Efficacy of sustainable cementitious materials on concrete porosity for enhancing the durability of building materials

1 Introduction

Concrete is a composite element characterized by its heterogeneity, multi-scale nature, and multi-layered composition, collectively contributing to its intricate structure. The macro-physical and mechanical behaviors of the material exhibit characteristics such as inconsistency, uncertainty, and non-linearity, which indicate its complex morphology. Although there has been extensive research on the macro and micro characteristics of cement-based substances, there has been comparatively less emphasis on comprehending the microstructure of concrete. The arrangement of pores and distribution of pore sizes in concrete are critical factors that directly impact its durability and strength [1]. Hence, developing a rapid assessment technique capable of evaluating these characteristics of concrete would hold significant value in forecasting the efficacy of concrete structures. The correlation between concrete’s porosity and transport characteristics has garnered excessive attention in academia. These characteristics include the chloride ion migration, diffusion coefficients of gas, electrical resistivity, and gas or water permeability [2,3,4]. Figure 1 illustrates the empirical correlation of the compressive strength (CS), porosity, and permeability of concrete. In general, the permeability of cement composite tends to increase with an increase in porosity, whereas its mechanical strength tends to decrease. Hence, the criterion of porosity plays a fundamental role in assessing the longevity and functionality of concrete structures subjected to harsh environmental conditions [5].

Figure 1

Relationship between porosity, permeability, and CS [6].

Concrete can be classified as a chemically bound ceramic product when formulated with a hydraulic binder. The cement reaction with water leads to the formation of a composite material comprising a solid phase and a network of pores. Pores are an inherent characteristic of concrete. The pore system plays a pivotal role in determining the critical characteristics of concrete, precisely its strength [7]. Insufficient compaction can also lead to the development of pores inside concrete. The pore structure seen in the mortar or concrete exhibits a distinct arrangement from the pores observed in well-compacted mortar or concrete manufactured separately with identical amounts of the corresponding constituents. The disparity in both pore systems can be attributed to interfacial transition zone (ITZ) pores at the interface between mortar and aggregate [8]. The porosity of cured cementitious composite is contingent on the water-to-binder (w/b) ratio. The w/b likewise regulates the porosity of ITZ in concrete. The increase in w/b leads to an expansion in the dimensions of the pore spaces within the hydrated cementitious composite. The reduction in porosity occurs as the duration of curing extends and the hydration process improves, primarily due to the sealing or connection of large-dimension voids by calcium-silicate-hydrate (CSH) hydrogel pores. A standard model for determining the volumetric makeup of the hardened cementitious composites has been established based on the w/b and the extent of cement hydration [9]. According to earlier experimental findings, it has been observed that an augmentation in both the size and percentage of coarse particles results in a corresponding increase in the porosity at the ITZ. Consequently, this leads to a decrease in the durability of conventional concrete [10].

The weight ratio between coarse and fine aggregates (CA/FA) significantly affects concrete’s permeability, porosity, and tortuosity [11]. Supplementary cementitious materials (SCMs) are currently employed as a means of partially substituting Portland cement (PC) to augment the durability as well as the strength of concrete [12,13]. Furthermore, SCMs, for instance, fly ash, which is a result of the burning of coal in the thermoelectrical factory [14], or ground granulated blast furnace slag (GGBFS), which is a derivative of pig iron manufacturing, have the potential to facilitate cleaner production processes by effectively mitigating CO₂ emissions [15]. The primary benefit of GGBFS in concrete is ascribed to its inactive hydraulic reaction. This reaction plays an imperative role in enhancing the hydration of cement by compacting the concrete’s compound and improving the pore formation. This phenomenon leads to decreased permeability and a surge in CS for concrete that undergoes maturation over extended periods. The alteration in the mineral constituents of the cement has the potential to improve the concrete’s ability to capture chloride ions and elevate its electrical resistance [16]. The decline in permeability of concrete modified with fly ash can be ascribed to the mutual impact of the diminished quantity of water necessary for specific workability and a more processed void structure resulting from the pozzolanic reaction. The benefits of the pozzolanic process become increasingly apparent in well-cured concrete due to its extended lifespan. Hence, the curing state, whether water or air curing, is an additional significant component that influences the porosity of concrete [17]. Moreover, the use of superplasticizers (SPs) has the potential to significantly decrease the extent of mix-up water, hence promoting the development of a more compact pore arrangement [18].

