Automated estimation of cementitious sorptivity via computer vision

Abstract

Monitoring water uptake in cementitious systems is crucial to assess their durability against corrosion, salt attack, and freeze-thaw damage. However, gauging absorption currently relies on labor-intensive and infrequent weight measurements, as outlined in ASTM C1585. To address this issue, we introduce a custom computer vision model trained on 6234 images, consisting of 4000 real and 2234 synthetic, that automatically detects the water level in prismatic samples absorbing water. This model provides accurate and frequent estimations of water penetration values every minute. After training the model on 1440 unique data points, including 15 paste mixtures with varying water-to-cement ratios from 0.4 to 0.8 and curing periods of 1 to 7 days, we can now predict initial and secondary sorptivities in real time with high confidence, achieving R² > 0.9. Finally, we demonstrate its application on mortar and concrete systems, opening a pathway toward low-cost and automated durability assessment of construction materials.

Monitoring water uptake in cementitious materials is important to assess their durability. Here, the authors introduce a low-cost computer vision method to predict initial and secondary sorptivity in real time in paste, mortar, and concrete systems.

Introduction

Global cement production exceeds 4 billion tons annually and is projected to increase until 2050 due to expanding urbanization and population¹. Ongoing aging and degradation of critical concrete infrastructure, such as dams, bridges, tunnels, and highways, highlight the importance of evaluating the durability of cementitious materials. With regard to durability, chloride-induced corrosion, physical salt attack, and freeze-thaw damage pose significant challenges to the reliability and safety of our built environment^2,3. For many durability-related issues, it is the transport properties, including fluid and ionic species penetration, that play a crucial role⁴.

The transport properties of cementitious systems are governed by three primary mechanisms: diffusion, absorption, and permeability, and they are significantly influenced by the connectivity, tortuosity, diameter, and volume fraction of pores^5–7. Absorption refers to the ability of an unsaturated cementitious surface to absorb water, initially fast through pure capillary suction within pore spaces (governed by Darcy’s law and Laplace equation)^8,9, and subsequently slow by either potential dissolution of trapped-air volume (governed by Henry’s law)^10,11 or by liquid diffusion into C-S-H layers^12,13. In the realm of absorption, sorptivity, as formally defined by Hall and Hoff¹⁴, refers to the tendency of a porous material to absorb or transmit liquid through capillary action. The precise mechanism behind the latter slow water uptake, also known as secondary sorptivity, is a matter of ongoing research and debate^11,15,16. Diffusion involves ion movement driven by concentration gradients in cementitious systems, while permeability measures liquid flow across a matrix under hydraulic pressure gradients¹⁴. Several standard test procedures evaluate the transportation properties of cement-based systems, including rapid chloride permeability¹⁷, non-steady-state chloride migration¹⁸, chloride ponding¹⁹, bulk diffusion²⁰, and water absorption²¹.

As detailed in a report from the US Federal Highway Administration (FHWA), the standard method for measuring water absorption in concrete in the US is the ASTM C1585^22,23. This test procedure determines the rate at which unsaturated concrete systems absorb water, a parameter that is closely associated with hydraulic diffusivity^24,25. The sorptivity represents a meticulously defined transport property inherent in diverse inorganic porous construction materials with inert (e.g., stone, ceramic, or brick) or chemically active (hydrated cement) matrices^9,14,24. Hence, determining the sorptivity in cementitious materials is crucial for predicting their long-term durability²⁶. However, despite its wide relevance, the ASTM C1585 sorptivity test is labor-intensive, requiring multiple, infrequent rounds of manual weighing over 24 hours to a few days.

In order to automate this labor-intensive test, researchers have proposed automated weight measurement while conducting the sorptivity test²⁷; however, the proposed methods may be impractical and yield inaccurate results in daily use due to errors in sample submersion, buoyancy, and surface tension effects. Predicting and visualizing liquid penetration by more advanced techniques such as Proton Nuclear Magnetic Resonance (¹H-NMR) Relaxometry²⁸, low-field Nuclear Magnetic Resonance (NMR)²⁹, Positron Emission Tomography (PET)³⁰, X-ray Computed Tomography (CT)^31–33, X-ray Radiography^34–36, X-ray Transmission/Attenuation³⁷, Neutron Radiography^38–40, and Neutron Imaging^41,42 have been demonstrated in the past decade, and has played a significant role in improving our fundamental understanding of water uptake. However, while these techniques are robust, they often come with a high capital cost. Hence, there is room to develop methods and techniques that can measure or predict water uptake in a low-cost and automated manner.

Nowadays, machine learning and computer vision models can automate model development based on user inputs, minimizing human intervention^43–46. Here, we introduce an automated and low-cost (<$200) device to address the issue of measuring the sorptivity of cement-based systems in the lab. Specifically, we introduce a computer vision model that can effectively detect water levels in real-time in prismatic samples that are absorbing water. To develop an efficient computer vision-based water detection, we substituted the computationally intensive Fully Convolutional Networks (FCNs) and Region Proposal Networks (RPNs) in the Mask R-CNN architecture with Feature Pyramid Networks (FPN). Our computer vision model is trained on 6234 images (4000 real + 2234 synthetic) and was tested on a set of separate 500 images. By training this water level detection model on 1440 (wetted area ratios and absorption times) experimental data points, we are able to accurately predict the penetration values and, subsequently, the relevant sorptivity of various systems, ranging from paste to mortar to concrete. Specifically, linear regression on penetration-time graphs allowed precise ‘indirect’ prediction of initial (R² = 0.99 for pastes, 0.96 for mortars, and 0.87 for concretes) and secondary (R² = 0.97 for pastes, 0.74 for mortars, and 0.65 for concretes) sorptivities.

