Prediction of microstructural evolution in fly ash-modified cementitious system: A computational study

The materials used in this study include Type I cement or ordinary Portland cement (OPC) and FA. The OPC utilized in this study was a commercially available cement, confirming ASTM C 150 specifications. FA cement confirming ASTM C 618 (AASHTO M 295) was also commercially available and was used to make an FA-blended mixture. All materials were stored in a controlled environment to prevent moisture absorption and contamination.

First of all, the investigation was initiated by determining the particle size distribution (PSD) and chemical composition of each cement. This step was undertaken to establish the PSD and oxide compositions, which are essential for subsequent computational modeling purposes. The PSD of the cements was obtained through the application of the laser diffraction (LD) technique, as detailed in Figure 1 below.

Fig. 1.

In cement, various oxides are found in the composition of cementitious materials. Some of the common oxides include SiO₂, CaO, Al₂O₃, Fe₂O₃, SO₃, MgO, K₂O, and Na₂O. These oxides are typically represented using chemical symbols and short forms as S=SiO₂, C=CaO, A=Al₂O₃, F=Fe₂O₃, S¯=SO3\[\overline{\text{S}}\text{=S}{{\text{O}}_{3}}\], M=MgO, K=K₂O, N=Na₂O, T=TiO₂, C¯=CO2\[\overline{\text{C}}\text{=C}{{\text{O}}_{2}}\], and H=H₂O. In this study, the oxide composition of the cements was obtained using the X-ray diffraction (XRD) technique, as presented in Figure 2. Using the characteristics of the cements, various cement pastes were created to replicate the microstructural evolution of cement pastes modified with FA.

Fig. 2.

The experimental investigation aimed to analyze the microstructural evolution within FA-modified cement paste. Cement paste specimens were created, each featuring distinct FA replacement levels of 10%, 20%, 30%, and 40%. To ensure a standardized approach, we rigorously maintained a constant w/c of 0.45 for all samples. The curing of the samples took place under controlled conditions at a standard temperature of 20°C, ensuring a saturated environment for optimal hydration development. The curing duration was determined based on the specific testing age required for analysis. A thermogravimetric analysis (TGA) technique was utilized to measure and assess the levels of hydrate water and calcium hydroxide (CH) present in both unmodified and FA-modified cement pastes. This technique involves subjecting samples to controlled temperature changes while measuring the weight variations and providing insights into the hydration process and resulting products. The porosity of FA-modified cement pastes was measured using the mercury intrusion porosimetry (MIP) technique. In order to determine the pore size distribution and porosity, this approach includes introducing mercury into the pore network of the sample while applying increasing pressure.

The extended version of a CEMHYD3D model was employed in this study to predict the microstructural evolution of FA-modified cement paste. This computational approach considers the various factors influencing microstructure formation, such as FA content, cement chemistry, and curing conditions. The modeling process involved inserting the experimental parameters, including FA replacement levels, w/c ratio, and curing conditions, into the CEMHYD3D model. The model then performed simulations based on these inputs to predict the progression of microstructural features over time, including hydration phases, porosity, and pore distribution. The predicted microstructural properties were subsequently compared to the experimental measurements obtained through TGA and MIP analyses. This validation process aimed to assess the accuracy of the prediction of the CEMHYD3D model and its application to simulate the microstructural evolution within FA-blended cement paste. By combining experimental analysis with the predictive capabilities of the CEMHYD3D model, this research helps to advance a comprehensive insight into the microstructural changes occurring in FA-blended cement paste over time.

The hydration process of Portland cement can be computed using the basic hydration equation expressed in Equation (1) for each chemical composition in the cement [22]. The chemical reactions as well as the diffusion processes during hydration of a single cement are all considered in this model: 1 dαdt=[ 3(SwS0)ρwCw−free(v+wg)r0ρc ]×[ 1(1kd−r0De)+r0De(1−α)−13+1kr(1−α)−23 ] \[\begin{array}{*{35}{l}} \frac{d\alpha }{dt}=\left[ \frac{3\left( \frac{{{S}_{w}}}{{{S}_{0}}} \right){{\rho }_{w}}{{C}_{w-free}}}{\left( v+{{w}_{g}} \right){{r}_{0}}{{\rho }_{c}}} \right] \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\times \left[ \frac{1}{\left( \frac{1}{{{k}_{d}}}-\frac{{{r}_{0}}}{{{D}_{e}}} \right)+\frac{{{r}_{0}}}{{{D}_{e}}}{{\left( 1-\alpha \right)}^{\frac{-1}{3}}}+\frac{1}{{{k}_{r}}}{{\left( 1-\alpha \right)}^{\frac{-2}{3}}}} \right] \\ \end{array}\] where α is the rate of hydration of cement, v is the mass ratio of water to cement, w_g is the physically-bound water in the C-S-H gel, S_w is the effective surface area of the cement particle that are in contact with water, S₀ is the total surface area, C_w–free is the physically free water from the C-S-H gel, r₀ is the radii of an unhydrated cement particle, ρ_c is the density of cement, and ρ_w is the density of water.

