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Probabilistic slope stability analysis using subset simulation enhanced by ensemble machine learning techniques

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Abstract

Within the field of geotechnical engineering, complex challenges arise due to uncertainties associated with variable loads, soil properties, ground stratification, and other related factors. In order to effectively address these uncertainties, it is recommended to employ reliability analysis based on probabilistic methodologies. The objective of this study is to investigate the effectiveness of ensemble machine learning methods in predicting the factor of safety (FOS) for railway embankments. The FOS is a critical indicator of the stability of cohesive slopes. By utilizing the recently developed Subset Simulation (SS) method for reliability analysis, we aim to investigate the potential of machine learning in improving predictions of FOS (Factor of Safety). We have obtained a comprehensive dataset consisting of 1400 instances from the subset simulation evaluation. This dataset serves as the foundation for our investigation. In the context of machine learning, we employ six commonly used methodologies, namely decision tree regression (DTR), multiple linear regression (MLR), K nearest neighbor regression (KNN), random forest regression (RF), extreme gradient boosting regression (XGB), and support vector regression (SVR), to develop predictive models for extrapolating FOS values. Afterwards, we utilize ensemble machine learning techniques to combine the outputs of these individual predictive models. Among the various ensemble strategies, the voting ensemble (VO-ENSM) stands out as a strong candidate, demonstrating significant proficiency in predicting the Factor of Safety (FOS) for the complex terrain of railway embankments.

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References

  • Al-Qahtani FH, Crone SF (2013) Multivariate k-nearest neighbour regression for time series data—A novel algorithm for forecasting UK electricity demand. In: The 2013 international joint conference on neural networks (IJCNN). pp 1–8

  • Ang AHS, Tang WH (1984) Probability concepts in engineering planning and design Decision risk and reliability. Wiley, New York

    Google Scholar 

  • Asare EN, Affam M, Ziggah YY (2023) A hybrid intelligent prediction model of autoencoder neural network and multivariate adaptive regression spline for uniaxial compressive strength of rocks. Model Earth Syst Environ 1:1–17

    Google Scholar 

  • Au S-K, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Eng Mech 16:263–277

    Google Scholar 

  • Au S-K, Wang Y (2014) Engineering risk assessment with subset simulation. Wiley, UK

    Google Scholar 

  • Au SK, Ching J, Beck JL (2007) Application of subset simulation methods to reliability benchmark problems. Struct Saf 29:183–193. https://doi.org/10.1016/j.strusafe.2006.07.008

    Article  Google Scholar 

  • Au SK, Cao ZJ, Wang Y (2010) Implementing advanced Monte Carlo simulation under spreadsheet environment. Struct Saf 32:281–292

    Google Scholar 

  • Baecher GB, Christian JT (2005) Reliability and statistics in geotechnical engineering. Wiley, USA

    Google Scholar 

  • Bardhan A, Samui P (2022) Probabilistic slope stability analysis of Heavy-haul freight corridor using a hybrid machine learning paradigm. Transp Geotech 37:100815. https://doi.org/10.1016/j.trgeo.2022.100815

    Article  Google Scholar 

  • Behar O, Khellaf A, Mohammedi K (2015) Comparison of solar radiation models and their validation under Algerian climate–The case of direct irradiance. Energy Convers Manag 98:236–251

    Google Scholar 

  • Breiman L, Friedman JH (1997) Predicting multivariate responses in multiple linear regression. J R Stat Soc Ser B (Statistical Methodol) 59:3–54

    Google Scholar 

  • Cao Z, Wang Y, Li D (2017) Probabilistic approaches for geotechnical site characterization and slope stability analysis. Springer, Berlin

    Google Scholar 

  • Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)?–Arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250

    Google Scholar 

  • Chang Y-C, Chang K-H, Wu G-J (2018) Application of eXtreme gradient boosting trees in the construction of credit risk assessment models for financial institutions. Appl Soft Comput 73:914–920

    Google Scholar 

  • Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng 120:2180–2207

    Google Scholar 

  • Cornell CA (1972) First-order uncertainty analysis of soil deformation and stability. Transportation research board, University of Hong Kong

  • Ditlevsen O (1981) Uncertainty modeling with applications to multidimensional civil engineering systems. McGraw-Hill International Book Company, USA

    Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39:665–683

    Google Scholar 

  • Engelund S, Rackwitz R (1993) A benchmark study on importance sampling techniques in structural reliability. Struct Saf 12:255–276

    Google Scholar 

  • Fenton GA, Griffiths DV et al (2002) Probabilistic foundation settlement on spatially random soil. J Geotech Geoenvironmental Eng 128:381–390

    Google Scholar 

  • Fishman GS (1996) Random Tours. In: Monte Carlo. Springer series in operation research, pp 335–491

  • Hammersley JM, Handscomb DC (1964) The general nature of Monte Carlo methods. Monte Carlo methods. Springer, Berlin, pp 1–9

    Google Scholar 

  • Hammersley JM, Handscomb DC (1964) Percolation processes. In: Jesy C (ed) Monte Carlo Methods. Springer, Berlin, pp 134–141

    Google Scholar 

  • Harr ME (1984) Reliability-based design in civil engineering. Department of Civil Engineering, School of Engineering, North Carolina State

  • Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100:111–121

    Google Scholar 

  • Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109

  • Kardani N, Aminpour M, Raja MNA et al (2022) Prediction of the resilient modulus of compacted subgrade soils using ensemble machine learning methods. Transp Geotech 36:100827

    Google Scholar 

  • Kulhawy FH (1992) On the evaluation of soil properties. ASCE Geotech Spec Publ 1:95–115

    Google Scholar 

  • Legates DR, McCabe GJ (2013) A refined index of model performance: a rejoinder. Int J Climatol 33:1053–1056

