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<p>This study developed a hybrid methodology integrating the node-based smoothed radial point interpolation method (NS-RPIM) with artificial neural networks (ANN) to determine the ultimate load of dual square tunnels in cohesive-frictional soils at varying depths. NS-RPIM performed effectively in upper bound limit analysis by eliminating mesh dependency and enhancing accuracy through smoothed strain fields, while allowing for flexible node distribution in complex tunnel geometries. Its integration with second-order cone programming ensures precise computation of critical surcharge loads with improved computational efficiency. ANN complements NS-RPIM providing reliable predictions of stability numbers <i>N</i> = <i>σ</i> <sub><i>s</i></sub><i>/c</i>, and its ability to model nonlinear soil-tunnel interactions and adapt to diverse geotechnical conditions. An ANN trained on 2587 NS-RPIM-generated data samples achieves exceptional predictive accuracy (R<sup>2</sup> ≈ 0.9967, RMSE ≈ 1.3482), enabling instantaneous stability predictions compared to NS-RPIM. The hybrid framework is validated against numerical simulations demonstrating superior performance in capturing the effects of tunnel depth <i>H/B</i>, the horizontal spacing ratio <i>S/B</i>, and the vertical spacing ratio <i>L/B</i>, soil properties <i>γB/c</i> and internal friction angle <i>φ</i>. The hybrid NS-RPIM and ANN approach is a powerful tool for geotechnical engineers addressing the stability of dual square tunnels under complex loading conditions.</p>

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Hybrid a Node-Based Smoothed Radial Point Interpolation Method and Artificial Neural Networks for Stability Analysis of Dual Square Tunnels at Different Depths

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • G. Mai-Hai,
  • Thanh Danh Tran,
  • T. Vo-Minh

摘要

This study developed a hybrid methodology integrating the node-based smoothed radial point interpolation method (NS-RPIM) with artificial neural networks (ANN) to determine the ultimate load of dual square tunnels in cohesive-frictional soils at varying depths. NS-RPIM performed effectively in upper bound limit analysis by eliminating mesh dependency and enhancing accuracy through smoothed strain fields, while allowing for flexible node distribution in complex tunnel geometries. Its integration with second-order cone programming ensures precise computation of critical surcharge loads with improved computational efficiency. ANN complements NS-RPIM providing reliable predictions of stability numbers N = σ s/c, and its ability to model nonlinear soil-tunnel interactions and adapt to diverse geotechnical conditions. An ANN trained on 2587 NS-RPIM-generated data samples achieves exceptional predictive accuracy (R2 ≈ 0.9967, RMSE ≈ 1.3482), enabling instantaneous stability predictions compared to NS-RPIM. The hybrid framework is validated against numerical simulations demonstrating superior performance in capturing the effects of tunnel depth H/B, the horizontal spacing ratio S/B, and the vertical spacing ratio L/B, soil properties γB/c and internal friction angle φ. The hybrid NS-RPIM and ANN approach is a powerful tool for geotechnical engineers addressing the stability of dual square tunnels under complex loading conditions.