Predicting the Open Porosity of Industrial Mortar Applied on Different Substrates: A Machine Learning Approach

Abstract

This study aims to evaluate the potential of machine learning algorithms (Random Forest and Support Vector Machine) in predicting the open porosity of a general-use industrial mortar applied to different substrates based on the characteristics of both the mortar and substrates. This study’s novelty lies in predicting the mortar’s porosity considering the substrate’s influence on which this mortar is applied. For this purpose, an experimental database comprising 1592 datapoints of industrial mortar applied to five different substrates (hollowed ceramic brick, solid ceramic brick, concrete block, concrete slab, and lightweight concrete block) was generated using an experimental program. The samples were characterized by bulk density, open porosity, capillary water absorption coefficient, drying index, and compressive strength. This database was then used to train and test the machine learning algorithms to predict the open porosity of the mortar. The results indicate that it is possible to predict the open porosity of mortar with good prediction accuracy, and that both Random Forest (RF) and Support Vector Machine (SVM) algorithms (RF = 0.880; SVM = 0.896) are suitable for this task. Regarding the main characteristics that influence the open porosity of the mortar, the bulk density and open porosity of the substrate are significant factors. Furthermore, this study employs a straightforward methodology with a machine learning no-code platform, enhancing the replicability of its findings for future research and practical implementations.

1. Introduction

The construction sector of the European Union (EU) generates over 35% of the region’s total waste and requires vast amounts of resources, accounting for about 50% of all extracted material [1]. This significant demand influences production and drives research to optimize existing materials and develop new products [2]. Machine learning is a data-driven approach that uses statistical concepts to create a mathematical model with existing information, making decisions about future data [3].

With the increase in data generation in material characterization, data science has emerged with tools that enable the exploration, mining, and processing of large information sets [4].

The predictive capability of material characterization reduces decision-making risks and identifies failures and successes [4]. It helps to predict a material’s lifespan and can minimize damage progression, for example, in terms of maintenance costs [5].

One of machine learning’s key advantages is its support for the decision-making process, due to its predictive nature and classification power. On the other hand, one of the main disadvantages is the need for a large volume of data to train the algorithms. Based on the learning process, machine learning can generally be divided into the following three major categories: supervised, unsupervised, and reinforcement learning [6,7].

Supervised learning is the primary type used in civil engineering problems [5,8,9], where algorithms are trained on labeled datasets. This approach is effective for tackling regression and classification tasks. The main difference between these two lies in the response variable, as follows: for classification, the response variable is categorical, aiming to identify patterns; while, for regression problems, the response variable is numerical, targeting the estimation of a regression function [10,11]. Figure 1 illustrates the main supervised learning algorithms for regression and classification problems [6,7,12]. Building machine learning algorithms (MLAs) generally involves randomly dividing the database into training, validation, and testing sets [6,9].

On the contrary, unsupervised learning algorithms are trained on unlabeled datasets. In reinforcement learning, the least common method used, the algorithm is trained through trial and error [6,7].

Research has demonstrated various applications of machine learning in the context of mortars. Tran and Hoang [13] proposed a hybrid machine learning model based on least squares support vector regression optimized using the flower pollination algorithm to estimate the growth time of algae on the mortar surface. Despite obtaining satisfactory results, the controlled conditions obtained in the laboratory limit the generalization and applicability of the prediction. Van Mullem et al. [14] segmented images using classification machine learning algorithms. This study aimed to determine the propagation of the healing agent in self-healing concrete and mortar using the Trainable Weka Segmentation plugin.

Morsali et al. [15] employed decision tree algorithms to delineate the boundaries of a good design space, highlighting the influence of the bricks’ appearance and the thickness of the horizontal mortar joint on the assembly’s performance. Sevim et al. [16] developed a model to predict the compressive strength of mortar samples with different properties using artificial neural networks and Fuzzy inference algorithms. They employed eight fly ashes in their research. Asteris et al. [2] studied the applicability of machine learning algorithms, such as Support Vector Machine, Random Forest, Decision tree, AdaBoost, and K-nearest Neighbors, finding higher accuracy with AdaBoost and Random Forest for analyzing the compressive strength of mortars. Oey et al. [17] also utilized decision tree algorithms to predict the compressive strength of cementitious systems, evaluating the effects of Portland cement characteristics on the properties and performance of cement pastes and mortars.

