Prediction of Three-Dimensional Orthotropic Frost Heave Deformation during Cross-Passage Construction Using Artificial Ground Freezing

Abstract The artificial ground freezing (AGF) method has been widely used in underground engineering to improve the stability and water tightness of water-rich weak ground. In projects with radial or inclined freezing pipe arrangements, the resulting deformation is strongly three-dimensional and direction-dependent, which may threaten adjacent tunnels, underground structures, and ground surface stability if it is not accurately predicted and controlled. To support deformation assessment in AGF engineering, this study develops a three-dimensional thermomechanical coupled numerical model for simulating frost heave deformation under complex freezing pipe layouts. The model incorporates the soil ice–water phase transition, convective heat transfer at the ground and structural surfaces, and orthotropic frost heave deformation associated with the heat-flow direction. In this framework, the frost heave ratio is introduced as an equivalent thermal strain, and an orthotropic deformation coefficient is used to characterize the difference between frost heave parallel and perpendicular to the heat-flow direction. A frost heave subroutine is implemented to update the temperature field, heat-flow direction, and frost heave strain during the freezing process. The proposed method is validated using field-monitored temperature and displacement data from a metro cross-passage freezing project. The results show that the model accurately reproduces the spatiotemporal evolution of the ground temperature field and effectively captures the orthotropic characteristics of frost heave. Compared with the isotropic frost heave assumption, the proposed method reduces the prediction error of ground surface uplift deformation from 17%–25% to <10%. The slightly conservative displacement predictions provide a reliable basis for safety-oriented frost heave control in AGF engineering.