Calculation of rigid body rotation and shearing dislocation deformation of adjacent shield tunnels due to excavation of foundation pits

Excavation of foundation pits has a significant impact on the deformation of the adjacent shield tunnels. Considering the additional stress at the tunnel axis due to the soil unloading during excavation, a tunnel deformation model combining the shear-dislocation and rigid-body rotation is established. The formulas for the longitudinal deformation, segment-joint dislocation displacement, rotation angle and segment-joint shear force of the tunnel are deduced based on the principle of the minimum potential energy. Two engineering cases are selected for analysis, and the calculated results are compared with the measured data. The results show that: the soil unloading stress of the adjacent parallel surrounding wall has the largest effect on the tunnel when the foundation pit is beside the tunnels. On the location of the maximum tunnel horizontal deformation, the dislocation and rigid-body rotation of tunnel segments are close to zero, and the segment-joint shear force is also very small. At the inflection point of the horizontal displacement curve, the segment-joint rotation angle and segment-joint shear force of the tunnel both reach the maximum. Under the excavation of the foundation pit, the tunnel deformation model is mainly composed of shear dislocation and complemented by rigid body rotation.