Texture Feature Analysis of the Microstructure of Cement-Based Materials During Hydration

Abstract

This study presents a comprehensive grayscale texture analysis framework for investigating the microstructural evolution of cement-based materials during hydration. High-resolution X-ray computed tomography (X-CT) slice images were analyzed across five hydration ages (12 h, 1 d, 3 d, 7 d, and 31 d) using three complementary methods: grayscale histogram statistics, fractal dimension calculation via differential box-counting, and texture feature extraction based on the gray-level co-occurrence matrix (GLCM). The average value of the mean grayscale value of slice (Mean_{G_AVE}) shows a trend of increasing and then decreasing. Average fractal dimension values (D_{B_AVE}) decreased logarithmically from 2.48 (12 h) to 2.41 (31 d), quantifying progressive microstructural homogenization. The trend reflects pore refinement and gel network consolidation. GLCM texture parameters—including energy, entropy, contrast, and correlation—captured the directional statistical patterns and phase transitions during hydration. Energy increased with hydration time, reflecting greater spatial homogeneity and phase continuity, while entropy and contrast declined, signaling reduced structural complexity and interfacial sharpness. A quantitative evaluation of parameter performance based on intra-sample stability, inter-sample discrimination, and signal-to-noise ratio (SNR) revealed energy, entropy, and contrast as the most effective descriptors for tracking hydration-induced microstructural evolution. This work demonstrates a novel, integrative, and segmentation-free methodology for texture quantification, offering robust insights into the microstructural mechanisms of cement hydration. The findings provide a scalable basis for performance prediction, material optimization, and intelligent cementitious design.

1. Introduction

Cementitious materials, as the most widely used manufactured construction materials globally, are essential for critical infrastructure including buildings, bridges, tunnels, and hydraulic projects [1]. Fundamentally, they are multi-phase, multiscale composites comprising cement, water, aggregates, and chemical admixtures [2]. During hydration and hardening, complex reactions form a binder phase dominated by calcium silicate hydrate (C-S-H) gel, accompanied by crystalline phases such as portlandite and ettringite, resulting in a heterogeneous system containing unhydrated particles, pores, and microcracks [3]. The dynamic evolution of this microstructure—including the spatial distribution of hydration products, pore network connectivity, and characteristics of the interfacial transition zone (ITZ)—directly governs macroscopic mechanical properties, durability, and long-term performance [4,5]. Consequently, elucidating spatiotemporal microstructural evolution during hydration and establishing quantitative microstructure–property correlations are fundamental for optimizing material design and enhancing engineering performance—core scientific challenges for achieving high-performance, long-service-life cementitious systems [6].

Researchers employ various characterization techniques to analyze cement hydration mechanisms, including hydration calorimetry for reaction monitoring [7,8], spectral analysis (e.g., X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR)) for phase identification [9], and image analysis for morphology assessment [10,11,12]. Because almost all chemical reactions are accompanied by heat generation, the hydration process of complex systems such as cement-based materials can be quantified by the hydration heat [8]. Reviewing the previous research [13,14] on the hydration heat of cement-based materials, it is confirmed that the TAM Air microcalorimeter is a reliable tool to study the hydration and hydration kinetics of cement-based materials. By tracking the change in the hydration exothermic curve, the overall reaction rate and product yield are indirectly reflected. However, the hydration heat can only reflect the thermal effect accompanying the chemical reaction and cannot represent the state and evolution process of microstructure formation in the hydration process [13]. Spectral analysis techniques (such as XRD and FT-IR) can accurately identify the phases’ chemical composition and crystal structure, but they are not sensitive enough to amorphous C-S-H gel, and it is difficult to capture the heterogeneity of local areas. In contrast, image analysis techniques have become key tools for microstructural studies due to their intuitive and spatially resolved capabilities [15,16]. Two-dimensional imaging techniques (such as scanning electron microscopy (SEM), backscattered electron imaging (BSE), and its spectral coupling (SEM-EDS)) can provide submicron-level morphology, elemental distribution, and phase composition information (such as the morphology of unhydrated particles, pores, and hydration products) [17,18]; three-dimensional imaging techniques (such as X-ray computed tomography (X-CT)) are able to reconstruct the internal structure of the material and to realize the connectivity of the pore network, crack extension, and the non-destructive quantification of the path of crack extension [19]. Although these technologies have their own advantages, traditional image processing—particularly threshold segmentation—has significant limitations [20]. Binarization via grayscale thresholds divides images into “target” and “background” regions, enabling porosity calculations but discarding critical texture details in transition zones (e.g., the surface roughness of hydration products, microcrack edge gradation). Segmentation results are highly sensitive to threshold selection, compromising the data’s comparability and reproducibility [20]. This underscores the need for grayscale-based analysis frameworks that preserve and extract deep image information.

