Open-Source Hardening Soil Material-Point Integrator and Neural-Network Surrogate for Ho Chi Minh City Soils

<title>Abstract</title> <p> The Hardening Soil (HS) model is widely used in deep-excavation and metro-tunnel analyses, but its reliance on closed-source software limits independent verification, reproducibility, and integration with machine-learning workflows. This study developed and validated an open-source HS-based material-point integrator and assessed its use as a physics-based data generator for a neural-network surrogate. Methods The Python implementation incorporated the stress-dependent stiffness law, Mohr–Coulomb failure criterion, and hyperbolic primary-loading relation. It was evaluated through internal consistency checks and comparison with consolidated-drained triaxial data from three representative Ho Chi Minh City soils comprising 274 measured points. The validated model generated 20,000 stress–strain curves for training a multilayer perceptron. The implementation was limited to drained primary loading and did not reproduce the complete multisurface HS formulation. Results Leave-one-out validation yielded a pooled R ² of 0.998, Pearson’s r of 0.999, and a mean absolute percentage error of 1.9%; the maximum internal consistency error was below 0.1%. The fitted exponent m ranged from 0.61 to 0.94. The surrogate achieved R ²  = 0.9999 and an RMSE of 1.47 kPa. The proposed platform provides a reproducible basis for inverse analysis and large-scale geotechnical simulations. </p>