Results and discussion

Detecting water levels in cementitious systems via computer vision

In the expansive field of computer vision, various models have been instrumental in revolutionizing sectors ranging from autonomous driving⁴⁷ and agricultural automation⁴⁸ to medical imaging⁴⁹ and infrastructure monitoring⁵⁰. The introduction of Convolutional Neural Networks (CNNs) and deep learning since the 2010s has significantly accelerated computer vision advancements, enabling more precise and efficient analysis across various applications⁵¹. Leveraging this technological momentum, we present a refined custom computer vision model tailored to detect water levels in cementitious samples during water uptake. Figure 1a illustrates the traditional ASTM C1585 test for sorptivity analysis, where the mass changes of the specimens are manually monitored using a weighing scale, attributing these changes to water absorption. This process spans hours to days, with only one surface of the specimen exposed to water, positioned above a water container with spacers beneath each sample. Subsequently, the absorbed water is quantified to derive the parameter i (penetration), which indicates the cumulative volume of fluid intake normalized by the area of absorption, see Fig. 1b. Then, the initial S_i and secondary S_s sorptivity values, as well as Nick times (when S_i and S_s lines intersect), are determined as the slopes derived from the fitted curves applied to the ‘infrequent’ penetration points, plotted against the square root of time.

Fig. 1. General outlines (existing and proposed) for measuring sorptivity.

a ASTM C1585 outlines a water absorption test on specimens in which mass changes can be monitored when a single surface is exposed to water. The 3D schematic was digitally hand-drawn in Procreate software. b Normalizing absorbed water yields i (penetration), indicating cumulative fluid intake. S_i (slope of the red line) and S_s (slope of the green line) values are derived from fitted curves at ‘infrequent’ penetration points against the square root of time. c In our proposed setup, the same specimen can be positioned at a fixed distance from two orthogonally aligned USB microscope cameras, capturing natural imagery data. The 3D model was created in Blender software. d By utilizing computer vision algorithms (Mask R-CNN or FPN), we can predict the average water level (wetted area) of two sides, shown as white pixels. e Using the water level and time values, our machine learning model can then continuously and frequently predict the penetrations (mm) or sorptivities (mm/√min). f It should be noted that sorptivity values can be ‘directly’ estimated (orange and blue points, by DM method) by our machine learning model based on time and wetted area ratio. Alternatively, these values can be ‘indirectly’ (green and red points, by IM method) predicted by fitting linear lines to the ‘highly frequent’ penetration-time data points estimated by our machine learning model.

Figure 1c shows our proposed automated method, positioning a specimen consistently between two orthogonally aligned USB microscope cameras. When a dry sample comes into contact with water, it transforms its optical properties⁵². The presence of water in capillary pores decreases the refractive index contrast between the pores and the solid material, reducing light scattering. This allows deeper penetration of light into the material, increasing the path length of scattered light, which enhances optical absorption and darkens the wetted regions. Thus, we propose quantifying the changes in the color of the outer surface of the specimen via USB microscope cameras during its interaction with water, see Fig. 1d.

Using computer vision algorithms, we can discern the average water level by analyzing the predicted white pixels in both captured images of each sample. Then, our machine learning model utilizes time (recorded from the initiation of solid-liquid interaction) and the wetted area ratio (i.e., the ratio of the wetted/darker area to the total sample area visible to the camera) to predict the penetration (mm) and subsequent sorptivity (mm/√min) of paste specimens over time, see Fig. 1d. It should be noted that sorptivity values can be ‘directly’ estimated (Direct Method, DM) via our machine learning model based on the time and wetted area ratio. Alternatively, these values can be predicted ‘indirectly’ (Indirect Method, IM) by fitting linear lines to highly frequent (every minute) penetration-time data points, again via our machine learning model. However, before predicting the sorptivity of cement-based systems, it is crucial to fine-tune our computer vision models to accurately mark the regions of interest (ROIs), i.e., wetted regions.

For this purpose, we used an intersection over union (or degree of matching DoM) parameter that normalizes the overlap between the predicted and ground-truth segmented masks⁵³. A DoM of ~ 1 denotes a perfect match between the estimated and ground truth masks, while a DoM of ~ 0 suggests a poor prediction, see Supplementary Fig. 1a. In Mask R-CNN (Supplementary Fig. 1a: left subplot), DoM rises from 0.39 to 0.77, with synthetic training images increasing from 50 to 2234, while the real dataset is absent. In contrast, FPN (Supplementary Fig. 1a: right subplot) shows minimal DoM change upon varying synthetic images. Supplementary Fig. 1b highlights the impact of training dataset size on model performance. The addition of synthetic data significantly improves the accuracy of the Mask R-CNN model for a small number of real datasets but has minimal effect on FPN estimations, as FPN focuses on object detection without a dedicated instance segmentation component. Supplementary Movie 1 shows extracting water level probability masks via the FPN model.

As shown in Supplementary Fig. 1b, a few hundred real training images reliably train FPN and Mask R-CNN models, irrespective of synthetic dataset size. The required number of training images depends on factors like dataset complexity. Simple, low-Kolmogorov complexity images may need a smaller set, while complex images require a larger, diverse set^54,55. In our study, the USB microscope cameras focused on ROIs with simple, small, and uniform backgrounds, exhibiting low complexity. Therefore, based on Supplementary Note 1 and Supplementary Figs. 2–9 and Supplementary Movie 2, a few hundred images are sufficient to adequately train both computer vision models for object detection. Finally, our FPN model (with 9 million operations) is nearly four times less computationally expensive than the Mask R-CNN model (with 44 million operations) and can deliver accurate object detections with a substantially smaller number of training datasets. Supplementary Movie 3 illustrates how we utilized the FPN-based water level detection model due to its optimized focus on image segmentation and faster training efficiency. Hence, in the course of the research, we consistently employed the FPN model for its superior computational efficiency, ensuring accurate water level detection.

