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Abstract：
To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25-0.5 (spilt and fracture), 0.5-0.9 (synergy between fracture and damage), 0.9-1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.
摘要：
为研究加载过程中岩石裂纹分布的分形特征,采用离散元法制作有节理的岩石样品，记录裂纹扩展。采用Box-counting方法对裂纹分布在各时刻的分形维数进行了定量分析,基于分形理论建立了裂纹分形维数与应变比的关系。结果表明，裂纹分布的分形维数与应变比之间表现出很强的线性特征。通过将这种线性关系转化为线性函数，发现函数的斜率与样本的失效模式有关，并从斜坡中确定了细化系数（损伤-断裂减少因子），作为确定样品损伤和断裂程度的有效依据。损伤-骨折缩小系数可以分类为：0.25-0.5（溢出和骨折），0.5-0.9（断裂和损伤之间的协同作用），0.9-1(微裂纹渐近损伤)。由于线性分形特征，可以从几何方面建立受失效模式影响的损伤变量的表达式。此外,在其他声发射和裂纹扩展实验中验证了裂纹的线性分形特征。