Despite the promising applications of machine learning in mortar research, studies in this area remain scarce compared to that of other scientific fields. However, an increasing interest in this topic is evident (Figure 2), as observed by the annual publication data in the Scopus database since 2020 using the following search query: (TITLE (mortar) AND TITLE-ABS-KEY (“Machine learning”) AND (LIMIT-TO (DOCTYPE, “ar”)).

The widespread use of machine learning algorithms in mortars underscores the necessity of a thorough understanding of the material, which allows for predicting behaviors and properties. Standardized laboratory tests characterize mortars; however, these tests do not account for interactions with substrates, as they are conducted in metal molds to assess the mortar’s quality and compliance with the requirements.

To predict a mortar’s performance, some authors have studied the interaction of the mortar with the substrate after its application, revealing that the substrates significantly influence the specific performance of the mortar. Carasek [18] evaluated the support/mortar bonds with different moisture contents and mortars, concluding that these factors influence adhesion. The author performed pull-off tests and made observations using a stereomicroscope and a scanning electron microscope to achieve this.

Kazmierczak et al. [19] used three types of supports and one mortar, concluding that the type of support affects the pore distribution and mortar adhesion. Torres et al. [20] used three supports (brick, concrete, and acrylic), three types of mortars (cement mortar, aerial lime mortar, and pre-dosed cement mortar), with one mix type for each mortar, and evaluated parameters such as open porosity, capillary water absorption, vapor permeability, dynamic modulus of elasticity, and compressive strength. The characteristics of the mortars detached from the supports were compared with those of the mortars molded and hardened in laboratory molds to analyze the influence of the support. This comparison revealed that various experimental factors significantly influence the mortars’ characteristics after their application to the supports. Matias et al. [21] studied the influence of the substrate on the porosimetry of hardened mortars, noticing that the substrate properties induce changes in the pore size, distribution, and apparent density. Bellei et al. [22] studied the effect of hollowed ceramic brick substrates on cement mortar with fine sand and regular sand, concluding that the substrate influences the bulk density and compressive strength of the mortar, leading to an increase in compressive strength when compared with the characterization carried out on laboratory molds.

Carvalho [23] investigated the adhesion system between a mortar and a substrate utilizing a scanning electron microscope (SEM-EDS) and an X-ray fluorescence spectrometer, aiming to correlate microstructural evaluations with the macrostructural characteristics of adhesion strength. This researcher concluded that the composition of a cement paste and its capacity for penetration into the substrate are interrelated with the adhesion properties.

Thus, the porosity of the mortar has an important role in its performance, since it influences other properties, such as mechanical resistance, water vapor permeability, and water absorption by capillarity. Predicting the mortar’s porosity is of great value when optimizing its formulation and adapting it to the built environment. This optimization should consider the substrate’s influence once it significantly influences the characteristics of the applied mortar.

This study aims to evaluate the potential of machine learning algorithms to predict mortars’ open porosity, considering the characteristics of the substrates. This paves the way for a better understanding of how the substrate can influence mortar performance, leading to the design of more tailored mortars that suit specific purposes and substrates. This study employs an easy-to-follow methodology using a machine learning no-code platform, making the findings more replicable for further research and practical applications.

2. Materials and Methods

This study aims to predict the open porosity of an industrial mortar based on the mortar’s bulk density, water absorption by capillarity, drying index, compression strength, and substrate characteristics (bulk density, open porosity, and water absorption by capillarity). This study used Orange software version 3.36.2, developed by Bioinformatics Lab at University of Ljubljana, Slovenia, in collaboration with the open source community [24].

The selected pre-dosed cement-based mortar is suitable for various substrates, indoor and outdoor use, can be applied manually or by spraying, and includes cement, aggregates, admixtures, and synthetic fibers. The mortar used has the following characteristics, according to the manufacturer’s declaration based on EN 998-1 [25]:

• Bulk density of the hardened product: 1400 to 1500 kg/m³;
• Compressive strength: >1.35 N/mm²;
• Adherence: ≥0.25 N/mm²;
• Water vapor permeability (µ): ≤35;
• Water absorption: Wc0.