Sorptivity prediction of pastes from water level and absorption time

After fine-tuning our computer vision model for detecting water levels, we analyzed a diverse set of cementitious systems of varying w/c ratios and curing periods. Thus, we establish definitions for several key physical quantities used to analyze water absorption dynamics in cementitious materials. The capillary transport of moisture in unsaturated porous materials such as paste, mortar, or concrete is a diffusion process. The dynamics of this process in one dimension are defined by Richard’s equation in the Klute form⁵⁶, presented in Eqs. 1 and 2¹⁴:

$$\frac{\partial \mathrm{\theta }}{\partial \mathrm{t}}=\nabla .\left(\mathrm{D}.\nabla \mathrm{\theta }\right)$$ 1

$$\mathrm{D}\approx {\mathrm{D}}_0\cdot {\mathrm{e}}^{\left({\mathrm{B}}_{\mathrm{r}}{\mathrm{\theta }}_{\mathrm{r}}\right)}$$ 2

For a typical capillary absorption test, the simplified one-dimension equation is subject to the following initial and boundary conditions:

$$\begin{array}{cc}\hfill \mathrm{initial}\mathrm{condition}:\hfill & \hfill \begin{array}{cc}\hfill \mathrm{\theta }\left(\mathrm{x},0\right)=0\hfill & \hfill \forall \mathrm{x}>0\hfill \end{array}\hfill \\ \hfill \mathrm{lower}\mathrm{boundary}\mathrm{condition}:\hfill & \hfill \begin{array}{cc}\hfill \mathrm{\theta }\left(0,\mathrm{t}\right)=1\hfill & \hfill \forall \mathrm{t}>0\hfill \end{array}\hfill \\ \hfill \mathrm{upper}\mathrm{boundary}\mathrm{condition}:\hfill & \hfill \begin{array}{cc}\hfill {\frac{\partial \mathrm{\theta }}{\partial \mathrm{X}}}_{\mathrm{x}=\mathrm{L}}=0\hfill & \hfill \forall \mathrm{t}>0\hfill \end{array}\hfill \end{array}$$

where,

θ = saturation at (x,t)

D = diffusion coefficient at relative saturation θ_r

D_o = unsaturated diffusion coefficient

θ_r= relative saturation at (x,t) = θ / θ_max

B_r = a constant

θ_max = maximum saturation.

From the empirically established Eq. 2, the process shows extreme nonlinearity due to the exponential dependence of the diffusion coefficient on saturation. This results in numerical solutions that depict the saturation profile with a sharp (almost vertical) drop along the moisture front, described as the Sharp Front Model (SFM). After applying the Boltzmann Transformation, Eq. 1 becomes Eq. 3, converting the partial differential equation (PDE) into an ordinary differential equation (ODE), which is widely used to determine capillary diffusion coefficients experimentally:

$$-\frac{\mathrm{\phi }}{2}\frac{\mathrm{d}\mathrm{\theta }}{\mathrm{d}\mathrm{\phi }}=\frac{\mathrm{d}}{\mathrm{d}\mathrm{\phi }}\left(\mathrm{D}\frac{\mathrm{d}\mathrm{\theta }}{\mathrm{d}\mathrm{\phi }}\right)$$ 3

where,

the transformation variable is φ(θ) = x(θ,t) t ^−1/2, thus:

$$\mathrm{x}\left(\mathrm{\theta },\mathrm{t}\right)=\mathrm{\phi }\left(\mathrm{\theta }\right){\mathrm{t}}^{1/2}$$ 4

Integration of Eq. 4 from θ_d (saturation at fully dry) to θ_max (maximum saturation which can be considered equal to the open porosity), the total amount of water absorbed at any time, called penetration i, is derived as:

$$\mathrm{i}={\int }_{{\mathrm{\theta }}_{\mathrm{d}}}^{{\mathrm{\theta }}_{\max }}\mathrm{x}\mathrm{d}\mathrm{\theta }={\mathrm{t}}^{\frac{1}{2}}{\int }_{{\mathrm{\theta }}_{\mathrm{d}}}^{{\mathrm{\theta }}_{\max }}\mathrm{\phi }\left(\mathrm{\theta }\right)\mathrm{d}\mathrm{\theta }=\mathrm{S}.{\mathrm{t}}^{\frac{1}{2}}$$ 5

From Eq. 5, we derive sorptivity S as the slope of the curve relating penetration i — defined as absorbed water volume normalized by the absorbing area — to the square root of time⁵⁷. Simplifying the water absorption profile as a sharp front, the visible wetted region can be assumed to have uniform saturation, approximately equal to the total open porosity. This assumption links the visible waterfront length x (captured by our USB camera) to the penetration i, with i ≈ f ⋅ x, where f is the open porosity. While x and i are mathematically related through f, in this study, x is represented by the wetted area ratio detected by our FPN computer vision model.

