A method for calculating unfrozen water content of silty clay with consideration of freezing point

A physical calculation model for the content of unfrozen water of silty clay was proposed with a consideration of freezing point. The freezing point of bulk water, capillary water and bound water was calculated. The freezing point of bulk water was assumed to be constant in the calculation. The Kelvin equation and the theory of water activity were used to calculate the freezing-point changes of the capillary and bound water during the volume decrease, respectively. The influence of soil-particle size on the freezing point was taken into account in the model. In the calculation, the unfrozen water content at a negative temperature was defined as the sum of the volume of capillary and bound water whose freezing point was lower than the given temperature. By using silty clay from the Qinghai-Tibet Plateau as an example, the results of the model calculations were validated by using the measured data from time-domain reflection and nuclear magnetic resonance. The calculations for four existing models as proposed by other scholars were listed for comparison with our model. The results show that the calculated results of our model are precise and reflect the hysteresis effect of the unfrozen water content during freezing and thawing. The model validated an order of freezing in soil: bulk water froze first, most capillary water froze next, and most bound water froze last. This paper explains the existence of unfrozen water from the perspective of freezing-point change and provides a theoretical basis for the calculation.