Due to the diverse compositions of cementitious compounds and the intricate reaction of cement hydration over time, the evolution of the pore system in concrete exhibits a high level of complexity, making it challenging to represent accurately by analytical modeling. The uncertainty of the pozzolanic reactivities of GGBFS and fly ash poses a significant difficulty. The chemical structure of SCMs exhibits considerable variability, posing difficulties in accurately determining the reactive fraction of these materials. Papadakis [19,20] introduced a theoretical framework for predicting fly ash-based cementitious compounds’ chemical makeup and related volume. The prototype deliberates the stoichiometry of PC’s hydration process and the pozzolanic reactivity of fly ash while also considering the molar weight of the components and byproducts involved. Nevertheless, this prototype operates under the assumption of complete hydration of PC and the occurrence of pozzolanic reactivity involving fly ash. Consequently, the prototype cannot account for the time-reliant changes in porosity. Similarly, Salih et al. [21] used distant modeling techniques, including artificial neural network (ANN), M5P tree, and nonlinear and linear regression (LR), to estimate the CS of fly ash-based modified concrete. Mohammed et al. [22] used 379 data points to compute the CS of fly ash-based modified concrete using neuro-imperialism and neuro-swarm models. Piro et al. [23] studied the optimization of full quadratic (FQ), multi-logistic regression (MLR), and ANN to predict the electrical resistivity and CS of concrete modified with GGBFS and steel slag as aggregate replacement. Piro et al. [24] developed MLR, ANN, and FQ models to forecast the CS and electric resistivity of concrete modified with steel slag as an aggregate replacement.

Several investigations have been conducted to compute concrete porosity [25,26,27]. However, manufacturing concrete compounds to compute the porosity and pore structure requires a significant allocation of resources, money, time, and labor. The process involves methodically choosing substances and their corresponding amounts, guided by a series of thorough experiments. Various scholars have proposed statistical methods to predict the advancement of cement hydration levels [28,29]. An empirical cement hydration model estimates the time-reliant changes in porosity and chloride diffusion coefficient in concrete [30]. To formulate empirical predictions regarding the permeability characteristics of concrete, Khan [31] employed multivariate regression analysis. This investigation entailed the computation of porosity by considering different constituents of the concrete mixture, such as the percentage of fly ash, the ratio of micro-silica, and w/b.

While these models were successfully employed to predict the porosity of concrete, their accuracy heavily relies on the underlying assumptions. Applying machine learning (ML) methods can provide numerous advantages in solving challenges and enhancing the efficiency of computing concrete porosity. In contemporary times, ML algorithms have been effectively utilized across several academic fields to predict multiple attributes precisely. Similarly, the implementation of these solutions in civil engineering has the capacity to generate significant advantages in terms of optimizing the testing process and thereby lowering time consumption. The implementation of such strategies has been utilized. Several methodologies have been utilized in the calculation of the strength and durability features of cementitious composites, such as genetic programming (GP) [32], ANN [33,34,35], decision tree (DT) [36], and support vector machine (SVM) [37]. The model findings demonstrate a significant correspondence between the anticipated values and the empirically derived concrete characteristics indicating that ML holds promise as a tool for modeling concrete with intricate mixed compositions. Nevertheless, there is a scarcity of research focusing on utilizing ML techniques for predicting concrete porosity. However, limited studies are available to describe the utilization of ML algorithms to forecast the porosity of concrete. For instance, using the ANN model, Pereira et al. [38] studied porous concrete’s airflow resistivity, open porosity sound absorption, and tortuosity. Similarly, the study of Sathiparan et al. [39] demonstrated the utilization of various ML algorithms like ANN, SVM, LR, RF, k-nearest neighbor, and DT to predict the permeability and porosity of concrete. Cao [6] developed three models, including XGBoost, RF, and XGB, to forecast the porosity of high-performance concrete. Wu et al. [40] studied the predictive performance of the ANN model using a permeability dataset of 3,252 observations. Similarly, the ML methodologies employed in the literature to compute the porosity of concrete are provided in Table 1.