The reaction coefficient, k_d, is supposed to be proportional to the rate of hydration of the cement, whereas the values of the coefficients B and C govern the initial rates of shell formation and decay, respectively. This can be expressed with Equation (2) below: 2 kd=Bα1.5+Cα3 \[{{k}_{d}}=\frac{B}{{{\alpha }^{1.5}}}+C{{\alpha }^{3}}\]

In the diffusion process, the effective diffusion coefficient value of the water, D_e, changes based on the radii of the gel pore in the cementitious system. Equation (3) presents an expression for this phenomenon in terms of the rate of hydration. 3 De0=ln(1α) \[{{D}_{e0}}=ln\left( \frac{1}{\alpha } \right)\]

While the mineral components in each cement undergo hydration, the quantity of free water, C_w–free within the capillary pores decreases. Therefore, the amount of water within the capillary pores changes in accordance with the hydration rate, which can be mathematically expressed by Equation (4) below: 4 Cw−free=W0−0.4αC0W0 \[{{C}_{w-free}}=\frac{{{W}_{0}}-0.4\alpha {{C}_{0}}}{{{W}_{0}}}\] where C₀ and W₀ represent the initial percentages by mass of cement and water, respectively, in the mix.

Hydration models essentially provide microstructural properties at different stages of hydration. Microstructural properties such as elastic modulus, rate of hydration, autogenous shrinkage, and transport properties can be predicted using these images. Cement particles are typically made up of tri-calcium silicate (C₃S), di-calcium silicate (C₂S), tri-calcium aluminate (C₃A), and tetra-calcium aluminate ferrite (C₄AF) mineral phases. The hydration model for a blended cement system is formulated by summing up the hydration processes involved in cement clinkers and the SCMs in the mix as a single component when considering the interaction between mineral components and the reaction of SCMs.

The rate of hydration in FA-blended cement can be computed based on the method described in [9, 12], and [23]. Therefore, the cumulative rate of hydration of both Portland cement and FA at a specific time, tj(αjcem,αjFA)\[{{t}_{j}}\left( \alpha _{j}^{cem},\alpha _{j}^{FA} \right)\] can be expressed with Equation (5) as follows: 5 αji=1Gi(xmaxi−1)∑z=xmincemxmaxi−1αz,ji.Wzi \[\alpha _{j}^{i}=\frac{1}{{{G}_{i}}\left( x_{max}^{i}-1 \right)}\sum\limits_{z=x_{min}^{cem}}^{x_{max}^{i}-1}{\alpha _{z,j}^{i}}.W_{z}^{i}\] where G_i(x) is the Rosin-Rammler function, which was used to determine the PSD of i particles. xmini\[x_{min}^{i}\] and xmaxi\[x_{max}^{i}\] represent the minimum and maximum particle size of i particle, respectively. Wzi\[W_{z}^{i}\] is the mass of i particles in a given fraction. With information on the PSD of i particles, it is possible to calculate the values of G_i(x) and Wzi\[W_{z}^{i}\]. αz,ji\[\alpha _{z,j}^{i}\] denotes the reaction degree of i particles with size j at time t_j; it can be calculated using the penetration depth of the i particles with size z, which can be determined using the basic hydration equation.

Hydration modeling basically covers the chemical effects of the cement minerals on hydration reactions. The amount of hydration products like calcium-silicate-hydrate (C-S-H) and calcium hydroxide (CH) in a cement paste can be calculated by the balance equation of pozzolanic reaction and cement hydration. According to the theories put forth by [24], the reactions that the minerals in Portland cement undergo during the hydration stage can be described with Equations (6)–(9) as follows: 6 2C3S+6H→C3S2H3+3CH \[2{{\text{C}}_{3}}\text{S}+6\text{H}\to {{\text{C}}_{3}}{{\text{S}}_{2}}{{\text{H}}_{3}}+3\text{CH}\] 7 2C2S+4H→C3S2H3+CH \[2{{\text{C}}_{2}}\text{S}+4\text{H}\to {{\text{C}}_{3}}{{\text{S}}_{2}}{{\text{H}}_{3}}+\text{CH}\] 8 C3A+CS¯H2→10H+C4ASH¯12 \[{{\text{C}}_{3}}\text{A}+\text{C}\overline{\text{S}}{{\text{H}}_{2}}\to 10\text{H}+{{\text{C}}_{4}}\text{AS}{{\overline{\text{H}}}_{12}}\] 9 C4AF+2CH→10H+C6AFH12 \[{{\text{C}}_{4}}\text{AF}+2\text{CH}\to 10\text{H}+{{\text{C}}_{6}}\text{AF}{{\text{H}}_{12}}\]

