Abstract
Reliability analysis approach provides a rational means to quantitatively evaluate the safety of geotechnical structures from a probabilistic perspective. However, it suffers from a known criticism of extensive computational requirements and poor efficiency, which hinders its application in the reliability analysis of earth dam slope stability. Until now, the effects of spatially variable soil properties on the earth dam slope reliability remain unclear. This calls for a novel method to perform reliability analysis of earth dam slope stability accounting for the spatial variability of soil properties. This paper develops an efficient extreme gradient boosting (XGBoost)-based reliability analysis approach for evaluating the earth dam slope failure probability. With the aid of the proposed approach, the failure probability of earth dam slope can be evaluated rationally and efficiently. The proposed approach is illustrated using a practical case adapted from Ashigong earth dam. Results show that the XGBoost-based reliability analysis approach is able to predict the earth dam slope failure probability with reasonable accuracy and efficiency. The coefficient of variations and scale of fluctuations of soil properties affect the earth dam slope failure probability significantly. Moreover, the earth dam slope failure probability is highly dependent on the selection of auto-correlation function (ACF), and the widely used single exponential ACF tends to provide an unconservative estimate in this study.
Similar content being viewed by others
References
Ahmed AA (2009) Stochastic analysis of free surface flow through earth dams. Comput Geotech 36(7):1186–1190. https://doi.org/10.1016/j.compgeo.2009.05.005
Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277. https://doi.org/10.1016/S0266-8920(01)00019-4
Au SK, Wang Y (2014) Engineering risk assessment with subset simulation. Wiley, Singapore
Babu GLS, Srivastava A (2010) Reliability analysis of earth dams. J Geotech Geoenviron Eng 136(7):995–998. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000313
Cao ZJ, Wang Y (2014) Bayesian model comparison and selection of spatial correlation functions for soil parameters. Struct Saf 49:10–17. https://doi.org/10.1016/j.strusafe.2013.06.003
Chen TQ, Guestrin C (2016) XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp 785–794. https://doi.org/10.1145/2939672.2939785
Childs EC, Collis-George N (1950) The permeability of porous materials. Proc R Soc Lond Ser A Math Phys Sci 201(1066):392–405. https://doi.org/10.1098/rspa.1950.0068
Cho SE (2010) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron Eng 136(7):975–984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309
Cho SE (2012) Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation. Eng Geol 133–134:30–39. https://doi.org/10.1016/j.enggeo.2012.02.013
Fan C, Sun Y, Zhao Y, Song M, Wang J (2019) Deep learning-based feature engineering methods for improved building energy prediction. Appl Energy 240:35–45. https://doi.org/10.1016/j.apenergy.2019.02.052
Fenton GA, Griffiths DV (1996) Statistics of free surface flow through stochastic earth dam. J Geotech Eng 122(6):427–436. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:6(427)
Fenton GA, Griffiths DV (1997) Extreme hydraulic gradient statistics in stochastic earth dam. J Geotech Geoenviron Eng 123(11):995–1000. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:11(995)
Fredlund DG, Rahardjo H, Fredlund MD (2012) Unsaturated soil mechanics in engineering practice. Wiley, Hoboken
GEO-SLOPE International, Ltd. (2012) Geostudio. https://www.geoslope.com/
Gui SX, Zhang RD, Turner JP, Xue XZ (2000) Probabilistic slope stability analysis with stochastic soil hydraulic conductivity. J Geotech Geoenviron Eng 126(1):1–9. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:1(1)
Hicks MA, Li YJ (2018) Influence of length effect on embankment slope reliability in 3D. Int J Numer Anal Methods Geomech 42(7):891–915. https://doi.org/10.1002/nag.2766
