Modelling Hysteresis in the Water Sorption and Drying Shrinkage of Cement Paste

Shrinkage can be critical for the strength and durability of drying cement pastes. Shrinkage becomes particularly severe at very low relative humidity, < 20%, which can be met in some activities involving extreme temperatures. Experiments and simulations suggest that small pores in the cement paste, with approximate thickness ≤ 1 nm, stay saturated unless the humidity drops below 20%. Here we suggest that this pore size can define two different categories of pores in the paste: pores thicker than 1 nm, where the Kelvin's equation and the corresponding capillary (Laplace) pressure apply, and pores thinner than 1 nm, which can be considered as part of the solid skeleton if the humidity stays above 20%. We show that a continuum model, incorporating a pore-blocking mechanism for desorption and equilibrium thermodynamics for adsorption, explains well the sorption hysteresis for a paste that remains above ∼ 20%. At lower humidities, we assume that (1) during adsorpion water re-enters the smallest pores throughout the entire RH range (supported by experiments and simulations) and (2) there exists a simple linear relationship between water and strain in the smallest pores. These minimal assumptions are sufficient to explain the low-humidity hysteresis of water content and strain, but the underlying mechanistic explanation is still an open question. Combining the low-humidity and high-humidity models allows capturing the entire drying and rewetting hysteresis, and provides parameters to predict the corresponding dimensional changes.