In this study, a Support Vector Regression (SVR) model was developed to predict the rate of penetration (ROP) during tunnel excavation, and its hyperparameters were optimized using Grid Search (GS), Random Search (RS), and Bayesian Optimization (BO). The results indicate that BO reached the optimal parameter set with only 30–50 evaluations, whereas GS and RS required approximately 1000 evaluations. In addition, BO achieved the highest predictive accuracy (R² = 0.9625) while reducing the computational time from 25.83 s (GS) to 17.31 s. Compared with the baseline SVM model, the optimized SVR demonstrated high accuracy (R² = 0.9610–0.9625), strong stability (NSE = 0.9194–0.9231), and low error levels (MAE = 0.0927–0.1099), clearly highlighting the critical role of hyperparameter optimization in improving model performance. To enhance interpretability, a feature importance analysis was conducted using four machine learning methods: Random Forest (RF), Bagged Trees (BT), Support Vector Machines (SVM), and the Generalized Additive Model (GAM). The relative contributions of BI, UCS, ALPHA, and DPW to ROP were evaluated, providing clearer insight into the model’s decision-making process and enabling more reliable engineering interpretation. Overall, integrating hyperparameter optimization with feature importance analysis significantly improves both predictive performance and model explainability. The proposed approach offers a robust, generalizable, and scientifically sound framework for TBM operations and geotechnical modeling applications.

The aim of this study is to prepare a mix that can be used in impermeable fill as an alternative to clay which can sometimes be difficult to find. In the study, bentonite and cement were chosen as admixtures and sand was chosen as the main material. The main reason for choosing bentonite and cement as admixtures is that they are impermeable and easy to find. Sand was chosen as the main material in the experiments to make use of the available sand pits at Yenicekent in Denizli, and to provide a pre-investigation for a possible future impermeable fill construction in the said region. Another reason for choosing sand as a main material was its low price. According to the result of the three mixtures tested, the mixture including 10% bentonite + 90% sand is the most economical solution that satisfies the limits values needed for clay core of earth fill dams and clay liners of solid waste storage areas. Key words: Bentonite, cement, earthfill, sand, unpermeable layer.

In this study, linear and nonlinear parametric models (M1–M6) were jointly evaluated alongside machine learning (ML)-based approaches to achieve reliable and interpretable prediction of the penetration rate (ROP) of tunnel boring machines (TBMs). The analyses incorporate key geomechanical and structural variables, including the brittleness index (BI), uniaxial compressive strength (UCS), mean spacing of weakness planes (DPW), the angle between the tunnel axis and weakness planes (α), and Brazilian tensile strength (BTS). The coefficients of the parametric models were optimized using the Differential Evolution (DE) algorithm. Variable effects were systematically examined through Jacobian-based elasticity analysis under both original and standardized data scenarios. The results indicate that the M6 model, which explicitly incorporates interaction terms, delivers superior predictive accuracy and a more balanced, physically meaningful representation of variable contributions compared to widely used parametric formulations reported in the literature. While the dominant influence of BI and UCS on ROP is consistently preserved across all models, the indirect contributions of variables such as DPW and BTS are more clearly revealed in M6 owing to its interaction-based structure. Model performance improves systematically with increasing complexity, with the coefficient of determination (R²) rising from 0.62 for M1 to 0.69 for M6. Relative to the linear model, M6 achieves a 9.07% reduction in RMSE and a 10.48% increase in R², while providing additional improvements of 2.47% in RMSE and 2.37% in R² compared with the closest competing model. ML-based variable importance analyses are largely consistent with the parametric findings, highlighting BI and α in tree-based models, and UCS and α in SVM and GAM frameworks. Notably, the GAM exhibits the highest predictive performance under both data scenarios. Overall, the integrated use of parametric and ML approaches establishes a robust hybrid modeling framework that enables highly accurate and engineering-interpretable prediction of TBM penetration rate.