The main focus of this investigation is to assess the microstructural characteristics of concrete, with a particular emphasis on porosity. To achieve the objective, ML techniques rooted in artificial intelligence were utilized, including adaptive boosting (AdaBoost), LR, SVM, and DT. The efficacy and precision of these algorithmic models exhibit a distinct correlation with the quantity of data elements. A comprehensive database of 240 data components regarding concrete porosity was compiled utilizing experimental results from previous studies. The modeling technique considered seven input elements: the quantity of binder, proportion of fly ash, water/binder ratio, percentage of slag, ratio of coarse-to-fine aggregates, SP, and number of curing days. A comparative evaluation has examined the outcomes derived from the ML models, specifically SVM, AdaBoost, DT, and LR. Statistical methodologies were utilized to compute and compare the model’s predictions, ability to generalize, inaccuracies, and proficiency. Furthermore, this study implemented the RReliefF algorithm to determine the key input variables that have the most significant influence on the porosity of concrete.

2 Data description

The rationale of this study was to predict the porosity of concrete. ML approaches necessitate the utilization of several inputs to produce the desired target variable. The data employed in this investigation for predicting the porosity of concrete are derived from previously published literature with specific standards for selection [45,46,47,48,49,50]. Initially, the concrete was blended with PC, which could be partially substituted with either GGBFS or fly ash. Furthermore, it is worth noting that the concrete matrix comprises both coarse and fine particles. The influence of carbonation on voids arrangement alteration was not considered in the concrete sample. In addition, a well-maintained equilibrium was preserved for each concrete variant, namely PC concrete, fly ash-based concrete and GGFBS-based concrete. The experimental setup for evaluating the porosity of concrete is shown in Figure 2(a)–(d). Seven distinct properties were selected as inputs to estimate the porosity of concrete. The specific information regarding these elements is listed in Table 2. The most critical stage while computing concrete properties via ML is the compilation of a comprehensive dataset. The accurate predictability of ML models is highly dependent on the quality and quantity of the dataset. As per literature studies, the adequate performance of the model is contingent upon the quantity of data in relation to inputs. An optimized model necessitates a ratio greater than 5 to analyze the relationship between the necessary variables effectively. The current study utilized a dataset of 240 records to calculate the porosity of concrete with seven potential inputs, hence fulfilling the requirement for the adequate performance of ML models [51,52]. A total of 240 data points were used to train the ML models in which 75 observations were of standard PC concrete, 120 observations were of fly ash-based modified concrete, and 45 records were of GGBFS-based modified concrete. Figure 3 shows the frequency distribution histograms of all the datasets utilized in constructing models.

Figure 2

Experimental setup for computing porosity of concrete: (a) oven drying of the sample; (b) sample cooling in a desiccator; (c) sample inside a vacuum container before beginning the test; and (d) sample in vacuum conditioning [53].

Figure 3

Frequency distribution histograms: (a) coarse aggregate/fine aggregate, (b) curing time, (c) binder, (d) fly ash, (e) SP, (f) slag, (g) water/binder, and (h) porosity (parameters similar to the study of Tian et al. [54]).

The process of normalizing and standardizing data is often considered crucial in preparing data for training ML models. Normalization may not be necessary or appropriate when the data are categorical or sparse. Alternative preparation techniques like data preprocessing may better suit specific situations [55]. The present study employed data preparation to assess its appropriateness for ML modeling. The primary processing of gathered data is a crucial and central phase in advancing and improving ML models. Data preparation encompasses a variety of commonly employed processes, including the management of missing data, the encryption of variables, the identification and treatment of outliers, and the partitioning of the data into sections. The database utilized in the present study was devoid of any missing information or outliers. Although the research did not employ a multivariate strategy to find outliers, a reliable data pre-treatment procedure successfully guaranteed the non-existence of abnormalities. Before training the ML models, a methodology was employed to detect outliers for each variable. The procedure involved the detection and exclusion of any data, if applicable that deviated from the predefined acceptable ranges. Additionally, a thorough demographical and statistical assessment was conducted on the dataset to sense and rectify any potential outliers. The statistical measurements offer boundaries, both higher and lower. The study incorporates various statistical metrics, including median, skewness, standard deviation, mode, standard error, mean, and kurtosis. The median, as well as the mode score of the SPs data, was found to be “0” due to the prevalence of values that are either 0 or in extreme proximity to 0. The frequency of values in proximity to 0 within the dataset for SPs can be credited to the constrained quantity of these constituents that were blended into the mixture. Skewness is the form of statistical indicator employed to quantify the severity of imbalance in the frequency distribution of a particular attribute with continuous values corresponding to its mean. In the present context, negative results typically indicate the presence of a long tail on the left side of the bell curve. Kurtosis is a statistical indicator used to evaluate the extent of the tail’s lightness or heaviness in a given data, as well as its suitability for a particular normal distribution. This provides valuable comprehension of probability distribution throughout the vertical axis. Table 3 provides an in-depth review of the statistical summary performed on all independent data features.

