1 Introduction

The frequent growth of citizens and urbanization was caused to the high development of massive concrete projects and road networks, afterward caused to increasing soil waterproofing due to the construction of impervious pavements and roads around the world [1,2,3]. This type of impervious of conventional concrete and pavements led to “downstream flooding”, sudden flash floods and earth erosion; however, these reasons led to increasing the risks of structural deterioration and reducing the benefits of pavement on the environmental [4, 5]. Concrete was “impermeable surfaces” which not penetrated water through it, then the rainwater was collected above these types of surfaces and flow into storm drains rather than allowing to penetration however cased to increase the risk of sudden flash flooding [6]. Moreover, increasing the flowing the flood and rain water for longer periods can account for natural hazards that affect the environmental negatively, such as unexpected landslides, sustained water logging, “reduction in soil moisture,” and changes in natural herbage [7,8,9]. Also, the higher temperatures measured in urban areas according to the surrounding countryside have enormous consequences for the health and wellbeing of people living in cities. The increased use of the construction of infrastructure materials which caused a large amount of heat production is the main cause of the urban heat island. Concrete roads and roofs constructed in the urban surface exposed to a solar ray of light. Concrete is one of the most utilization materials for pavement surfacing and is a higher effective contributor to this action. Densely graded concrete pavement has high volumetric heat capacity, which effective in surface temperatures and led to reaching high temperature up to 60 C˚ on hot summer days [10, 11]. Pervious concrete pavement systems are a perfect alternative for impermeable concrete that permits to recharge of groundwater from infiltration, thus reducing and eliminating runoff, also help control the contaminants in waterways. This treatment numerates as a result of reducing initial rainfall and allowing it to penetrate into the ground, which permits the soil chemistry and biology to the water naturally. Porous pavements allow to increase groundwater, recharge, decrease water flow through drainage pipes and channels, and minimize flooding. A porous concrete produce enough water storage capacity to exclude the requirement for waterhole, swales, and other downfall runoff containment strategies. Porous concrete contains the same constituent materials of conventional concrete but not including fines aggregate, the mix contain of uniform and usually single size coarse aggregates which produce a higher porosity, voids and permeability, also reduce inter particle connectivity [12]. Also, different names used for this type of concrete such as pervious concrete pavements, Sometimes, it also named no fines concrete, permeable concrete, or porous concrete (PC), are defined as a type of concrete surface that contain an open network of voids and pores to permit infiltration of rain and storm water through the concrete into the base and sub-base layers [13]. A typical PC can feature a wide range of properties such as effective air voids from about 15 to 30 percent, permeability from 0.23 to 20 mm/s, and compressive strength from 5 to 20 MPa [14]. In the beginning the experimentally porous concrete was built in England in the 1960s [15]. The main content that creates the porous concrete difference from the normal concrete was the size and gradation of coarse aggregate content. The major requirement of porous concrete is to have perfect voids to allow the flow of the water through its pores and voids [16]. Moreover, this type usually not included a fine aggregate, also some of the investigations were used fine aggregates of sizes 9.5– 2.36 mm in order to increase mechanical properties of the concrete such as compressive strength, but the use of very fine aggregate is strictly disallowed as the fine aggregates which fill the void areas, this caused of reducing the infiltration rate [1, 17], However, according to Crouch et al. [17] fine aggregate will result in higher compressive strength than the larger size aggregates with a similar porosity distribution, but low permeability, and the study suggested to use uniformly graded aggregate for beneficial field installation. Another research carried out, indicates that single size aggregates provide higher permeability rate, but with a low concrete compressive strength [18].