The product’s technical data sheet does not disclose the proportions of the mortar components or the binder’s chemical composition. However, the manufacturer advises using 4 to 5 L of water for each 25 kg bag of mortar. The experimental campaign used 4.5 L of water for every 25 kg mortar.

The substrates selected for this study comprised hollow ceramic brick measuring 300 × 200 × 70 mm³, solid ceramic brick at 215 × 110 × 55 mm³, concrete block sized 500 × 200 × 100 mm³, lightweight concrete block also at 500 × 200 × 100 mm³, and concrete plate with dimensions of 300 × 200 × 40 mm³, all of which were chosen due to their prevalent application within the construction sector.

To facilitate the application of the mortars to the substrates, wooden molds were constructed to ensure a uniform thickness of 15 mm. Moreover, a fiberglass mesh was incorporated at the interface between the mortar and the substrate to aid in the detachment process following curing. The utilized mesh exhibited resistance to alkaline conditions, possessed a mesh opening of 5 × 5 mm², and had a specific weight of 158 g/m². The mortar detachment was ultimately executed manually.

According to the specifications provided by the mortar manufacturer, the substrates must be pre-moistened exclusively under elevated temperature conditions; however, this condition was not met, leading to the decision to refrain from pre-moistening the substrates.

Preliminary tests conducted on the employment of fiberglass mesh at the interface between the substrate and mortar demonstrated that the mesh does not substantially affect the properties of the mortar applied [26].

For the curing conditions of the mortars applied to the substrates, they were stored in a sheltered environment without regulation of relative air humidity or ambient temperature. Consequently, the average relative air humidity and ambient temperature recorded were 66% and 17 °C, respectively, over 28 days. After detachment, the samples had dimensions of 40 × 40 × 15 mm³.

2.1. Test Procedures

The bulk density (BD) and open porosity (OP) were determined according to the Standard EN 1936 [27].

The capillary water absorption coefficient (Aw) was determined following ISO 15148 [28], with the necessary adaptations to the dimensions of the samples. The samples were waterproofed on their side faces to ensure unidirectional flow. The samples were removed from the water, weighed, and replaced again after 5 min, 10 min, 20 min, 30 min, 1 h, 1 h and 30 min, 2 h, 4 h, 8 h, 24 h, 48 h, and 72 h.

The drying index test (DI) was carried out using Standard EN 16322 [29] and recommendation No. II.5 of RILEM [30]. The saturated samples, except the upper face, had their faces waterproofed and were placed in a climatic chamber at 23 ± 2 °C and relative humidity of 50 ± 5 °C.

Standard EN 1015-11 [31] procedures were used for compressive strength tests.

2.2. Database

The database was obtained experimentally using a general industrial cement mortar. This mortar was applied and detached from the substrates after a 28-day curing period for characterization. The authors have also used this characterization methodology in previous works [32,33,34,35].

The substrates used were hollowed ceramic brick (HCB), solid ceramic brick (SCB), concrete slab (CS), concrete block (CB), and lightweight concrete block (LCB).

The constructed database contained 1592 datapoints. The data were homogenized for this composition by removing outliers and missing values. The outliers were identified and removed using Peirce’s method [36]. They were removed due to having measurement errors or being defective samples.

Considering only the mortar’s characterization, the database comprised 200 datapoints per mortar–substrate. The data were divided into test and training subsets, and the cross-validation technique was used to avoid overfitting.

2.3. Machine Learning Algorithms for Predicting Mortar Open Porosity

Machine learning algorithms were used to predict the open porosity of the applied mortars. The algorithms selected for this study were Random Forest (RF) and Support Vector Machine (SVM). These algorithms were chosen for their wide use, effectiveness in regression tasks, and availability in Orange software version 3.36.2.

