Horizontal convergence reconstruction in the longitudinal direction for shield tunnels based on conditional random field

Tunnel horizontal convergence monitoring is essential to ensure the operation safety. However, only a few representative tunnel sections are chosen for monitoring due to the cost limitation. It is difficult to capture the horizontal convergence of each tunnel ring with limited measurements. Confronted with this difficulty, the paper proposes a horizontal convergence reconstruction method based on the measurements of deployed sensors. The tunnel horizontal convergence along the longitudinal direction is seen as a one-dimensional stationary and ergodic random field. The reconstruction problem is then transformed into the generation of conditional random fields. Monte Carlo simulation is adopted to generate possible realizations and the mean of realizations is considered as the maximum likelihood reconstruction. Error analysis proves the effectiveness of the proposed reconstruction method. The proposed method is proved to be applicable in reconstructing the time-variant horizontal convergence and is verified by the monitoring results of the shield tunnel of Shanghai Metro Line 2. The effect of sensor numbers is parametrically studied, and an optimal sensor placement scheme is decided. Additional sensors placed at the deformation drastically changed location can significantly improve the performance of the proposed method.