Thus, we discuss how sorptivity can be continuously and reliably estimated utilizing our setup. Figure 2a (Supplementary Fig. 10 and Supplementary Data 1.xlsx) summarizes the penetration of paste cubes made with w/c ratios of 0.4–0.8 and curing periods of 1–7 days. Based on Supplementary Figs. 11,12, it is observed that the sorptivity values of different mixtures vary significantly as a function of w/c ratio and curing age. The secondary sorption rate exhibits a slower progression in contrast to the initial sorption rate⁵⁸. Secondary sorptivity likely arises from the gradual liberation of entrapped air (with a pressure higher than atmospheric air) within the material during the primary imbibition process. This entrapped air slowly dissolves and diffuses through the water-filled pores, ultimately reaching the specimen’s external unsealed (including inflow) surfaces. This air diffusion is driven by the pressure difference between the trapped air and the surrounding atmosphere, resulting in a system that is initially at mechanical equilibrium but not at mass-transfer equilibrium. Governed by the material’s porosity, tortuosity, and the solubility of air in water, the concentration difference of dissolved air leads to a diffusive flow toward the specimen’s unsealed surfaces. As the trapped air gradually escapes, it is replaced by water drawn into the pores, thereby extending the duration of the secondary sorptivity phase^11,14.

Fig. 2. Extracting the sorptivity of paste specimens using machine learning.

a Predicting paste sorptivity via ASTM C1585 shows consistent and repeatable water penetration dynamics across systems. The error bar represents the standard deviation of six replicates. b Initial and secondary sorptivity values in paste specimens are inversely correlated. c A heatmap scatter plot illustrates the relationship between wetted area ratio, time, and mass change. d Three random paste specimens highlight that porous matrices with larger wetted areas at shorter durations show higher mass change, while denser matrices with smaller wetted areas over longer durations exhibit lower mass change. In this subplot, ‘pre’ and ‘post’ refer to original and FPN-analyzed images, respectively. e The machine learning model accurately predicts penetration patterns for the training dataset (R² = 0.97). f The model also shows strong performance on the testing dataset, matching predicted and measured penetration values (R² = 0.93). g Indirectly estimating sorptivity from predicted penetration-versus-time data yields high accuracy (R² > 0.97), while (h) direct estimation using only wetted area and time data results in lower accuracy (for Both S_i= blue points and S_S = red points), particularly for secondary sorptivities (R² = 0.83). Source data are provided as a Source Data file.

Figure 2a also confirms a strong linear relationship between penetration i and the square root of time, called the t^0.5 law. This is attributed to factors such as one-dimensional liquid movement, homogeneity in cementitious systems, unchanged matrix structure during the short testing period (~ 24 h), uniform drying of specimens before liquid absorption, consistent initial water content, maintained cross-sectional area, and negligible gravitational forces compared to capillary forces in fine-pored materials during the capillary rise^{10,14,59–61}. The ability of different paste systems to absorb and retain moisture was repeatably quantified. Figure 2b suggests an inverse correlation between initial and secondary sorptivity values. Possible explanations include the influence of a parameter other than porosity, such as increased C-S-H content, leading to the diffusion of water molecules into the C-S-H sheets^16,31. Another hypothesis is that reducing curing time or increasing w/c ratios decreases entrapped air pressure, thereby increasing the slope of secondary sorption. Further, the correlation between mass change and penetration shows a steady absorption rate, but linearity decreases in matrices with higher porosities, see Supplementary Notes 2, 3, and Supplementary Figs. 13–17.

Figure 2c displays a heatmap scatter plot illustrating the correlation among wetted area ratio, time, and mass change. For porous matrices with higher wetted areas at shorter times, mass change is notably elevated, while denser matrices with lower wetted areas at larger times show comparatively lower mass change. Figure 2d illustrates mass changes in three randomly selected samples, with the top-row specimen suggesting low porosity (3.5% predicted mass change) and the bottom-row sample indicating higher porosity (23.2% total absorbed water content). Coupling ‘water level’ (wetted area ratio) and ‘absorption time’ (square root of liquid absorption duration) as the pivotal parameters, our machine learning model adeptly analyzes patterns and establishes relationships within the training data. This approach enables the model to provide accurate estimations of penetration values in pastes, achieving a commendable R² of 96% and 93%, shown in Fig. 2e and f, respectively. Notably, slight deviations from the linear regression line are observed at higher penetration values (> 2 mm), reflecting matrices with greater absorption capacities. The discrepancy between the neural network predictions and experimental results at higher penetration levels arises from the network’s inability to capture the complex nonlinearities of fluid flow in highly porous cement pastes. These nonlinearities arise from capillary action, pore connectivity, and material heterogeneity, creating unpredictable fluid pathways, though the carbonation is unlikely a factor, see Supplementary Note 4 and Supplementary Fig. 18.

In addition, our findings confirm that estimating sorptivity values from the predicted penetration-versus-time data allows for highly accurate determination of both initial and secondary sorptivity values (R² > 0.97). This approach is referred to as the ‘indirect’ prediction of sorptivities, where the relationship between water level and time results in a penetration-versus-time graph, and the S_i and secondary S_s sorptivities are estimated subsequently, see Fig. 2g. Nevertheless, if we attempt to ‘directly’ estimate sorptivity values using only water level and time data, i.e., in the absence of penetration values, the accuracy tends to be lower (R² = 0.83, especially for secondary sorptivities), as many data points (of different mixtures) may correspond to similar secondary sorptivity values, see Fig. 2h.

