Analytical solutions for the performance of existing shield tunnel caused by overlying excavation in the presence of the portal frame

The heave of the existing shield tunnel would be induced due to the above excavation, and then structural damages, including leakage and cracking, easily happen. The combination of the shaft excavation and anti-uplift portal frame is an effective technique to limit the heave of the existing tunnel, while the theoretical method is absent presently to guide the design of the anti-portal frame. Thus, analytical solutions for the performance of the existing tunnel are proposed. Both the longitudinal and cross-section deformation of the existing tunnel during the shaft excavation and foundation pit excavation, respectively. The flow chart is also provided. The results predicted by the analytical solution are in good agreement with that of field measurement and 3D numerical simulation, which proves the reliability of the analytical solution. The mechanism of the anti-uplift portal frame is carefully investigated and sensitivity analysis of the buried depth of the existing tunnel and the excavation size of the shaft is performed. The results show that the anti-uplift portal frame could effectively control the deformation of the existing tunnel caused by the above excavation, strongly depending on the thickness of the soil above the existing tunnel. The efficiency of the anti-uplift portal frame is stronger as the decrease of the thickness of the soil above the existing tunnel. The effect of the anti-uplift portal frame mainly depends on the force between the anti-floating slab and the soil, and the uplift pile shows a minor influence on the deformation of the existing tunnel.