Awareness of granulated soils’ internal instability is an important parameter when designing granulated filters, and the ability of a granulated soil’s internal stability can be verified using the soil PSD (Particle Size Distribution) curves’ secant slopes. The current work presents a new method to calculate the soil PSD curves’ secant slopes automatically, and a synthetic diagram is presented for the potential examination of the granulated soils’ internal stability. To verify the feasibility and accuracy of this synthetic diagram, 80 specimens of soil were investigated in this work and categorized into two groups: 50 sand–gravel soils and 30 (clay)–silt–sand–gravel soils. The obtained conclusions indicate that the internal stability and instability potentials of sand–gravel soils can be distinguished successfully with a synthetic chart and the Kenney and Lau criterion but cannot be assessed with the Kezdi and Sherard criteria. None of the criteria studied here can be used for the internal stability assessment of silt–sand–gravel and clay–silt–sand–gravel soils.

Accurate prediction of tunnel water inflow in water-rich fault zones is important for groundwater control design and construction risk prevention. In this study, a per-linear-meter tunnel water inflow database containing 425 valid samples was established through orthogonal numerical simulations based on a three-dimensional steady-state seepage model with a grouting ring. The input variables included four hydraulic and grouting parameters and two excavation-position descriptors, namely the excavation-position distance and excavation-position category, thereby reflecting both the water-blocking effect of grouting reinforcement and the spatial variation in water inflow as the excavation face approached the fault zone. Considering that the samples were generated from 25 orthogonal simulation cases at different excavation positions, grouped validation was adopted to reduce information leakage at the simulation-case level. Four baseline machine learning models, including SVM, RF, XGBoost, and CatBoost, were evaluated using ten repeated grouped hold-out validations. CatBoost achieved the best overall baseline generalization performance, with an average test R² of 0.6209 ± 0.0405, MAE of 0.1084 ± 0.0079, and RMSE of 0.1555 ± 0.0085. CatBoost was therefore selected for further hyperparameter optimization. Subsequently, random search, Bayesian optimization, the Osprey Optimization Algorithm, and the Grey Wolf Optimizer were compared under the same search space and computational budget. Hyperparameter optimization was conducted only within the training set using grouped cross-validation, and the independent grouped test set was used only for final evaluation. The results showed that the unoptimized CatBoost model achieved the best overall balance between prediction accuracy, stability, and computational efficiency. Although RS-CatBoost slightly improved MAE and MAPE among the optimized models, none of the optimization strategies consistently outperformed the unoptimized CatBoost baseline, indicating that the choice of hyperparameter optimization algorithm played a secondary role under the current dataset and grouped-validation framework. The proposed framework is intended as a preliminary modeling reference under controlled numerical simulation conditions, and its practical engineering reliability requires further validation using field monitoring data or independent benchmark cases.