The limitations of threshold segmentation have spurred grayscale-based analytical methods, among which, fractal theory and the gray-level co-occurrence matrix (GLCM) excel at quantifying complex textures [21,22,23]. Fractals characterize irregular, self-similar, scale-invariant objects or phenomena, with the fractal dimension (D_B) quantifying the complexity [24]. Zhou et al. [25] combined SEM with differential box-counting to calculate the D_B of hydration products, demonstrating its correlation with methylene blue (MB) value effects on hydration and compressive strength. Lü et al. [26] noted that D_B from SEM images reflects both the surface structure and compositional distribution, though BSE imaging reduces overestimation of surface irregularity. Furthermore, GLCM analyzes the spatial relationship between pixel intensities, effectively characterizing the material surface features [27]. Its success in diverse fields extends to cementitious materials. Guo et al. [28,29] quantified internal curing concrete textures via GLCM, revealing strong correlations (R² > 0.9) between compressive strength and features like energy (negative correlation) and contrast/entropy (positive correlation). Guo et al. [30] used Micro-CT-derived GLCM features with deep belief networks for accurate strength prediction. Wang et al. [31] coupled X-CT and GLCM to analyze damage in magnesium oxychloride cement concrete, while Zhu et al. [32] correlated GLCM bandwidth changes with microstructural damage progression. Collectively, these methods form a segmentation-free “texture feature analysis system” converting geometric morphology, spatial correlations, and statistical distributions into quantifiable indices, providing multidimensional insights into microstructural evolution.

This study investigates microstructural evolution during cement hydration by innovatively integrating three texture analysis methods: grayscale histogram statistics, fractal dimension calculation, and GLCM feature extraction. First, high-resolution grayscale im-ages were acquired via X-CT at different hydration ages. Second, histogram statistics characterized the phase distribution concentration and dispersion. Third, fractal dimension (D_B) was computed directly from grayscale images using differential box-counting to quantify overall microstructural roughness. Finally, GLCM parameters (energy, entropy, correlation, contrast) quantified directional dependencies and spatial correlations at 0°, 45°, 90°, and 135°. Through this multiscale, multi-parameter approach, we establish a dynamic atlas of microstructural texture evolution during hydration, providing theoretical support for intelligent design and performance optimization of cement-based materials.

2. Materials and Methods

2.1. Data Sources and Processing

All X-ray computed tomography (X-CT) slice images used in this study were from published datasets provided by J Fernandez-Sanchez et al. [33]. A detailed description of the dataset is contained in the literature [34]. The sample analyzed was PC-525, prepared using CEM I 52.5 R commercial Portland cement (Spain). For sample preparation, 8 g of cement was mixed with twice-boiled distilled water (4.00 g), maintaining a water-to-binder ratio of 0.5.

The paste was injected into glass capillaries (outer diameter: 2.0 mm, wall thickness: 0.01 mm). Capillaries were mounted in a custom-designed holder enabling repeated scanning of identical volumes (field of view: 2.2 × 1.5 mm, horizontal × vertical). A Bruker SKYSCAN 2214 CT system acquired datasets at hydration ages of 12 h, 1 d, 3 d, 7 d, and 31 d (Figure 1).

This dataset contains high-resolution 2D cross-sectional grayscale images that represent the internal microstructure of cement-based materials at different hydration stages, ensuring excellent spatial resolution and consistent imaging parameters across the hydration timeline.

2.2. Texture Analysis Based on X-CT Slice Images

Prior to analysis, the original X-CT images were cropped. Within the XY-plane (slices), a square region spanning Rows 388–1412 and Columns 388–1412 was selected. Along the z-direction, slices 150–449 were used. The cropped grayscale images underwent statistical histogram evaluation, fractal analysis, and GLCM-based texture analysis (as shown in Figure 2). Detailed texture data for all slices at various curing ages are summarized in Tables S1–S6.

2.2.1. Statistical Analysis of Grayscale Histograms

Grayscale histograms of X-CT images were analyzed first. Each histogram represents the frequency distribution of pixel intensities (0–255), reflecting the relative proportions of phases (pores, hydration products, unhydrated cement). Evolution of histogram shape across hydration ages enables qualitative assessment of phase content changes and material densification [35,36]. Typically, increasing skewness toward higher grayscale values indicates greater hydration product formation and reduced porosity (as shown in Figure 3).

