Hybrid a node-based smoothed radial point interpolation method and artificial neural networks for stability evaluation of dual square tunnels at different depths in cohesive-frictional soils

Abstract This study introduces a hybrid approach combining the node-based smoothed radial point interpolation method (NS-RPIM) and Artificial neural networks (ANN) to evaluate the limit load capacity of dual square tunnels at different depths in cohesive-frictional soils. NS-RPIM performs effectively in upper bound limit analysis by eliminating mesh dependency and enhances accuracy through smoothed strain fields, while enabling flexible node distribution for 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 provides reliable predictions of stability numbers N = σ s/c, and its ability to model nonlinear soil-tunnel interactions and adapt to diverse geotechnical conditions. Trained on extensive NS-RPIM-generated datasets, the ANN model achieves high predictive accuracy with minimal computational cost. 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 vertical spacing ratio L/B, soil properties γB/c and internal friction angle φ. This approach offers significant advantages over traditional finite element methods, including reduced computational time, enhanced robustness, and applicability to practical tunneling design. Hybrid NS-RPIM and ANN approach is a powerful tool for geotechnical engineers addressing the stability of dual square tunnels under complex loading conditions.