The evaluation of the relationship between inputs has been recognized as a crucial measure for assessing their influence on the target inside the employed dataset. Figure 4 depicts a plot of the Pearson correlation coefficient, which showcases the statistical relationship between variables for the complete dataset employed in the present study. Correlation coefficients are utilized as a quantitative matrix to evaluate the intensity and direction of the linear correlation between two entities. The correlation tool is a frequently employed gadget in the domain of statistics to examine the interaction between different attributes. Potential outcomes encompass an entirely (−ive) correlation, symbolized by −1, a wholly (+ive) correlation, expressed by +1, and the non-appearance of any correlation, indicated by 0. A +1 score implies that the increase in one entity is consistently associated with an increase in another entity. At the same time, a −1 correlation says that a decline in another entity usually accompanies the increase in one entity. The input variable that had the peak level of prominence was fly ash, which revealed a more pronounced (+ive) correlation with the target parameter (porosity). The association between these variables was additionally substantiated by a correlation value of 0.32. A positive connection was seen between the CA/FA, fly ash, and w/b, while the correlation between the binder, GGBFS, SP, and CT showed a (−ive) alliance with the target variable. The complete database was arbitrarily subdivided into two definite subsets: training data, comprising 70% of the total data points, and testing data, comprising 30% of the remaining data.

Figure 4

Pearson correlation coefficient chart.

3 Research methodology

ML algorithms are utilized in several research fields to anticipate materials’ serviceability. As nonlinear interaction exists between various concrete components, which includes binder, coarse aggregates/fine aggregates, water/binder, fly ash, curing time, GGBFS, and SP, this research utilizes AdaBoost, LR, DT, and SVM techniques to predict the porosity of cement-containing compounds. These techniques are well recognized for capturing the non-linear pattern between the concrete components, ensuring the problem of oversimplification and overfitting. These models utilized sufficient parameters and hyperparameters, which allowed us to learn the complex pattern between inputs and output variables, enabling the algorithm to predict the outcomes precisely. These approaches are adopted due to their extensive practice, reliable predicting capacities in related research, and identification as the most efficient data-driven techniques. The utilization of the correlation coefficient (R ²), which falls within an interval of 0 to 0.99, is a prevalent method for evaluating the level of accuracy in foreseeing properties by contrasting them to their observed values. A higher R ² signifies that the selected algorithm has produced satisfactory results. The in-depth flowchart of the current investigation is depicted in Figure 5. The model’s algorithms are run in Orange (3.35.0), a software platform based on Python. The inclusive arrangement of models in orange software is provided in Figure 6.

Figure 5

Flow diagram of research.

Figure 6

Model arrangements in software.

3.1 DT algorithm

A DT is a controlled learning technique that may handle input and target variables that are either categorical or continuous. The algorithm is capable of making predictions for both categorical data, using a classification tree, and continuous variables, using a regression tree. The algorithm operates by iteratively dividing a dataset into smaller segments using the most influential attribute, defined by a splitting criterion such as variance reduction, information gain, or gini impurity. Each division yields nodes, and this process continues until a stopping criterion is met. Typically, the threshold is reached when each of the points in a node is part of the same class (in classification) or when further divisions do not appreciably enhance predictions [56]. The DT is an extensively employed regression approach that offers an understandable framework for analysis. The key benefit of DT is its ability to imitate decision-making in humans, rendering it more accessible compared to other ML algorithms. A rudimentary hierarchical structure is constructed to model prospective outcomes, consisting of root systems, limbs, and leaf nodes, representing the predictions [57]. The outcomes, as shown by the leaf nodes, are situated at the terminus of the flow chart representing the DT [58]. The flow chart commences with root buds and thereafter turns to branches. The hierarchical structure of the given database commences with the primary root bud, which commonly functions as a symbolic description of the complete database. The effectiveness of a particular modeling approach is determined by the functions assigned to each root bud. The classification concept is determined by the direction every parent node (Root) takes as it advances the leaf, as shown in Figure 7. These buds are categorized into three distinct geometric shapes: triangles, rectangles, and circles. The DT classification technique is widely considered to be bare, with a simplicity that facilitates comprehension and use [59]. The functions applied to develop the DT algorithm for the prediction of porosity are summarized in Table 4.