2.2.2. Calculation of Fractal Dimension

Fractal theory provides a mathematical framework for characterizing irregular, self-similar, and scale-invariant structures prevalent in natural systems. The fractal dimension (D_B) serves as a quantitative descriptor of geometric complexity, enabling the analysis of intricate microstructural patterns that resist simple Euclidean characterization [37,38]. While the spatial distribution of cement microstructures can be qualitatively observed in X-CT images, traditional methods lack the capacity for rigorous quantitative assessment. Fractal analysis addresses this limitation by establishing that cementitious microstructures obey fractal scaling laws, allowing D_B to quantify spatial complexity and surface roughness.

Various computational approaches exist for D_B estimation, including box-counting, Hausdorff dimension, similarity dimension, Brownian motion algorithms, and differential box-counting (DBC) [39,40]. Among these, the DBC method was selected for this study due to its superior accuracy, computational efficiency, and dynamic applicability—attributes that are essential for characterizing evolving hydration textures.

Grayscale images represent three-dimensional surfaces (x, y, z), where (x, y) denote spatial coordinates and z corresponds to pixel intensity. This intensity surface encapsulates textural information, with D_B quantifying its topological complexity: higher D_B values indicate greater surface irregularity and structural intricacy, while lower values reflect smoother, more homogeneous morphologies. Critically, D_B integrates spatial and intensity information, providing a holistic measure of microstructural complexity.

Conventional D_B computation relies on image binarization, which discards critical grayscale information by reducing continuous intensity gradients to binary states. This simplification fails to capture nuanced features of hydration products, pores, and microcracks, compromising analytical accuracy. To overcome this limitation, we implemented a direct grayscale DBC algorithm. The methodology proceeds as follows.

For an M × M grayscale image treated as a 3D surface:

(1)

Partition the (x, y) plane into grids of size L × L;

(2)

Define the scale ratio r = L/M;

(3)

Each grid column corresponds to a stack of boxes with a height h, where h satisfies G/h = M/L (G = total grayscale levels);

(4)

Within grid (i, j), let l and k represent the maximum and minimum grayscale levels. The number of boxes spanning the intensity range is

$$n_r\left(i,j\right)=l-k+1$$

(1)

(5)

The total number of boxes needed to cover the whole image is

$$N_r={\sum }_{i,j}{n}_r\left(i,j\right)$$

(2)

(6)

The fractal dimension D_B is derived from the limit

$$D_B=lim {\displaystyle \frac{\mathit{log}{N}_r}{\mathit{log}\left(1/r\right)}}$$

(3)

For multiple L values, logN_r and log(1/r) are computed. D_B is obtained as the slope of the linear regression of logN_r versus log(1/r) in a log–log plot, as shown in Figure 4.

2.2.3. Gray-Level Co-Occurrence Matrix (GLCM)

The concept of the gray-level co-occurrence matrix (GLCM) was introduced by Haralick [41]. This matrix represents the probability that two pixels with specific grayscale values occur simultaneously at a given distance and direction in an image. It characterizes image texture by describing the relative positional relationships between pairs of pixels [42]. Since the distribution of cement particles and internal structural features can be reflected by the texture features of cement microstructure images, texture features can indirectly describe the intrinsic patterns of microstructural phases during cement hydration [30,43]. The GLCM captures two characteristics of cement hydration Micro-CT images: phase composition and distribution. The grayscale distribution of the image expresses its texture. It describes the spatial distribution characteristics and correlations of different phases in cement hydration Micro-CT images, representing comprehensive information about the direction, spacing, and amplitude of variation between hydration products and unhydrated materials [30,43]. This information can be used to analyze the local features and texture arrangement rules of microscopic phase particles in the image.

For an M × N image, the GLCM element P(i, j, d, θ) corresponds to the relative occurrence frequency of pixel pairs with grayscale values i and j separated by a spatial displacement (dx, dy) at a given distance d and angle θ. Specifically, i is located at coordinates (x, y), and j is located at coordinates (x + dx, y + dy). The formula is defined as

$$P\left(i,j,d,\theta \right)=\#\left\{\left[\left(x_i,y_i\right),\left(x_j,y_j\right)\right]|f\left(x_i,y_i\right)=i,f\left(x_j,y_j\right)=j,d,\theta \right\}$$

(4)

where i, j denotes the number of elements in the set. In two-dimensional SEM images, with a distance d, and angles θ chosen as 0°, 45°, 90°, and 135°, GLCMs in different directions can be obtained. The selection of angles is illustrated in Figure 5.

Fourteen Haralick features can be derived from GLCMs [41]; this study focuses on four that are most relevant to cement hydration.

