岩石在细观尺度上是由矿物颗粒胶结而成，除细观结构的力学特性外，其几何特征（颗粒界面网络结构和颗粒粒度分布）也对宏观断裂能具有一定的影响。为了探索这种几何特征与大理岩断裂能之间的相关性，从而进一步揭示岩石细观断裂机制，首先通过三点弯曲试验测定大理岩的断裂能，然后在试验后的三点弯试件断口处取岩石切片，进行电镜（SEM）扫描以获取岩石细观结构图像。利用图像处理技术获取岩石细观颗粒的界面网络图。通过对颗粒界面网络图分析，发现颗粒界面网络拓扑结构与颗粒粒度分布具有较强的分形特征。将二者分形维数与试件宏观断裂能相对比，发现它们之间具有很强的相关性。界面网络分形维数与宏观断裂能具有很强的二次相关性，而粒度分布维数与宏观断裂能之间具有较强的线性相关性。宏观断裂能随着两种分形维数的增大而增大。该研究结果揭示了宏观断裂能与岩石细观结构几何特征的相关性，加深了对宏观断裂能细观机制的理解。

Rock consists of mineral grains at the mesoscale. The grain boundaries form an interface network and grain sizes are also uniformly distributed. Besides mechanical properties of mesostructure, the geometrical characters (i.e., topology of grain interface network and grain size distribution) also contribute to fracture energy. The aim of this paper is to explore the effects of geometrical characters on the fracture energy and get insight into the mesomechanism of macro fracture energy of rock. Three-point-bending tests are carried out on marble specimens to obtain the fracture energy of marble. Then a rock slice is taken from fracture surface to obtain the image of mesostructure of rock using the scanning electron microscopy (SEM). The technique of digital image processing is used to obtain the grain interface network. Through analyzing of the interface network, it is found that both the topology of interface network and the grain size distribution present a strong fractal feature. There exists a close correlation between macro fracture energy and the fractal dimensions, in which the fracture energy increases with the increase of the fractal dimension. The relationship between fracture energy and fractal dimension of interface network can be well characterized by the quadratic function, while the relationship between fracture energy and fractal dimension of grain size distribution can be characterized by the linear function. The research results reveal a mesomechanism of macro fracture energy.