LSSVM-based approach for refining soil failure criteria and calculating safety factor of slopes

Abstract

The failure criteria of practical soil mass are very complex, and have significant influence on the safety factor of slope stability. The Coulomb strength criterion and the power-law failure criterion are classically simplified. Each one has limited applicability owing to the noticeable difference between calculated predictions and actual results in some cases. In the work reported here, an analysis method based on the least square support vector machine (LSSVM), a machine learning model, is purposefully provided to establish a complex nonlinear failure criterion via iteration computation based on strength test data of the soil, which is of more extensive applicability to many problems of slope stability. In particular, three evaluation indexes including coefficient of determination, mean absolute percentage error, and mean square error indicate that fitting precision of the machine learning-based failure criterion is better than those of the linear Coulomb criterion and nonlinear power-law criterion. Based on the proposed LSSVM approach to determine the failure criterion, the limit equilibrium method can be used to calculate the safety factor of three-dimensional slope stability. Analysis of results of the safety factor of two three-dimensional homogeneous slopes shows that the maximum relative errors between the proposed approach and the linear failure criterion-based method and the power-law failure criterion-based method are about 12% and 7%, respectively.

Graphical abstract

Keywords

slope stability / safety factor / failure criterion / least square support vector machine

References

[1] Collins I F, Gunn C I M, Pender M J, Yan W. Slope stability analyses for materials with a non-linear failure envelope. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(5): 533–550

[2] Kang F, Li J J. Artificial bee colony algorithm optimized support vector regression for system reliability analysis of slopes. Journal of Computing in Civil Engineering, 2016, 30(3): 04015040

[3] Chen W F, Scawthorn C R. Limit analysis and limit equilibrium solutions in soil mechanics. Soil and Foundation, 1970, 10(3): 13–49

[4] Sun D A, Wang L, Li L. Stability of unsaturated soil slopes with cracks under steady-infiltration conditions. International Journal of Geomechanics, 2019, 19(6): 04019044

[5] Wang L, Sun D A, Yao Y, Tan Y. Seismic stability of 3D piled unsaturated earth slopes using kinematic limit analysis. Soil Dynamics and Earthquake Engineering, 2019, 126: 105821

[6] Lian J, Wu J. Surficial stability analysis of soil slope under seepage based on a novel failure mode. Frontiers of Structural and Civil Engineering, 2021, 15(3): 712–726

[7] Sheng K, Hong B N, Liu X, Shan H. Modified Bishop method for stability analysis of weakly sloped subgrade under centrifuge model test. Frontiers of Structural and Civil Engineering, 2021, 15(3): 727–741

[8] Matsui T, San K C. Finite element slope stability analysis by shear strength reduction technique. Soil and Foundation, 1992, 32(1): 59–70

[9] Yuan W, Li J X, Li Z H, Wang W, Sun X Y. A strength reduction method based on the Generalized Hoek-Brown (GHB) criterion for rock slope stability analysis. Computers and Geotechnics, 2020, 117: 103240

[10] FelleniusW. Calculation of the stability of earth dams. In: Transactions of The 2nd Congress on Large Dams, International Commission on Large Damsof The World Power Conference. 1936, 4: 445–462

[11] Bishop A W. The use of the slip circle in the stability analysis of earth slopes. Geotechnique, 1955, 5(1): 7–17

[12] JanbuN. Slope Stability Computations. Hoboken: John Wiley, 1973

[13] Morgenstern N R, Price V E. The analysis of the stability of general slip surfaces. Geotechnique, 1965, 15(1): 79–93

[14] Spencer E. A method of analysis for stability of embankments using parallel inter-slice forces. Geotechnique, 1967, 17(1): 11–26

[15] BellJ M. General slope stability analysis. Journal of the Soil Mechanics and Foundations Division, 1968, 94(6): 1253−1270

[16] Zhu D Y, Lee C F. Explicit limit equilibrium solution for slope stability. International Journal for Numerical and Analytical Methods in Geomechanics, 2002, 26(15): 1573–1590

