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.