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<p>This study presents an integrated reliability-based framework combining deterministic analysis, probabilistic modeling, system reliability assessment, and hybrid machine-learning techniques to evaluate the seismic external stability of gravity retaining walls. External failure modes were analyzed under varying seismic conditions using horizontal seismic coefficients ranging from 0.03 to 0.25. Input uncertainty was incorporated using a Latin Hypercube-Monte Carlo approach, while reliability indices were estimated through the First Order Second-Moment method, followed by system reliability evaluation. Results indicate a pronounced reduction in reliability with increasing seismic intensity. In low seismic zones, the reliability index (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:\beta\:\)</EquationSource> </InlineEquation>) remained extremely high (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:\beta\:\:&gt;\:17\)</EquationSource> </InlineEquation>), whereas in Zones V and VI, overturning and bearing capacity exhibited negative reliability indices, indicating failure probabilities approaching unity. Under extreme seismic demand, system reliability declined more rapidly than individual failure modes, reaching <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:{\beta\:}_{system}\)</EquationSource> </InlineEquation>= -7.67, demonstrating that bearing capacity governs overall stability. To reduce computational burden, hybrid extreme gradient boosting (XGB) models optimized using the Sparrow Search Algorithm (SSA) and Differential Evolution (DE) were developed for factor-of-safety prediction and reliability assessment. Among the proposed models, XGB-SSA consistently outperformed XGB-DE. Model performance was further validated through statistical analyses, including the Anderson-Darling test and examinations of regression error characteristics curve.</p>

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A Hybrid Machine Learning Paradigm for Seismic External Stability and System Reliability Assessment of Gravity Retaining Walls

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Md Shayan Sabri,
  • Amit Kumar Verma,
  • Nitish Kumar,
  • T. N. Singh

摘要

This study presents an integrated reliability-based framework combining deterministic analysis, probabilistic modeling, system reliability assessment, and hybrid machine-learning techniques to evaluate the seismic external stability of gravity retaining walls. External failure modes were analyzed under varying seismic conditions using horizontal seismic coefficients ranging from 0.03 to 0.25. Input uncertainty was incorporated using a Latin Hypercube-Monte Carlo approach, while reliability indices were estimated through the First Order Second-Moment method, followed by system reliability evaluation. Results indicate a pronounced reduction in reliability with increasing seismic intensity. In low seismic zones, the reliability index ( \(\:\beta\:\) ) remained extremely high ( \(\:\beta\:\:>\:17\) ), whereas in Zones V and VI, overturning and bearing capacity exhibited negative reliability indices, indicating failure probabilities approaching unity. Under extreme seismic demand, system reliability declined more rapidly than individual failure modes, reaching \(\:{\beta\:}_{system}\) = -7.67, demonstrating that bearing capacity governs overall stability. To reduce computational burden, hybrid extreme gradient boosting (XGB) models optimized using the Sparrow Search Algorithm (SSA) and Differential Evolution (DE) were developed for factor-of-safety prediction and reliability assessment. Among the proposed models, XGB-SSA consistently outperformed XGB-DE. Model performance was further validated through statistical analyses, including the Anderson-Darling test and examinations of regression error characteristics curve.