Analytical solutions of ground settlement induced by yaw in a space curved shield tunnel

This paper aims to provide the analytical solutions of the ground settlement for a space curved shield tunnel in the case of yaw construction. Settlement inducements include ground loss and construction loads, and two corresponding analytical models have been proposed in this study. Three-dimensional image theory has been adopted to calculate the ground settlement due to ground loss. Yawrelated parameters are introduced into the calculation model to deduce the relevant laws of the ground settlement. Based on modified Mindlin solutions, analytical models are established to calculate the ground settlement induced by construction loads, such as the frontal additional thrust, axial friction of shield shell, and the grouting pressure. The method of calculating the position of the shield machine in the ground is refined, and the influence area of construction loads from the shield machine is optimized. Subsequently, the obtained solutions are validated by a numerical model and field data. Besides, a comparison reveals that the proposed model is the composition of three classical analytical models, thus it excels them in solving the problem mentioned. Finally, parametric analyses of yaw are conducted to examine yaw angle and pitch angle on ground settlement. The proposed model can effectively predict ground settlement caused by the spatial linear shield tunneling process.