The Random Forest (RF) algorithm, developed by Breiman [37] in 2001, can be defined as an ensemble of structured decision trees (classification and/or regression). Each tree grows according to a randomly selected subset of the training set, with replacement (i.e., bagging). This means that the selected sample is not eliminated from the dataset, so some samples may be selected multiple times while others may not be selected at all in a new set. The replacement improves the accuracy by reducing the variance of classification errors [2]. In RF, each prediction of an individual regression tree is averaged to produce the final result [38].

The Support Vector Machine (SVM), developed by Cortes and Vapnik [39], can handle classification and regression problems [40]. SVM is an effective pattern recognition tool suitable for cases with small sample sizes [41]. In this method, a hyperplane, the decision boundary, must be defined. When a set of objects belongs to different classes, a decision plane is needed to separate them [40]. Support vectors modify the original low-dimensional input data into high-dimensional output data through nonlinear transformation. This transformation allows for identifying nonlinear separation features that could not be recognized in a low-dimensional space [41]. In this system, the support vectors are the points closest to the ideal hyperplane [2].

2.4. Evaluation Metrics

An efficient technique for performance evaluation is cross-validation (k-fold). Cross-validation randomly divides the database into K parts and trains the model K times using one part as a test and the remaining parts for training [10]. It is essential to compare different algorithms to find the most suitable one for the problem [6]. A 10-fold cross-validation technique was used with the Test and Score widget [42].

The trained model evaluates the algorithm’s performance using the test dataset [5]. Then, predictions can be made using a new dataset. This study randomly divided the database into 20% for testing and 80% for algorithm training.

Regarding the evaluation metrics for the algorithms [9,10,11], the following were used:

• MAE (Mean Absolute Error);
• MSE (Mean Squared Error);
• RMSE (Root Mean Squared Error);
• R² (Coefficient of Determination).

The metrics can be expressed according to the following equations [9,10,11]:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}|{\mathrm{y}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}}|$$

(1)

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}}\right)}^2$$

(2)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\mathrm{M}\mathrm{S}\mathrm{E}}=\sqrt{{\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}}\right)}^2}$$

(3)

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum {({\mathrm{y}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}})}^2}{\sum {({\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}^{\ast })}^2}}$$

(4)

where the following applies:

$y$ is the real value

$x$ is the predicted value

$y$* is the mean of the real values

Figure 3 shows the model scheme created in Orange. In this workflow, the following used widgets are visible: Data Sampler (which randomly divides the database in a chosen proportion: 20% for testing and 80% for training), RF and SVM (the algorithms used), Test and Score (used for cross-validation), Prediction (used for predicting porosity), and Feature Importance (used to evaluate the importance of features in the prediction).

3. Results and Discussion

As stated, two machine learning algorithms were used to predict open porosity for an industrial-cement-based mortar. According to the data, 1274 samples were used for the simulation.

Table 1. Substrate characterization.

Substrates		Bulk Density (kg/m3)	Open Porosity (%)	Aw (kg/(m2·s0.5)
Mean	CS	2224 ± 9	11.5 ± 0.4	0.023 ± 0.003
	CB	2113 ± 21	14.5 ± 1.0	0.332 ± 0.003
	LCB	1319 ± 72	16.8 ± 1.4	0.308 ± 0.021
	HCB	2071 ± 13	16.5 ± 1.5	0.037 ± 0.004
	SCB	2059 ± 2	18.3 ± 0.3	0.104 ± 0.023
Min/Max	CS	2216/2241	10.9/11.8	0.013/0.026
	CB	2084/2138	13.3/15.6	0.326/0.336
	LCB	1194/1401	15.1/18.3	0.289/0.348
	HCB	2051/2082	15.1/18.7	0.031/0.042
	SCB	2002/2096	17.0/19.3	0.066/0.134

CS—substrate concrete slab; CB—concrete block; LCB—lightweight concrete block; SCB—solid ceramic brick; HCB—hollow ceramic brick; ±standard deviation.

(substrate characterization) and

Table 2. Mortar characterization.

