A Mathematical Model for Predicting Frost Penetration in Saturated Porous Materials

Abstract

A two-dimensional finite element computer model for predicting frost penetration in saturated porous materials is presented together with a comprehensive literature review regarding mechanisms of frost action. Based on available second order parabolic differential equations for predicting temperature and moisture content, and equations relating freezing temperature and water potential, the finite element model predicts temperature, water and ice content, frost penetration, and generated pore water pressures as a function of freezing time. The model is validated using field and laboratory data presented in the literature, and a sensitivity analysis performed on such important variables like tensile strength and density of material, the moisture characteristic curve, and hydraulic and thermal conductivity. A discussion on limitations and experiences with the model is also offered. The influence of the desorption characteristics on freezing progress is illustrated leading to the important finding that the pore size distribution is represented by the desorption curve and plays a major role in the freezing performance of porous materials. It is further concluded that the latent heat of fusion is temperature dependent to the extent that the prediction of freezing temperature as a function of time is changed significantly by assuming a constant value. The surface tension is likewise a function of temperature. This change, however, can be ignored in the prediction of the freezing process.