Various modeling approaches have been explored in the literature to forecast different properties of cement-based concrete composites. For instance, Philip et al. [19] effectively utilized a range of tree-based machine learning algorithms to forecast the mechanical characteristics of fiber-reinforced GGBS geopolymer concrete, and Ahmed et al. [20] employed six distinct modeling techniques to anticipate the compressive strength of recycled plastic aggregate geopolymer concrete that was enhanced with Nano-silica. Similarly, Faraj et al. [21] used a variety of modeling challenges to project the tensile strain capacity of engineered cementitious composites. On the other hand, another study used a dataset of 1030 records from University of California Irvine’s machine learning repository. Four conventional models were trained and validated. These predictions were combined using ANN to create the Hybrid Ensemble Model (HENSM), which outperformed individual models in predictive accuracy. The HENSM mitigated overfitting issues and shows promise for sustainable concrete construction design [22]. Moreover, ANN models were employed to predict the ultimate compressive load of rectangular concrete filled steel tube columns [23]. Additionally, Asteris et al. [24] investigated the prediction of the fundamental period of infilled reinforced concrete structures through artificial neural networks. They employed a substantial dataset for training and validating the ANN, taking into account diverse parameters that influence the fundamental period. The comparison with analytical values indicates the efficacy of ANNs in forecasting the fundamental period while considering essential influencing factors. Also, Armaghani and Asteris [25] employed ANN and adaptive neuro-fuzzy inference system (ANFIS) models for predicting the compressive strength of cement-based mortar. Finally, in a study [26], artificial neural network and M5P-tree models, along with other techniques, were proficiently applied to predict the failure stress of alkali-activated concrete under ambient curing conditions and different mixture proportions. These studies showcase the versatility and adaptability of different modeling methodologies in addressing specific properties and compositions within the realm of cement-based concrete composites.

The primary objective of this research is to develop a comprehensive model aimed at estimating and forecasting the permeability and compressive strength of porous concrete across multiple scales. To achieve this, a large dataset comprising 139 samples with varying water-to-cement ratios, cement content, curing durations, porosity levels, and coarse aggregate contents was utilized. Through various modeling techniques, including statistical analysis, the study aims to investigate the impact of key mixture components such as coarse aggregate, cement, porosity, curing time, and water-to-cement ratio. The ultimate goal is to enable concrete producers to optimize their production processes, reduce the need for extensive experimental testing, and save both time and costs. The study also seeks to identify the most effective model for predicting porous concrete properties among linear, nonlinear, and Artificial Neural Network (ANN) models through rigorous statistical evaluation.

The application of these models in optimizing concrete mix design yields multiple benefits. Not only does it enhance efficiency, but it also significantly conserves raw materials and reduces energy consumption. These advancements play a crucial role in lowering carbon emissions and promoting sustainable practices within the construction industry. By minimizing the environmental impact and fostering the use of eco-friendly materials, these models contribute to a more sustainable and responsible approach to construction, aligning with global efforts to combat climate change and preserve natural resources.

2 Methodology

In this paper review, the numbers of data were 139 experimental data which collected from the “previous papers” and investigations, and then by static process, they analyzed and split into three groups of data. The first grouped data was the larger group and consisted of 85 data used for generating and creating “the models”. However, the second group consisted of 27 data and was used as testing data while third group was validating data which also consist of 27 data to validate and check the created models. The main primary purpose of this study was to predict permeability (k) and compressive strength (σ) by static analysis. From Table 1, the parameters of these two properties of the pervious concrete contained water-to-cement ratio (w/c), curing time (T), coarse aggregate (CA), porosity (n), and cement content (C.C). The presented dataset containing several independent parameters that were highlighted above was used to predict the value of compressive strength (CS) and permeability (k) by various equations model and compared with the experimentally measured data of CS and k. The flowchart in Fig. 1 was represented to demonstrate the procedure of collected data, analysis, modeling, and evaluation.

Table 1 Summary of a different proportion for pervious concrete mixtures
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Fig. 1
figure 1

The process by flow chart diagram executed in this work

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3 Statistical evaluation

In this section of the study, a statistical and numerical analysis was generated to indicate the best and strong relationship between the collected parameters with permeability and also with compressive strength separately. All variable which used in this process containing (i) w/c, (ii) T, (iii) CA, and (iv) C.C was represented by a graph and analyzed with compressive strength, but for permeability, variable of (vi) porosity was added, also the statistical properties such as “standard deviation”, “skewness”, “kurtosis”, maximum, minimum, and variance obtained to represent the distribution of each parameter with permeability and compressive strength of pervious concrete. In below all information related to the input parameters and variables indicated:

  1. (i)

    w/c

From the data set Table 1, which consists of 139 data samples, the w/c ratio in the mix proportion has a minimum value of 0.2, and the maximum value was 0.4, median equal to 0.33. The other variables were determined by statistical analysis; consist of “standard deviation”, skewness, kurtosis and variances are 0.044, -0.22, -0.53, and 0.00188, “respectively”. Also, the variation of permeability with w/c ratio and Histogram was indicated in Fig. 2a, from the relationship, one can observes that by increasing the w/c ratio, the permeability was increased because this type of concrete different from the conventional concrete, as discussed in the introduction section above. Also, the variation of the permeability with w/c ratio and the Histogram (Fig. 2c) of PC is indicated in Fig. 2b, from the relationship, one can observe that by increasing the w/c ratio, the compressive strength was decreased.

  1. (ii)

    Curing time (T)

Fig. 2
figure 2

The relation between: A permeability and water to cement ratio; B “compressive strength” and water to cement ratio with C Histogram of the collected data

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For the hydration process and progression, curing time is required for an adequate age to produce sufficient compressive strength also for permeability. However, according to the data collected from the literature, the curing age range started from 7 to 42 days as maximum curing time with a median of 28 days. From the statistical analysis the variance, skewness, standard deviation and kurtosis were 12.68, -4.67, 3.56, and 29.10, respectively. Relationship between permeability and curing time and Histogram of porous concrete represented in the Fig. 3a, also the variation between the compressive strength and parameter of curing time and Histogram (Fig. 3c) of permeable concrete represented in the Fig. 3b.

  1. (iii)

    Coarse aggregate (CA)

Fig. 3
figure 3

The relation between: A permeability and curing time; B “compressive strength” and curing time with C Histogram of the collected data

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Natural coarse aggregate used as reported in Table 1 with minimum coarse aggregate size was 4 mm and maximum aggregate size of 20 mm. Also, with maximum aggregate content of 1692 kg/m3 and minimum coarse aggregate content was 1178 kg/m3 from the statistical analysis of collected data, the skewness, variance, standard deviation, median, and kurtosis were -0.83, 14616.9, 120.9, 1560, and 0.23, respectively. The relation between coarse aggregate content with the permeability (Fig. 4a) and the compressive strength (Fig. 4b), and the Histogram of the collected datasets shown in Fig. 4c.

  1. (iv)

    Cement content (C.C)

Fig. 4
figure 4

The relation between: A permeability and coarse aggregate content; B “compressive strength” and coarse aggregate content with C Histogram of the collected data

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According to the collected data in Table 1, the minimum cement content of data was 158 kg/m3 and the maximum cement content was 590 kg/m3, with a median of 367 kg/m3, the standard deviation of 80.58 kg/m3, variance equal to 649.99 kg/m3, skewness is -0.29, and kurtosis equal to 0.14. The relation between cement content with the permeability (Fig. 5a) and the compressive strength (Fig. 5b), and the Histogram of the collected datasets shown in Fig. 5c.

  1. (xxii)

    Porosity

Fig. 5
figure 5

The relation between: A permeability and cement content; B “compressive strength” and cement content with C Histogram of the collected data

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Porosity in the porous concrete was higher than conventional concrete because to produce this type of concrete, no fine aggregate content was used. From Table 1, the porosity was ranged from minimum with 3 % and a maximum of 37.61 %. Also, from the statistical analysis, the standard deviation, skewness, variance, median, and kurtosis were equal to 7.612, -.09, 57.94, 22.33, and -0.22, respectively. The relationship between the permeability of porous concrete with porosity and Histogram shown in Fig. 6.

  1. (vi)

    Permeability (k)

Fig. 6
figure 6

The relationship between permeability and porosity with Histogram of porous concrete

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From the total collected data in Table 1 the permeability of pervious concrete ranged from a minimum of 0.3 mm/s and the maximum value equal to 22.8 mm/s, variance of 48.89 mm/s, the standard deviation of 6.99, kurtosis of -1.29, and skewness of 0.26.