Similar to other pozzolanic materials, the main effect of FA substitution into cement is to lower the ratio of Ca/Si in C-S-H by reducing the amount of portlandite generated. The main constituents of FA are calcium, silicon, and aluminum oxide, which combine to form a glassy material [25]. Higher concentrations of SiO₂ can be found in the glassy phases, while magnetite, mullite, quartz, and hematite are the most common crystalline phases. Some FA have a higher concentration of CaO in their glassy phases, and their crystalline phases are more likely to be quartz, lime, and periclase [26]. Based on the study of [27], the equation for the chemical reaction of FA-modified cementitious systems can be described with Equations (10)–(14) as follows: 10 S+1.1CH+2.8H→C1.1SH3.9 11 AS+2CH+6H→C2ASH8 \[\text{AS}+2\text{CH}+6\text{H}\to {{\text{C}}_{2}}\text{AS}{{\text{H}}_{8}}\] 12 CAS2+C3A→16H+2C2ASH8 \[\text{CA}{{\text{S}}_{2}}+{{\text{C}}_{3}}\text{A}\to 16\text{H}+2{{\text{C}}_{2}}\text{AS}{{\text{H}}_{8}}\] 13 CAS2+C4AF+20H→2C2ASH8+CH+FH3 \[\text{CA}{{\text{S}}_{2}}+{{\text{C}}_{4}}\text{AF}+20\text{H}\to 2{{\text{C}}_{2}}\text{AS}{{\text{H}}_{8}}+\text{CH}+\text{F}{{\text{H}}_{3}}\] 14 CS¯+2H→CS¯H2 \[\text{C}\overline{\text{S}}+2\text{H}\to \text{C}\overline{\text{S}}{{\text{H}}_{2}}\]

The amount of CH in the paste decreases due to the pozzolanic reaction involving FA in cementitious systems. Therefore, the CH content, m_CH, in the system can be computed with Equation (15). This computation accounts for the chemical composition and reactivity of the specific FA being used: 15 mCH=mCH0−mCHFA \[{{\text{m}}_{\text{CH}}}={{\text{m}}_{\text{C}{{\text{H}}_{\text{0}}}}}-{{\text{m}}_{\text{C}{{\text{H}}_{\text{FA}}}}}\] where m_CH is the total CH content in the system after the pozzolanic reactions, mCH0\[{{m}_{C{{H}_{0}}}}\] is the initial CH content in the system before the pozzolanic reactions, and mCHFA\[{{\text{m}}_{C{{H}_{FA}}}}\] is the amount of CH consumed due to the pozzolanic reactions with FA.

Over past few decades, numerous distinct hydration models have been meticulously formulated and widely adopted, each specifically applied for the analysis of pure Portland cement. The best approach to developing a hydration model for a cement system containing FA blends would be to extend the verified model for Portland cement. Therefore, this study employed the extended CEMHYD3D modeling program from the open source.

The microstructural evolution of FA-modified cement pastes with various substitution levels of FA was simulated using the extended CEMHYD3D model. In the simulation, it is possible to calculate a wide range of microstructural parameters such as heat of hydration, phase volume fractions, chemical shrinkage, and porosity. In the computer model, microstructural properties like heat of hydration, CH formation, and pore structure were simulated.

The prediction yielded valuable insights into the progression of phases and the distribution of hydration products within the cementitious system containing FA. An intriguing observation was made as the FA content increased, subtle shifts occurred in the composition of reaction products. The introduction of FA particles brought about additional nucleation sites, fostering the generation of hydrates and consequently promoting a more extensive formation of C-S-H. This phenomenon bears significance for the material’s mechanical properties, as the secondary C-S-H gel enhances both the acceleration of strength development and the improvement of microstructural compaction.

Additionally, the simulations revealed the formation of C-A-S-H gels in the presence of FA, further contributing to the overall densification of the microstructure of cement paste. The simulated figures (a, b, c, and d) in Figure 3, corresponding to various levels of FA replacement, vividly depict this phenomenon. Over a span of 180 days, the extended CEMHYD3D model aptly predicted the rate of hydration and the evolution of microstructure in FA-modified cement pastes, underscoring its reliability.

