eng Geol Environ 80(2):735–749. https://doi.org/10.1007/s10064-020-01940-6
Spencer E (1967) A method of analysis of the stability of embankments assuming parallel inter-slice forces. Géotechnique 17(1):11–26. https://doi.org/10.1680/geot.1967.17.1.11
Spencer E (1973) Thrust line criterion in embankment stability analysis. Géotechnique 23(1):85–100. https://doi.org/10.1680/geot.1973.23.1.85
Wang FW, Zhang YM, Huo ZT, Matsumoto T, Huang BL (2004) The July 14, 2003 Qianjiangping landslide, Three Gorges Reservoir. China Landslides 1(2):157–162. https://doi.org/10.1007/s10346-004-0020-6
Wang Y, Huang K, Cao ZJ (2013) Probabilistic identification of underground soil stratification using cone penetration tests. Can Geotech J 50(7):766–776. https://doi.org/10.1139/cgj-2013-0004
Wang Y, Aladejare AE (2016a) Bayesian characterization of correlation between uniaxial compressive strength and Young’s modulus of rock. Int J Rock Mech Min 85:10–19. https://doi.org/10.1016/j.ijrmms.2016.02.010
Wang Y, Aladejare AE (2016b) Evaluating variability and uncertainty of geological strength index at a specific site. Rock Mech Rock Eng 49(9):3559–3573. https://doi.org/10.1007/s00603-016-0957-5
Wang Y, Cao ZJ, Li DQ (2016) Bayesian perspective on geotechnical variability and site characterization. Eng Geol 203:117–125. https://doi.org/10.1016/j.enggeo.2015.08.017
Xu B, Low BK (2006) Probabilistic stability analyses of embankments based on finite-element method. J Geotech Geoenviron 132(11):1444–1454. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:11(1444)
Yao WM, Li CD, Zhan ZQJ, HB, Criss R (2019) Spatiotemporal deformation characteristics and triggering factors of Baijiabao landslide in Three Gorges Reservoir region, China. Geomorphology 343:34–47. https://doi.org/10.1016/j.geomorph.2019.06.024
Yao WM, Li CD, Zhan HB, Zhou JQ, Criss R (2020) Estimation of geological strength index through a Bayesian sequential updating approach integrating multi-source information. Tunn Underg Sp Tech 102:103426. https://doi.org/10.1016/j.tust.2020.103426
Zeng P, Jimenez R (2014) An approximation to the reliability of series geotechnical systems using a linearization approach. Comput Geotech 62:304–309. https://doi.org/10.1016/j.compgeo.2014.08.007
Zhang J, Huang HW, Juang CH, Li DQ (2013) 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, Huang HW (2016) Risk assessment of slope failure considering multiple slip surfaces. Comput Geotech 74:188–195. https://doi.org/10.1016/j.compgeo.2016.01.011
Zhao LH, Zuo S, Lin YL, Li L, Zhang YB (2016) Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory. Landslides 13:711–724. https://doi.org/10.1007/s10346-015-0604-3
Zhao J, Duan XR, Ma LN, Zhang J, Huang HW (2020) Importance sampling for system reliability analysis of soil slopes based on shear strength reduction Georisk 1–12. https://doi.org/10.1080/17499518.2020.1780618
Zhao HB, Chen BR, Li SJ, Li Z, Zhu C (2021) Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference. Geosci Front 12(5):101198. https://doi.org/10.1016/j.gsf.2021.101198
Zienkiewicz OC, Humpheson C, Lewis RW (1975) Associated and non-associated viscoplasticity and plasticity in soil mechanics. Géotechnique 25(4):671–689. https://doi.org/10.1680/geot.1975.25.4.671
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This work was supported by the National Natural Science Foundation of China (grant numbers 42107181 and 41972270), the National Key R&D Program of China (grant numbers 2018YFC1507200 and 2017YFC1501304), and the National Science Foundation for Excellent Young Scholars of China (grant number 41922055).
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Yao, W., Li, C., Yan, C. et al. Slope reliability analysis through Bayesian sequential updating integrating limited data from multiple estimation methods. Landslides 19, 1101–1117 (2022). https://doi.org/10.1007/s10346-021-01812-4
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DOI: https://doi.org/10.1007/s10346-021-01812-4