Hu JL, Liu HB (2019) Bayesian network models for probabilistic evaluation of earthquake-induced liquefaction based on CPT and Vs databases. Eng Geol 254:76–88. https://doi.org/10.1016/j.enggeo.2019.04.003
Hu Y, Zhao TY, Wang Y, Choi C, Ng CWW (2019) Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling. Stoch Environ Res Risk Assess 33(8–9):1477–1496. https://doi.org/10.1007/s00477-019-01718-7
Huang HW, Wen SC, Zhang J, Chen FY, Martin JR, Wang H (2018) Reliability analysis of slope stability under seismic condition during a given exposure time. Landslides 15(11):2303–2313. https://doi.org/10.1007/s10346-018-1050-9
Huang XX, Chen JQ, Zhu HP (2016) Assessing small failure probabilities by AK-SS: an active learning method combining Kriging and subset simulation. Struct Saf 59:86–95. https://doi.org/10.1016/j.strusafe.2015.12.003
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
Khalilzad M, Gabr MA, Ellen M (2015) Assessment of remedial measures to reduce exceedance probability of performance limit states in embankment dams. Comput Geotech 67:213–222. https://doi.org/10.1016/j.compgeo.2015.02.010
Le TMH, Gallipoli D, Sanchez M, Wheeler SJ (2012) Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments. Int J Numer Anal Methods Geomech 36(8):1056–1076
Le TMH, Gallipoli D, Sánchez M, Wheeler S (2015) Stability and failure mass of unsaturated heterogeneous slopes. Can Geotech J 52(11):1747–1761. https://doi.org/10.1139/cgj-2014-0190
Leong EC, Rahardjo H (1997) Permeability functions for unsaturated soils. J Geotech Geoenviron Eng 123(12):1118–1126. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:12(1118)
Li DQ, Jiang SH, Cao ZJ, Zhou W, Zhou CB, Zhang LM (2015) A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Eng Geol 187:60–72. https://doi.org/10.1016/j.enggeo.2014.12.003
Li DQ, Wang L, Cao ZJ, Qi XH (2019) Reliability analysis of unsaturated slope stability considering SWCC model selection and parameter uncertainties. Eng Geol 260:105207. https://doi.org/10.1016/j.enggeo.2019.105207
Li DQ, Xiao T, Cao ZJ, Zhou CB, Zhang LM (2016) Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using subset simulation. Landslides 13(2):293–303. https://doi.org/10.1007/s10346-015-0569-2
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 XY, Zhang LM, Zhang S (2018) Efficient Bayesian networks for slope safety evaluation with large quantity monitoring information. Geosci Front 9(6):1679–1687. https://doi.org/10.1016/j.gsf.2017.09.009
Liu LL, Cheng YM (2016) Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation. Comput Geotech 79:41–54. https://doi.org/10.1016/j.compgeo.2016.05.001
Liu LL, Cheng YM, Jiang SH, Zhang SH, Wang XM, Wu ZH (2017) Effects of spatial autocorrelation structure of permeability on seepage through an embankment on a soil foundation. Comput Geotech 87:62–75. https://doi.org/10.1016/j.compgeo.2017.02.007
Liu LL, Zhang SH, Cheng YM, Liang L (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
Liu Y, Zhang WG, Zhang L, Zhu ZR, Hu J, Wei H (2018) Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods. Geosci Front 9(6):1657–1664. https://doi.org/10.1016/j.gsf.2017.09.003
Montoya-Noguera S, Zhao TY, Hu Y, Wang Y, Phoon KK (2019) Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen–Loève expansion. Struct Saf 79:66–79. https://doi.org/10.1016/j.strusafe.2019.03.006
Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 12:513–522. https://doi.org/10.1029/WR012i003p00513
Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624. https://doi.org/10.1139/t99-038
Phoon KK, Santoso A, Quek ST (2010) Probabilistic analysis of soil–water characteristic curves. J Geotech Geoenviron Eng 136:445–455. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000222
Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1(5):318–333. https://doi.org/10.1063/1.1745010
