Analytical solution of mechanical response in cold region tunnels under transversely isotropic freeze–thaw circle induced by unidirectional freeze–thaw damage

During the operation stage of cold region tunnels, the isotropic surrounding rock in a freeze–thaw circle suffers long-term unidirectional freeze–thaw cycles and gradually transforms into transversely isotropic material, which induces the variation of stress and displacement distribution of cold region tunnels. Aimed at this phenomenon, an analytical solution of mechanical response in cold region tunnels under transversely isotropic freeze–thaw circles induced by unidirectional freeze–thaw damage is proposed. The analytical solution is derived under two different states of the freeze–thaw circle: 1) transversely isotropic and unfrozen state (state TU) and 2) transversely isotropic and frozen state (state TF). In addition, the stress distribution in the lining and surrounding rock with a transversely isotropic freeze–thaw circle is analyzed. The transformation of the surrounding rock in a freeze–thaw circle from isotropic material into transversely isotropic material leads to the increase of stress in the lining, especially for a significant increase under state TF. Finally, the influence of the deterioration coefficient and the degree of anisotropy on the stress distribution in the lining is analyzed. The stress in the lining increases linearly as the deterioration coefficient decreases, while it increases nonlinearly as the degree of anisotropy decreases. The smaller the degree of anisotropy is, the greater the increase rate of the stress is. Moreover, the increase of stress with deterioration coefficient and degree of anisotropy under state TF is much greater than that under state TU. Both deterioration coefficient and degree of anisotropy decrease from 1.0 with increasing unidirectional freeze–thaw cycles suffered by surrounding rock, and, thus, induce the increase of stresses in the lining. In addition, the deterioration coefficient has a greater influence than the degree of anisotropy on the stress in the lining.