Following the validation of our computer vision model, we estimated the penetration (and subsequently sorptivity) values of paste cubes. For this purpose, we chose images of cement paste samples placed inside a glass vial, exhibiting either specular reflection (captured in a dark room with LEDs on) or diffuse reflection (captured under normal room lighting conditions with LEDs off) to investigate if a single camera could consistently measure penetration values over time, see Supplementary Fig. 19. In a single-camera system, occasional discrepancies arose between weighing scale readings and computed penetration values. Thus, our real-time dual-camera analysis, illustrated in Fig. 3a–d and Supplementary Movie 4, improves penetration estimations in cement paste measurements. This setup also ensures a thorough analysis to better capture 3D unsaturated flow dynamics. Figure 3e shows the absorption time-lapse in paste samples with varying initial sorptivity. Water levels change rapidly in porous matrices, while denser matrices show a gradual rise, supported by Supplementary Movie 5. Additionally, Supplementary Fig. 20 shows how the real-time measurements of S_i and S_s in paste cubes were performed using our FPN and machine learning models.

Fig. 3. Real-time prediction of penetration/ sorptivity values via our setup.

a Predicted penetration-time values obtained using our dual-camera setup (Camera 1 = blue points/masks, Camera 2 = green points/masks) for a denser matrix, (b) alongside their corresponding time-lapse images. c Predicted penetration-time values for a more porous matrix, (d) along with their corresponding time-lapse images. The use of a single-camera system may result in sporadic disparities between the weighing scale readings and the computed sorptivity values. This is due to the variability in sorptivity values, which are influenced by factors such as tortuosity and capillary pore distribution in different areas of the paste specimens, thus reducing reliability. The dual-camera system thus enhances the reliability of absorption measurements through computer vision. In this subplot, ‘Pre’ and ‘Post’ refer to the original and FPN-analyzed images, respectively. e Time-lapse of paste specimens with varying porosities, showing real-time sorptivity analyses. f In more porous matrices (higher initial sorptivity), there is a rapid evolution in the water level (∆ area/√min) over time, while in denser matrices, water levels increase more gradually. Our machine learning successfully combines water level data (predicted by machine vision) and absorption time to accurately estimate cementitious absorption rates. Source data are provided in the Source Data file.

Next, we analyze paste samples, with absorption times (0–1440 minutes on the theta axis) and wetted area ratios (0 to 1 on the radial axis) at S_i and S_s stages, see Fig. 4d. Upon careful analysis of our data, we realized that most initial sorptivity values have wetted area ratios smaller than 0.8 (left subplot, Fig. 4d). However, the secondary sorptivities show higher wetted area ratios (> 0.8), with a skewing distribution toward higher values (right subplot, Fig. 4d). Observations suggest that Nick time mostly occurs at 70–90% wetted area ratio, averaging around 85% (Fig. 4e and Supplementary Figs. 21, 22). This finding differs from earlier research, which only observed secondary sorptivity after complete coverage of the entire sample height¹². To justify this, we can argue that after primary sorptivity, entrapped air impedes water flow to the remaining 15% area³³. Subsequently, secondary sorption occurs as entrapped air gradually dissolves into water, initiating forced imbibition⁶². It should be noted that the rate of secondary imbibition in five-faced coated paste samples is highly influenced by entrapped air pressure. Thus, higher secondary sorption is observed when compared to samples with an uncoated top face (Supplementary Fig. 23).

Fig. 4. Sorptivity measurement across varied sample sizes, aspect ratios, and geometries.

a This subplot shows water absorption in pastes with aspect ratios from 1 to 2.5. Wetted area ratios remain consistent, ranging between 81.7% and 84.2% at Nick times for the tested samples. b Confirms that the Nick time is mainly determined by the square root of the prism aspect ratio (√(h/a). It also emphasizes that the primary and secondary sorptivities will stay uniform, irrespective of the aspect ratios. c Paste prisms with aspect ratios of 1.5 and 2.5 were split in half. Wetted area ratios closely matched surface measurements with USB microscope cameras, differing by only 3.2%. This supports the robustness of single-side camera measurements and suggests potential accuracy enhancement with dual-side measurements, especially for shorter samples, e.g., aspect ratio = 1.5. d Analyzing sorptivity distribution reveals dominance of initial values with wetted area ratios below 0.8. In contrast, secondary sorptivities exhibit a trend of ratios exceeding 0.8, leading to a skewed distribution towards higher values. e Our observations reveal that Nick time typically occurs between a wetted area ratio of 70–90%, averaging around 85%. This marks the intersection of the initial and secondary sorptivity fitted lines. Source data are provided as a Source Data file.

The capillary forces are strongest in dry conditions, decreasing as saturation occurs. This highlights the role of capillarity in both initial and secondary imbibition for water transport (Supplementary Fig. 24)^11,63. In simpler terms, in the initial sorption phase, water quickly fills the largest pores. During the secondary sorption phase, all pores saturate from bottom to top, with smaller pores ascending more slowly³³. Consequently, we believe that the rate of secondary imbibition is controlled by excess entrapped-air pressure, with the assumption that air diffuses outward solely through the unsealed surface at the bottom, i.e., the liquid inflow face^11,58.

Our ANN model was trained on a dataset of paste prisms with aspect ratios ranging from 0.7 to 1.4, with an average of around 1.0 (Supplementary Fig. 25). To analyze prisms outside this range, we normalize the time input by √(h/a) for non-cubic samples or by √(h (mm)/10) for large (> 10 mm) cubic samples, where h and a are height and width/depth, respectively. This ensures similar penetration-time behavior for prisms of different dimensions, see Supplementary Fig. 26a. Figure 4a illustrates water absorption in pastes with aspect ratios ranging from 1 to 2.5, encompassing the initiation of initial sorption, sorption at Nick time, and the end of secondary sorption. Upon the conclusion of the secondary period, the sample reaches near-complete saturation, and the exclusive mode of water transport ensues through a wick action¹⁴. Moreover, we confirm that the wetted area ratio for these prisms is constrained between 81.7% and 84.2% at Nick times. These ratios align with the average 85% wetted area ratio observed during Nick times in Fig. 4e and schematically shown in Supplementary Fig. 26b.

