Tunnel-wall-monitoring-based probabilistic risk assessment and inverse control of train-induced ground vibration in metro tunnels

Long-term vibration monitoring in operational metro tunnels provides valuable information for evaluating train-induced ground-surface vibration and its environmental impact. However, it remains challenging to determine whether the ground-surface vibration satisfies environmental limits based on tunnel wall response and, more importantly, to identify the allowable tunnel wall vibration level required to ensure ground-surface compliance. To address this issue, this study proposes a probabilistic framework for uncertainty quantification, exceedance risk assessment, and reliability-based inverse control of train-induced ground-surface vibration. In this framework, a multi-layer perceptron (MLP) model is used as the deterministic prediction backbone to establish the mapping between tunnel wall response and ground-surface vibration, while a Gaussian residual model is introduced to quantify aleatoric uncertainty. The proposed framework is validated using field measurements from an independent monitoring section of Beijing Metro Line 6. The results indicate that the framework provides satisfactory prediction accuracy for ground-surface vibration, with the coverage probability of the constructed 95 % confidence interval reaching 95.45 %. The prediction residuals are approximately consistent with a Gaussian distribution, supporting the adopted probabilistic assumption. The exceedance probability of ground-surface vibration increases nonlinearly with increasing tunnel wall vibration level, and clear differences are observed under different environmental vibration limits. Furthermore, a deterministic prediction trap is identified, in which compliant mean predictions may conceal a hidden exceedance risk of 11.0 %. Based on the probabilistic relationship among tunnel wall vibration, exceedance probability, and reliability index, a reliability-based inverse control strategy is developed. For the investigated section, the tunnel wall vibration level should be controlled below 64.19 dB to satisfy a target reliability of 99 % under the nighttime vibration limit for residential, cultural, and educational areas. The proposed framework provides a monitoring-based decision-support tool for environmental vibration assessment and source-side vibration control in operational metro tunnels.