Energy (ENG): Measures textural uniformity and phase homogeneity. Higher values indicate ordered microstructures with evenly distributed phases.

$$ENG={\sum }_{i=0}^{L-1}{\sum }_{j=0}^{L-1}{\left\{P\left(i,j\right)\right\}}^2$$

(5)

Entropy (ENT): Quantifies disorder and complexity. Higher values reflect heterogeneous microstructures with diverse phase boundaries.

$$ENT=-{\sum }_{i=0}^{L-1}{\sum }_{j=0}^{L-1}P\left(i,j\right)\times \mathit{log}P\left(i, j\right)$$

(6)

Correlation (COR): Measures linear grayscale dependencies in specific directions. Higher values suggest anisotropic alignment of hydration products.

$$\left\{\begin{array}{c}COR=-{\sum }_{i=0}^{L-1}{\sum }_{j=0}^{L-1}{\displaystyle \frac{\left(i\times j\right)P\left(i,j\right)-{\mu }_x\times {\mu }_y}{{\sigma }_x\times {\sigma }_y}}\\ {\mu }_x={\sum }_{i=0}^{L-1}i{\sum }_{j=0}^{L-1}P(i,j)\\ \begin{array}{c}{\mu }_y={\sum }_{i=0}^{L-1}j{\sum }_{j=0}^{L-1}P(i,j)\\ {\sigma }_x^2={\sum }_{i=0}^{L-1}{\left(i-{\mu }_x\right)}^2{\sum }_{j=0}^{L-1}P(i,j)\\ {\sigma }_y^2={\sum }_{i=0}^{L-1}{\left(j-{\mu }_y\right)}^2{\sum }_{j=0}^{L-1}P(i,j)\end{array}\end{array}\right.$$

(7)

Contrast (CON): Sensitive to local intensity variations and edge sharpness. Higher values indicate pronounced phase boundaries (e.g., sharp pore–solid interfaces).

$$CON={\sum }_{n=0}^{L-1}{n}^2{\sum }_{i=1}^L{\sum }_{j=1}^{L}P\left(i,j\right),\left|i-j\right|=n$$

(8)

GLCM feature parameters were extracted from X-CT images using a self-compiled program. During extraction, the grayscale levels of the X-CT images ranged from 0 to 255, the distance d in the GLCM was set to 1, and the angles θ were 0°, 45°, 90°, and 135°, resulting in GLCMs in four different directions, as shown in Figure 6. The elements in the GLCMs of the four directions were normalized to obtain the final GLCMs

$$P(i,j)={\displaystyle \frac{P\left(i,j\right)-P_{max}}{P_{max}-P_{min}}}$$

(9)

where P(i, j) is an element in the GLCM, P_max is the maximum value of the elements in the matrix, and P_min is the minimum value. The GLCM feature parameters were extracted from the normalized GLCM, and the average values and standard deviations of the different feature values in the four directions were recorded.

3. Results

3.1. Statistical Analysis of Grayscale Histograms

The microstructural evolution during cement hydration manifests as progressive pore filling and densification of the gel network, quantifiable through grayscale variations in X-CT images. The mean grayscale value (Mean_G) serves as a statistical indicator of overall image brightness, effectively tracking density’s evolution throughout hydration.

Figure 7a–e show frequency histograms of the mean grayscale values of the 300 slices fitted with normal distribution functions at each hydration age (12 h, 1 d, 3 d, 7 d, 31 d). Figure 7f shows the temporal variation of Mean _G across all slices, while Figure 8 plots the evolution of the average of the Mean_G values of the samples at each age (Mean_{G_AVE}). The unimodal, symmetric normal distributions at all ages indicate statistical consistency in structural grayscale characteristics across slices within each hydration stage. However, the observed slice-to-slice variation in Mean_G (maximum range ≈ 1.5) demonstrates inherent microstructural heterogeneity, reflecting localized variations in phase distribution (e.g., clusters of unhydrated particles or pores).

As shown in Figure 8, Mean_{G_AVE} exhibited significant progression. It increased continuously from 78.68 (12 h) to 79.35 (7 d), indicating progressive hydration product accumulation, porosity reduction, and structural densification. This corresponds to rapid C-S-H gel formation during primary hydration, which increases X-ray attenuation and elevates grayscale intensity. Notably, from 7 d to 31 d, Mean_{G_AVE} decreased slightly (79.35~78.95), deviating from conventional expectations of a monotonic increase in grayscale. This anomaly may be attributed to redistribution of microcracks and micropores during microstructural maturation, slightly increasing the proportion of low-intensity regions.

3.2. Fractal Dimension

Fractal dimension (D_B), computed via differential box-counting of grayscale surfaces, quantifies geometric complexity and surface roughness in hydrating cement paste. This metric captures the hierarchical, self-similar characteristics of evolving microstructures during pore filling and gel network development.