  1. (vii)

    Compressive Strength (CS)

From the total collected data in Table 1, the important mechanical property of porous concrete, which is the compressive strength, ranged from a minimum of 5.05 MPa and the maximum value equal to 25.67 MPa, variance of 26.77 MPa, the standard deviation of 5.17 MPa, kurtosis of -0.59, and skewness of 0.42.

  1. (viii)

    Size of aggregate

This content is one of the more effective parameters in the pervious concrete, as shown in Fig. 7a by increasing the maximum size of aggregate then the permeability was increased, but has adversely relation with compressive strength, by increasing the size of the aggregate in the porous concrete then the compressive strength was decreased, as shown in Fig. 7b.

Fig. 7
figure 7

The relationship between A permeability; B Compressive strength and coarse aggregate size of porous concrete

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4 Modeling

From the statistical analysis and Figures in Section 3 of this study and based on the R2 value, clearly can observe no direct relationship between the permeability and other composition of pervious concrete such as w/c, curing time, porosity, coarse aggregate content, and cement content, also the same for compressive strength and pervious concrete’s composition. Therefore, six various models, which are represented below, are generated to indicate the effect of all various contents in the mixture of the porous concrete. The models proposed in this review are used to predict the values of permeability and compressive strength of pervious concrete and then select the best model of them which gain the better estimation value of permeability and compressive strength compared with the experimental and measured value of them. However, the comparison of predicted data for different proposed models executed according to criteria of the “model” should have “scientifically” form and should have the minimum error which obtained from the different experimental and predicted value which mean has lower “RMSE”, “OBJ”, “SI”, and greater R2 value.

4.1 Linear” regression “model” (LR)

Linear regression model is one of the models that used to predict concrete properties from different work in literature [43, 44]. The common form of linear regression to predicting the value of k and σ of the pervious concrete in this type of model, as indicated in Eq. (1) and (2)

$$k=a+b({}^{w}\!\left/ \!{}_{c}\right.)$$
(1)
$$CS=a+b({}^{w}\!\left/ \!{}_{c}\right.)$$
(2)

a, b, k, and w/c are symbol equation “parameters”, permeability, and water to “cement” ratio, and CS is compressive strength, respectively. However, other constituent and parameters of pervious concrete mixture proportion are not contained on the equation above, but for having more accuracy and scientific considerations, the Eq. (2) is proposed that may impact the permeability and compressive strength

$$k=a+b\left({}^{w}\!\left/ \!{}_{c}\right.\right)+d\left(T\right)+e\left(n\right)+f\left(CA\right)+g(C.C)$$
(3)
$$CS=a+b\left({}^{w}\!\left/ \!{}_{c}\right.\right)+d\left(t\right)+f\left(CA\right)+g(c)$$
(4)

Where, w/c is water to cement “ratio” (%), “T is curing age, n is porosity (%), CA is coarse aggregate content (kg/m3), C.C is cement content (kg/m3), and CS is compressive strength. Moreover, the letters of a, b, d, e, f, and g are parameters of the model. The obtained Eq. (3) and (4) can be considered as an extent for Eq. (1) and (2), all variables recognized linearly. Also, all the variables can influence on the value of pervious concrete and inter-act with each other.

4.2 Nonlinear “regression” Model (NLR)

This form of models used for these independent parameters that have non linears relation with dependent parameters [45]. As shown in the Eq. (5) and (6) and can be applied as a universal form for producing a nonlinear “regression” model. The relation between the different parameters in Eq. (1), (2) and Eq. (3), (4), however, indicated in Eq. (5), and (6) to predict the permeability and compressive strength of the porous concrete.

$$k=a{\left({}^{w}\!\left/ \!{}_{c}\right.\right)}^{b}+{ c\left(T\right)}^{d}{+ h\left(n\right)}^{e} {+ i\left(CA\right)}^{f} {+ j(C.C)}^{g}$$
(5)
$$CS=a{\left({}^{w}\!\left/ \!{}_{c}\right.\right)}^{b}+{ c\left(T\right)}^{d}+ {e\left(CA\right)}^{f}+ {h(C.C)}^{g}$$
(6)

where the w/c, T, n, CA, C, represented the water to cement ratio (%), curing time (days), porosity (%), coarse aggregate content (kg/m3), and cement content (kg/m3), respectively. Also, a, b, c, d, e, f, g, h, i, and j are symbols of the model parameters that are obtained from the calculation according to the least “square” method.

