Freezing Strain Model for Estimating the Unfrozen Water Content of Saturated Rock under Low Temperature

The freeze-thaw damage of rock is mainly induced by the 9% volumetric expansion of frozen water. It has already been demonstrated that unfrozen water exists in porous material at the freezing point. Accurate estimation of unfrozen water content is important for evaluating freeze-thaw damage and understanding freezing processes in rock. To derive the unfrozen water content, the freezing process of pore water and freezing strain of saturated rock under low temperature were studied. Based on the cumulative distribution curve of pore size, the unfrozen water content is proved to be an exponential function of freezing temperature. Unfrozen water mainly occupies nanopores and has no effect on the freezing strain of rock. The freezing strain of rock under subzero temperature is composed of matrix shrinkage caused by falling temperature and pore expansion by pore-ice pressure. Thus, a theoretical model that accommodates the relationship between freezing strain and unfrozen water content considering the phase transition is proposed according to saturated poroelasticity theory. Using this model, the unfrozen water content can be accurately calculated by measuring the freezing strain of saturated rock. Three examples of freezing strain tests demonstrate that the freezing strains derived from this theoretical model are in good agreement with the experimental values for saturated rock with different porosities and that the unfrozen water content can be easily and accurately determined.