Cement Hydration Model Research Articles

A Numerical Hydration Model to Predict the Macro and Micro Properties of Cement–Eggshell Powder Binary Blends

This study aims to propose a hydration kinetic model for the cement–eggshell powder binary system and predict the performance development of composite concrete through this model. The specific content and results of the model are as follows. First, based on the cumulative hydration heat of the cement and eggshell powder binary system in the first seven days, the parameters of the cement hydration model and the eggshell powder nucleation parameter are calibrated. These parameters remain constant regardless of the mix ratio. Secondly, the hydration heat of the cement–eggshell powder binary system over 28 days is calculated using the hydration model. The results show that at 28 days, for specimens with 0%, 7.5%, and 15% eggshell powder substitution, the cement hydration degrees are 0.832, 0.882, and 0.923, respectively. The hydration heat per gram of cement is 402.69, 426.88, and 446.73 J/g cement, respectively, while the hydration heat per gram of binder is 402.69, 394.86, and 379.72 J/g binder, respectively. Additionally, the hydration model is used to calculate the chemically bound water and calcium hydroxide content of the cement–eggshell powder binary system. At 28 days, for samples with 0%, 7.5%, and 15% eggshell powder, the chemically bound water content is 0.191, 0.188, and 0.180 g/g binder, respectively, and the calcium hydroxide content is 0.183, 0.179, and 0.173 g/g binder, respectively. Finally, a power function is used to regress the calculated hydration heat with experimentally measured compressive strength and surface electrical resistivity. The correlation coefficients for compressive strength and surface electrical resistivity are 0.8474 and 0.9714, respectively. This is because the strength weak point effect of eggshell powder has minimal impact on hydration heat and surface electrical resistivity experiments but significantly affects the strength experiment.

Modelling the hydration of cement ‐ Does chemical shrinkage influence autogenous self‐healing?

AbstractAutogenous self‐healing of cracks in water retaining concrete structures is included in Eurocode 1992‐3 as a possible measure to heal cracks up to a width of 200 μm without additional repair. Water flow through the crack leads to the closure of the fracture, mainly due to CaCO3 precipitation. However, despite standardization, the healing effect seems to be random in practice. This study uses thermodynamic modelling of cement hydration to examine how the timing of crack formation affects crack widening or closure due to chemical shrinkage or swelling and discusses the implications for autogenous self‐healing. It is found that the exact timing of early‐age crack formation can lead to crack widening or closure in the range of a few micrometres. This effect is most prominent for cracking within the first two days of curing and dependents on the cement type, the fraction of inert material in the mix design and the amount of shrinkage that translates into a macroscopic volume reduction. However, it is concluded that other more dominant factors must be at play leading to the discrepancy between laboratory results and the unpredictable healing efficiency observed in practice.

Development and verification of an integrated hydration, geochemical and transport model for the hydrated cement paste exposed to an aggressive chemical environment

This study established a new transport model by using the COMSOL-IPHREEQC interface to simulate the changes in the morphology of hydrated cement paste due to the diffusion of carbon dioxide and chloride ion. A series of constitutive models such as the cement hydration model (to compute the dissolution rate of each clinker mineral), thermodynamic model (to perform the hydration reaction, reaction due to transport of ions, chemical and physical adsorption of chloride ion during the chloride ion ingression and dissolution rate of calcium-silica-hydrate (C–S–H) simultaneously with portlandite for the carbonation), porosity determination, and COMSOL Multiphysics (for the calculation of transport problems) were integrated using MATLAB language to determine the pore solution chemistry, hydrates assemblage, and porosity of the cement paste exposed to aggressive environments. During the diffusion of carbon dioxide gas, the decalcification of C–S–H was realistically considered by assuming that the Ca/Si ratio of C–S–H decreased from 1.67 (Jennite type C–S–H) to 0.67 (Tobermorite C–S–H), and then from 0.67 to 0 (silica gel). The proposed integrated platform was well verified with different sets of reported and raw experimental results and existing models, indicating a realistic predictability for chloride ion ingression and carbonation. The developed model discloses the effect of coupling the progression of hydration with reaction due to the transport of ions by using the free chloride ion profile and phase assemblages during the chloride ion ingression.

