Elastoplastic Analytical Solution for the Stress and Deformation of the Surrounding Rock in Cold Region Tunnels Considering the Influence of the Temperature Field

It is very important to accurately calculate the frost heave force for the frost resistance design of tunnels in cold regions. A computational model will divide the lining and surrounding rock into eight parts, such as the support zone, the frozen zone (e.g., isothermal Rings I, II, III, IV, V, and VI), and the unfrozen surrounding rock Zone VII. The model will consider the influence of the inhomogeneity of the mechanical parameters of the frozen surrounding rocks that are caused by the temperature field on the calculation results for the frost heave force. Based on the case analysis, the elastoplastic analytical solution of the stress and deformation of the surrounding rock in a cold region tunnel will be obtained. The results show that: (1) if the basic physical and mechanical parameters of the frozen surrounding rock are taken as constants, the calculation results of frost heave force, plastic radius (rp), and circumferential stress (σθ) at the excavation radius will be smaller than that of the model proposed in this paper, and the freezing resistance design of the tunnel lining in cold regions based on the uniform parameter model might lead to lining damage due to insufficient support strength in the later stage; (2) the results of variance analysis show that the inner radius of the lining (ra) and radius of Zone 7 (r7) had a significant effect on the frost heave force in all cases, and the elastic modulus of the lining (E0) was significant. The influence of the elastic modulus of Zone 7 (E7) and in situ stress (p0) on the frost heaving force was not significant; and (3) the influence law of the displacement release coefficient (η), E0, and p0 on the force that acted on the lining will be analyzed. The model to calculate the frost heave force and the related conclusions could have guiding significance for the frost resistance design and numerical simulation of tunnels in cold regions.

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