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Application of AI models for reliability assessment of 3d slope stability of a railway embankment

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Abstract

In this work, three machine learning (ML) techniques i.e., multivariate adaptive regression splines (MARS), support vector machine (SVM), and least square vector machine (LSSVM) have been used to conduct a reliability analysis of a railway embankment situated in the Mokama district of the state of Bihar, India based on 3D slope failure investigation. The probabilistic assessment of the railway embankment is important as it incorporates risk estimates of a real-life structure against various uncertain loading conditions. The main goal of the analysis is to evaluate the stability of the embankment in three dimensions while taking pore pressure and seismic impacts into consideration. Using Scoops-3D software, the Factor of Safety (FOS) of the embankment is calculated based on Bishop’s Simplified Method. Notably, to determine the reliability index (β), the study takes uncertainties resulting from geographical differences in soil parameters into account. Our findings show that the railway embankment functions admirably under various loading conditions. For the training and testing datasets, error markers such as root mean squared error (RMSE), Weighted Mean Absolute Percentage Error (WMAPE), Nash–Sutcliffe coefficient (NS), Performance index (PI), Maximum determination coefficient value (R2), Adjusted R2, Scatter Index (SI), Uncertainty at 95% (U95), Objective function (OBJ) criterion values are determined to assess the models’ capacity for prediction. By proving the effectiveness of machine learning approaches in capturing complex interactions and uncertainties, this research advances the subject of railway embankment stability evaluation. Among the evaluated models, the LSSVM model proved to be the best accurate predictor.

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Data will be made available on request.

Abbreviations

\(c^{\prime}\) :

Cohesion

\(\phi^{\prime}\) :

Internal frictional angle

\(\gamma\) :

Unit weight of soil

\({k}_{h}\) :

Horizontal seismic coefficient

\({r}_{u}\) :

Pore water pressure coefficient

\({\sigma }_{n}\) :

Normal stress

\(u\) :

Developed pore water pressure on the shearing surface

H :

Horizontal shear force

X :

Vertical shear force

E :

Inter-column normal force

\({\varepsilon }_{j,k}\) :

True angle of dip

\({\propto }_{j,k}\) :

Apparent angle of dip

\({S}_{j,k}\) :

Mobilized shear resistance

\({N}_{j,k}\) :

Normal force acting on a column \(j,k\)

\({U}_{j,k}\) :

Uplifting force normal

\(\tau\) :

Shear force

\({W}_{j,k}\) :

Weight of \(j,k\) column

\({h}_{j,k}\) :

The moment arm for horizontal driving force on a \(j,k\) column

\({R}_{j,k}\) :

The distance from the axis of rotation to the centre of the base of a \(j,k\) column;

\({\gamma }_{t}\) :

Is the total unit weight

\({B}_{m} \left(x\right),\left({C}_{m}\right)\) :

Basis function used in MARS

\({a}_{0}\) and \({a}_{m}\) :

Undetermined constants

GCV:

Generalized cross-validation

\(C\left(B\right),C(M)\) :

Penalty factor

\(\xi\) :

Relaxation variable

\({X}_{\mathrm{max}}\),\({ X}_{\mathrm{min}}\) and \({X}_{j}\) :

Maximum, minimum, and any values of the parameter under consideration, respectively

R 2 :

Maximum determination coefficient value

\({\mathrm{Adj}.R}^{2}\) :

Adjusted determination coefficient

RMSE:

Root-mean-square error

WMAPE:

Weighted mean absolute percentage error

NS:

Nash–Sutcliffe coefficient

PI:

Performance index

SI:

Scatter Index

\(\beta\) :

Reliability index

\({P}_{\mathrm{f}}\) :

Probability of failure

SD:

Standard deviation

U95 :

Uncertainty at 95% confidence

OBJ:

Objective function

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Acknowledgements

The authors acknowledge the support of the colleagues in the Dept. of Civil Engineering, National Institute of Technology, Patna.

Funding

No external funding was used for the present work.

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Authors and Affiliations

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

    Brijbhan Rao, Avijit Burman & Lal Bahadur Roy

Authors
  1. Brijbhan Rao
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  2. Avijit Burman
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  3. Lal Bahadur Roy
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Contributions

BR (first author): conceptualization, analysis, writing of the manuscript. AB (second and corresponding author): conceptualization, analysis, writing of the manuscript, overall supervision. LBR (third author): conceptualization and overall supervision.

Corresponding author

Correspondence to Avijit Burman.

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As per authors’ knowledge, the present work has no conflict interest with any other work. No financial assistance was required for this work.

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Rao, B., Burman, A. & Roy, L.B. Application of AI models for reliability assessment of 3d slope stability of a railway embankment. Multiscale and Multidiscip. Model. Exp. and Des. 7, 1007–1029 (2024). https://doi.org/10.1007/s41939-023-00255-9

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