A failure criterion model for concrete integrating egret swarm optimization algorithm and back propagation neural networks

Concrete demonstrates pronounced nonlinear failure behavior under multiaxial loading. However, conventional failure criteria, constrained by predefined functional forms, are inadequate for representing the complex and path-dependent failure mechanisms observed in experiments. To overcome these limitations, this study develops a hybrid modeling framework that couples the Egret Swarm Optimization Algorithm (ESOA) with a back propagation (BP) neural network to improve the representation of concrete failure behavior. The proposed framework exploits the strong capability of neural networks to approximate high-dimensional nonlinear mappings and extract the essential geometric features of the failure surface in stress space. Meanwhile, ESOA improves convergence robustness and global optimization efficiency, resulting in more reliable predictions under diverse multiaxial loading scenarios. The model is evaluated using several benchmark datasets from multiaxial strength tests. The results demonstrate that the ESOA-BP model consistently surpasses both the conventional BP network and the classical Ottosen criterion in terms of prediction accuracy, generalization capacity, and computational stability. The resulting failure surface exhibits smooth and physically consistent deviatoric sections that closely match the experimental observations. Both the tensile and compressive meridians reproduce the overall experimental trends, and the curvature evolution in the tension–compression transition zone is captured with high fidelity. Overall, the findings offer a high-accuracy, robust, and practically applicable modeling strategy for developing multiaxial failure criteria for concrete.