In general, simultaneous heat and moisture transfer model in three phases is established as a numerical model to calculate the distribution of ice content in porous materials. This numerical model is based on thermodynamic equilibrium theory that the freezing point of water in pore is uniquely depended on own pore size. However, it is commonly considered that frost damage is caused by sudden freezing of supercooled water, which is a random phenomenon. Because the supercooling phenomenon is thermodynamic non-equilibrium phenomenon, the previous analytical model as the thermodynamic equilibrium model cannot investigate influence of the supercooling phenomenon. Although an establishment of the thermodynamic non-equilibrium analytical model is expected, the freezing point is not determined uniquely since the freezing of the supercooled water is probabilistic phenomenon. Thus, in order to predict the probability of frost damage adequately by using numerical analysis based on physical model, it is essential to build the supercooling phenomenon as a probabilistic event into the analytical model.
Therefore, the aims of this study are to establish a prediction model for the probability of freezing until any lowest reached temperature, and to obtain the probability distribution function of the freezing point for the proposed analytical prediction model.
First, theoretical prediction model for the probability of the instantaneous increment of ice content when lowest achieving temperature was known was derived based on these assumptions that building structure is an aggregation of small elements and probability distribution of the freezing point in small elements is independent from each other. The applicability of the proposed model for small continuum will be validated as the future task.
Next, the freezing point measurement was carried out by using saturated mortar samples as the small element. As the results, it could be found that the first freezing due to supercooling occurred from -4 to -11 deg. C and the maximum probability was appeared at -7.5 deg. C. From comparison between the average increment of ice content based on the measurement result and the 40 % volume of pore water until the thermodynamically-based freezing point, there was a good agreement for both of them. Moreover, the standard deviations were 0.6 % constantly in the measurement temperature range.
Moreover, the probability distribution of the increment of ice content could be regarded as a normal distribution. And the method that can calculate the probability distributions of the instantaneous increment of ice content for any lowest achieving temperature from pore size distribution was proposed. Because the calculation results of the proposed method had good agreements with the measurement results, it can be concluded that the proposed method has enough validity.
