Analytical elasto-plastic solution of frost heaving force in cold region tunnels considering transversely isotropic frost heave of surrounding rock

Numerous cold region tunnels have been constructed in recent decades. To prevent frost damage, problem of frost heaving force calculation is to be solved urgently. During the freezing process of cold region tunnels, temperature gradient occurs mainly in radial direction, whereas the temperature gradient in circumferential and axial directions is negligibly gentle. Hence, the surrounding rock of cold region tunnels freezes unidirectionally along the radial direction, which results in the transversely isotropic frost heave of surrounding rock. Therefore, an analytical elasto-plastic solution of frost heaving force is proposed, in which an anisotropic frost heave coefficient k is introduced to consider the transversely isotropic frost heave. And the surrounding rock is considered as ideal elasto-plastic material conforming to Mohr-Coulomb yield criterion in the solution. Moreover, the method to determine the elastic or plastic state of the surrounding rock after frost heave is proposed. For the condition that the frozen surrounding rock doesn't reach the plastic state, an elastic solution of frost heaving force considering the transversely isotropic frost heave is also established. Then, the analytical elasto-plastic solution is verified with the existing solutions and a model test, and proved to be reasonable and applicable. Finally, the influence of the related factors, such as the frost heaving property (the anisotropic frost heave coefficient and the volumetric frost heaving strain) of surrounding rock, the initial ground stress, and the mechanical parameters of surrounding rock on the frost heaving force and plastic zone radius is analyzed. Results show that as the anisotropic frost heave coefficient k increases, the frost heaving force increases significantly, which demonstrates that the transversely isotropic frost heave of surrounding rock has considerable impact on the frost heaving force and should be considered.