Simulation of the effect of nano-CaCO3 agglomeration on the hydration process and microstructural evolution of cement paste

In this study, three-dimensional simulations of cement hydration are conducted to investigate the effect of nano-CaCO3 (NC) agglomeration on the hydration process and microstructural evolution of cement pastes (CPs). Few experimental studies have reported on the effect of NC agglomeration on the properties of CPs because the degree of NC agglomeration is difficult to control in experiments. Herein, NC agglomeration was first investigated in a simulation by assigning different contents of NC in water-filled voxels in a three-dimensional cement hydration and microstructure development model (CEMHYD3D). CPs containing 3 wt% NC with a water-to-cement ratio (w/c) of 0.3 were considered in the simulation. Four levels (1, 2, 3, and 4) of NC agglomeration were investigated by assigning 8.5, 13.7, 19.8, and 27 vol% of NC in a C–H voxel, respectively. Agglomeration level 0 refers to the condition in which no NC particles are deposited in a water-filled voxel. An isothermal calorimetry test was conducted to validate the simulation results obtained for plain CPs. A comparison of experimental data and simulation results in terms of heat flow rate and heat formation revealed that level 3 showed better agreement than the other levels. The effect of NC agglomeration on cement hydration was more evident in the early stages of the process than in the later stages. Lower levels of agglomeration resulted in a faster hydration rate, a higher degree of hydration (DOH), and higher C–S–H and CH contents at an early age. However, the addition of NC particles did not result in an increase in ultimate DOH.

Quantitative study on growth and porosity of C-S-H structures: Experiments and simulations

Coupling of microstructural and physico-chemical modelling of cement hydration is a key step towards prediction of material performance. In this paper, a physico-chemical model based on surface reactions and ion transports is proposed to capture the development of calcium-silicate-hydrate (C-S-H) not only at an early age but also at later ages of hydration (e.g, up to 28 days). Furthermore, we introduce a random sampling method to quantify pore size distribution and phase fractions in the 3D simulation, which are available for the comparison with experimental data. The latest experimental techniques were used to quantify the development of the C-S-H as well as its pore sizes, e.g. SEM, 1H NMR , XRD during hydration. By combining observations from experiments and simulations, we can explain the densification of C-S-H during the hydration.

A hierarchical creep model for cement paste: From decoding nano-microscopic C-S-H creep to considering microstructure evolution

The creep of cement paste significantly affects the long-term performance of concrete structures. However, the accurate prediction of cement paste creep remains to meet enormous challenges. This work proposes a hierarchical creep model of cement paste considering the hydration microstructure evolution. First, the microstructural evolutions are quantitatively captured by a cement hydration model. The creep property of cement paste is upscaled from high-density (HD) and low-density (LD) calcium silicate hydrate (C-S-H) at the nanoscale, via C-S-H gels at the sub-micrometer scale to the microscopic scale by coupling the mean-field theory with the transfer function method. The creep behavior of HD and LD C-S-H is described using a fractional Maxwell model in the time domain and its corresponding transfer function in the Laplace-Carson domain. The creep parameters of HD and LD C-S-H are identified through a back-analysis approach. The determined creep parameters and the hierarchical creep model are validated by comparing them with extensive experimental data. Furthermore, the proposed model quantitatively evaluates the influences of various factors on the creeps of cement paste and C-S-H gels. The results indicate that C-S-H gels should not be treated as a phase with stable viscoelastic creep properties, and cement paste creep can be tailored via proper design for these factors.

Hydration kinetics of Portland cement shifting from silicate to aluminate dominance based on multi-mineral reactions and interactions

A theoretical model for cement hydration was proposed to study multi-mineral reactive transport processes under various mineral compositions and determine the effect of multi-mineral reactions and interactions on cement hydration kinetics shifting from silicate to aluminate dominance. The reaction rates of each mineral dissolution, product precipitation, ionic diffusion, and adsorption were calculated individually through the degrees of undersaturation and supersaturation associated with the ionic concentration, all of which were coupled in the modified Poisson–Nernst–Planck equation. The hydration heat flow was then theoretically calculated by the superposition of the reaction rates of silicate and aluminate phases, which was derived from the calculated ionic concentration. The model was validated by comparison with experimental data obtained under various conditions, showing consistency. The combined effect of multi-mineral reactions and interactions on hydration kinetics was investigated using the model, and the results indicated that (1) faster dissolution of gypsum or a higher ratio of tricalcium aluminate to tricalcium silicate leads to a larger time interval between silicate and aluminate peaks; (2) faster precipitation of calcium silicate hydrate results in a more significant difference between silicate and aluminate peaks; and (3) the sulfate ion retards cement hydration kinetics shifting from silicate to aluminate dominance.