Figure 9a–e display the statistical distributions of D_B for 300 slices per hydration age. Figure 9f shows the slice-wise D_B values, while Figure 10 presents the temporal evolution of average fractal dimension (D_{B_AVE}).

Figure 9a–e present the frequency distributions of D_B values for 300 slices at each hydration age (12 h, 1 d, 3 d, 7 d, and 31 d), all of which adhere to unimodal normal distributions. At 12 h of hydration, D_B values ranged from 2.45 to 2.52, with a mean (D_{B_AVE}) of 2.48, reflecting the highest geometric complexity observed. This elevated complexity arises from the initial formation of disordered fine-scale hydration products (e.g., nascent C-S-H gels) and interconnected capillary pores, which collectively generate intricate surface textures and high spatial heterogeneity. As hydration progressed to 1 d, D_B decreased to a range of 2.42~2.48 (D_{B_AVE} = 2.45), indicating the onset of microstructural consolidation. By 3 d, D_B values further declined to 2.39~2.46 (D_{B_AVE} = 2.43), demonstrating a continued reduction in surface roughness. At 7 and 31 d, D_B stabilized within lower ranges of 2.39~2.44 (D_{B_AVE} = 2.41) and 2.38~2.44 (D_{B_AVE} = 2.41), respectively.

The gradual decrease in D_{B_AVE} is consistent with the logarithmic decay model (y = −0.016 ln(x) + 2.4561, R = 0.7953), as shown in Figure 10. The continuous decrease in the fractal dimension indicates a decrease in microstructural complexity and surface irregularity over time. Physically, this trend may be closely related to (i) the coalescence of C-S-H gels into denser, more continuous phases; (ii) refinement and isolation of pores, reducing interfacial tortuosity; and (iii) gradual smoothing of microcrack networks as hydration approaches completion. The stabilization of D_{B_AVE} values beyond 7 d of age suggests that the microstructure reaches a state of near equilibrium in which further hydration minimally alters the topological roughness. These findings quantitatively demonstrate that hydration drives homogenization and geometric simplification of the microstructure.

3.3. GLCM Characteristic Parameters

Gray-level co-occurrence matrix (GLCM) analysis provides a statistical framework for quantifying the spatial distribution and directional dependencies of grayscale patterns within X-CT images. Four key GLCM parameters—energy (ENG), entropy (ENT), contrast (CON), and correlation (COR)—were extracted to characterize the evolving microtexture of cement-based materials during hydration. The directional GLCMs were computed at angles of 0°, 45°, 90°, and 135° with a pixel distance d = 1, and theresults were averaged across all directions to ensure rotational invariance.

Figure 11, Figure 12, Figure 13 and Figure 14 present the frequency distributions of each GLCM parameter across 300 slices per hydration age. The evolution of parameter averages (denoted as Parameter~_AVE~) is summarized in Figure 15.

Energy quantifies the homogeneity of grayscale distribution, with higher values indicating greater phase uniformity and spatial regularity. As depicted in Figure 11a–e, the energy values for all hydration ages follow a unimodal normal distribution, confirming the statistical consistency of the microstructural texture within each age group. At 12 h, energy values are concentrated around 0.0007, reflecting the initial heterogeneous microstructure, dominated by sharp transitions between unhydrated cement particles and surrounding pores. By 1 d, the energy distribution shifts significantly upward to approximately 0.00095, indicating the onset of hydration product formation and pore filling. This trend continues at 3 d, with energy values reaching 0.0012, demonstrating progressive microstructural homogenization. Beyond 3 d, the increase in energy slows, and by 31 d, a slight decline is observed, suggesting stabilization of the microstructure with minimal further morphological changes.

The temporal evolution of the average energy (Energy_{_AVE}) is well-described by the logarithmic model y = 0.0002 ln(x) + 0.0009 (R² = 0.792), as shown in Figure 15a. The initial surge in energy (∼87% increase from 0.5 to 7 d) corresponds to the rapid formation of C-S-H gel and capillary pore filling, which smooths grayscale transitions and reduces local intensity fluctuations. The plateau and slight decline after 7 d imply that the microstructure approaches a near-steady state, where further hydration primarily involves densification of existing phases rather than significant structural reorganization.