Accurate prediction of TBM penetration rate (ROP) is of critical importance for the planning of tunneling operations and performance assessment. In this study, both classical multiple linear regression (MLR) and machine learning approaches—namely Random Forest, Bagged Trees, Support Vector Machine, and LSBoost—were employed to investigate the contributions of BI, UCS, DPW, α, and BTS parameters to ROP prediction. Univariate and MLR analyses exhibited limited explanatory power (R² = 0.365), confirming that ROP is governed by complex, multivariate, and nonlinear interactions. Comparative machine learning analyses revealed that LSBoost provides the most reliable predictions, achieving the highest accuracy (R² = 0.9565) and the lowest error metrics (RMSE = 0.1794; MAPE = 5.63%) for both original and normalized datasets. While Random Forest and Bagged Trees demonstrated comparable performance, SVM showed limited predictive capability on the original dataset (R² = 0.452; RMSE = 0.637; MAPE = 18.60). However, its performance improved substantially following data normalization, approaching that of LSBoost (R² = 0.936; RMSE = 0.218; MAPE = 4.87). Feature importance analyses based on PDP-driven Jacobian sensitivity and SHAP methods indicate that UCS, BI, and DPW are the dominant factors governing TBM penetration performance, while also demonstrating that model outputs remain interpretable in an interaction-aware manner. These findings highlight that machine learning-based approaches can deliver both reliable prediction and interpretability even with small and heterogeneous datasets, and suggest that future research should focus on integrating larger datasets, hybrid modeling strategies, and advanced explainability techniques.

This study evaluated the predictive performance of Random Forest, Bagged Trees, Support Vector Machines (SVM), and Least Squares Boosting (LSBoost) for estimating Tunnel Boring Machine (TBM) penetration rate (ROP). While all models achieved acceptable accuracy, LSBoost outperformed the others, showing the highest correlation (R = 0.965) and coefficient of determination (R² = 0.909), along with the lowest RMSE and MAE. Its performance remained robust after Z-score normalization, highlighting its ability to capture nonlinear parameter interactions and generalize well on limited geotechnical datasets. Random Forest and Bagged Trees showed similar performance, with Bagged Trees only slightly improved by normalization. SVM performed less effectively, indicating limited capacity to model complex TBM penetration behavior. Feature importance and SHAP analyses identified discontinuity spacing (DPW) and uniaxial compressive strength (UCS) as the primary controlling factors, while brittleness index (BI) was more influential within the SVM model. Agreement between Jacobian-based derivative analyses and SHAP results confirmed both mathematical sensitivity and engineering interpretability. Overall, TBM penetration prediction is a multivariate and inherently nonlinear problem. LSBoost provides reliable and high-accuracy predictions even under data-constrained conditions. The combination of SHAP- and PDP-based feature importance analyses enhances interpretability, supporting engineering decision-making in TBM design and operation. These findings emphasize the applicability of machine learning approaches for accurate, interpretable, and robust TBM performance prediction.

In this study, both linear and nonlinear parametric models (M1–M6) and machine learning (ML)–based approaches were evaluated for the reliable and interpretable prediction of tunnel boring machine (TBM) penetration rate (ROP). The analyses incorporated rock hardness index (BI), uniaxial compressive strength (UCS), joint angle (α), excavation depth (DPW), and BTS as input variables. Parametric model coefficients were optimized using the Differential Evolution (DE) algorithm, and variable effects were examined via Jacobian-based elasticity analysis under both original and standardized data scenarios. Parametric results indicate that the proposed M6 model outperforms existing literature correlations in terms of prediction accuracy and represents variable contributions in a more balanced and physically meaningful manner. While the dominant influence of BI and UCS on ROP is preserved across all models, interaction terms allow the indirect contributions of variables such as DPW and BTS to be captured more clearly. Model performance systematically improves when moving from linear to nonlinear and interaction-inclusive structures, with R² increasing from 0.62 for M1 to 0.69 for M6. Machine learning–based variable importance analyses largely corroborate the parametric findings, highlighting BI and α in tree-based methods, and UCS and α in SVM and GAM models. Notably, the GAM model exhibited the highest predictive performance under both data scenarios. Overall, the combined use of parametric and ML approaches provides a robust hybrid framework for accurate and interpretable prediction of TBM penetration rates.