Abstract: Brittle material such as rock deteriorates subjected to freezing and thawing. It is generally observed that the primary reason of rock deterioration is the water phase transition caused by the change of temperature. Hydraulic pressure is generated by 9% volumetric increase of freezing water in a closed crack, which expands crack, meanwhile water flows into new cracks as the temperature is raised. Therefore, the repeated cycles generate the new damage of rock. The freezing and thawing process of rock is also affected by a number of factors such as the length of cracks, permeability, and heaving stress. Considering the extension length of one single crack subjected to frost heave forces, a formula of the relationship between the macroscopic damage and freezing-thawing cycles is established on the basis of elastoplastic mechanics and fracture mechanics. An analytical model is developed to predict the deterioration degree. The validity of the model is examined by comparing its predictions with the experimental results. The effect of elastic modulus on freezing-thaw cycles, heaving stress and permeability coefficient is also discussed. In addition, the theoretical solutions are compared with the existing experimental results. The conclusions are drawn as follows. Firstly, the crack extension length is dominated by heaving stress and the permeability of rock which increases nonlinearly with the decrease of temperature and the coefficient of permeability. On the other hand, the connectivity increases with increasing crack length, and the permeability of fractured rock mass increases. Secondly, elastic modulus decreases nonlinearly due to freezing-thawing cycles. Thirdly, the initial crack length has great effect on the variability of elastic modulus, according to stress intensity factor theory, the heaving stress decreases as the initial crack length increases, which reduces the elastic modulus to some extent. Finally, by comparing the theoretical results with the experiment data of sandstone under uniaxial compression, it is interesting to note that the results are in good agreement. Although the number of cracks is not affected by the freeze-thaw cycles due to the limitation of the initial assumption, the assumption needs to be improved with the measured data.

Key words: heaving stress, permeability coefficient, crack expansion, elastic modulus, freezing-thawing cycles