Prediction of initial fracture energy governing crack propagation in concrete specimens using hybrid machine learning and empirical approaches

The examination of crack growth's energy consumption in concrete structures has been of primary importance since the origin of fracture mechanics. A quasi-brittle material like concrete heavily depends on the available fracture energy for reliable design of structures and for modeling the failure spill. Yet, the approaches to evaluate the initial fracture energy of concrete (IFEC) remain unsatisfactory because of complexity, time consuming costs and monetary budget constraints of orthodox laboratory experiments. In this regard, this research suggested two predictive models: one is AdaGrad gated recurrent unit (AdaG-GRU) and other is adaptive response surface method with KNN (ARSM-KNN). Chi-square automatic interaction detection-decision tree (CHAID-DT) and automatic linear regression with boosting overfitting criteria (ALR-OPC) were also included in the ensemble of the models, along with the stacking approach. Data from three-point load tests for single-edge notched beams (SENB) conducted in the laboratory were used to train and validate these models. With the introduction of the new empirical model using ALR-OPC, different scenarios of concrete strength were incorporated. The training was conducted on a dataset which consisted of five features of concrete and one dependent variable as compressive strength, aged at 28 days, and indexed by 500 datapoints, divided in 85 percent training and 15 percent testing set. These features included maximum size of coarse aggregate and the ratio of water to cement. Between the offered metrics, multitask sensitivity analysis and importance ranking identified the most crucial features of the IFEC as compressive strength and water-to-cement ratio. These results proved the strongest correlation between the predicted and observed values using stacking-ensemble and AdaG-GRU models, which obtained the highest accuracy at R2 = 0.98 and 0.95, respectively. Empirical laboratory tests and advanced machine learning based models also agreed that the optimum water-to-cement ratio of 0.2 to 0.4 resulted in the maximum IFEC. In addition, the increase of IFEC values with time was observed as maximum aggregate size and specimen age were increased from 1 mm to 35 mm and 3 to 180 days, respectively.