[17] Zheng H, Tham L G. Improved Bell’s method for the stability analysis of slopes. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(14): 1673–1689

[18] Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[19] RabczukTBelytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29−30): 2777−2799

[20] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37−40): 2437–2455

[21] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[22] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

[23] Areias P, Msekh M A, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

[24] Areias P, Reinoso J, Camanho P P, César de Sá J, Rabczuk T. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360

[25] Hedayat A A, Ahmadi Afzadi E, Kalantaripour H, Morshedi E, Iranpour A. A new predictive model for the minimum strength requirement of steel moment frames using artificial neural network. Soil Dynamics and Earthquake Engineering, 2019, 116: 69–81

[26] Rivera J I, Bonilla C A. Predicting soil aggregate stability using readily available soil properties and machine learning techniques. Catena, 2020, 187: 104408

[27] Oommen T, Baise L G, Vogel R. Validation and application of empirical liquefaction models. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(12): 1618–1633

[28] Bikmukhametov T, Jäschke J. Combining machine learning and process engineering physics towards enhanced accuracy and explainability of data-driven models. Computers & Chemical Engineering, 2020, 138: 106834

[29] Merghadi A, Yunus A P, Dou J, Whiteley J, ThaiPham B, Bui D T, Avtar R, Abderrahmane B. Machine learning methods for landslide susceptibility studies: A comparative overview of algorithm performance. Earth-Science Reviews, 2020, 207: 103225

[30] Smiti A. When machine learning meets medical world: Current status and future challenges. Computer Science Review, 2020, 37: 100280

[31] Sheil B B, Suryasentana S K, Cheng W C. Assessment of anomaly detection methods applied to microtunneling. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146(9): 04020094

[32] Zhang N, Shen S L, Zhou A, Jin Y F. Application of LSTM approach for modelling stress–strain behaviour of soil. Applied Soft Computing, 2021, 100: 106959

[33] Samui P. Slope stability analysis: A support vector machine approach. Environmental Geology (Berlin), 2008, 56(2): 255–267

[34] Garg A, Garg A, Tai K, Sreedeep S. An integrated SRM-multi-gene genetic programming approach for prediction of factor of safety of 3-D soil nailed slopes. Engineering Applications of Artificial Intelligence, 2014, 30: 30–40

[35] Koopialipoor M, Jahed Armaghani D, Hedayat A, Marto A, Gordan B. Applying various hybrid intelligent systems to evaluate and predict slope stability under static and dynamic conditions. Soft Computing, 2019, 23(14): 5913–5929

[36] Ferentinou M, Fakir M. Integrating Rock Engineering Systems device and artificial neural networks to predict stability conditions in an open pit. Engineering Geology, 2018, 246: 293–309

[37] Zhou J, Li E, Yang S, Wang M, Shi X, Yao S, Mitri H S. Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories. Safety Science, 2019, 118: 505–518

[38] Huang F M, Cao Z, Guo J, Jiang S H, Li S, Guo Z Z. Comparisons of heuristic, general statistical and machine learning models for landslide susceptibility prediction and mapping. Catena, 2020, 191: 104580

[39] Wang Y K, Huang J S, Tang H M, Zeng C. Bayesian back analysis of landslides considering slip surface uncertainty. Landslides, 2020, 17(9): 2125–2136

[40] Wei X, Zhang L L, Yang H Q, Zhang L M, Yao Y P. Machine learning for pore-water pressure time-series prediction: Application of recurrent neural networks. Geoscience Frontiers, 2021, 12(1): 453–467

[41] Safa M, Sari P A, Shariati M, Suhatril M, Trung N T, Wakil K, Khorami M. Development of neuro-fuzzy and neuro-bee predictive models for prediction of the safety factor of eco-protection slopes. Physica A: Statistical Mechanics and its Applications, 2020, 550: 124046

[42] Suykens J A K, Vandewalle J. Least squares support vector machine classifiers. Neural Processing Letters, 1999, 9(3): 293–300

