Utilizing genetic programming to evaluate and predict roller-compacted concrete pavements reinforced with coal powder and basalt fiber

Roller-compacted concrete (RCC) pavement technology has drawn significant attention in recent years, thanks to its many advantages over conventional paving materials. The main benefits of RCC include decreased shrinkage, reduced life-cycle expenses, early access to traffic and a decrease in the urban heat island effect. This study proposed a cost-effective method to address the disposal of coal powder (CP), which is an important contributor of environmental problems, by integrating it into the manufacturing of RCC. Cement was replaced with CP at weight ratios of 5%, 10%, 15%, and 20%. CP was substituted for cement, with weight ratios of 5%, 10%, 15% and 20%. The albedo and mechanical properties of the obtained RCC mixtures were measured. The albedo of the RCC mixture with 20% CP decreased approximately 2.3 times in comparison to that of the reference mixture. After 28 days, RCC mixes had compressive strengths of 26–38 MPa and flexural strengths of 4.3–6.1 MPa. Flexural and splitting tensile strengths increased substantially with BF. RCC mixtures with 5% CP and 0.5% BF improved freeze-thaw resilience after 100 cycles. The genetic algorithm approach may improve RCC design optimisation. Thus, RCC made with CP may be environmentally friendly and Sustainable.


Introduction
Coal is one of the most extensively used forms of carbon, and the amount of 756.2 million tons produced in the United States alone in 2018 underscores its critical role in energy production (Masi et al. 2021).In addition to being utilized for thermal energy production, municipal heating and coal chemical conversion (Ren et al. 2022), coal currently accounts for 41% of worldwide electrical generation, demonstrating its widespread usage in the power industry (Xu et al. 2022).In addition to energy production, a significant amount of coal is used in metallurgical processes, gasification and cement industry, and as a source of activated carbon and numerous other common and industrial compounds (Dai and Finkelman 2018).Nevertheless, coal has considerable environmental effects, leading to pervasive water and air pollution (Kopas et al. 2020, Suárez-Ruiz et al. 2023).To address these difficulties, it is necessary to develop new approaches to effectively utilize coal and its by-products in environmentally advantageous ways.
Coal powder (CP) and waste have been considered promising options for construction materials.It was reported in a previous study that integrating CP for soil stabilization improved the mechanical properties over time (Kinuthia and Nidzam 2009).It was stated in another study that the plasticity of soils increased at a rate of 12% (Modarres and Nosoudy 2015).In addition, this product was studied as a partial replacement for sand and cement in concrete slabs for paving applications (Li et al. 2022, Zhenli et al. 2023).Previous studies examined the utilization of coal dust as a partial replacement for sand and cement in concrete.The results suggest that substituting up to 50% of aggregate with coal dust does not affect the compressive strength (CS) of the material negatively and may even improve it (Luo et al. 2022).Further studies indicated that CS and flexural strength (FS) of concrete made with a 5% substitution of CP for cement are similar to those of the reference specimen (Hesami et al. 2016).Based on these findings, the replacement of traditional cement with CP drew increased academic interest due to its dual benefits of sustainability and reduced environmental impact.Comprehensive studies thoroughly examined this replacement's practicality, long-lasting nature, and ecological consequences.These studies emphasised its ability to make a substantial contribution to the development of more environmentally friendly building materials and the adoption of circular economy principles in the construction industry (Shamsaei et al. 2019, Babajide Olabimtan andMosaberpanah 2023).The potential benefits and challenges of this substitution specified in the literature highlight its relevance in achieving greener building materials (Ashish 2018, Aghayan et al. 2021, Lo et al. 2021).Furthermore, as reported in a recent study, CP can be added to concrete mixtures without calcining, and remarkable improvements in durability were achieved (Wu et al. 2023).However, the use of in concrete causes a considerable decrease in FS of concrete (Zhang et al. 2021, Su et al. 2022).Therefore, it is essential to use fibers such as glass, steel, and basalt to improve this property as well (Ahmad et al. 2022, Yildizel et al. 2022, Zhang et al. 2023b).
