Mesoscopic crack pattern fractal dimension-based concrete damage identification

The randomness and irregularity of concrete cracking present a challenge of quantitatively identifying the developing of damage degree of concrete subjected to complex external conditions. In this study, a concrete meso-mechanical model is established to quantitatively analyze crack propagation and damage evolution under uniaxial tension. Fractal dimension (FD) is used to quantify the crack distribution and track the entire process of concrete cracking. A novel calculation method for the damage identification based on crack FD is proposed, so that the quantitative correlation among the three curves of stress-strain, crack fractal dimension-strain, and damage variable-strain for concrete is obtained. During the hardening stage, the microcracks initiate at interface transition zone between aggregates and mortar, causing an increase in crack FD. As the load reaches its maximum, some micro-cracks tend to localize and form a crack aggregation zone. At the subsequent softening stage, the micro-cracks in other regions undergo a rebound phenomenon, resulting in a decrease in crack FD. Once the crack aggregation zone is formed, the macro-crack concentrates and continues to propagate, leading to an increase in crack FD again. This FD-based damage degree accumulates with crack development throughout the tensile process and varies with the aggregate gradation, specimen size, and aggregate distribution. This study suggests that the mutation point of the crack FD-strain curve after the peak stress point is the critical point at which concrete enters the local failure stage, and the corresponding damage value approximates 0.8.