4.3 Artificial neural network (ANN)

The ANN model in this study utilized the Weka software package (version 3.8.5). Artificial Neural Networks (ANNs), regarded as reliable models that mimic the functioning of the human brain, comprise input, hidden, and output layers. ANNs lack a fixed structure, and the analytical process is contingent on the provided parameters and the nature of the presented problems [45]. Used structure for predicting compressive strength of pervious concrete is as shown in Fig. 8 while for predicting permeability is as in Fig. 9.

Fig. 8
figure 8

Used stracture for predicting compressive strength of pervious concrete using ANN

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Fig. 9
figure 9

Used stracture for predicting permeability of pervious concrete using ANN

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5 Assessment criteria for models

For determine and estimate the efficiency of the “proposed” models, different execution parameters containing coefficient of “determination” (R2), Root “Mean” Squared Error (RMSE), Mean “Absolute Error (MAE), Scatter Index (SI), and “OBJ” are used; these parameters can be defined as:

$${\text{R}}^{2}={\left[\frac{{\sum }_{{\varvec{p}}=1}^{{\varvec{p}}}\left({\varvec{t}}{\varvec{p}}-{\varvec{t}}\boldsymbol{^{\prime}}\right)\left({\varvec{y}}{\varvec{p}}-{\varvec{y}}\boldsymbol{^{\prime}}\right)}{\sqrt{\left[{\sum }_{{\varvec{p}}=1}^{{\varvec{p}}}{\left({\varvec{t}}{\varvec{p}}-{\varvec{t}}\boldsymbol{^{\prime}}\right)}^{2}\left[{\sum }_{{\varvec{p}}=1}^{{\varvec{p}}}{\left({\varvec{y}}{\varvec{p}}-{\varvec{y}}\boldsymbol{^{\prime}}\right)}^{2}\right.\right]}}\right]}^{2}$$
(7)
$$RMSE=\sqrt{\frac{\sum_{{\varvec{p}}=1}^{{\varvec{p}}}({\varvec{y}}{\varvec{p}}-{\varvec{t}}{\varvec{p}})}{{\varvec{p}}}}$$
(8)
$${\varvec{S}}{\varvec{I}}=\boldsymbol{ }\frac{RMSE}{t^{\prime}}$$
(9)
$$MAE=\frac{\sum_{p=1}^{p}|(yp-tp)|}{n}$$
(10)
$$OBJ=\left(\frac{{n}_{tr}}{{n}_{all}}*\frac{{{RMSE}_{tr}+ MAE}_{tr}}{{R}_{tr}^{2}+1}\right)+\left(\frac{{n}_{tst}}{{n}_{all}}*\frac{{{RMSE}_{tst}+ MAE}_{tst}}{{R}_{tst}^{2}+1}\right)+\left(\frac{{n}_{val}}{{n}_{all}}*\frac{{{RMSE}_{val}+ MAE}_{val}}{{R}_{val}^{2}+1}\right)$$
(11)

Where, “yp” and “tp” are the symbol of predicted value and experimental value of the path specimen, “respectively”, t΄ and y΄ are the mean value of predicted value and experimental value. tr, and tst, are symbols of training, testing data, respectively, and “n” is the number of “data” in the “dataset”. For all parameters except the R2 value, the “best” value is zero, and for R2, the best value is one. According to SI value, the proposed model is (“poor” performance) when SI > 0.3, (fair performance) when the value is 0.2 < SI < 0.3, and (“excellent” performance) when the value of SI < 0.1. Also, the OBJ used to evaluate the efficiency of the “proposed” model as an integrated “performance” parameter [45].

