The Gene Expression Programming Method to Generate an Equation to Estimate Fracture Toughness of Reinforced Concrete

Complex and intricate preparation techniques, the imperative for utmost precision and sensitivity in instrumentation, premature sample failure, and fragile specimens collectively contribute to the arduous task of measuring the fracture toughness of concrete in the laboratory. The objective of this research is to introduce and refine an equation based on the gene expression programming (GEP) method to calculate the fracture toughness of reinforced concrete, thereby minimizing the need for costly and time-consuming laboratory experiments. To accomplish this, various types of reinforced concrete, each incorporating distinct ratios of fibers and additives, were subjected to diverse loading angles relative to the initial crack (α)in order to ascertain the effective fracture toughness (Keff) of 660 samples utilizing the central straight notched Brazilian disc (CSNBD) test. Within the datasets, six pivotal input factors influencing the Keff of concrete, namely sample type (ST), diameter (D), thickness (t), length (L), force (F), and α, were taken into account. The ST and a parameters represent crucial inputs in the model presented in this study, marking the first instance that their influence has been examined via the CSNBD test. Of the 660 datasets, 460 were utilized for training purposes, while 100 each were allotted for testing and validation of the model. The GEP model was fine�tuned based on the training datasets, and its efficacy was evaluated using the separate test and validation datasets. In subsequent stages, the GEP model was optimized, yielding the most robust models. Ultimately, an equation was derived by averaging the most exemplary models, providing a means to predict the Keff parameter. This averaged equation exhibited exceptional proficiency in predicting the Keff of concrete. The significance of this work lies in the possibility of obtaining the Keff parameter without investing copious amounts of time and resources into the CSNBD test, simply by inputting the relevant parameters into the equation derived for diverse samples of reinforced concrete subject to varied loading angles.