Mortar		Bulk Density (kg/m3)	Open Porosity (%)	Aw (kg/(m2·s0.5)	Drying Index	CS (MPa)
Mean	MHCB	1574 ± 14	22.1 ± 0.9	0.18 ± 0.02	0.138 ± 0.012	4.96 ± 0.70
	MSCB	1570 ± 13	22.5 ± 0.6	0.26 ± 0.03	0.123 ± 0.008	6.27 ± 0.66
	MCP	1528 ± 17	25.8 ± 1.0	0.16 ± 0.02	0.135 ± 0.012	3.94 ± 0.51
	MCB	1540 ± 23	25.3 ± 1.3	0.17 ± 0.03	0.155 ± 0.014	3.97 ± 0.44
	MLCB	1475 ± 18	30.3 ± 0.6	0.31 ± 0.02	0.117 ± 0.008	3.99 ± 0.35
Min/Max	MHCB	1551/1606	20.1/24.0	0.13/0.24	0.112/0.160	3.5/6.4
	MSCB	1533/1607	21.1/23.4	0.20/0.32	0.104/0.148	4.6/7.5
	MCP	1499/1566	23.6/28.3	0.13/0.20	0.115/0.160	2.9/4.9
	MCB	1496/1590	23.3/27.9	0.12/0.24	0.131/0.189	3.1/4.9
	MLCB	1441/1518	29.3/31.5	0.26/0.35	0.104/0.133	3.2/4.7

MCP—mortar applied to concrete slab; MCB—mortar applied to concrete block; MLCB—mortar applied to lightweight concrete block; MHCB—mortar applied to hollow ceramic brick; MSCB—mortar applied to solid ceramic brick; ±standard deviation.

(applied mortar characterization) show the mean and standard deviation separated by variables and characteristics to assist in visualizing and understanding the database used.

The results indicate that the characterization values for ceramic substrates (HCB and SCB) and concrete substrates (CS and CB) are similar in magnitude. In contrast, the lightweight concrete block (LCB) shows approximately 60% lower bulk density and 29% higher open porosity than the other concrete substrates. This pattern observed in the substrate characterization is also reflected in the applied mortar.

Concerning constructing the machine learning models, eighty percent of the data was used to train the models, and twenty percent was used to predict the mortar’s open porosity. The widget Data Sampler randomly divided the data. The widget Test and Score was used to evaluate the training set using a cross-validation technique, and the Predictions widget was used to evaluate the algorithm performance.

Table 3. Training results.

ML Models	Training Set
	MSE	RMSE	MAE	R2
Support Vector Machine	0.865	0.930	0.731	0.908
Random Forest	0.901	0.949	0.735	0.904

MAE (Mean Absolute Error); MSE (Mean Squared Error); RMSE (Root Mean Squared Error); R² (Coefficient of Determination).

shows the training results. The parameters used in the SVM configuration were as follows: cost (C) = 1.00; and regression loss epsilon = 0.10, Kernel linear. For RF, they were as follows: number of trees = 10; and number of attributes considered at each split = 6. One of the disadvantages of using low-code software is the limitation of parameter configuration. However, the possibility of testing different algorithms with extreme simplicity reduces the time it takes to design the model.

The database was randomly divided into the indicated proportion ten times to construct the evaluation metrics for testing the models.

Table 4. Test results for Support Vector Machine (SVM).

Runs	MSE	RMSE	MAE	R2
1	1.101	1.049	0.796	0.889
2	1.117	1.057	0.793	0.870
3	0.954	0.771	0.587	0.942
4	0.953	0.976	0.814	0.907
5	1.011	1.005	0.816	0.868
6	0.810	0.900	0.690	0.909
7	0.914	0.956	0.749	0.897
8	1.045	1.022	0.748	0.905
9	1.121	1.059	0.814	0.880
10	0.839	0.916	0.748	0.894
Mean	0.987 ± 0.112	0.971 ± 0.090	0.756 ± 0.072	0.896 ± 0.022

MAE (Mean Absolute Error); MSE (Mean Squared Error); RMSE (Root Mean Squared Error) R² (Coefficient of Determination); ±standard deviation.

shows the results and the mean value for SVM, and

Table 5. Test results for Random Forest (RF).

