The models to be presented in this section depend critically on the volume fractions of water-filled and total capillary porosity (φW(t) and φT(t)) and unhydrated cement (γ(t)), as a function of time, t. Based on Power's model for cement hydration, for an ordinary portland cement paste, these quantities are given by [3, 4]:
where (w/c) is the water-to-cement mass ratio, α is the degree of hydration (reacted fraction) of the cement at time t, ρcem is the specific gravity of cement (here taken to be 3.2), ƒexp is the volumetric expansion coefficient for the "solid" cement hydration products relative to the cement reacted (here taken to be (2.15-1.)=1.15) [2,4], CS is the chemical shrinkage per gram of cement (here taken to be 0.07 mL/g), and a density for water of 1.0 g/cm3 has been assumed. The ρcemCSα/(1+ρcem(w/c)) term in equation (1) represents the empty porosity created under sealed curing conditions by the chemical shrinkage occurring during hydration. Under saturated curing conditions, the chemical shrinkage is assumed to be exactly compensated for by the imbibition of external curing water (i.e., CS=0), and the total and water-filled porosities are thus equivalent.