6 “Analysis” and outputs

6.1 The model of LR

The relation between the measured and predicted value of permeability and compressive strength of the porous concrete for training, testing and validating data sets are shown in Figs. 10 and 11 with Eq. 12 and 13. The model parameters can observe that the w/c ratio and porosity have a remarkable effect on the permeability of the porous concrete. The w/c ratio with curing time has a major effect on the compressive strength for porous concrete:

$$\mathbf{k}=1.003+\mathbf{w}/\mathbf{c}-0.0189\mathbf{\ *\ }\mathbf{C}.\mathbf{C}+0.6\mathbf{\ *\ }\mathbf{n}+0.0035\mathbf{\ *\ }\mathbf{C}.\mathbf{A}-0.19\mathbf{\ *\ }\mathbf{T}$$
(12)
$${\varvec{\upsigma}}\mathbf{P}=0.988-0.99\mathbf{\ *\ }\mathbf{w}/\mathbf{c}+0.0554\mathbf{\ *\ }\mathbf{C}.\mathbf{C}-0.009\mathbf{\ *\ }\mathbf{G}.\mathbf{C}+0.247\mathbf{\ *\ }\mathbf{T}$$
(13)

from the Eq. (12), the w/c ratio has the maximum effect on increasing the permeability of the porous concrete. However, for compressive strength from Eq. (13), increasing the value of the w/c ratio, the amount of compressive strength was decreased.

Fig. 10
figure 10

Scatter graph for initial compressive strength (MPa) to predicted compressive strength by linear model

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Fig. 11
figure 11

Scatter graph for initial permeability (mm/sec) to predicted permeability by linear model

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6.2 The model of NLR

The relation between the measured and predicted value of permeability and compressive strength of the porous concrete for training, testing and validating data sets is shown in Figs. 12 and 13. The model parameters can observe that the w/c ratio, cement content and void ratio have a remarkable effect on the permeability of the porous concrete. The w/c ratio with cement content has the major effect on the compressive strength for porous concrete. For this NLR model with different parameters, the equation can be written and represented as follows (Eq. 14) for permeability and (Eq. 15) for the compressive strength:

Fig. 12
figure 12

Scatter graph for initial compressive strength (MPa) to predicted compressive strength by Non-linear model

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Fig. 13
figure 13

Scatter graph for initial permeability (mm/sec) to predicted permeability by Non-linear model

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$$\mathbf{k}={(\mathbf{w}/\mathbf{c})}^{1.38}-1.647\mathbf{\ *\ }{(\mathbf{C}.\mathbf{C})}^{0.382}+2.227\mathbf{\ *\ }{(\mathbf{n})}^{0.731}+0.763\mathbf{\ *\ }{(\mathbf{C}.\mathbf{A})}^{0.286}-0.93\mathbf{\ *\ }{(\mathbf{T})}^{0.464}$$
(14)
$$\mathbf{C}\mathbf{S}=-0.01\mathbf{\ *\ }{\mathbf{w}/\mathbf{c}}^{1.17}+0.0534\mathbf{\ *\ }{\mathbf{C}.\mathbf{C}}^{1.003}-0.01\mathbf{\ *\ }{\mathbf{C}.\mathbf{A}}^{1.006}+0.247\mathbf{\ *\ }{\mathbf{T}}^{0.301}$$
(15)

6.3 The model of ANN

The Figs. 14 and 15 depict the correlation between the anticipated and observed values of permeability and compressive strength of porous concrete across various sets of data, including training, testing, and validation for the output of the ANN model.

Fig. 14
figure 14

Scatter graph for initial C.S to predicted C.S by ANN model

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Fig. 15
figure 15

Scatter graph for initial permeability to predicted permeability by ANN model

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Since ANN forms proposed using artificial intelligent, provide higher accuracy compare to other methods. Based on the proposed structures as in Fig. 8 for the prediction of compressive strength according to the independent parameters, the coefficient of determination for obtained form is 0.966 for training data, while for testing data is 0.92 and 0.93 for validation data.

Also, according to the proposed structures as in Fig. 9 for the prediction of permeability according to the independent parameters, the coefficient of determination for obtained form is 0.937 for training data, while for testing data is 0.977 and 0.980 for validation data.