Hydration simulation of cement pastes reinforced with carbon nanotubes

The study proposed a cement hydration model based on multiphase voxels and a novel dissolution rate to simulate the hydration of a carbon nanotube (CNT)-reinforced cement paste. The proposed multiphase voxels and dissolution rates were validated by considering accelerated or delayed hydration owing to CNTs and superplasticizers. The model can simulate the formation of low-density and high-density calcium silicate hydrates (CSHs) using multiphase voxels and was validated using previous experimental data for cement pastes containing 0.05–0.25 wt% CNTs. The simulation results, including those on the heat flow and heat of hydration, are consistent with the experimental results.

Employing Discrete Solid Phases to Represent C-S-H Solid Solutions in the Cemdata07 Thermodynamic Database to Model Cement Hydration Using the PHREEQC Geochemical Software

This paper presents a cement hydration model over time using the cemdata07 thermodynamic database and a series of derived discrete solid phases (DSPs) to represent calcium silicate hydrate (C-S-H) as a binary solid solution with two end-members. C-S-H in cement is amorphous and poorly crystalline with a range of molar Ca/Si ratios from 0.6 to 1.7. It displays strongly incongruent dissolution behaviour, where the release of calcium into solution is several orders of magnitude greater than silicon. It is, therefore, important that any cement hydration model provides a credible account of this behaviour. C-S-H has been described in the cemdata07 thermodynamic database as a number of solid solutions using different end-members with differing levels of complexity. While solid solutions can be included in most modern geochemical software programs, they often lead to a significant increase in computation time. This paper presents how an incongruent solid solution between two C-S-H end-members may be represented as a number of DSPs to model cement hydration over time using the PHREEQC geochemical software. By using DSPs rather than modelling C-S-H as a nonideal solid solution, this gives the user full control of the input for the model, reducing the computational demand and analysis time with no loss in accuracy in predicting stable-phase assemblages and their associated pore chemistry over time.

Experimental investigation of fiber content and length on curing time‐dependent mode‐I fracture behavior and properties of cemented paste backfill and implication to engineering design

AbstractThe inclusion of fiber in cemented paste backfill (CPB) can significantly alter the mechanical response of the CPB body. The intrinsic defects in CPB and the potential dynamic loading condition make it necessary to investigate the fracture properties of fiber‐reinforced CPB (FR‐CPB). The mode‐I fracture behavior and properties are crucial to the successful engineering application of FR‐CPB technology used in underground mines. The contribution of fiber length and content to the evolutive mode‐I fracture behavior and properties of FR‐CPB was examined in this study. The results show that the addition of fiber reduces the prepeak stiffness but improves the mode I fracture toughness (KIc), and the improvement in KIc increases with fiber length. In contrast, the initial increase in fiber content (from 0% to 0.5%) benefits the KIc acquisition, while a further increase in fiber content from 0.5% to 0.75% poses a negative influence on the KIc development. Moreover, with the adoption of the cement hydration model, four predictive functions are proposed to describe the contribution of fiber length and content to the development of fracture properties. In addition, KIc is identified as a more reliable fracture property for assessing the immediate ground support role played by the FR‐CPB structure. The findings are helpful when it comes to the determination of the fiber length and content in FR‐CPB design.

Incorporating elastic and creep deformations in modelling the three-dimensional autogenous shrinkage of cement paste

A structure-based modelling framework was established to simulate the three-dimensional autogenous shrinkage of cement paste. A cement hydration model, HYMOSTRUC3D-E, was used to obtain the microstructures and ionic concentrations of the cement paste. A lattice fracture model based on the effective stress and effective modulus was used to consider the elastic and creep parts of autogenous shrinkage. For Portland cement pastes with water-to-cement ratios of 0.3 and 0.4 (where the time zero of autogenous shrinkage was set as the time of the drop in internal relative humidity), the simulated linear elastic autogenous shrinkage was respectively −188 and −79 μm/m at 160 h. The obtained linear total autogenous shrinkage including elastic and creep deformations was respectively −501 and −236 μm/m at 160 h. These values of the elastic autogenous shrinkage and total autogenous shrinkage are close to the predications of poromechanical models and experimental data obtained using a corrugated tube.

Numerical Study on Transient Annular Pressure Caused by Hydration Heat during Well Cementing

Annular pressure has been recognized as one of the most challenging problems in the petroleum industry, posing a series of threats to wellbore integrity. Annular pressure caused by thermal expansion during the cement hydration process is rarely studied by researchers. In light of the hydration heat generation process, a kinetics model for cement hydration under different curing temperatures is demonstrated in this paper. Considering interactions between temperature and cement hydration, a transient temperature prediction model during well cementing is built. On the basis of these assumptions, the prediction model of annular pressure is established, considering the change in cement temperature and the change in annulus volume. Using the models illustrated in this paper, a series of numerical simulations are performed. The changing roles of transient cement hydration degree and temperature in wellbores are analyzed thoroughly. The annular pressure during well cementing shows a rapid increase and then a decrease, which is similar to that of the temperature. In addition, a sensitive analysis of annular pressure is conducted. The analysis shows that the annular pressure increases with the geothermal gradient, the cement hydration heat, and the wellbore diameter. Suggestions and conclusions can provide safety guidance for the management of annular pressure during well cementing.