Entropy measures the complexity and randomness of texture patterns, with higher values denoting greater disorder. Figure 12a–e reveal that entropy values for all ages also adhere to a unimodal normal distribution, but their trend opposes that of energy. At 12 h, entropy peaks at ∼11.16, reflecting a highly disordered microstructure with large connected pore networks, sharp gel–pore interfaces, and incomplete hydration. As hydration progresses, entropy declines to ∼10.385 by 7 d (a 7% reduction), signaling the transition to a more ordered solid framework. This reduction is attributed to pore isolation, diminished phase boundaries, and the coalescence of C-S-H gels into continuous networks. After 7 d, entropy stabilizes, with only a marginal decline to 10.38 at 31 d, indicating microstructural equilibrium. The slight rebound in some slices at 31^st day (Figure 12f) may arise from localized self-desiccation microcracks or interfacial reconfiguration, introducing minor heterogeneity. The logarithmic model y = −0.18 ln(x) + 10.849 (R² = 0.7744) captures the entropy decline, as shown in Figure 15b, aligning with the progressive homogenization observed in the energy analysis.

Contrast quantifies local intensity variations and is sensitive to phase boundaries. Figure 13a–e show that contrast values for each age group follow a unimodal normal distribution, but with higher intra-sample variability compared with energy and entropy. This variability underscores the sensitivity of contrast to spatial sampling location, particularly during rapid hydration stages.

The temporal evolution of contrast (Figure 15c) mirrors that of entropy, declining continuously with age. The logarithmic model y = −6.395 ln(x) + 45.151 (R² = 0.7389) describes this trend. From 0.5 to 1 d, contrast plummets by 29.2% (57.56 to 40.73), reflecting the rapid attenuation of phase boundaries as pores are filled and gel layers bridge unhydrated particles. Between 1 and 3 d, contrast further decreases by 19.5%, indicating continued reduction in grayscale discontinuities. Beyond 3 d, the decline becomes more gradual, reaching 29.14 at 7 d and 28.53 at 31 d, suggesting near-saturation of interfacial smoothing. These trends highlight the transition from a multi-phase composite to a more continuous matrix.

Correlation measures the linear dependency of grayscale values in specific directions. Figure 14a–e demonstrate that correlation values for all ages follow a unimodal normal distribution, but with minimal inter-sample variability. Unlike the other parameters, correlation does not exhibit a well-defined monotonic trend (Figure 15d). Instead, it shows a slight initial increase followed by a decrease, broadly aligning with the evolution of mean grayscale values (Mean_G). Correlation remains high (>0.95) across all hydration stages, indicating consistently strong directional grayscale dependencies.

All in all, the evolution of GLCM parameters provides a detailed portrait of microstructural transformations during cement hydration. The initial stage (0.5–1 d) is dominated by the rapid precipitation of hydration products and the disruption of pore networks, leading to sharp changes in ENG, ENT, and CON. In the mid-stage (1–7 d), ongoing gel coarsening and pore refinement continue to drive textural homogenization and reduction in complexity. By the late stage (7–31 d), the microstructure approaches equilibrium, characterized by marginal variations in texture parameters, indicative of slowed hydration kinetics and structural stabilization.

4. Discussion

This study employed a multi-parameter approach to characterize the evolving texture of cement-based microstructures during hydration, utilizing high-resolution X-CT slice images. A total of six quantitative descriptors were extracted from each image: the mean grayscale value (Mean_G), fractal dimension (D_B), and four gray-level co-occurrence matrix (GLCM) parameters (energy, entropy, contrast, correlation). The analysis encompassed five distinct hydration ages (12 h, 1 d, 3 d, 7 d, and 31 d), with each age represented by a sample containing 300 slices. A critical challenge in such large-scale image-based analysis lies in evaluating the reliability and discriminatory power of these parameters for tracking microstructural evolution. An ideal parameter should exhibit (1) low intra-sample variability (high stability) i.e., minimal fluctuation across different slices within the same hydration age sample, indicating robustness to spatial sampling location and reflecting a consistent microstructural state characteristic of that age; and (2) high inter-sample discrimination (high sensitivity), i.e. significant differences in the parameter’s average value between different hydration ages, enabling clear differentiation of the microstructural states associated with the hydration progression. This section rigorously assesses these two aspects for each parameter and introduces a combined metric (signal-to-noise Ratio, SNR) to holistically evaluate their suitability for characterizing cement hydration microtexture.

4.1. Volatility Analysis

The reliability of a parameter for representing a specific hydration age hinges on its stability within the sample at that age. High intra-sample stability ensures that the calculated average value (μ(i) for sample i) is a robust and representative descriptor of the microstructural state at that age, minimizing the uncertainty introduced by slice selection.

