冻融循环条件下岩石弹性模量变化规律研究

岩体冻融损伤机制为温度降低使岩体中的水发生相变、体积膨胀、产生冻胀力的作用，岩体中的微裂隙在冻胀力的作用下扩展延伸，温度升高时，融化的水进入新的裂隙，冻结成冰再次产生冻胀作用，反复循环使裂隙网络扩展，最终造成岩体的损伤。基于此，从弹塑性力学、断裂力学的角度出发，研究了在冻胀力的作用下单裂隙扩展特性，推导了冻胀力与裂纹扩展长度之间的关系，利用Mori-Tanaka方法建立了岩体宏观损伤量与冻胀力及冻融次数之间的关系式，讨论了岩体弹性模量与冻融次数、冻胀应力以及渗透系数的变化规律，并与试验结果进行了比较分析。结果表明，岩体在冻融循环条件下的弹性模量随冻融次数的增加呈非线性减小；冻胀应力越大，岩体弹性模量衰减越快；岩体的渗透系数越大，弹性模量衰减越慢。

Variability of elastic modulus in rock under freezing-thawing cycles

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.