Crack Coalescence and Damage Evolution Laws of Concretes with Different Strengths Based on the Zhang‒Hou Damage Calculation Model

The study of concrete crack propagation is always challenging. A Zhang‒Hou damage calculation model is developed based on the theoretical framework of the concrete damaged plasticity (CDP) model and incorporates Sidoroff's damage theory to analyze the inherent patterns between crack coalescence and damage evolution in concrete of different strengths. This model quantitatively describes the uniaxial compressive and tensile damage behavior of concrete, enabling an in-depth investigation of crack propagation and damage evolution in concrete. The study finds that the damage evolution patterns under uniaxial compression and tension are generally consistent across concretes of different strengths. A critical damage crossover point is identified, where the damage values for compression and tension are 0.57 and 0.62, respectively. This crossover point marks a transition from rapid to slow damage evolution. The damage evolution patterns before and after this point remain consistent across different strengths: before the crossover, higher-strength concrete exhibits lower damage, while after the crossover, the trend reverses. Based on these findings and the implications of the catastrophe criterion, the identified damage crossover point is proposed as a critical criterion for the crack coalescence of concrete, and the corresponding damage values are interpreted as a damage threshold that characterizes the crack coalescence in concrete. In addition, a validated finite element model of reinforced concrete (RC) is utilized to comprehensively analyze its damage state and crack coalescence regions under various loading displacements, confirming the validity of the proposed damage threshold. The findings provide a theoretical basis for concrete damage analysis and crack simulation within the framework of continuum mechanics.