Figure 7

Hierarchical structure of DT [60].

Table 4

Functions adopted for the DT algorithm

Parameters	Assigned function
Least no. of instances in leaves	2
Maximum tree depth	50
Induce binary tree	Yes
Minimal subset	5
Stopping criteria	95%

3.4 Adaptive boosting algorithm

A single DT, when used as a separate model, is sometimes referred to as a poor learner due to its inherent limitations in terms of predictive power and generalization ability. The likelihood of attaining a robust learner by amalgamating several weaker learners is an active research area. The central concept is to prioritize instances that pose the most significant challenge in terms of classification. AdaBoost operates in an iterative manner: with each round, it modifies the weights of wrongly classified instances, increasing their importance in the subsequent training phase. During each step of this ongoing process, a new weak learner is introduced and trained to rectify the errors made by the prior ensemble. The speculation was proven by Freund et al. [65] in 1990, establishing the fundamental principles for the boosting algorithm, a technique that consecutively combines numerous weak learners. As demonstrated in Eq. (4) [66], incorporating a new tree algorithm into the overall structure eliminates the typical tree, with just the most robust tree included. Through the process of iterative computation, the performance of the entire model will continuously enhance. Following the acquisition of the primary rudimentary tree model, specific sections within the dataset are accurately identified, while the others are erroneously labeled:

(4) f j ( x ) = f j − 1 ( x ) + argmin k ∑ i = 1 n a y i f j − 1 x i + k x i ,

where f _j (x) represents the entire model, f _j–1 (x) represents the entire mode in the prior round, y _i represents the forecasted outcome of the ith tree, and kx _i represents the freshly incorporated tree.

The AdaBoost algorithm is an iterative method for enhancing the performance of weak classifiers by iteratively learning from the data. This iterative process aims to increase the algorithm’s overall classification ability. The first poor classifier is derived by the process of training on the provided samples, wherein the misclassified samples are mixed alongside the untrained data to create a novel trained prototype. Moreover, the succeeding poor classifier is acquired through the process of learning from this prototype. The incorrect prototype is merged alongside the untrained data to create a novel trained prototype, which may be used to derive the third poor classifier for training purposes. Afterward, iteratively executing this procedure multiple times can eventually obtain the reboot-resilient classifier. To boost the accuracy of classification, the AdaBoost methodology assigns multiple weights to the data [65]. The appropriately categorized samples are assigned relatively low weights, while the misclassified samples need to be given higher weights. This compels the algorithm to allocate more importance to the misclassified data [67]. Figure 8 provides a comprehensive depiction of the computational procedure employed by the AdaBoost method. To train any basic DT model, altering the weight distribution that appears for each sample inside the dataset is mandatory. Given that each training data point changes, the training results will similarly demonstrate variability. Consequently, the cumulative sum of all outcomes is obtained [68]. Table 6 provides detailed insight into all the parameters adopted to run the AdaBoost algorithm.

Figure 8

Schematic diagram for AdaBoost algorithm [69].

Table 6

Functions utilized to run the AdaBoost model

Parameters	Assigned value/function
Basic estimator	Tree
Classification algorithm	SAMME.R
Learning rate	0.50
Regression loss function	Linear
Estimator’s number	100

4 Results and analysis

4.1 LR outcomes

The analysis focused on the outcomes of the prediction and the error associated with the LR algorithm. Figure 9(a) exhibits the association between the experimental and anticipated outcomes, as indicated by an R ² score of 0.763. This correlation implies that the precision of outcomes is inferior to that of the DT model. Figure 9(b) demonstrates the distribution of observed, forecasted, and errors in the LR model. The training set exhibited maximal upper limit, minimal limit, and mean limit error readings of 4.52, 0.00, and 1.13%, respectively. Overall, 51.67% of the errors were found to be below 1%, while 45.00% were within the range of 1–3%. The remaining 3.3% of error values exceeded 3%.