Basalt fibers (BFs) recently drew attention as potential reinforcement materials in concrete owing to their exceptional mechanical features, such as high tensile strength, resilience to chemical and thermal degradation, and cost-effectiveness compared to those of conventional fibres such as glass or polypropylene fibres (Zhou et al. 2020).In terms of fire, chemical attack and sudden load resistance, BFs outperform carbon fibers (Meesaraganda et al. 2023).To produce BF-reinforced concrete, BFs can be incorporated as chopped fibers into concrete to avoid defects (Ralegaonkar et al. 2018, Zhang et al. 2023a).The impact of BF on CS in concrete varies across investigations.With a specific dosage of BF, CS has increased in some studies, decreased in others, and was not exhibited in others (Al-Rousan et al. 2023).The amount of BF and the ratio of BF's length to width (aspect ratio) can significantly impact the mechanical properties of BF-reinforced concrete.Consequently, many researchers evaluated the mechanical properties of concrete reinforced with BF in static environments (John and Dharmar 2021).BF was used to improve the mechanical properties of different types of concrete, including various pavements (Wu et al. 2020, Hui et al. 2022, Shen et al. 2022).
Since pavements play an essential role in the social and economic developments of urban areas, they constitute a substantial element of the urban landscape.Manufactured or constructed surfaces such as concrete and asphalt absorb more solar radiation in comparison to naturally forming surfaces such as vegetation and soil.The urban heat island effect is caused by pavements' capacity to absorb and emit heat.When compared to asphalt, concrete has a higher initial albedo owing to its light grey color rather than black color.However, due to weathering and accumulation of debris, the albedo of concrete decreases over time.Fresh concrete typically has an albedo between 0.35 and 0.40, whereas that of weathered concrete ranges between 0.25 and 0.40 (Reza and Boriboonsomsin 2015).A decrease in the albedo increases the urban heat island phenomenon, in which urban regions experience much higher temperatures than their rural counterparts.The solar reflectance of construction materials used in buildings, walls, roofs, and roadways, which are mainly made of hardened Portland cement concrete, impacts solar reflectance (Boriboonsomsin andReza 2007, Marceau andVangeem 2007).It is essential to increase the albedo or solar reflectivity of these surfaces in order to reduce the heat island effect by minimizing the transfer of heat from surfaces to the air through convection (Qin et al. 2019).
Roller-compacted concrete (RCC) consists of grit, Portland cement, dense-graded aggregate, and water.Typically, an asphalt paver is installed and compacted by using standard vibratory roller compactors (Mardani-Aghabaglou and Ramyar 2013, Adresi and Lacidogna 2021).In comparison to standard concrete, RCC contains more aggregates, less cement, and less water.It is required to implement compaction energy in order to increase the density (Meddah et al. 2014, Lam et al. 2017).Regular or high-density asphalt paver equipment and vibrating rollers are employed to achieve the appropriate density and uniform surface on the pavement.In comparison to conventional rigid pavement or asphaltic pavement, RCC can reduce the cost of pavement construction by 15% to 30% and also allow for traffic to start earlier (Meddah et al. 2014, Rao et al. 2016, Aghaeipour and Madhkhan 2020).
Even though cool pavements, namely those utilizing RCC, offer numerous benefits, their adoption is not as widespread as that of cool roofs.Due to the lack of incentives, property owners and contractors have limited motivation to build cool pavements.There are few studies on the genetic programming (GP) of the solar reflectance and FS of RCC, particularly on fiber-reinforced specimens.A novel application of CP as a black pigment in the production of concrete coatings of different colors was examined in the present study.This study also evaluates how this modification affects the albedo values of textures.The extent to which CP can change the reflectivity and its prediction of RCC pavements was not well investigated, creating a notable deficiency in the existing studies.
This study aims to fill these knowledge gaps by developing a genetic algorithm that can predict the flexural performance of a material, taking into account the composition of fibers and albedo values and establishing a correlation with the fraction of CP utilized.The lack of predictive models to be used for these properties in RCC applications emphasizes a distinct opportunity for innovation.The present research intends to reduce the time and financial resources needed for pavement design by establishing these models.It was also aimed to make it more practicable to use algorithms as prediction tools in RCC applications.This study provides novel perspectives in the field, making use of previous studies and expanding the limits of what can be accomplished utilizing contemporary concrete technology.