Runs	MSE	RMSE	MAE	R2
1	1.080	1.039	0.834	0.891
2	0.933	0.966	0.663	0.891
3	0.930	0.964	0.745	0.909
4	0.845	0.919	0.734	0.918
5	1.136	1.066	0.824	0.852
6	1.643	1.282	0.942	0.815
7	1.082	1.040	0.840	0.878
8	1.184	1.088	0.841	0.892
9	1.235	1.111	0.860	0.868
10	0.942	0.971	0.769	0.881
Mean	1.101 ± 0.228	1.045 ± 0.104	0.805 ± 0.079	0.880 ± 0.029

MAE (Mean Absolute Error); MSE (Mean Squared Error); RMSE (Root Mean Squared Error); R² (Coefficient of Determination); ±standard deviation.

shows the same for RF.

The R² of the RF and SVM models were generally almost the same (0.904 and 0.908 for the training data, respectively). The SVM performance was also slightly better than that of RF for the test data (0.896 and 0.880, respectively).

The Feature Importance widget was used to evaluate each feature’s contribution to the model. This widget explains regression models using a trained model and reference data as the input; in addition, the method calculates each feature’s contribution to the prediction by assessing the increase in the model’s prediction error after permuting the feature’s values, thereby disrupting the relationship between the feature and the target [23]. Figure 4 and Figure 5 show the results for the RF and SVM algorithms, where the bar indicates the mean with the standard deviation after five permutations.

Both algorithms indicate that the substrate’s features (bulk density and open porosity) are the most significant factors influencing the mortar’s open porosity.

Kazmierczak et al. [19], Carasek [18], and the authors observed the tendency of the substrate’s porosity to influence the mortar’s characteristics, which reinforces the theory of active pores. However, the substrate’s porosity not only influences the mortar’s adhesion to the substrate, but also determines the physical and mechanical behavior of the applied mortar. These characteristics depend on the mortar’s porosity.

From this, the porosity of the substrate and its capillary absorption capacity are determining factors in the actual porosity of the mortar. The mortar–substrate interaction creates a surface with finer pores close to the interface. This water absorption from the substrate during the curing process makes the mortar less porous and mechanically more resistant. Therefore, the Feature Importance analysis indicates that the substrate porosity is important for mortar open porosity.

Consequently, in practical terms, the formulation of the mortar must consider the influence of the substrate where it will be applied. This way, it is possible to obtain more sustainable mortars while reducing the use of natural resources in their production.

Concerning the R² obtained with the ML models, Asteris et al. [2] used the same algorithms (SVM and RF) to predict the compressive strength of cement mortars, obtaining 0.420 for SVM and 0.944 for RF using the testing set. Sevim et al. [16] also predicted the compressive strength of cementitious composite with fly ash. Still, they used different algorithms, such as artificial neural networks (ANN), and obtained 0.894 for R² in the testing set.

In our case, we obtained R² values ranging from 0.8890 to 0.9088, indicating that the model accurately predicts the open porosity of cement-based industrial mortar based on the substrate, showing a good match between the performance of the two MLAs and the database size. However, the fact that R² is not a perfect fit means that the model does not explain 100% of the phenomenon. The factors that influence the porosity of the mortar, such as temperature, humidity, and application methods, were not considered within the features used. This fact can be considered a limitation of the prediction model.

4. Conclusions

As previous studies have demonstrated, open porosity changes according to the substrate characteristics. Therefore, it is essential to tailor mortars to account for the substrate where they will be applied.

This study evaluated the machine learning algorithms used to predict the open porosity of mortars applied to different substrates.

The machine learning algorithms demonstrated good prediction accuracy (R²) (SVM = 0.896; RF = 0.880), although the Support Vector Machine algorithm performed slightly better than the Random Forest.

This analysis revealed that the substrates’ bulk density and open porosity are important features that influence the mortar’s open porosity.

For future work, the database will be extended to industrial mortars and substrates to enhance the algorithms’ robustness and permit model generalization. This database will also be used to test other machine learning algorithms, such as artificial neural networks, KNNs, and GPR. The software’s use will be compared with a manual algorithm development approach. Moreover, a long-term performance evaluation will be carried out in further research.