Figure 9

LR model outcomes: (a) R ² graph and (b) error tracing.

4.2 DT outcomes

The values derived from the DT approach exhibit a satisfactory level of accuracy and only a minimal magnitude of divergence between observed and predicted outcomes. Figure 10(a) presents the data analysis evaluation of the observed and projected results for the porosity of cementitious composites. R ² indicates that the model accurately predicts outcomes with a value of 0.838. The DT model outperformed the LR model, as suggested by a higher R ² score. DT models can capture complex interactions and non-linear patterns within the data. This characteristic makes them particularly well-suited for tasks in which the linear assumptions of LR may not be valid. Figure 10(b) displays the distribution of data obtained from experiments, projected scores, and errors for the DT algorithm. The training set was analyzed to find the maximum upper limit, lowest limit, and mean limit values, which were found to be 5.55, 0.00, and 0.82%, respectively. Furthermore, approximately 73.75% of the error values observed in the study were found to be less than 1%. Around 23.75% of the error values also fell within the 1–3% range, while approximately 2.50% exceeded 3%.

Figure 10

DT models outcomes: (a) R ² graph and (b) error tracing.

4.3 SVM outcomes

The analysis focused on the prediction outcomes and errors associated with the SVM model. Figure 11(a) showcases the interaction between experimental and anticipated results, indicating higher precision in outcomes relative to the DT and LR models, as supported by an R ² value of 0.870. SVMs have exceptional performance in identifying ideal hyperplanes or non-linear transformations that optimize the margin between distinct classes, hence offering a robust separation between data points. Moreover, SVM models have a lower susceptibility to overfitting in comparison to DT and LR algorithms and possess the ability to effectively handle datasets with a high number of dimensions. Figure 11(b) demonstrates the distribution of observed, forecasted, and errors in the SVM model. The training set exhibited maximal limit, minimal limit, and mean limit error readings of 3.64, 0.01, and 0.80%, respectively. Overall, 71.25% of the errors observed were found to be less than 1%, while 26.67% were within the range of 1–3%. The remaining 2.08% of the error values exceeded 3%. The superior accuracy of the SVM algorithm, in contrast to the DT algorithm, is additionally substantiated by the presence of lower error values.

Figure 11

SVM model outcomes: (a) R ² graph and (b) error tracing.

4.4 Adaptive boosting outcomes

Figure 12(a) depicts the correlation between the experimental findings of the AdaBoost and the projected outcomes. The R ² value of 0.914 for this model suggests that it possesses a higher degree of accuracy in predicting responses. AdaBoost shows higher accuracy than SVM, DT, and LR due to its iterative adaptation and aggregation of several weak classifiers. This collective approach effectively improves model performance by mitigating misclassification errors. Figure 12(b) displays a graphical depiction of the distribution of observed, forecasted, and error values within the AdaBoost model. Within the training set, the highest upper boundary, lowest upper boundary, and average boundary values were recorded as 5.10, 0.00, and 0.62%, respectively. Nevertheless, 83.33% of the inaccurate approximations were below 1%, whereas only 0.83% were above 3%. The AdaBoost model demonstrated greater precision in forecasting concrete’s porosity relative to the LR, DT, and SVM models, as supported by the comparison of R ² values and error distributions. All of the model’s R ² values and error percentages fell within acceptable levels, indicating improved predictive outcomes.

Figure 12

AdaBoost model outcomes: (a) R ² graph and (b) error tracing.

4.5 Statistical error analysis

The outcome of this study contributed to the creation of ML algorithms, which were optimized to predict the porosity of concrete and subsequently compare the performance of these models. Table 7 presents the statistical deviations observed between the anticipated and experimental results. The statistical error analysis reveals a strong association between the observed and projected responses for the AdaBoost model, demonstrating a high accuracy level in forecasting the porosity of concrete. The AdaBoost model has exceptional performance, as demonstrated by its R ² score of 0.914 and the following evaluation metrics: RMSE (0.858%), SI (0.083), MAE (0.617%), OBJ (0.771%), and MAPE (6.3%). Nevertheless, the LR model demonstrates the lowest level of accuracy, as specified by an R ² score of 0.763 and errors in terms of RMSE, SI, MAE, OBJ, and MAPE, which amount to 1.410, 0.136, 1.128, 1.440, and 12.6%, respectively. The violin plot shown in Figure 13 demonstrates the error propagation of ML models. The MAE of the AdaBoost model is 0.617%, lower than 0.796% for SVM, 0.824% for DT, and 1.128% for the LR model. Thus, the violin plot testifies to the boosting performance of the AdaBoost model against DT, SVM, and LR models in terms of forecasting the porosity of concrete.

