The theoretical freezing model of sandstone considering the statistical arrangement of pore structure

It is of great significance to understand the evolution law of unfrozen water content in frozen rocks to maintain the stability of geotechnical engineering in cold regions. Due to the different particle sizes and shapes, coupled with the diversity of cements, the internal pore structures of rocks are complex and diverse. In this study, a theoretical model for freezing point of sandstone is proposed based on the characteristics of microscopic pore structures. The characteristic of freezing point is analyzed by considering the mineral particle arrangement. A statistical theoretical model of unfrozen water in sandstone is established according to the random arrangement of mineral particles. The influence of the stacking angle of mineral particles following the normal distribution on unfrozen water content is analyzed. Finally, the NMR freezing process analysis for sandstones was carried out. The results show that the statistical theoretical model of unfrozen water fits the experimental results well. The effect of the average value of stacking angle on unfrozen water content is mainly due to the change of pore size, which leads to the change of pore water content. The standard deviation of stacking angle determines the residual water content. •A freezing point model was proposed based on the characteristic of pore structure.•The evolution of unfrozen water during the freezing process was analyzed.•A statistical theoretical model of unfrozen water content was established.•The influence of the stacking angle on unfrozen water content was analyzed.