Multi-Scale Multi-Phase field model for Shrinkage Performance of Concrete

Concrete, as a porous composite material, is susceptible to moisture loss, which can initiate degradation mechanisms such as autogenous and drying shrinkage. These shrinkage phenomena lead to crack initiation and propagation, compromising structural safety and durability. Therefore, understanding concrete shrinkage under varying hydric conditions is critical for extending the service life of concrete structures. However, existing research lacks the precision needed to accurately predict moisture loss, crack development, and shrinkage behaviour.
This study introduces innovative mesoscale numerical models to simulate moisture diffusion, mechanical properties, and shrinkage in concrete, aiming to assess its long-term performance. The inclusion of a pore phase in the model enables accurate monitoring and solution derivation. Autogenous shrinkage is modelled through chemical shrinkage in the matrix phase (mortar), while drying shrinkage is attributed to moisture loss in the pore phase during hydration. The latter is described via capillary stress evolution induced by moisture evaporation.
To develop and calibrate the proposed model, extensive experiments were conducted to characterize concrete’s physical properties at the mesoscale, including moisture transport, mechanical degradation, crack propagation, and shrinkage. The approach integrates numerical modelling with laboratory testing to monitor early-age moisture content, temperature, and strain in concrete elements. Mechanical behaviour and crack propagation in mortar and concrete specimens were also experimentally evaluated.
A novel micro–meso model is presented, utilizing random packing and Voronoi tessellation to generate aggregates, the interfacial transition zone (ITZ), and pore structure. The Rayleigh–Ritz and Brunauer–Skalny–Bodor (BSB) models are employed to simulate pore distribution and calculate moisture diffusion coefficients for both vapor and liquid water. This diffusion model considers critical variables such as the water-to-cement (w/c) ratio, concrete maturity, and environmental conditions.
Crack development is simulated using an elasto-plastic phase-field model, which is calibrate through compressive.
By integrating moisture diffusion and mechanical behaviour across four phases—aggregate, mortar, ITZ, and pores—a comprehensive coupled system is proposed to predict shrinkage behaviour and mechanical performance. Given that shrinkage is primarily driven by moisture loss, accurate modelling of moisture diffusion is essential, as it governs the drying process and controls the development of shrinkage-induced strains. These strains, in turn, affect both short- and long-term deformation and cracking in structural elements.
This study addresses these challenges by using common variables such as the w/c ratio and concrete maturity to assess the effects of pore relative humidity and ambient temperature on concrete diffusivity through inverse numerical analysis. Results show strong agreement between the model and experimental data, confirming the model’s capability to capture the influence of mix design and environmental conditions on moisture evolution in drying concrete.