Experimental program
In the experimental study, crushed limestone was used as coarse aggregate (CA) and silica sand (SS) as fine aggregate.After the air-drying process, the organic material from the aggregates was eliminated.A maximum aggregate size of 20 mm was chosen to prevent segregation and its effects.Figure 1 illustrates the gradation curves of the aggregates.CEM II (42.5R)-type white cement (WC) conforming to the BS EN 197-1 (BS EN 197-1 2011) standard was also employed.CP, a commercially available product, was used as the filling and cement replacement material.Cement was replaced with CP in proportions of 5%, 10%, 15%, and 20% by the weight of cement.The chemical compositions of CP and WC are listed in Table 1.The mixes had BFs (8 mm length) at 0.25%, 0.5%, 0.75%, and 1.0% by the volume.Water-to-cement ratios between 0.40 and 0.44 were selected to meet the requirements of ACI 207.R-11 (ACI 207.5R-11 2011) regarding allowable compaction and water content limits.Figure 2 displays the utilized CP and BF.Following the ASTM C 1435 standard, the mixtures were compacted in three layers at 1850 rpm (10 kg surcharge) by using a compactor.The optimal amounts of water in the prepared mixtures were well within the allowed range.
The albedo values of the specimens were determined using a UV-VIS-NIR spectrophotometer (Figure 3).For this purpose, rectangular specimens with dimensions of 24 mm × 24 mm × 5 mm were prepared (Figure 4).Moreover, albedo values were determined at the wavelengths of 200-2500 nm.The mean reflection percentages and spectrophotometer readings were used to calculate albedo values for each sample.
The mixtures were blended using a 60-liter pan mixer at a constant rate of 250 rpm.The CS and splitting tensile strength (STS) tests were conducted on 150 mm × 300 mm cylindrical samples as per the guidance of ASTM C39 (ASTM C39 2016) and ASTM C496 (ASTM C496/C496M − 2011) for 7, 28, and 90 days, respectively.Rectangular samples with dimensions of 100 mm × 100 mm × 500 mm were produced for the FS test.The loading rate was maintained at 0.9 MPa/min following ASTM C39 (ASTM C39 2016).The frost resistance of the samples (100 cycles) was evaluated by using ASTM C 666 (ASTM C666/C666M-03 2008).While performing all the mechanical tests, the methodologies of previous studies were also obtained to achieve more accurate results and make performance comparisons (Hesami et al. 2016, Modarres et al. 2018).More detailed material tests and evaluations are presented in the literature (Yildizel and Armagan 2023).
In the first stage of the experimental studies, the albedo of the specimens was measured after 28 days of curing.The average of three measurements of the spectral reflectance of each specimen was recorded.Then, the mechanical and durability tests were conducted.The proportions of the mixture design and flowchart of the experimental processes are presented in Table 2 and Figure 5, respectively.Twenty pieces for each type of mixture (120 samples in total) were poured, and their arithmetic averages were considered.

GP
GP is an evolutionary computation method and a symbolic optimisation technique that is used in developing computer programs to solve problems based on the Darwinian principle of natural selection (Koza 1992, O'Neill 2009).This approach is commonly utilized to create algorithms, programs, mathematical functions, etc.Researchers have progressively introduced many forms of representation for GP over time.However, the form of representation does not alter the steps of the system (Turner andMiller 2017, Sudhir andBeulah 2023).The flowchart of the general GP steps is depicted in Figure 6.Linear representation was also employed in this study.In a linear GP, programs in the population consist of a sequence of instructions (Dal Piccol Sotto et al. 2022).Table 3 lists the instructions utilized during the analysis.As seen in Table 3, the GP system used in this study consists of 27 instructions.The numbers in Table 3 indicate the indexes provided in the instructions.R 1 and R 2 are registers; RS swaps the programs in registers to store the relevant program or reuse the previously stored program; and I 1 -I 3 are the input symbols.The inputs for the FS formulation include WC, CP, and W/C, whereas those for the albedo formulation include WC, BF, and W/C.The chromosomes in the populations retained the instruction indexes in their genes.The program executed by each chromosome is obtained from R 1 by successively following the relevant instructions specified in that chromosome's indexes.
Instructions using simple mathematical operators and key input elements were designed for GPs to return simple programs.The terminal set includes the inputs and some constants, and the function set consists of fundamental mathematical operations, subtraction, and multiplication-excluding division.
The population size of the GP system was set at 1000.The chromosome length, crossover probability, and mutation probability were defined to be 40%, 85%, and 15%, respectively.However, for the first instruction, the chromosome length varied between 0 and 40 since there was no operation in the first phase of the analysis.
The fitness function is another essential configuration component of GP, guiding GP to search for the solution in the search space (Oltean 2005;Lui et al. 2023).It can be any function designed by the user that measures how to fit the programs in the GP population to the optimal solution.In this study, the mean absolute percentage error function (MAPE) was used as the fitness function, which is given in the following equation: where n refers to the number of samples in the training data, y designates the actual output, and ŷ represents the predicted output of the corresponding sample.