To quantify the variability of each parameter within a given sample (i.e., across its 300 slices), we employed the Volatility Index (VIX(i)), defined as

$$\begin{array}{cc}VIX\left(i\right)={\displaystyle \frac{SD\left(i\right)}{\mu \left(i\right)}}\times 100\%& i=1,\dots ,5\end{array}$$

(10)

where SD(i) is the standard deviation of the parameter values across all 300 slices within sample i

$$SD\left(i\right)=\sqrt{{\displaystyle \frac{1}{M}}{\sum }_{j=1}^M{(y_{i,j}-\mu \left(i\right))}^2}$$

(11)

where M is the data volume of a single group of data. In this paper, each group of samples contains 300 slices of data for each parameter, so we take M = 300. Moreover, y_i,j is the parameter value corresponding to the j-th slice of the i-th sample, and μ(i) is the mean value of all the slices of data of the i-th group of samples. The larger the value of VIX, the higher the fluctuation in the parameter value of the group and the more susceptible it is to the influence of the sampling location (different slice locations).

The calculated VIX values for all parameters across all ages are summarized in Figure 16. Contrast exhibited the highest VIX values, indicating the largest intra-sample variability. Notably, its VIX reached 5.76 for the Day 1 sample and consistently exceeded 2.5 for all other ages. This signifies that contrast is highly sensitive to the specific location sampled within the microstructure at a given age. Energy showed the next highest level of variability, with VIX values ranging between 2.30 and 3.00. This suggests that energy is also considerably influenced by the sampling position. D_B, Mean_G, entropy, and correlation demonstrated significantly lower intra-sample variability. Their VIX values were all below 1.0. Correlation displayed the highest stability, with remarkably low VIX values consistently below 0.11 across all ages. This indicates that its value is relatively consistent regardless of the slice location within a sample, making it a stable descriptor within an age group.

The parameters correlation, Mean_G, entropy, and D_B exhibit excellent intra-sample stability, implying that their calculated mean values (μ(i)) reliably represent the microstructural texture for their respective hydration ages. In contrast, contrast and energy show substantial variability within samples, meaning their single-slice values are less representative, and their sample means have higher associated uncertainty.

4.2. Discrimination Analysis

While intra-sample stability ensures reliable characterization within an age, the ability to distinguish between different ages is paramount for tracking evolution. A high level of discrimination means the parameter’s characteristic value shifts significantly as hydration progresses.

To quantify the ability of a parameter to differentiate between the five hydration ages at a given slice position j, we introduced the Discrimination Index (DIX(j))

$$\begin{array}{cc}DIX\left(j\right)={\displaystyle \frac{SD\left(j\right)}{\mu \left(j\right)}}\times 100\%& j=1,\dots ,300\end{array}$$

(12)

where SD(j) is the standard deviation of the parameter values across the five different age samples at the same slice position j

$$SD\left(j\right)=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{(z_{i,j}-\mu \left(j\right))}^2}$$

(13)

where N is the number of samples. In this paper, we mainly used five samples of 0.5 d, 1 d, 3 d, 7 d, and 31 d of age, so the value of N was taken as 5. Also, z_i,j is the parameter value corresponding to the j-th slice of the i-th sample, and μ(j) is the mean value of the parameter of all the samples at the position of the j-th slice. The larger the value of DIX, the larger the parameter difference between different samples, and the better the differentiation of data.

The distribution of DIX values across slice positions for each parameter is presented in Figure 17. Contrast consistently achieved the highest DIX values (up to 39), signifying its exceptional ability to differentiate between hydration ages at any given slice location. Visual inspection of Figure 13f confirms this strong separation among age groups. Energy also demonstrated high discriminatory power, with DIX values ranging between 23 and 28. Its effectiveness in distinguishing ages is evident in Figure 11f. Entropy showed moderate discrimination (DIX values lower than contrast and energy but still substantial). D_B, Mean_G, and correlation exhibited progressively lower discrimination. Their DIX values were significantly smaller than those of the top three parameters. Correlation had the lowest DIX values (between 0.13 and 0.29), indicating minimal change across hydration ages at any fixed slice position. Consequently, its ability to reflect the evolution of microstructure between ages is very limited, as seen in Figure 14f.

The parameters contrast, energy, and entropy possess strong discriminatory power, enabling clear differentiation between the microstructural textures characteristic of different hydration ages. In contrast, D_B, Mean_G, and especially correlation show weak inter-sample discrimination, making them less effective for tracking temporal evolution.

All in all, the preceding analyses reveal a trade-off. Parameters with high inter-sample discrimination (contrast, energy, entropy) tend to exhibit higher intra-sample variability, while parameters with high intra-sample stability (correlation, Mean_G, D_B) often lack strong discriminatory power. An ideal parameter for robustly characterizing hydration evolution should optimally balance both low intra-sample noise (high stability) and high inter-sample signal (strong discrimination).