    Google Scholar 

  • Low BK (2003) Practical probabilistic slope stability analysis. Proceedings, Soil Rock Am 12:22–26

    Google Scholar 

  • Low BK, Tang WH (1997a) Probabilistic slope analysis using Janbu’s generalized procedure of slices. Comput Geotech 21:121–142

    Google Scholar 

  • Low BK, Tang WH (1997b) Efficient reliability evaluation using spreadsheet. J Eng Mech 123:749–752

    Google Scholar 

  • Low BK, Tang WH (2004) Reliability analysis using object-oriented constrained optimization. Struct Saf 26:69–89

    Google Scholar 

  • Low BK, Tang WH (2007) Efficient spreadsheet algorithm for first-order reliability method. J Eng Mech 133:1378–1387

    Google Scholar 

  • Lumb P (1974) Application of statistics in soil mechanics. Soil Mech New Horizons IK Lee, ed

  • Malkawi AIH, Hassan WF, Abdulla FA (2000) Uncertainty and reliability analysis applied to slope stability. Struct Saf 22:161–187

    Google Scholar 

  • Melchers RE, Beck AT (2018) Structural reliability analysis and prediction. Wiley, USA

    Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN et al (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    CAS  Google Scholar 

  • Phoon K-K (2008) Reliability-based design in geotechnical engineering: computations and applications. CRC Press, Florida

    Google Scholar 

  • Raghuram G, Verma A (2019) Dedicated freight corridor: current challenges. In: World Conference on Transport Research-WCTR

  • Ren Y, Zhang L, Suganthan PN (2016) Ensemble classification and regression-recent developments, applications and future directions. IEEE Comput Intell Mag 11:41–53

    Google Scholar 

  • Ribeiro MHDM, dos Santos Coelho L (2020) Ensemble approach based on bagging, boosting and stacking for short-term prediction in agribusiness time series. Appl Soft Comput 86:105837

    Google Scholar 

  • Robert CP, Casella G, Casella G (1999) Monte Carlo statistical methods. Springer, Berlin

    Google Scholar 

  • Schuëller GI, Pradlwarter HJ (2007) Benchmark study on reliability estimation in higher dimensions of structural systems–an overview. Struct Saf 29:167–182

    Google Scholar 

  • Sihag P, Al-Janabi AMS, Alomari NK et al (2021) Evaluation of tree regression analysis for estimation of river basin discharge. Model Earth Syst Environ 7:1–13

    Google Scholar 

  • Singh A (1972) How reliable is the factor of safety in foundation engineering, Soil Mechanics-new horizons. Newness Butterworths 1974, pp 44–111

  • Sivakumar Babu GL, Mukesh MD (2004) Effect of soil variability on reliability of soil slopes. Geotechnique 54:335–337

    Google Scholar 

  • Stone RJ (1993) Improved statistical procedure for the evaluation of solar radiation estimation models. Sol Energy 51:289–291

    Google Scholar 

  • Tamiru H, Wagari M (2022) Machine-learning and HEC-RAS integrated models for flood inundation map** in Baro River Basin, Ethiopia. Model Earth Syst Environ 8:2291–2303

    Google Scholar 

  • Tang WH, Yucemen MS, Ang A-S (1976) Probability-based short term design of soil slopes. Can Geotech J 13:201–215

    Google Scholar 

  • Tso GKF, Yau KKW (2007) Predicting electricity energy consumption: A comparison of regression analysis, decision tree and neural networks. Energy 32:1761–1768

    Google Scholar 

  • Wang Y, Cao Z, Au S-K (2011) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Can Geotech J 48:162–172

    Google Scholar 

  • Willmott CJ (1984) On the evaluation of model performance in physical geography. Spatial statistics and models. Springer, Berlin, pp 443–460

    Google Scholar 

  • Wong FS (1985) Slope reliability and response surface method. J Geotech Eng 111:32–53

    Google Scholar 

  • Yahyaoui N, Neji M, Kallel M et al (2023) A comparative approach of ML algorithms to rank irrigation water quality: case of Oriental-Coast shallow aquifer in Cap-Bon, northeastern of Tunisia. Model Earth Syst Environ 9:1–14

    Google Scholar 

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Acknowledgements

The authors express their sincere gratitude to Prof. Siu-Kui Au, University of Liverpool, UK; Prof. Yu Wang, City University of Hong Kong, China and Prof. Zijun Cao, Wuhan University, China, for providing the MS-Excel Add-In UPSS module which has been used in the present work.

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Authors and Affiliations

  1. Civil Engineering Department, National Institute of Technology Patna, Patna, India

    Furquan Ahmad, Pijush Samui & S. S. Mishra

Authors
  1. Furquan Ahmad
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  2. Pijush Samui
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  3. S. S. Mishra
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Contributions

FA: Research Methodology, Resources, Software, Validation, Visualization, Original Draft, Review & Editing Writing; PS: Guidance. SSM: Guidance.

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Correspondence to Furquan Ahmad.

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Appendix

Appendix

See Figs. 9, 10 and 11.

Fig. 9
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In Excel VBA codes built to determine the FS values concerning various center coordinates and slip surface radius

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Fig. 10
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MATLAB code for Cholesky’s decomposition of correlation matrix and lower triangular matrix

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Fig. 11
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In Excel VBA codes built to determine the FS values concerning various center coordinates and slip surface radius

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Ahmad, F., Samui, P. & Mishra, S.S. Probabilistic slope stability analysis using subset simulation enhanced by ensemble machine learning techniques. Model. Earth Syst. Environ. 10, 2133–2158 (2024). https://doi.org/10.1007/s40808-023-01882-4

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