A damage model for frost heaving pressure in circular rock tunnel under freezing-thawing cycles

The failure of rock tunnel lining in cold region involves the evaluation of frost heaving pressure in surrounding rock. Although many theoretical models of frost heaving pressure have been proposed, the combination effect of reduction in rock elastic modulus and increase of rock void ratio due to freezing-thawing cycles has not been considered. For this issue, on basis of the elastic model for frost heaving pressure in the circular tunnel surrounding rock, this study establishes the relationship between the rock elastic modulus and the number of freezing-thawing cycles based on fracture mechanics and mesodamage theory. Thereafter, we propose the damage model for frost heaving pressure by considering the combination of rock elastic modulus and void ratio. It is assumed that frost heaving pressure mainly occurs when water in microcracks is frozen into ice. The calculation example shows that frost heaving pressure gradually increases and tends to be a constant with increasing the number of freezing-thawing cycles. It indicates that the proposed model is capable of calculating the variation of frost heaving pressure with the number of freezing-thawing cycles.