6.4 Comparison between developed models

As investigated and mentioned before, five different statistical values and tools, which consist of RMSE, MAE, SI, OBJ, and R2 were applied to assess the effectiveness and efficiency of suggested and proposed models. The ANN model has greater R2 and smaller RMSE and MAE values compare to NLR, and LR models, as indicated in Table 2 for predicting compressive strength and in Table 3 for predicting Permeability. The value of SI assessment parameters for the suggested models in the training, testing and validating as expressed in Tables 2 and 3, for ANN model are lower than 0.1.

Table 2 Statistical tools value for proposed models to predict C.S
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Table 3 Statistical tools value for proposed models to predict k
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6.5 Limitations of the proposed models

The developed models represent a significant advancement in the field of pervious concrete technology, offering a comprehensive approach to predicting both permeability and compressive strength. Their versatility extends across a broad spectrum of mixture proportions, encompassing the full range of ingredients typically found in pervious concrete formulations. By encompassing maximum and minimum contents of these ingredients, the models provide a robust framework for engineers and researchers to analyze and optimize pervious concrete mix designs for various applications and environmental conditions. This adaptability ensures that the models remain relevant and effective in diverse contexts, contributing to the ongoing evolution and refinement of pervious concrete technology.

The simplicity of linear and nonlinear models makes them easy to implement, which is a significant advantage. However, its limitations become apparent when it comes to predicting compressive strength and permeability of pervious concrete. In this regard, they show a lower level of accuracy and a higher margin of error compared to alternative models. Despite their straightforward application, its reduced precision in forecasting compressive strength and permeability poses a challenge. This limitation could affect the reliability of predictions, especially in scenarios where accurate forecasts of compressive strength and permeability are essential. It may be necessary to enhance the model’s predictive accuracy, particularly concerning compressive strength and permeability, to address this limitation and ensure its effectiveness across a broader range of applications.

Despite their effectiveness in the construction field, the black-box nature of ANN-based models presents a significant limitation. Users can only observe the outputs after conducting numerous trials, without any understanding of the model's internal mechanisms. While these models excel at handling complex construction data, their lack of transparency hampers comprehension and informed decision-making. Efforts to tackle this issue include the utilization of advanced visualization techniques and explanatory tools, with the aim of improving the interpretability of ANN-based models. Striking a balance between efficiency and interpretability is essential for optimizing the application of these models in construction contexts.

7 Conclusions

An accurate model that reliably forecasts permeability and compressive strength of porous concrete has the potential to significantly reduce costs and time. Based on the statistical analysis and modeling of the dataset utilized in this study, gathered from previous investigations and studies, the findings of this research can be summarized as follows:

  1. 1-

    The median water-to-cement ratio employed was 0.33, with a range spanning from 0.2 to 0.4. Experimental programs utilized various curing times, generating data spanning from 7 to 42 days, with a median duration of 28 days.

  2. 2-

    Through various assessment criteria and statistical analysis results, it was found that the ANN model outperformed other models. This conclusion was drawn from its higher R2 value, lower RMSE, lower MAE, lower OBJ, and lower SI value for both training and testing/validation data.

  3. 3-

    Across all sections of the dataset, the SI value was consistently lower in the ANN model when compared to the LR and NLR models.

  4. 4-

    The OBJ value for predicting compressive strength and permeability is lower in the ANN model compared to both the NLR and LR models. Also, The OBJ value of the ANN model is lower than the NLR, and LR model for compressive prediction strength and permeability.

  5. 5-

    From the all results and analysis of this study in the production of porous concrete, the curing time and cement content has a negative effect on the permeability and positive effectiveness in the compressive strength of the porous concrete; however, the w/c and coarse aggregate content has positive effect in the permeability but negatively effect on the compressive strength.

8 Recommendation

Conducting a detailed study focused on how these modeling techniques can reduce CO2 emissions is essential. Additionally, such a study should explore ways to minimize the time and material trials required to produce pervious concrete with the desired properties. This research would provide a deeper understanding of the environmental benefits and efficiency improvements offered by these models. It would also contribute to the development of more sustainable construction practices by highlighting the potential for significant reductions in carbon footprints and resource consumption. This, in turn, would support the broader goal of creating more eco-friendly and efficient construction methods.