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<p>Accurate prediction of lateral pile response requires computationally intensive nonlinear finite element analysis, limiting its use in routine design and large-scale parametric studies. This study presents a machine learning surrogate framework trained on 15,351 Beam on Nonlinear Winkler Foundation simulations, generated by Latin Hypercube Sampling across an eleven-variable parametric space covering pile geometry, soil properties, loading conditions, and head fixity. Six structural response quantities were predicted simultaneously: maximum bending moment (<i>M</i><sub>max</sub>), lateral deflection (<i>δ</i><sub>max</sub>), shear force (<i>V</i><sub>max</sub>), pile head rotation (<i>θ</i><sub>head</sub>), peak soil reaction (<i>p</i><sub>max</sub>), and the soil capacity utilization ratio (<i>p/p</i><sub>ult</sub>). Extreme Gradient Boosting achieved R<sup>2</sup> of 0.989 (<i>M</i><sub>max</sub>), 0.819 (<i>δ</i><sub>max</sub>), 0.999 (<i>V</i><sub>max</sub>), 0.824 (<i>θ</i><sub>head</sub>), 0.988 (<i>p</i><sub>max</sub>), and 0.981 (<i>p/p</i><sub>ult</sub>) on a 20% hold-out set, with normalized root mean squared error not exceeding 5.86% across all targets. SHAP TreeExplainer analysis confirmed that lateral load and pile diameter are the dominant predictors, with opposing roles: lateral load governs moment demand while diameter controls deflection and rotation. Undrained shear strength ranked third across most targets. Head fixity reduces deflection by approximately 30 to 40% at high loads while increasing peak bending moment by 25 to 30%, indicating a clear trade-off between deflection control and structural moment demand. Three practical design tools were derived from the surrogate: a joint fixity and eccentricity design chart, closed-form power-law expressions for hand calculation, and a soil utilization index quantifying proximity to plastic failure. The framework provides a computationally efficient and physically interpretable basis for sensitivity analysis and preliminary design of laterally loaded piles in soft clay.</p>

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Explainable machine learning surrogates for lateral pile response prediction in soft clay

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Saif Ahmed Santo,
  • Md. Majidur Rahman,
  • Matiur Rahman Raju

摘要

Accurate prediction of lateral pile response requires computationally intensive nonlinear finite element analysis, limiting its use in routine design and large-scale parametric studies. This study presents a machine learning surrogate framework trained on 15,351 Beam on Nonlinear Winkler Foundation simulations, generated by Latin Hypercube Sampling across an eleven-variable parametric space covering pile geometry, soil properties, loading conditions, and head fixity. Six structural response quantities were predicted simultaneously: maximum bending moment (Mmax), lateral deflection (δmax), shear force (Vmax), pile head rotation (θhead), peak soil reaction (pmax), and the soil capacity utilization ratio (p/pult). Extreme Gradient Boosting achieved R2 of 0.989 (Mmax), 0.819 (δmax), 0.999 (Vmax), 0.824 (θhead), 0.988 (pmax), and 0.981 (p/pult) on a 20% hold-out set, with normalized root mean squared error not exceeding 5.86% across all targets. SHAP TreeExplainer analysis confirmed that lateral load and pile diameter are the dominant predictors, with opposing roles: lateral load governs moment demand while diameter controls deflection and rotation. Undrained shear strength ranked third across most targets. Head fixity reduces deflection by approximately 30 to 40% at high loads while increasing peak bending moment by 25 to 30%, indicating a clear trade-off between deflection control and structural moment demand. Three practical design tools were derived from the surrogate: a joint fixity and eccentricity design chart, closed-form power-law expressions for hand calculation, and a soil utilization index quantifying proximity to plastic failure. The framework provides a computationally efficient and physically interpretable basis for sensitivity analysis and preliminary design of laterally loaded piles in soft clay.