## 2 Literature Review
### Literature on Numerical Methods  
ANNs and FL have gained significant popularity as innovative and effective tools in scientific and engineering research, particularly in the analysis and prediction of concrete behavior. [PERSON] et al. [47] investigated the application of ANNs in optimizing the mix design of self-consolidating concrete (SCC). Their study focused on the properties of SCC, particularly reinforcement with fibers and the utilization of agricultural and industrial waste as partial cement replacements. The authors reported that some studies indicate a confidence level of approximately 0.9995 for ANN predictions, with significantly lower errors than linear regression. [PERSON] et al. [48] explored the application of ANNs in conjunction with data envelopment analysis (DEA) for designing SCC mixes containing fly ash. The ANN served as a comparative model to validate the DEA approach, which estimated efficiency based on input parameters such as superplasticizers and aggregates. The study indicated that the ANN model correlated well with the experimental results, enhancing theunderstanding and optimization of SCC mix design. [PERSON] et al. (2019) developed a deep neural network (DNN) model to predict the compressive strength of rubber concrete. A comprehensive database was utilized, with input parameters related to binders and aggregates and compressive strength as the output. They reported that DNN outperformed other neural network architectures across various performance metrics, demonstrating superior accuracy compared to existing machine learning methods. [PERSON] and [PERSON] (2019) compared the performance of two ANN models in predicting explosive spalling in polypropylene fiber-reinforced concrete subjected to elevated temperatures. One model was based on concrete mix proportions, while the other was based on concrete strength. The results, obtained from training datasets of 306 and 300 tests, showed that both models achieved high prediction accuracies, with ANN1 attaining 100% accuracy and ANN2 reaching 90%, indicating the effectiveness of ANNs in assessing the risk of explosive spalling. [PERSON] et al. (2019) developed a hybrid ANN model to predict the compressive strength of SCC, considering factors such as cement replacement and aggregate types. The ANN, optimized using the Runge-Kutta optimization algorithm, achieved high prediction accuracy (R\({}^{2}\) = 0.933 for training and R\({}^{2}\) = 0.9203 for testing), surpassing the performance of traditional models. Feature importance and Taylor diagram analyses further supported the effectiveness of the ANN as a predictive tool for the mechanical properties of SCC. [PERSON] et al. (2019) proposed an ANN model optimized using the Levenberg-Marquardt backpropagation algorithm to predict compressive strength in both normal and high-strength concrete. By evaluating 1637 samples with eight input variables, the study optimized the model's architecture. K-fold cross-validation confirmed its reliability, and the statistical results were promising. The ANN demonstrated significant accuracy and efficiency, revealing that cement content and superplasticizers had a notable impact on compressive strength. [PERSON] et al. (2019) introduced an FL system to predict the shear bond strength of fiber-reinforced self-consolidating concrete (FRSCC). They reported high prediction accuracy, with R\({}^{2}\) values reaching up to 0.96 depending on the applied t-norms. The study highlighted the potential of FL in guiding the precise selection of pozzolan and optimizing mechanical performance. [PERSON] et al. (2019) presented an FL numerical model designed to predict the complete stress-strain behavior of hybrid fiber-reinforced concrete (HFRC). Using data from 27 mixes (including 18 self-made and 9 collected from the literature), the FL model exhibited strong predictive capabilities compared to existing equations. The model was particularly suitable for HFRC, with strengths ranging from 60 to 90 MPa, encompassing both metallic and non-metallic fibers.