[43] SuykensJ A KGestelT VBrabanter J DMoorB DVandewalleJ. Least Squares Support Vector Machines. Singapore: World Scientific, 2002

[44] Duncan J M. State of the art: Limit equilibrium and finite-element analysis of slopes. Journal of Geotechnical Engineering, 1996, 122(7): 577–596

[45] Li S G. A reflection on the Mohr failure criterion. Mechanics of Materials, 2020, 148: 103442

[46] JohnstonI W. Strength of intact geomechanical materials. Journal of Geotechnical Engineering, 1985, 111(6): 730–749

[47] Zhang X J, Chen W F. Stability analysis of slopes with general nonlinear failure criterion. International Journal for Numerical and Analytical Methods in Geomechanics, 1987, 11(1): 33–50

[48] Drescher A, Christopoulos C. Limit analysis slope stability with nonlinear yield condition. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(3): 341–345

[49] Jiang J C, Baker R, Yamagami T. The effect of strength envelope nonlinearity on slope stability computations. Canadian Geotechnical Journal, 2003, 40(2): 308–325

[50] Yang X L, Yin J H. Slope stability analysis with nonlinear failure criterion. Journal of Engineering Mechanics, 2004, 130(3): 267–273

[51] Rafiai H, Jafari A, Mahmoudi A. Application of ANN-based failure criteria to rocks under polyaxial stress conditions. International Journal of Rock Mechanics and Mining Sciences, 2013, 59: 42–49

[52] Wu S, Zhang S, Guo C, Xiong L. A generalized nonlinear failure criterion for frictional materials. Acta Geotechnica, 2017, 12(6): 1353–1371

[53] Xue X H, Xiao M. Deformation evaluation on surrounding rocks of underground caverns based on PSO-LSSVM. Tunnelling and Underground Space Technology, 2017, 69: 171–181

[54] Barzegar R, Ghasri M, Qi Z, Quilty J, Adamowski J. Using bootstrap ELM and LSSVM models to estimate river ice thickness in the mackenzie river basin in the northwest territories, Canada. Journal of Hydrology (Amsterdam), 2019, 577: 123903

[55] Adnan R M, Liang Z, Heddam S, Zounemat-Kermani M, Kisi O, Li B. Least square support vector machine and multivariate adaptive regression splines for streamflow prediction in mountainous basin using hydro-meteorological data as inputs. Journal of Hydrology (Amsterdam), 2020, 586: 124371

[56] Wei J, Chen H. Determining the number of factors in approximate factor models by twice K-fold cross validation. Economics Letters, 2020, 191: 109149

[57] Chandler R J. Lias clay: The long-term stability of cutting slopes. Geotechnique, 1974, 24(1): 21–38

[58] MATLAB. Version 9.4.0. Natick, MA: The Mathworks, Inc., 2018

[59] Perry J. A technique for defining non-linear shear strength envelopes, and their incorporation in a slope stability method of analysis. Quarterly Journal of Engineering Geology and Hydrogeology, 1994, 27(3): 231–241

[60] Tordesillas A, Zhou Z Z, Batterham R. A data-driven complex systems approach to early prediction of landslides. Mechanics Research Communications, 2018, 92: 137–141

[61] Zhou X P, Huang X C, Zhao X F. Optimization of the critical slip surface of three-dimensional slope by using an improved genetic algorithm. International Journal of Geomechanics, 2020, 20(8): 04020120

[62] Xiao S G, Guo W D, Zeng J X. Factor of safety of slope stability from deformation energy. Canadian Geotechnical Journal, 2018, 55(2): 296–302

[63] VapnikV N. Statistical Learning Theory. New York: Wiley-Interscience, 1998

[64] BrabanterK DKarsmakersPOjedaF AlzateCBrabanter J DPelckmansKMoorB DVandewalle JSuykensJ A K. LS-SVMlab Toolbox User’s Guide. Heverlee: Katholieke Universiteit Leuven, 2010

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 51578466).

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