Fig. 3.

From the model predictions, the influence of FA on cement hydration appears to be minimal when up to 10% FA is incorporated into the cement mixture. As the FA content increases to 20% in Portland cement, the rate of hydration for the blend surpasses that of a cement system containing only Portland cement, particularly during the later stages beyond 90 days. However, the rate of hydration in early ages, up to 28 days, is a little slower than that of the later ages when compared with the hydration of pure Portland cement pastes. When about 30% FA is replaced with cement, the rate of hydration in the system is still higher than that of pure Portland cement, and this is true when up to 40% FA is substituted. The simulation shows that the rate of hydration for FA-blended cement demonstrates an increased trend after 28 days, which is consistent with an increase in the FA substitution level.

When FA is added to cementitious systems, it can have a significant effect on the formation of CH and the microstructural evolution of the resulting cement pastes. FA reacts chemically with CH to form additional cementitious compounds, such as C-S-H. As a result, when FA is added to cement paste, it reduces the amount of CH as illustrated in Figure 4. This reduction in CH content can be simulated in terms of volume fractions with the CEMHYD3D model.

Fig. 4.

The initial parameters for pore structure analysis of the cement paste were set before the simulation started. The chemical composition of the mixture, FA content, w/c ratio, temperature, and curing condition were normally considered when determining the pore structure. Based on these parameters, the CEMHYD3D model simulated the microstructure images of hydrated blended cements with various substitution levels of FA at the age of 180 days.

The microstructure images in Figure 5 shows the pore structure of various cement pastes denoted as A, B, C, and D, each featuring different levels of FA substitution. It is evident that as the FA content in the cement increases, the rate of hydration notably increases in the later stages, beyond 90 days, and this continues until the particular curing period of 180 days. When the hydration time increases, the hydrated products take up a larger volume and the mineral phases shrink, and this determines the pore structure of the system. The colors in the microstructure images indicate the various mineral phases present in cement.

Fig. 5.

The CEMHYD3D modeling program tracks changes in the pore structure of the cement paste, including the size and distribution of pores. FA can affect the pore structure by filling some of the voids or influencing the formation of smaller pores. Therefore, understanding the evolution of porosity is crucial for predicting the mechanical and durability properties of cementitious materials.

The microstructure simulation encompassed various levels of FA substitution, denoted as A (10% FA), B (20% FA), C (30% FA), and D (40% FA), all simulated at the age of 180 days with a constant w/c of 0.45. Distinct cement phases are represented by different colors within the images. Specifically, C₃S is depicted in brown, C₂S in blue, C₃A in gray, C₄AF in white, K₂SO₄ in red, gypsum in yellow, free lime in green, free silica in aqua, periclase in pink, and the pore structure in black.

The simulations revealed that elevating the FA replacement level yielded finer and betterconnected pore networks. This phenomenon can be attributed to the pozzolanic reaction of FA, which fosters the creation of supplementary reaction products and the refinement of pore sizes. The intensified pore interconnectivity signifies improved durability, reduced permeability, and heightened resistance against detrimental agents like chlorides and sulfates.

From the simulation results, the porosity of cement blended with FA demonstrates an upward trend with increasing percentages of FA addition, extending up to the age of 180 days, as illustrated in Figure 6. These simulations also probed the interactions between FA particles and the cementitious system. It was observed that FA particles played a role as nucleation spaces for the formation of reaction products, consequently fostering an intensified interfacial transition zone between the FA and the encompassing cement paste. This phenomenon impacted the connectivity of the pore network, adding to the overall reduction in pore sizes and the improvement of mechanical performance. The presence of FA particles also exerted an influence on the distribution of CH crystals, which formed around the FA particles, influencing the overall pore filling and connectivity. These findings underscore the role of FA in modifying the microstructure and mechanical behavior of the cementitious system. Microstructures from a scale of nanometers to micrometers govern the permeability of cement-based materials [14]. That is why microstructural properties are important to exhibit excellent durability properties in concrete. Using sufficiently small voxels, a detailed microstructural property can be obtained with simulation [28]. From the simulation results, as the degree of hydration increases, the outer hydrate layer expands while the volume of small capillary pores in the system decreases.

Fig. 6.

The small capillary pores result from insufficient packaging of hydrates in the layer of outer products, while the large capillary pores are left out of the layer of outer products. The large capillary pores can percolate throughout the entire material; high permeability can be anticipated, or they can be connected through small capillary pores, and low permeability can be anticipated. Further developments in computational models will incorporate some algorithms to simulate the pore structure of blended cement pastes, which will result in more refined microstructures and may improve the accuracy of the pore structure of hydrated phases in blended cements.