Table 7

Error evaluation of models

Models	MAE (%)	RMSE (%)	R 2	MAPE (%)	OBJ	SI
AdaBoost	0.617	0.858	0.914	6.3	0.771	0.083
SVM	0.796	1.059	0.870	8.5	0.992	0.103
DT	0.824	1.166	0.838	7.9	1.083	0.114
LR	1.128	1.410	0.763	12.6	1.440	0.136

Figure 13

Violin graph for various developed models.

4.6 Feature importance evaluation

To forecast the porosity of concrete, this research employed CA/FA, SP, w/b, GGBFS, CT, fly ash, and binder as input features. Further, this study employed the RReliefF algorithm to order the input features according to their importance while estimating the output target. Figure 14 presents the findings of the RReliefF test. According to this radial plot, the binder content, w/b, and GGBFS percentage significantly influence the porosity of concrete with the RReliefF factors of 0.167, 0.151, and 0.150, respectively. However, SPs and curing time have the most negligible effect on the output target (porosity), as suggested by the RReliefF factors of 0.085 and 0.084, respectively. The porosity of cementitious composite is greatly affected by the amount of binder present, as the binder is responsible for the hydration process that bonds the aggregate fragments together. The quantity and composition of the binder are key factors in determining the size and arrangement of the hydration products, such as CSH, that occupy the voids in the concrete structure. The calcium-to-silica ratio (C/S ratio) in CSH has an impact on the pore structure and permeability [78]. Inadequate binder causes incomplete hydration, leading to an increase in capillary pores and increased porosity. On the other hand, an ideal quantity of binder decreases porosity by guaranteeing a more compact microstructure through efficient filling of pores [79]. Prior research has also demonstrated that fluctuations in the amount of binder significantly impact concrete’s mechanical properties and permeability, highlighting the significance of regulating the ratio of binder to water to attain the necessary porosity and strength [80]. Since the binder and w/b ratio are the controlling factors affecting the concrete porosity, while preparing a concrete mix, one can prioritize these variables and compute the other quantities. Moreover, optimal concrete mix designs can be achieved by modifying the quantity of binder to attain the required porosity level.

Figure 14

Radial plot for feature importance.

4.7 Sieve diagram

Figure 15(a)–(d) demonstrates the sieve diagram for DT, LR, SVM, and AdaBoost models. The sieve diagram is a graphic technique applied to visually characterize frequencies in a two-way contingencies table and assess them concerning the expected frequencies based on a presumption of independence. The presented visualization depicts rectangles whose areas are proportionate to the expected frequency, while the quantity of squares represents the experimental frequency within each rectangle. The shading density visually represents the distinction between actual and forecasted frequency, which is proportional to the standard Pearson residual (χ ²). This shading utilizes color to show whether the divergence from independence is red (−ive) or blue (+ive). The χ ² value for AdaBoost is 375.09, which is higher than 208.80 for DT, 319.29 for SVM, and 99.47 for the LR model. The higher χ ² suggests a strong correlation between actual and anticipated outcomes. Hence, AdaBoost shows an excellent correlation of experimental porosity with predicted porosity.

Figure 15

Sieve diagrams: (a) LR model, (b) DT model, (c) SVM model, and (d) AdaBoost model.

