Review of several existing models simulating the hydration of cementitious materials
In the late 1980s, Johnson and Jennings wrote a program which was based on the idea that cement hydration is considered as nucleation and growth of spherical particles in three-dimensional space.
HYMOSTRUC was built by K. van Breugel, this model is based on the assumption that the growth of new layers of hydration products is deposited on the surface of cements particles (mostly alite particles considered), which leads to a more heterogeneous distribution of hydration products. The hydrating cement particles are represented as expanding spheres. At the contact zone, where two hydrating cement particles meet, the overlapping volume of hydration products is redistributed around the two touching particles. The model can simulate the development of properties of Portland cement, e.g. the development of hydration and microstructure, the volume changes of the hardening cement pastes, and the effect of geometrical changes of the microstructure on the creep of the hardening concrete. The emphasis of the model is on the formation of the microstructure and the corresponding bulk properties, while the evolution of hydrating product phases is less focused.
Based on HYMOSTRUC model, Liu Xian et al. made an improvement to take account of the addition of limestone into Portland cement. Due to large substitution level (say 33% and 42%) of Portland cement, limestone particles are considered as no-expanding particles and inert filler without taking part in the hydration process.
To better represent the accurate microstructure of hardening Portland cement, Integrated Particle Kinetics Model (IPKM) was developed, the assumption of IPKM is that the evolution of alite hydration is modeled by the deposition of C-S-H on the surface of C3S particles but the formation of new portlandite is assumed to take place in pores, which is not considered in HYMOSTRUC; therefore, it is possible to enable the calculation of interaction between particles and evolution of individual particles, thus enabling the modeling of the evolution of each particle independently. However, due to the explicit calculation of all possible interactions, the simulations using IPKM is very slow, which leads to the simulations only within relatively small number of particles.
Similar to IPKM, a new platform for modeling the hydration of cements called µic is developed, which is claimed to have improved the performance of the continuous approach enabling simulations with millions of particles within acceptable times compared with IPKM. Besides the high calculation efficiency, the application enables the customization of all aspects of microstructural development of hardening cement paste.
One of the best known models using discretization approach is called CEMHYD3D which was launched by Garboczi and Bentz. The model is used to simulate the development of properties of cement-based materials, e.g. the microtructure development of hardening cement paste, the adiabatic temperature rise of Portland cement and silica fume blended concrete, and the diffusivity of chloride ions in silica fume blended cement paste. The features of this model are digital image basis, accurate microstructure representation, and rule-based to mimic reaction and diffusion. The drawback is that there is little or no kinetic information corresponding to the hydration process and requiring magic resolution which substantially increases the computation time of a relatively large volume cement paste. As for binary cement, preliminary work were tried to incorporate the reaction of fly ash and slag; however, due to the complexity of the reaction of slag blended cement, more effort is needed for this model to deal with the reaction kinetic constant and activation energy of fly ash and slag, meanwhile, the induction period of slag or fly ash blended cement is not explicitly considered in the model limiting the application of the model in predicting the properties of early-age concrete.
Originally based on the CEMHYD3D, Chen Wei extended the model to simulate the hydration and microstructure development of slag cement. Some modifications were made to consolidate the chemical background of the model and eliminate the effect of system resolution on the model predictions, especially the hydration degree of cement. The model can be used to investigate the various stages of cement hydration. As the author stated, the new version model has its own drawbacks, such as the reactivity of slag has not been taken into account adequately, the role of activator is constrained only to the activation from Portland cement/clinker.
Maekawa et al. proposed an integrated program named DUCOM (DUrability COncrete Model), which evaluates both the early-age properties of hardening concrete (such as the cement heat hydration and thermal conduction, pore structure formation and moisture equilibrium) and durability of concrete (e.g. chloride ion transport, carbonation, corrosion of steel re-bar and calcium ion leaching). The old version DUCOM model can be used to evaluate the temperature history of slag or fly ash blended concrete. In the latest updated DUCOM model, the effect of limestone powder and the reaction of silica fume are incorporated. However, DUCOM model did not consider too much on the chemical aspects of the hydration of binary cements. The influence of mineral compositions of fly ash or silica fume on reaction stoichiometry is not considered in DUCOM model yet. The evolution of chemical and volumetric composition of silica fume-cement blends or fly ash cement blends cannot be evaluated.
G. De Schutter proposed a kinetic hydration model which is valid for Portland cement and blast furnace slag cement. In his model, the heat evolution of blast furnace slag cement is obtained by the superposition of the heat release of the Portland reaction (P reaction) and the slag reaction (S reaction). The evolution of mechanical properties in early-age concrete is described using functions of the degree of hydration. However, the interactions between the cement hydration and the reaction of mineral admixtures, e.g. the production of calcium hydroxide by cement hydration and the consumption calcium of hydroxide by slag reaction, are not considered in the hydration model yet. On the other hand, The generalization of the reaction parameters depending on the actual slag replacement ratios is not yet possible.
Considering the production of portlandite from cement hydration and the consumption in the reaction of mineral admixtures, a numerical hydration model is recently developed by Wang et al. In this model, the heat evolution rate of fly ash- or slag-blended concrete is determined by the contribution of both cement hydration and the reaction of mineral admixtures, where the total heat generation content of fly ash and slag is set as 110 kcal/kg and 50 kcal/kg, respectively. With regards to CH, it is assumed the amount of CH is directly proportional to the degree of hydration of cement, and the reaction of slag is accelerated by the presence of CH and be dependent on the mass of CH. Using this model, the prediction of temperature rise from modeling results in blended cement agrees well with the experimental results, as well as the temperature distribution in blended cement is predicted. However, influence of the chemical compositions of admixtures on the reaction stoichiometry of admixture is not taken account for in the model, and hydration product phase’s distribution and microstructure development are not included in the model.