<p>This research focuses on evaluating the stability of circular tunnels under plane strain conditions by applying advanced machine learning approaches, specifically artificial neural networks (ANNs) and deep neural networks (DNNs). The primary objective is to support the effective, safe, and inclusive management of road infrastructure systems. The investigation examines tunnel stability in soils that exhibit both cohesion and internal friction, using the Mohr‒Coulomb failure model to represent soil strength behavior in a two-dimensional deformation context. A wide range of input parameters is systematically analyzed via finite element limit analysis (FELA) to assess the stability load coefficient (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{\sigma\:}_{i}/c\)</EquationSource> </InlineEquation>) at the tunnel circumference. By evaluating <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{\sigma\:}_{i}/c\)</EquationSource> </InlineEquation>, engineers can identify potential failure mechanisms such as excessive deformation, collapse, or ground instability. The predictive accuracy of the constructed machine learning model was assessed via several performance indices and regression plots. Additionally, a Taylor chart and triangle diagram are also plotted for the developed models. The developed DNN model is identified as the best performing model, with an R<sup>2</sup> value of 0.974 in the training phase and 0.966 in the testing phase. The RMSE value for the DNN model is 0.053, and that for the ANN model is 0.080 in the testing phase, confirming the superiority of the DNN in predicting <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:{\sigma\:}_{i}/c\)</EquationSource> </InlineEquation>. SHAP analyses were performed to assess the importance of the input variable on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:{\sigma\:}_{i}/c\)</EquationSource> </InlineEquation>. The SHAP analysis identified the normalized unit weight as the most influential parameter, with a mean SHAP value of 0.329, followed by the friction angle (φ) (0.129), whereas <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\:{k}_{h}\)</EquationSource> </InlineEquation> (0.029) and H/D (0.016) showed only minor effects, indicating that the normalized unit weight and φ are the primary drivers of prediction variability. The results indicate that the proposed models strongly agree with the numerical FELA <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\:{\sigma\:}_{i}/c\)</EquationSource> </InlineEquation> values. By conducting comprehensive stability analyses, engineers can design and maintain tunnels that meet safety standards, accommodate diverse traffic needs, and contribute to efficient road infrastructure management. This ensures the long-term sustainability and safety of transportation networks, fostering economic development and social inclusion.</p>

Integrating machine learning for efficient and safe tunnel design: an analysis of stability load coefficients in circular tunnels

期刊论文
发表日期：

2026年2月9日

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Divesh Ranjan Kumar,
Warit Wipulanusat,
Pradeep Thangavel,
Chaiyathawat Boonyong

摘要

This research focuses on evaluating the stability of circular tunnels under plane strain conditions by applying advanced machine learning approaches, specifically artificial neural networks (ANNs) and deep neural networks (DNNs). The primary objective is to support the effective, safe, and inclusive management of road infrastructure systems. The investigation examines tunnel stability in soils that exhibit both cohesion and internal friction, using the Mohr‒Coulomb failure model to represent soil strength behavior in a two-dimensional deformation context. A wide range of input parameters is systematically analyzed via finite element limit analysis (FELA) to assess the stability load coefficient ( \(\:{\sigma\:}_{i}/c\) ) at the tunnel circumference. By evaluating \(\:{\sigma\:}_{i}/c\) , engineers can identify potential failure mechanisms such as excessive deformation, collapse, or ground instability. The predictive accuracy of the constructed machine learning model was assessed via several performance indices and regression plots. Additionally, a Taylor chart and triangle diagram are also plotted for the developed models. The developed DNN model is identified as the best performing model, with an R² value of 0.974 in the training phase and 0.966 in the testing phase. The RMSE value for the DNN model is 0.053, and that for the ANN model is 0.080 in the testing phase, confirming the superiority of the DNN in predicting \(\:{\sigma\:}_{i}/c\) . SHAP analyses were performed to assess the importance of the input variable on \(\:{\sigma\:}_{i}/c\) . The SHAP analysis identified the normalized unit weight as the most influential parameter, with a mean SHAP value of 0.329, followed by the friction angle (φ) (0.129), whereas \(\:{k}_{h}\) (0.029) and H/D (0.016) showed only minor effects, indicating that the normalized unit weight and φ are the primary drivers of prediction variability. The results indicate that the proposed models strongly agree with the numerical FELA \(\:{\sigma\:}_{i}/c\) values. By conducting comprehensive stability analyses, engineers can design and maintain tunnels that meet safety standards, accommodate diverse traffic needs, and contribute to efficient road infrastructure management. This ensures the long-term sustainability and safety of transportation networks, fostering economic development and social inclusion.