Analytical solution for the response of an existing tunnel induced by above-crossing shield tunneling

The shield tunneling above an existing line has been a commonly encountered problem in urban construction in recent years. It is obvious that the over-crossing tunneling will adversely affect and even damage the existing tunnels if the induced deformation exceeds the design limit of tunnel structures. In order to obtain a better understanding of the effects of the above-crossing tunneling on the existing tunnels and provide a quick and effective tool for evaluating the behaviors of underlying tunnels prior to construction, in this study a simplified analytical method is proposed. In this model, the tunnel is represented by a series of short beams resting on a Winkler foundation connected by tensile springs, compressional springs and shear springs, so that the rotational effect and shearing effect of the joints between lining rings can be captured. Our new model is compared with some existing models, such as Euler-Bernoulli beam and a series of short beams connected only by shear springs, by comparing their predictions with the field-measured longitudinal deformation of two Shanghai subway tunnels. Results of these case studies show that the predictions of our model are much closer to field monitored data than those existing models. In addition, a parametric analysis is also conducted to investigate the influences of the different factors, including advancing distance, clearance distance and stiffness of joints, on the behaviors of the existing tunnels.