A unified model for frost heave pressure in the rock with a penny-shaped fracture during freezing

In order to investigate the mechanisms of rock deterioration at low temperature, a unified model for frost heave pressure in the rock with a penny-shaped fracture during freezing was proposed, in which the main influencing factors can be classified into four groups: 1) the mechanical properties of ice and rock (Ei, υi, Es and υs); 2) the external loading conditions (q and λ); 3) shape characteristic of the fracture (η); and 4) effective volume expansion coefficient (βe). The model attempts to unify the volume expansion theory, water immigration theory and combination theory. Validation was carried out, and the comparisons indicated that the proposed model can accurately reflect the variation of the frost heave pressure. Parametric sensitivity analyses were performed to examine the effect of various parameters and to improve the understanding of the damage of fractured rock mass subjected to frost heave. The results showed that βe is the most important parameter that affects the magnitude of frost heave pressure, apart from it, the mechanical properties of ice (Ei and υi) are also crucial, and then is the parameters of Es, q and η. Relatively speaking, υs and λ have little influence. Besides, some discussions were given to the newly defined variableβe, which is a crucial parameter that can unite the three existing frost heave mechanics of rock.