Figure 4b (right subplot) reports the penetration-time behavior of the four paste prisms shown in Fig. 4a, confirming that the Nick time is mainly controlled by the square root of the prism aspect ratio, or √(h/a). It further highlights that the S_i and S_s values would remain consistent, regardless of the prisms’ aspect ratios; see Fig. 4b (left subplot) and Supplementary Fig. 26c. Alongside, Supplementary Fig. 27 investigates how sample size and aspect ratio affect sorptivity values in paste cubes (5 to 25 mm). Larger samples result in more reliable measurements, and the aspect ratio does not significantly impact sorptivity coefficients, aligning with the ‘scaled’ capillary rule¹⁴. Notably, across all measurements, the error bar for S_s is higher than that for S_i, suggesting that the initial sorptivity can be more reliably measured⁶³.

A previous numerical estimation indicated that when the moisture profile exhibits a steep leading edge, ~ 70% of the water content change occurs within the initial 10% of its length¹⁰. While the SFM model focuses on relative moisture content and one-dimensional liquid flow, cumulative absorption can be approximated using USB cameras. However, to validate this, paste prisms with aspect ratios of 1.5 and 2.5 were split in half using a razor blade and a hammer after water absorption, as shown in Fig. 4c. The measured wetted area ratios closely matched those obtained from surface measurements using USB cameras. This confirms that single-side camera measurements are reliable, and using dual-side cameras would further improve accuracy. For smaller samples, a razor blade and hammer were used, whereas thicker specimens were cut with a saw, and magenta dye was added to the water to better visualize water levels (Supplementary Note 5 and Supplementary Fig. 28), confirming that 2D optical imaging accurately estimates water penetration depth in both paste and concrete samples.

Application to mortar and concrete samples

Following the successful application of our model to predict the sorptivity of cement pastes, we now explore its potential in more complex systems such as mortar and concrete. These materials are of particular interest due to their widespread use in real-world construction projects, where understanding moisture dynamics is crucial for assessing their durability and performance. Mortar and concrete introduce complexities due to having a mixture of paste, aggregates, and interfacial transition zone (ITZ) between aggregate and paste. Although traditionally considered a key pathway for moisture ingress, recent findings suggest that water movement around aggregates in the ITZ is less uniform and does not consistently follow expected paths, particularly under unsaturated conditions⁶⁴. This variability complicates the role of the ITZ in influencing moisture dynamics, especially during secondary sorptivity phases where diffusion predominates.

Figure 5 showcases the ability of our model to predict the sorptivity values in mortar as well as 4% air-entrained concrete samples trained solely on the paste dataset. For this purpose, Fig. 5a displays mortar cubes and cylindrical concrete samples subjected to a water absorption test. In the subsequent step, penetrations (measured with a weighing scale) and wetted area ratios (determined using computer vision) were recorded over four days, shown in Fig. 5b. It should be noted that for similar cubic mortar samples, increasing the sample dimensions has no impact on the sorptivity values but proportionally increases the penetration values. Based on Supplementary Table 1 (also summarized in Fig. 5d), mortar samples with a leaner mix (lower cement content relative to sand; in this case, cement: 1 part by mass, and sand = 2.75 part by mass) exhibit higher initial sorptivity values, attributed to greater porosity, confirming findings by Hall and Tse⁶⁵. In addition, the w/c ratio impacts the initial sorptivities of both mortar and concrete samples, with higher w/c ratios leading to a higher volume fraction of pores, thereby increasing sorptivity. Although we anticipated significant changes in sorptivity with variations in the duration of moist curing, these changes are marginal, with extended curing slightly reducing initial sorptivity values.

Fig. 5. Predicting sorptivity in mortar and concrete samples from the pastes dataset.

a Selecting cubic mortars and 4% air-entrained cylindrical concretes, drying them at 105 °C, coating their sides and tops with epoxy resin, and subjecting them to a water absorption test, (b) measuring the penetration vs. time (and area ratio vs. time) for mortar and concrete specimens over a period of 4 days, (c) utilizing our trained FPN model to mark the water level in mortar and concrete samples using yellow masks, (d) applying our machine learning model (trained on the paste dataset) to take the normalized time value (based on the aspect ratio and size of the specimens) and the area ratio of the wetted region to predict the initial and secondary sorptivity values, (e) our FPN model is also able to accurately mark water levels in more complicated shapes. Results show accurate water level predictions for I-shaped mortar (featuring CEE & Illinois logos) and vertically cut 4% air-entrained concrete cylinders. Future work includes training our machine learning model for sorptivity analyses of these complex geometries. Source data are provided as a Source Data file.

Our study aligns with the findings of Hall and Yau’s research on concrete^65,66 and Hall and Tse’s work on mortars⁶⁶, which demonstrate that both materials exhibit reproducible absorption characteristics where the cumulative absorption varies linearly with the square root of time. This alignment with established research enhances the relevance of our computational models in understanding water transport dynamics in cementitious materials. Figure 5c demonstrates that the FPN performed admirably in marking the water levels from orthogonal directions for both mortar and concrete samples. Figure 5d expands our research by applying our machine learning model (trained on paste dataset) to predict the primary and secondary sorptivity values based on the estimated wetted area ratios and normalized time values. This result underscores the ability of our proposed model to accurately predict both initial (R² = 0.96 for mortar and 0.87 for concrete) and secondary sorptivities (R² = 0.74 for mortar and 0.65 for concrete) in more complex systems, relying solely on the paste datasets. It is worth noting that the accuracy of predicting initial sorptivity in mortar/concrete samples is generally higher due to the simpler, more uniform process of capillary absorption and the relatively stable material properties at this stage. In contrast, secondary sorptivity involves more complex physical processes and interactions, leading to increased difficulty in accurate measurement and prediction, see Supplementary Note 6 and Supplementary Fig. 29. Further, our method applies to various inert and chemically active inorganic systems, extensively detailed in Supplementary Notes 7–10, Supplementary Figs. 30–33, Supplementary Data 2, 3.xlsx, and Supplementary Tables 2–6.

