Complex Variable Solution for Twin Tunneling-Induced Ground Movements Considering Nonuniform Convergence Pattern

The construction of twin tunnels in crowed urban cities requires tunnel excavations in close proximity to one another, in which the interaction between tunnels significantly affects the ground movements generated by tunneling. However, little information was provided for the effects of twin tunnels interaction on the ground movements during tunneling. In this paper, a new analytical approach is introduced to efficiently assess the ground surface settlements induced by twin tunneling in clay, with the nonuniform contraction deformation pattern richly considered at the tunnel opening boundary. Other than simply using linear superpositions of results of a single tunnel, special attention is paid in this literature to the interaction of twin tunnels in various configurations, on the basis of the complex variable theory and Schwartz alternating control method. The analytical presented solution is then verified by comparisons with a total of four centrifuge model tests and two engineering case records, together with the superposition of each single tunnel result. It is revealed that the presented complex variable solution considering the nonuniform contraction deformation model can provide a prediction of soil subsidence in good agreements with the experimental data and field measurements. Finally, a parametric study is performed to investigate the influence of different configurations and spacing of twin tunnels on the interaction degree. The configurations of twin tunnels are of horizontal, vertical, and diagonal arrangements. It is revealed that the twin tunnels interaction contributes to significantly large ground movements when the tunnels are in small spacing and shallow depths, but the interaction progressively decreases as the tunnel spacing increases. The ground settlements induced by twin tunneling are generally same with the results for combined superpositions from two single tunnels at a horizontal tunnel spacing of 10D. The complex variable solution proposed in this paper provides an effective insight into the interaction of shallow twin tunnels in clay, and can serve as an appropriate approach for conservatively estimating the ground movements in the preliminary design of twin tunnels.