An evolutionary approach to formulate the compressive strength of roller compacted concrete pavement
Introduction
The high cost of producing roads asphalt pavement and the large volume of oil products polluting the environment have necessitated the use of alternative technologies. Roller-compacted concrete pavement (RCCP) is a rigid pavement that has been of interest to researchers due to the accelerated construction and reduced maintenance costs [1], [2]. The lower cement pastes and higher aggregates make RCCP has low consistency, and to be compacted, the roller and compactor are used. Compared with the tropical and temperate asphalt, the long-term durability of RCCP has received interest due to the resistance to rising temperatures, low water absorption, and proper compressive strength, and consequently, it experiences less deformation under loading [3]. Also, in cold areas, the concrete pavement is resistant to frost cycles in the face of possible damage. In addition, due to the impermeability of the constituting materials, as consistent pavement, there is no environmental problem in its application range [4]. The gray and neutral color of the RCCP also has a good temperature absorption coefficient and helps lower the ambient temperature. Due to the lower cost of production than cement and improved strength properties, the use of pozzolanic materials has also been considered in the production of the RCCP [4]. Therefore, in this study, the RCCP incorporating binder-based pulverized fly ash (PFA) powder is investigated. The PFA is well combined with the gel produced in concrete and increases the hydration of concrete [5] and, as a result, increases the density of the produced concrete and improves the mechanical and chemical properties of RCCP.
The mechanical properties of RCCP required important factors [6]. The compressive strength (fc) as a prominent mechanical property of RCCP is necessary to investigate experimental and computational intelligence analysis in construction materials. Developing models with an accurate estimation for this key characteristic caused to an eco-friendly benefit, saving cost and time of production and designing an optimal blend. In the last years, an evolutionary approach presented an enhanced potency for solution of civil engineering challenges [7]. Some of the data-driven methods named multiple linear regression (MLR) [8], [9], artificial neural network (ANN) [10], [11], [12], [13], support vector machine (SVM) [14], [15], adaptive neuro-fuzzy inference systems (ANFIS) [16], [17] that have been implemented to predict the properties of concretes. Chen [8] employed the MLR method to predict fc based on physical properties of concrete. He investigates five series of input variables and reports results of all scenarios in terms of error metrics. The capability of the ANN methodology for prediction of properties of SCC investigated by Asteris and Kolovos [11] and Getahun et al. [12]. They reported the ANN technique as an alternative to the experimental program to simulate characteristics of concretes. Wang et al. [13] Compared MLR, ANN and ANFIS techniques to estimate the expansion behavior of self-stressing concrete. The detail of the result illustrates the ANFIS model outperforms ANN and MLR in terms of acceptability and accuracy. Sonebi et al. [14] derived SVM method for modeling of self-compacting concrete using kernel functions named radial basis and polynomial. The modeling process demonstrates that the SVM based radial basis method robustness and accurate in their study. Regarding the entire aforementioned, machine learning methods generally considered as black-box methodology since they are not capable to formulate linear relation between predictor and target variables. Genetic Programming (GP) [18], [19], [20] is another heuristic regression method that automatically generates computational models on the basis of evolutionary genetic [21]. González-Taboada et al. [19] focused on a comprehensive database to forecast a high accuracy model of mechanical properties of structural recycled concrete using GP technique. GEP is the extended form of GP, which evolves intelligence process with different shapes and sizes that are encoded chromosomes in the form of simple linear with a fixed length [22]. Several other studies have proved the estimation capability and potential of the evolutionary data-driven models in the field of concrete technology and material design [23], [24], [25].
As stated above, the classical data-driven models provide reliable tools to predict the compressive strength of concrete. However, it is not a robust method to formulate this fundamental property. The main focus of this attempt is presented initially as a new interpretation and conceptualization GEP-based formulas in three forms of inputs combination to calculate the fc of RCCP for the first time. Performance criteria of the proposed formula-based GEP models are compared with the previous investigation. Moreover, the uncertainty analyses inspired by Monte-carlo simulation (MCS) method of all of the developed GEP models are performed. To verify the developed models, external validations based on some performances indicators and parametric studies are evaluated.
Section snippets
Overview of gene expression programming
Based on evolution biological theory of Darwin, evolutionary algorithms are a type of computational techniques used for problem-solving through natural selection and heuristic search amongst a population of solutions to find the “best-fit”. Each candidate solution which belongs to the population is referred to as an individual. Poor solutions are eliminated through the iteration of an evolutionary algorithm, which includes a competitive selection by evaluating the quality of solutions based on
Modeling of the compressive strength of RCCP
In this study, three different models based on volumetric/weighted content (dimensional) consisting six predictors, ratio of different constituents (non-dimensional) of the variables consisting five predictors and percentage form of variables consisting six predictors are implemented by the GEP-based method to clarify between the fc and each important predictors in the functional relationship as bellow:
Result and discussion
In the present study, the performances of the GEP-based models for training and testing phases were compared. To evaluate the accuracy of the models, statistical metrics in terms of r, MAE, RMSE, AAE, PI, and OBJ have been performed. Moreover, the validity of the derived GEP-based models performed using external validation and uncertainty analysis. The error measures of the developed models for the training and testing performances are indicated in Table 4. Considering Table 4, the GEP approach
Limitations and future work
Although, this study was the first attempt to propose artificial intelligence (AI)-based formula for estimation of the compressive strength of RCCP, several limitations should be addressed for future work. As can be seen from computational process, GEP-based models could predict the fc of RCCP in different inputs combination forms with high accuracy. One of the disadvantages of evolutionary-based model (e.g., GEP) is that its implementation is time-consuming because it optimized user manual
Conclusion
In this study, the evolutionary approach based on GEP was applied as a soft computing technique proposed new predictive formulations of the compressive strength of roller compacted concrete pavement in three forms of inputs combination. The models were implemented using 235 datasets of RCCP mixture proportions. The wide range database containing components of RCCP caused to ensure that the GEP models will be suitable and generalized. Implemented models based on weighted/volumetric content,
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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