Interestingly, our FPN algorithm can accurately mark the water levels in the mortar (Fig. 5e, top row) and 4% air-entrained concrete (Fig. 5e, bottom row) specimens with complex microstructures. The existing literature strongly emphasizes the importance of using specimens with a constant cross-section for such measurements. However, in the future, our proposed method can potentially address and surpass this limitation by demonstrating its applicability to diverse geometries²⁴. Also, in contrast to our previous work, which provided quick initial sorptivity estimates but was less effective for secondary sorptivities⁶⁷, the current study now offers automated measurement of both S_i and S_s. Even though our camera setup cannot directly observe the internal reduction of entrapped air, our model captures subtle surface changes reflecting internal processes, coupled with machine learning to predict secondary sorptivity. Our observations indicate that the sorption transition generally occurs when the wetted area ratio is between 70–90% (Fig. 4e and Supplementary Figs. 21, 22). Thus, this study demonstrates the potential of our model for reliable, repeatable, and autonomous sorptivity estimation in various cementitious systems.

Limitations and outlook

Precise assessment of initial and secondary sorptivity values can be achieved with our computer vision and machine learning models, but some technical constraints need future attention. Our Mask R-CNN and FPN models were trained on a relatively small dataset with low Kolmogorov complexity. As shown in Supplementary Fig. 34 and Supplementary Movie 6, the images were captured with cameras close to the specimen and limited background variation. Accurate water level detection requires an ROI ratio above ~ 45%. Augmenting the training set is essential for better model generalization for more complex datasets.

In addition, our machine learning model, trained on w/c ratios of 0.4–0.8, struggled to predict sorptivity for lower w/c ratio samples (0.2 and 0.3), with R² values dropping to 0.71 for S_i and 0.63 for S_s (see Supplementary Fig. 35). This highlights the need for a more extensive dataset to improve accuracy across a broader range of conditions. Moreover, our trained FPN model accurately identifies water levels in single samples but struggles with adjacent samples (Supplementary Fig. 36), often detecting only one. Possible solutions include using separate cameras or cropping images to isolate samples, along with training on a more diverse dataset to enhance performance.

Finally, using two orthogonally aligned cameras with computer vision and machine learning, our current method efficiently estimates 2D unsaturated moisture flow in cement-based materials. In the future, a potential next step could involve comparing these results with 3D unsaturated moisture flow as measured by more advanced techniques including but not limited to Electrical Resistance/Impedance Tomography (ERT/EIT)^68,69, Electrical Capacitance Tomography (ECT)⁷⁰, and dual-method approaches such as neutron + X-ray tomography (NeXT)⁶⁴, ERT + Neutron Radiography⁷¹, or EIT + X-ray Tomography⁷². It is worth noting that ECT is more effective for unsaturated flow, while ERT/EIT is better suited for saturated flow due to the need for good ohmic contact. These electrical methods are also less expensive than X-ray or Neutron Tomography, making them viable alternatives for future studies. Comparing these methods will help determine if our 2D analysis can accurately represent the 3D behavior of unsaturated flow in complex systems.

Methods

Mask R-CNN implementation

Following real (Supplementary Note 11, Supplementary Figs. 37–46, Supplementary Table 8, Supplementary Appendix 1, and Supplementary Movie 7) and synthetic (Supplementary Note 12 and Supplementary Figs. 47–49) image generation, we used the imagery data to train our computer vision models. Our first Mask Region-based Convolutional Neural Network (Mask R-CNN) computer vision model (available in Supplementary Appendix 2 and GitHub repository⁷³) was implemented by constructing the “maskrcnn_resnet50_fpn” function, a feedforward pre-trained CNN architecture on the COCO dataset from the torchvision library⁷⁴. Mask R-CNN is an extension of the Faster R-CNN model designed for pixel-level object instance segmentation⁶⁸. To optimize the model, various data augmentations such as random cropping, vertical and horizontal flipping, and padding were applied⁷⁵. Two callbacks were defined for the trainer, ModelCheckpoint and EarlyStopping, in which (for the latter callback) a patience level of 6 epochs and an initial learning rate of 0.001 helped the model achieve optimal performance with a binary cross-entropy loss function. We also disabled the ResNet gradients backbone by setting ‘disable_resnet_gradients = True’ to speed up the transfer learning process⁷⁶. Furthermore, we implemented the Adam optimizer (torch.optim.Adam) to update the model parameters during training and to facilitate its convergence⁷⁷. The number of classes defined for the model was 2, i.e., 1 class for the background and 1 class for the foreground = water. Finally, during the model evaluation, only the segmentation mask corresponding to the instance prediction with the highest score was used to mark the ROIs. An overview of the architecture of the Mask R-CNN model is shown in Supplementary Fig. 50.

FPN Implementation

The Feature Pyramid Network (FPN) model (available in Supplementary Appendix 2) was implemented by constructing the ‘EfficientNet-B2’ function, a pre-trained CNN with compound scaling, depth-wise separable convolutions, and squeeze-and-excitation modules, imported from the torchvision library, i.e., the SMPModel class⁷⁸. Our modified architecture reduced feature maps to 128 channels with 1 × 1 convolution, performed up-sampling, added them with corresponding bottom-up layers via skip connections, and passed them through a 14 × 14 MLP for dense segmentation⁷⁹.

