Analytical Solution of Three-Dimensional Heaving Displacement of Ground Surface during Tunnel Freezing Construction Based on Stochastic Medium Theory

Many studies indicate that the heaving displacement during tunnel freezing construction can be regarded as a plane strain problem. However, due to the fact that many of the frozen pipes are placed obliquely in practical engineering, it should be a three-dimensional problem. Therefore, considering stochastic medium theory, the analytical solution of three-dimensional heaving displacement of ground surface during tunnel freezing construction is established, and the analytical solution is applied to the project case in Beijing. The calculation results show that, considering the inclination angle between the freezing pipe and the center axis of the tunnel, the maximum heaving displacement of the ground surface occurs at the tunnel center. When the inclination angle is equal to 0°, the analytical solution of three-dimensional ground surface heaving displacement is in good agreement with that of the two-dimensional prediction model, which further verified the reliability of the established analytical solution of the three-dimensional frost heave prediction model.