Mathematical Model for Freeze‐Thaw Durability of Concrete

Although the equations governing the individual basic physical processes involved in freezing and thawing of concrete are known, a mathematical model for this complex phenomenon is unavailable. Its formulation is attempted in the present study. Desorption and absorption isotherms for concrete below 0°C are constructed on the basis of isotherms for concrete above 0°C, using pore size distribution functions. Water movement during freezing or thawing is described as a double diffusion process, involving both macroscopic diffusion through concrete and local diffusion of water into or out of air‐entrained bubbles. Heat conduction is formulated taking into account the latent heat of freezing. Pore pressures are used in a two‐phase material model, which makes it possible to predict the stress in the solid structure of concrete caused simultaneously by freezing and applied loads. This in principle reduces the freeze‐thaw durability problem to the calculation of stresses and strains. However, development of the model to full application would require various new types of tests for calibration of the model, as well as development of a finite element code to solve the governing differential equations. Such a mathematical model could be used to assess the effect of cross‐section size and shape, the effect of cooling rate, the delays due to diffusion of water and of heat, the effect of superimposed stresses due to applied loads, the role of pore size distribution, the role of permeability, and other factors which cannot be evaluated at present in a rational manner.