Effect of curing temperature on hydration, microstructure and ionic diffusivity of fly ash blended cement paste: A modelling study

This paper presents an integrated modelling framework to investigate the effect of curing temperature on hydration, microstructure and ionic diffusivity of fly ash blended cement. A 3D cement hydration model, i.e. CEMHYD3D, was modified by incorporating the parameters representing the temperature-dependent dissolution of Portland cement and fly ash and then used to simulate the hydration and microstructural evolution of blended cement with different fly ash replacement ratios and types and water-to-binder ratios cured at various temperatures. Based on the generated 3D microstructure, a lattice Boltzmann model for diffusion was employed to simulate the ionic diffusivity and estimate the relationship between ionic diffusivity and microstructure in hydrating fly ash blended cement paste. Results indicate the simulated hydration process of blended cement cured at various temperatures agrees well with experimental data. The elevated curing temperature leads to a lower capillary porosity and connectivity, less diffusible C-S-H and lower ionic diffusivity at early ages but higher ionic diffusivity later due to the denser hydration products in fly ash blended cement paste.

Effects of Water-to-Cement Ratio on Pore Structure Evolution and Strength Development of Cement Slurry Based on HYMOSTRUC3D and Micro-CT

Changing the water-to-cement ratio is one of the major ways to develop cement slurry with different densities, which in turn will greatly affect the pore structure and mechanical properties of cement slurry. In the current study, the cement hydration model HYMOSTRUC3D was used to investigate the effects of water-to-cement (w/c) ratio (0.40, 0.44, 0.50) on the pore structure evolution and strength development of cement slurry. The microstructure of the cement stone was characterized via scanning electron microscope (SEM) and micro-computed tomography (micro-CT), and the mechanical strength of the cement stone was tested and analyzed via a mechanical tester. The simulated compressive strength and capillary porosity are in good agreement with the measured data, where the relative error between the simulated results and measured results are within 0.6~10.7% and 13.04~25.31%, respectively. The capillary porosity is proved as the main factor affecting the compressive strength of cement stone with different w/c ratios. Herein, the mathematical relationship between the measured capillary porosity and compressive strength could be well fitted via the mathematical prediction models of the Balshin function (R2 = 0.95), Ryshkewitch function (R2 = 0.94), Schiller function (R2 = 0.96), and the linear regression function (R2 = 0.95). Moreover, the linear regression function (y = −2.38x + 82.76) can be used to characterize and predict the quantitative relationship between the compressive strength and capillary porosity of cement stone. The findings in this study will provide a reference value in the fields of oil and gas cementing and building concrete.

CO2 uptake model of limestone-powder-blended concrete due to carbonation

In this study, a model for evaluating the CO2 uptake rate of plain concrete and limestone-powder-blended concrete in both the service and recycling phases was proposed. First, a blended cement hydration model was proposed to evaluate the content of carbonatable substances, porosity and carbon dioxide diffusivity. In the service phase, a one-dimensional carbonation model was proposed to evaluate the carbonation depth. In the recycling stage, an unreacted core model was proposed to evaluate the carbonation process of spherical recycled concrete. Secondly, considering the concrete materials, structural elements and environmental exposure, a CO2 uptake model at the service stage and recycling stage was proposed. The total CO2 uptake rate is the sum of the CO2 uptake rates in the service stage and the recycling stage. The analysis results showed (1) as the limestone replacement rate increased from 0% to 20% (water–binder ratio is 0.3), the CO2 uptake rate in the service phase increased from 3.12% to 3.84%, and the total CO2 uptake rate increased from 22.82% to 26.11%. (2) Given a certain concrete mixture, as the surface area to volume ratio of structural units increased, or the amount of recycled concrete decreased, the CO2 uptake rate increased, but the total CO2 uptake rate did not change. (3) Given a certain limestone powder replacement ratio, as the water/binder ratio increased, the total CO2 uptake ratio increased. The contributions of this study are 1) propose an integrated hydration-carbonation-CO2 uptake model for limestone blended concrete, 2) clarify the differences of carbonation equations between service stage and recycling stage, and 3) determine the effects of concrete mixtures, structural element sizes and types, life cycle stages, and recycled concrete sizes on CO2 uptake.