It is worth noting that the “predict_step” method was also employed to predict the probability masks via sigmoid with the highest score for a batch of input images during inference. Similar to Mask R-CNN, to expedite the model convergence, we utilized the Adam optimizer (torch.optim.Adam) to update the parameters during training⁷⁷. Finally, the trainer implemented two callbacks, namely ModelCheckpoint and EarlyStopping. For optimal performance, EarlyStopping was configured with a patience level of 6 epochs and an initial learning rate of 0.001. Supplementary Fig. 50 provides an overview of the FPN model architecture, which includes a top-down pathway, a bottom-up pathway, and lateral connections.

Machine learning implementation

Available in Supplementary Appendix 3 and GitHub repository⁷³, a feedforward neural network (Artificial Neural Networks ANN) with a TensorFlow dataset was developed that splits the data into training and testing sets⁸⁰. To ensure that the sequential model can perform computations efficiently and accurately, we converted the data to float32 format⁸¹. The input layer consists of two input features: wetted area ratio and time. These features are mapped to a hidden layer that has 64 nodes with the ReLU activation function, followed by two more hidden layers with 32 and 16 nodes, each with the ReLU activation function (Supplementary Note 13, Supplementary Fig. 51, and Supplementary Appendix 4). The output layer consists of 1 node, either penetration or sorptivity as a function of time. A training dataset, with 1440 data points (from Cement A, listed in Supplementary Table 8), was used to train the ANN, while the testing dataset, with 144 data points (from Cements B to E, also listed in Supplementary Tables 8) was kept separate. The Adam optimizer optimized the model with a learning rate of 0.00005. The training was performed for 500 epochs with a batch size of 16. During the training, the model was validated using the test dataset. The performance of the model was tracked using the R² and the mean squared error (MSE) metric (Supplementary Fig. 52 and Supplementary Appendix 5).

Traditional weighing scale sorptivity measurement

As per the ASTM C1585, detailed in Fig. 1a²¹, the mass change of paste samples (cast in accordance with Supplementary Note 14 and Supplementary Fig. 53) due to one-dimensional unsaturated flow was recorded at regular intervals throughout a 24-h period of solid-liquid interaction. Then, the absorbed water quantity was normalized as i = m/($\mathrm{a}.\mathrm{\rho }$), where m represents the mass change over time, a is the exposed area of the specimen that comes into contact with water, $\rho$ is the density of water, and i is the normalized cumulative volume of fluid that the specimen has absorbed. To estimate the S_i and S_s values, the penetration values against the square root of time were plotted, and the slopes of the first and second fitted linear lines were calculated using the least square method.

Hardware configuration for the proposed device

To establish the experimental setup (detailed in Supplementary Table 9), a transparent glass vial with dimensions larger than 15 mm (width) by 27 mm (height) was selected; see Supplementary Fig. 54a. The vial’s lid has a soft polypropylene snap-top cap to facilitate controlled water introduction via syringe (Supplementary Fig. 54b). The paste cubes, measuring ~ 10 mm on each side, are positioned atop the metallic beads, ensuring that their faces are precisely perpendicular to the orthogonally aligned cameras for optimal visibility while allowing a slight tilt in the camera itself as computer vision models can accommodate a minor rotation in the region of interest (Supplementary Fig. 54e). To capture focused images, adjustments in the camera lens distance from the region of interest are made (Supplementary Fig. 55), with code provided in Supplementary Appendix 6 to enforce image acutance requirements. The syringe needle punctures the vial cap at a distance from the paste cubes, dispensing liquid over approximately 3 seconds to ensure uniform wetting for accurate water absorption analysis in computer vision (Supplementary Fig. 56). Maintaining water levels between 0.5–2 mm guarantees continuous capillary water suction during absorption. The image acquisition employs inexpensive USB microscopy cameras, each priced at less than $30, offering Full HD (1920 × 1080 pixels) or 4 K resolutions (3840 × 2160 pixels) with a minimum spatial resolution of 10 µm, magnifications ranging from 50 to 1000x and a real Angle of View (AOV) of 120 degrees. The USB cameras are encircled by LED lights, enabling the capture of images under different conditions: diffuse reflections with LEDs turned off or specular reflections with LEDs turned on (Supplementary Fig. 54c, d).

Author contributions

The experimental design was conceptualized by H.K. and N.G. The computer vision models were developed and optimized by H.K., and J.W. Furthermore, J.W. developed the water annotator algorithm. H.K. developed the machine learning model and settled the hardware setup. In addition, S.D. contributed to the preparing, and absorption measurements of mortar, concrete, and masonry samples. All the authors collaboratively conducted the data analysis, figure preparation, and manuscript composition. In addition, the annotation of real images was partly done by H.K., J.W., and T.J. Finally, N.G. led and supervised the study.

Peer review

Peer review information

Nature Communications thanks Laura Dalton, who co-reviewed with Qinyi Tian, Danny Smyl, and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The experimental data is available in Supplementary Data 1–3.xlsx. Source data are provided in this paper as well.

Code availability

All Python codes are available in Supplementary Appendices 1–6. Furthermore, the GitHub repository can be accessed via the following link:

https://github.com/hosseinkabiruiuc/Sorptivity-Analysis-via-Computer-Vision

Our GitHub repository can also be accessed via Zenodo: 10.5281/zenodo.13835635⁷³.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-53993-w.