混凝土断裂能尺寸效应的细观方法

A mesoscopic approach for the size effect on fracture energy of concrete

本文提出了混凝土断裂能尺寸效应的细观方法 .首先 ,根据混凝土细观结构的边界效应确定主宏观裂缝的分形维数 ,发现此分形维数随着离边界距离的不同而变化 .为了计算这一变分形维数主宏观裂缝的长度 ,通过延伸分形曲线长度的定义 ,提出了分形长度与欧几里得长度的微分关系 .其次 ,应用能量等价原理 ,将混凝土名义断裂能表示成分形断裂能、分形维数、细观结构参数和混凝土试件尺寸的函数 .进一步的理论分析表明该名义断裂能的基本力学特征与混凝土宏观实验现象一致 .最后 ,本文的理论预测与一些混凝土实验结果进行了比较 ,证实了该方法的有效性 .

A mesoscopic approach for the size effect on fracture energy of concrete is presented. Based on the wall effect on mesostructure of concrete, the fractal dimension of the macro crack in a concrete specimen is determined, which is found to change with the distance from the specimen boundaries. To calculate the length of the main macro crack with variable fractal dimension, a differential relationship between the fractal length of a curve and the corresponding Euclidian length is put forward by extending the definition of the fractal length of a curve. By applying the principle of energy equivalence, the nominal fracture energy of concrete is expressed in terms of the fractal fracture energy, the fractal dimension, some mesostructural dimensions and the cross sectional dimension of the specimen. A further theoretical analysis reveals that the basic mechanical characteristics of the nominal fracture energy agree with the observed macroscopic experimental phenomena of concrete. The theoretical prediction is compared with experiment data to confirm the effectiveness of the approach.