Rodríguez JD, Pérez A, Lozano JA (2010) Sensitivity analysis of k-fold cross validation in prediction error estimation. IEEE Trans Pattern Anal Mach Intell 32(3):569–575. https://doi.org/10.1109/TPAMI.2009.187
Santoso AM, Phoon KK, Quek ST (2011) Effects of soil spatial variability on rainfall-induced landslides. Comput Struct 89:893–900. https://doi.org/10.1016/j.compstruc.2011.02.016
Sheridan RP, Wang WM, Liaw A, Ma J, Gifford EM (2016) Extreme gradient boosting as a method for quantitative structure–activity relationships. J Chem Inf Model 56(12):2353–2360. https://doi.org/10.1021/acs.jcim.6b00591
Sillers WS, Fredlund DG (2001) Statistical assessment of soil–water characteristic curve models for geotechnical engineering. Can Geotech J 38:1297–1313. https://doi.org/10.1139/cgj-38-6-1297
Silvestrini RT, Montgomery DC, Jones B (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
Srivastava A, Babu GLS, Haldar S (2010) Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Eng Geol 110(3–4):93–101. https://doi.org/10.1016/j.enggeo.2009.11.006
van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x
Vanapalli SK, Fredlund DG, Pufahl DE, Clifton AW (1996) Model for the prediction of shear strength with respect to soil suction. Can Geotech J 33(3):379–392. https://doi.org/10.1139/t96-060
Vanmarcke EH (1983) Random fields: analysis and synthesis. MIT Press, Cambridge
Wang B, Chen YL, Wu C, Peng Y, Song JJ, Liu WJ, Liu X (2018) Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. J Hydrol 562:692–702. https://doi.org/10.1016/j.jhydrol.2018.05.049
Wang L, Cao ZJ, Li DQ, Phoon KK, Au SK (2018) Determination of site-specific soil–water characteristic curve from a limited number of test data—a Bayesian perspective. Geosci Front 9(6):1665–1677. https://doi.org/10.1016/j.gsf.2017.10.014
Wang L, Zhang WG, Chen FY (2019) Bayesian approach for predicting soil–water characteristic curve from particle-size distribution data. Energies 12:2992. https://doi.org/10.3390/en12152992
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
Wang Y, Cao ZJ, Au SK (2010) Efficient Monte Carlo simulation of parameter sensitivity in probabilistic slope stability analysis. Comput Geotech 37(7–8):1015–1022. https://doi.org/10.1016/j.compgeo.2010.08.010
Wang Y, Cao ZJ, Au SK (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
Wang Y, Zhao TY, Phoon KK (2018) Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation. Can Geotech J 55(6):862–880. https://doi.org/10.1139/cgj-2017-0254
Wang Y, Zhao TY, Hu Y, Phoon KK (2019) Simulation of random fields with trend from sparse measurements without detrending. J Eng Mech 145(2):1–12. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001560
Wong TT (2015) Performance evaluation of classification algorithms by k-fold and leave-one-out cross validation. Pattern Recognit 48(9):2839–2846. https://doi.org/10.1016/j.patcog.2015.03.009
Zhang WG, Goh ATC (2013) Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Comput Geotech 48:82–95. https://doi.org/10.1016/j.compgeo.2012.09.016
Zhang WG, Goh ATC (2016) Multivariate adaptive regression splines and neural network models for prediction of pile drivability. Geosci Front 7(1):45–52. https://doi.org/10.1016/j.gsf.2014.10.003
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(4):711–724. https://doi.org/10.1007/s10346-015-0604-3
Acknowledgements
This work was supported by the National Key R&D Program of China (No. 2019YFC1509600), Natural Science Foundation of Chongqing (Nos. cstc2019jcyj-bshX0043 and cstc2019jcyj-bshX0032), Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering (No. 2019018), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K201900102). The financial support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, L., Wu, C., Tang, L. et al. Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method. Acta Geotech. 15, 3135–3150 (2020). https://doi.org/10.1007/s11440-020-00962-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11440-020-00962-4