A Simple Cement Hydration Model Considering the Influences of Water-to-Cement Ratio and Mineral Composition

A simple hydration model is used here by taking the composition of the cement and the initial water: cement ratio (w/c) into account explicitly. Its conceptual basis is a combination of the Avrami equation and Bentz’s model based on simple spatial considerations. In this model, the Avrami equation determines the initial reaction, and Bentz’s model describes the following hydration stage. The model favors engineers for it relies on one experimental parameter and has a reliable approximation in the practice.

Carbonation process simulation for cement-based materials based on microstructure by a cement hydration model

Based on three-dimensional distributions of cement particles, cement hydration was simulated to obtain the hydrate content and the pore structure of cement paste. Additionally, the porosity of mortar and concrete was obtained by considering aggregate inclusion and interfacial transition zones (ITZ). Then, a coupled model for heat transfer, moisture transport and carbonation in cement-based materials was established. The experimental carbonation results agreed well with the simulated results for mortars and concretes with different water-cement ratios. The carbonation reaction front was far beyond the complete carbonation depth. The aggregate dilution had a more significant effect on carbonation than the ITZ did.

Modelling of sand cement hydration in normal conditions

The paper considers the hardening mechanisms of the sand cement composition (0.75 sand and 0.25 Portland cement) during 28 days. In this study, the VCCTL tool is used for computer modelling of the sand cement hardening process. It is found that after 28 days, the sand cement hydration is ∼0.75, the porosity is over 0.20 and 0.32 at the water-cement ratio of 0.40 and higher, respectively. Calcium silicate hydrate (C–S–H) and portlandite (CH) are the main hydration products of Portland cement and responsible for the sand cement strength. Owing to the high porosity of sand cement, free moisture is present in it in large quantities. It is shown that the effective elastic moduli of sand cement rapidly grow during 200 hours and then monotonically lower. The yield stress monotonically grows during sand cement curing, and at 0.40 and 0.44 water-cement ratios achieves the maximum value. This growth thus depends on the water-cement ratio and affects Young’s modulus during the curing process. At the qualitative level, a correlation is observed between the yield stress and Young’s modulus depending on the curing time of sand cement with the discussed water-cement ratios.

Evolution of microstructures of cement paste via continuous-based hydration model of non-spherical cement particles

As the soul of cement-based materials, hydration is a complex process involving many chemical reactions, which is one of the intrinsic driving forces for the evolution of the microstructure and macroscopic properties of cementitious composites. The predominant lines of previous researches on cement hydration models are dominated by spherical particles. However, the actual shape of cement grains is non-spherical. Herein, a continuous-based hydration model of non-spherical cement particles (HYD-NSP) is developed, in which the hydration kinetics strongly depend on the morphological features of cement grains. Subsequently, the proposed HYD-NSP model is validated by experimental results. By applying the HYD-NSP model, we further investigate the evolution of microstructures of cement paste including icosahedron-shaped cement grains over time. Results reveal that the influence of the shape of cement particles on the degree of hydration and the porosity of cement paste is mainly reflected by their specific surface area.

Simulating cement hydration using HYDCEM

HYDCEM is a new cement hydration model to simulate volumetric changes and predict phase assemblage, degree of hydration, heat release, compressive strength and chemical shrinkage over time for PC and limestone binders undergoing hydration for any w/c ratio and curing temperatures between 5 and 45 °C. While models should never completely remove experimental analysis, they are an aid to better understand cement hydration and microstructure development by allowing users analyse different binders in a relatively short time. HYDCEM, written in MATLAB®, is aimed at complementing more sophisticated thermodynamic models giving users a reasonable prediction of hydration behaviour over time, using user-customisable inputs. A number of functions based on up to date cement hydration behaviour from the literature are included along with user-changeable inputs such as the cement chemical (oxide) composition, cement phase densities, species molar mass, phase and product densities and heat of hydration enthalpies. HYDCEM uses this input to predict the cement phase and gypsum proportions, volume stoichiometries and growth of hydration products including C-S-H, calcium hydroxide, hydrogarnet (if applicable), hydrotalcite, ettringite, monosulphate, hemicarbonate and monocarbonate if limestone is present. A number of comparisons with published experimental and thermodynamic model results and HYDCEM predictions are provided to demonstrate its accuracy and usefulness. Previous work has shown that HYDCEM can reasonably accurately predict phase assemblages in terms of volume change and behaviour for a range of cements and curing temperatures.