To integrate these two critical aspects, we propose the signal-to-noise ratio (SNR) metric:

$$\mathrm{S}\mathrm{N}\mathrm{R} = {\displaystyle \frac{{\sum }_{j=1}^{M}DIX\left(j\right)/M}{{\sum }_{i=1}^{N}VIX\left(i\right)/N}}$$

(14)

This metric represents the ratio of the average inter-sample discrimination strength (the “signal” reflecting true hydration-induced change) to the average intra-sample variability (the “noise” obscuring that signal). A higher SNR indicates a parameter that provides a clearer, more reliable signature of microstructural evolution across ages, effectively overcoming the inherent spatial heterogeneity within samples. The calculated SNR values for all six parameters are presented in

Table 1. The SNR of all parameters.

Parameter	SNR
MeanG	0.95
DB	1.85
Energy	9.34
Entropy	8.78
Contrast	8.09
Correlation	2.23

.

Energy, entropy, and contrast emerge as the superior parameters, achieving significantly higher SNR values (9.34, 8.78, and 8.09, respectively). This confirms that despite their inherent intra-sample spatial variability, their sensitivity to changes between hydration ages is exceptionally strong relative to that noise. D_B and correlation show moderate SNR (1.85 and 2.23), indicating a less favorable balance between discrimination and stability. Mean_G exhibits the lowest SNR (0.95), signifying that its inter-age discrimination is barely stronger than the intra-age noise level. The superiority of energy, entropy, and contrast is quantified by their massive improvement in SNR over Mean_G—increases of 883%, 824%, and 752%, respectively.

The SNR metric provides a holistic and quantitative assessment of parameters’ suitability for tracking hydration evolution via texture analysis. It robustly identifies energy, entropy, and contrast as the most effective descriptors. They successfully combine sufficient intra-sample stability (ensuring reliable age-specific averages) with high inter-sample discrimination (enabling clear detection of microstructural evolution across ages), as visually corroborated in Figure 11, Figure 12 and Figure 13. Parameters like correlation and Mean_G, while stable within an age, lack the necessary sensitivity to temporal changes to be primary evolution trackers. The SNR framework thus offers a powerful criterion for selecting optimal image-derived features in complex, heterogeneous materials like hydrating cement paste.

5. Conclusions

This study established a multi-parameter grayscale texture analysis framework to systematically characterize the microstructural evolution of cement-based materials during hydration. By integrating histogram statistics, fractal theory, and gray-level co-occurrence matrix (GLCM) analysis, the research offers a non-destructive, quantitative, and segmentation-independent approach to mapping hydration-induced microstructural transitions. The main conclusions are summarized as follows.

(1)

The average value of mean grayscale value of the slices (Mean_{G_AVE}) increased significantly during the early hydration period (12 h to 7 d), reflecting the accumulation of hydration products and the progressive filling of pores. A slight decline at 31 d indicates microstructural stabilization or potential local porosity redistribution.

(2)

Fractal dimension analysis provides an important insight into the microstructural evolution of cement-based materials during hydration. The evolution trend of the average fractal dimension (D_{B_AVE}) with time shows that the complexity of the microstructure in the process of cement hydration decreases logarithmically (y = −0.016 ln (x) + 2.4561, R² = 0.7953). Due to disordered hydration products, the value of D_{B_AVE} reached the maximum at the early age (12 h), reaching 2.48, and then the interface became smooth with pore refinement and gel coalescence, and gradually decreased to 2.41 (31 d). This shows that hydration drives homogenization of the microstructure instead of increasing roughness.

(3)

The four key GLCM descriptors captured hydration-induced changes in texture. Energy increased logarithmically, indicating enhanced grayscale uniformity and material homogenization. Entropy declined rapidly during early hydration, reflecting reduced grayscale randomness and microstructural disorder. Contrast decreased continuously, suggesting the blurring of phase boundaries and a reduction in interfacial gradients. Correlation remained high and slightly increased, indicating stable and coherent spatial relationships among grayscale values.

(4)

Through the combined analysis of intra-sample volatility, inter-sample discrimination, and signal-to-noise ratio (SNR), energy, entropy, and contrast were identified as the most robust and sensitive indicators for capturing microstructural evolution across hydration ages.

This research proposes a segmentation-free, full-grayscale analysis framework, integrating statistical, geometric, and spatial–textural dimensions to quantify microstructural development during hydration. Unlike conventional binary image methods, this approach retains intricate grayscale information, enhances reliability, and avoids thresholding bias. It provides a powerful, scalable methodology for non-destructive evaluation, performance prediction, and intelligent optimization of cement-based materials.