Unified strength-based elastoplastic solution for frost heaving force of cold-region tunnels considering dual non-uniform frost heaving of surrounding rock

Precise evaluation of the frost heaving force and surrounding rock plastic zone is an important basis of the prevention of freezing damage in cold-region tunnels. The temperature gradient along the radial direction of cold-region tunnels surrounding rock results in the dual non-uniform frost heaving of surrounding rock, namely, the gradual change of frost heave ratio along the radial direction and the unequal frost heaving deformation in the circumferential and radial directions. A new elastoplastic solution of tunnel frost heaving force considering double non-uniform frost heave and intermediate principal stress was derived based on the elastoplastic mechanics theory, thick-cylinder theory, and unified strength theory to better guide the frost resistance design of tunnels in cold regions. The rationality and advantages of the unified plastic solution of tunnel frost heaving force were verified by model tests and engineering examples. Results showed that the theoretical calculation value of frost heaving force was in good agreement with the measured value. When the gradual change in the frost heave ratio of surrounding rock in the radial direction was ignored, the frost heaving force and radius of the surrounding rock plastic zone were large and conservative. The solution in this paper can accurately evaluate the tunnel frost heaving force and surrounding rock plastic zone. Finally, this paper studies the influences of intermediate principal stress coefficient, the frost heaving coefficient of unit temperature of frozen surrounding rock, non-uniform frost heaving coefficient in different directions, and maximum freezing depth on the evolutionary law of frost heaving force and plastic zone of cold-region tunnels are studied.