5 Discussion

The current research employed a random split of the porosity database, with a ratio of 70% for training and 30% for testing. This partition was used for all ML models, including DT, SVM, AdaBoost, and LR. The intent was to evaluate and contrast the predictive accuracy of these techniques and study the applicability of these optimized models for calculating the porosity of concrete without any lab experimentation. The correlation coefficient of all developed models showed acceptable performance, while AdaBoost outperformed SVM, LR, and DT models in terms of accuracy and predictive capabilities. AdaBoost shows higher accuracy than SVM, DT, and LR due to its iterative adaptation and aggregation of several weak classifiers. This collective approach effectively improves model performance by mitigating misclassification errors. AdaBoost is an ML algorithm that focuses on complex data points and iteratively enhances its predictive performance by allocating more weights to previously misclassified instances. The effectiveness of this technique lies in its adaptability and ensemble nature, which allows it to effectively capture complicated decision boundaries and address difficulties related to overfitting. Additionally, it demonstrates versatility by accommodating different types of base classifiers. In addition, AdaBoost exhibits less sensitivity to feature scaling, has a simplicity of implementation, and has the capacity to effectively handle non-linear data, which collectively contributes to its strong performance in many datasets and applications. Compared to the LR model, which is primarily based on linear assumption, the DT and SVM models perform well as both models can trace out intrinsic correlation among the variables. However, the efficiency of these algorithms is highly dependent on the database. Any potential outlier in the database yields false results in computation modeling.

The approach described above exhibits promising potential for several applications, such as optimizing mix compositions to enhance the performance-driven design of concrete structures and mitigating the adverse ecological effects associated with concrete production. Furthermore, the ML technique under consideration can be utilized to provide empirical predictions regarding the specific durability characteristics of concrete, including but not limited to the water and gas permeability, chloride diffusion coefficient, electrical resistivity, and degree of cement hydration. Subsequent research endeavors should focus on developing a dependable and balanced database encompassing concrete porosity, which can be utilized to train the ML model. The integration of diverse ML techniques can achieve the enhancement of forecasting accuracy. The applications of ML for industry and academics are described in Figure 16. However, some constraints are associated with utilizing these ML techniques. The exploitation of large, superior databases is crucial for ensuring the effectiveness of training ML models. However, the process of obtaining a comprehensive and diversified database that includes specific compositions of cementitious compounds and their accompanying porosity values may present significant difficulties. The lack of available data has the potential to compromise the accuracy and relevance of the algorithm. The algorithm’s ability to make accurate predictions for unfamiliar mixtures or unusual processing parameters may be compromised if the training data lacks coverage of the full range of compositions of cementitious compounds or unique situations of interest.

Figure 16

Applications of ML for academics and industry.

6 Conclusions

This research introduced an innovative machine learning (ML) framework that demonstrated exceptional precision and adaptation performance in predicting the porosity of concrete. ML techniques include DT, AdaBoost, LR, and SVM. The models were subjected to intensive training and testing utilizing data sourced from reputable scholarly publications. Statistical analyses have demonstrated that ML algorithms exhibit superior performance compared to conventional approaches, characterized by enhanced generalization capabilities and greater reliability. The study main findings are as follows:

1. The ML procedures suggested in this study exhibited a notable level of efficiency and generalization capability when employed for predicting the porosity of concrete. The correlation coefficient (R ²) for AdaBoost was observed to be 0.914. Meanwhile, R ² values for DT, SVM, and LR were 0.838, 0.870, and 0.763, respectively.

2. The results of RMSE (0.858), MAPE (6.3), SI (0.083), MAE (0.617), and OBJ (0.771) for the AdaBoost-model confirmed the superior efficiency than the LR-model (1.410, 12.6, 0.136, 1.128, and 1.440), the DT-model (1.166, 7.9, 0.114, 0.824, and 1.083), and the SVM model (1.059, 8.5, 0.013, 0.796, and 0.992).

3. As evident from the R ² score and minimum observed errors, the AdaBoost algorithm exhibited reliable accuracy and predictive capabilities against SVM, LR, and DT for computing the porosity of concrete.

4. The outcomes of RReliefF analysis demonstrated the comparative importance of each independent variable, with the following order of significance: binder > water/binder > slag > coarse/fine particles > fly ash > superplasticizer > curing time.

5. The AdaBoost model’s 375.09 chi-square value (χ ²) showed a significant correlation of inputs with the target variable. However, the χ ² values for DT, SVM, and LR were observed to be 208.50, 319.29, and 99.47, respectively.

The research findings suggest that the formulated models yield higher accuracy and precision. However, the use of a diverse dataset with a greater number of input features can lead to the formation of a universal ML model capable of capturing the intrinsic correlation among the variables. Further studies can be conducted to generate a dataset that includes the chemical composition of SCMs and curing conditions to create a universal ML model for estimating the porosity of concrete.