Experimental results
Figure 7 shows the calculated albedo values of the mixtures.
The test results ranged between 0.28 and 0.16.As expected, the reference mixture without CP and BF had the highest albedo value of 0.28.The color change properties of CP and BF were significant (Kaloush et al. 2008).This higher albedo in the reference mixture can also be attributed to the inherent properties of the cement and aggregates used, which typically influence the albedo of conventional concrete (Levinson and Akbari 2002).Furthermore, a noticeable reduction was observed in the albedo as the amount of CP increased, potentially because the CP's darker color influenced the overall mixture's reflectivity (Emery et al. 2014).The albedo values of concrete samples increase as the water-to-cement ratio increases (Qin et al. 2019) due to the increased possibility of the role of Ca(OH) 2 as a hydration product (Chaussadent et al. 2000).In detail, this phenomenon was not observed, and it suggests that color additives might interfere with the reflective properties typically enhanced by hydration products.Figure 8 illustrates CSs derived from an average of three samples containing identical ingredients.The inclusion of 5% CP and 0.25% BF increased CS by 10.1% and resulted in the best performance compared to the other mixtures.In   addition, the results demonstrated that replacing more than 5% of cement with CP decreased CS.These results were consistent with those reported in a previous study (Hesami et al. 2016).At 28 days, there was a noticeable decrease of almost 50% in CS when using 20% CP and 1% BF.It indicates the harmful impact of large concentrations of CP and BF on the overall strength of concrete (Radović et al. 2021).The use of more BFs (Liang et al. 2021) could lead to an increase in the number of poor interfaces between the fibers and cement matrix (Algin and Ozen 2018).Figure 9 displays the results of the FS test.A significant improvement of up to 20% was found in FS at 28 days when 0.5% BF and 10% CP were used in the mix.This enhancement is line with other research that has pointed out that moderate quantities of CP and BF increase the strength and ability of the composite material to withstand bending forces (Hesami et al. 2016, Modarres et al. 2018, Haido et al. 2021, Liang et al. 2021).Beyond these values, FS declined, confirming earlier research showing that high CP and BF can remarkably affect the mechanical properties of concrete due to poor dispersion and weak surfaces (Reid and Marchand 1998).
Figure 10 depicts the results of the STS tests.The results achieved in this study demonstrate that STS ranged between Mean albedo test results.2.41 MPa and 3.84 MPa.The ratios of STS to CS were determined to be within the range of 6.8%-11.9%,which aligns with the results reported in previous investigations (Choi andYuan 2005, Gaedicke et al. 2016).An increase in CP and BF contents beyond 5% and 0.5%, respectively, caused a reduction in STS, highlighting a trend where excessive additives compromise tensile integrity, likely owing to the same issues affecting FS and CS.

GP results
Preliminary runs with different configurations, including normalized and nonnormalized data, were performed at the beginning of the GP-based study.Considering the initial runs, it was decided to set the GP parameters to the configuration explained in the previous section and to apply the normalization process to the input data.A straightforward normalization procedure was conducted by dividing the data in each column by its highest value.At the end of the evolution process, the following functions were obtained: The blue and yellow plots in Figure 11  However, these values are 0.014 and 0.93 for the test samples, respectively.A correlation coefficient R 2 higher than 0.90 suggests that the model is suitable for predicting the outcome.Consequently, all the results illustrate that the proposed method is appropriate for predicting the outcomes (Chen and Wang 2021, Gonçalves et al. 2021, Li et al. 2021).
Figure 12 displays the actual and estimated albedo values that correspond to the parametric samples, which are WC, CP, and W/C.The only difference between the parameters in Figure 12    the testing samples, respectively.These results also show that the method proposed here is appropriate for predicting the outputs.

Conclusions
A GP-based algortihm was developed to evaulate the solar reflectance and the mechanical and durability properties of BF-reinforced and CP-added RCC mixtures in the present study.The combined effect of BF and CP was also investigated.The main conclusions of the study are summarized as follows: . The combined utilization of 5% CP and 0.5% BF improved the mechanical properties of the RCC samples. .The potential replacement of CP in RCC production was also examined, and the use of CP as a supplementary cement material up to 5% can lead to a greener concrete design. .Based on the albedo values analyzed in this study, it is possible to develop concrete materials that can either decrease or enhance the urban heat island effect.
. Traditional laboratory tests are costly and time-consuming, and empirical methods were shown to have limited effectiveness.Therefore, machine learning-based regression methods offer a viable option for RCC.
present the actual and estimated values of FS, respectively.The actual values refer to the values that are measured experimentally, whereas the estimated values refer to the results of the FS function evolved by GP.The training and testing figures have 95 and 22 parametric samples, respectively: WC, BF, and W/C.Considering Figure 11, the maximum error between the actual and estimated values in both training and testing is approximately 0.1, while the minimum error is almost zero.MAPE and R 2 are 0.012 and 0.95 for the training samples, respectively.
and Figure 11 is that CP was used instead of BF.MAPE and R 2 of the training samples are 0.05 and 0.92, respectively, while these values are 0.04 and 0.094 for 9. Results of FS tests.

Figure 11 .
Figure 11.Comparison of training and testing FS plots: (a) Training and estimated training FS plots, (b) Testing and estimated testing FS plots.

Figure 12 .
Figure 12.Comparison of training and testing Albedo plots; (a) Training and estimated training Albedo plots, (b) Testing and estimated testing of Albedo plots.

Table 1 .
Chemical ingredients of WC and CP (provided by supplier).

Table 2 .
Mixture codes and proportions.

Table 3 .
Instructions in GP system.