节理岩体表征单元体的分形几何研究

FRACTAL STUDY ON THE REPRESENTATIVE ELEMENTARY VOLUME OF JOINTED ROCK MASSES

节理岩体的尺寸效应是其内在结构复杂性的体现,应归因于岩体内裂隙网络系统的存在。提出在岩体结构宏观分区的基础上研究表征单元体,应用分形几何的观点进行研究。结果表明,分区内岩体结构具有统计自相似性。进一步的计算表明,用于描述岩体结构特征的分形维数随岩石试样尺寸的增加而减小;但当尺寸增加到某特定值时,分形维数趋于稳定,将此特定值称为结构表征单元体,即尺寸大于结构表征单元体的样本其结构具有代表性。根据表征单元体的定义,尺寸大于表征单元体的岩体试样,其力学性质具有代表性;而结构相似是性质相似的前提,由此可以推知,结构表征单元体为表征单元体取值的下限。

The scale effects of the jointed rock masses are the external behaviors of the inherent complexity of the structure, and could be attributed to the fracture network inside. The paper determines representative elementary volume on the basis of the evaluation of statistical homogeneity of rock mass structure. The study shows that the rock masses structure has statistical self-similarity, and the fractal dimension of the rock structure decreases with the size of the specimen increasing; but when the specimen dimension increases to a certain value, the fractal dimension varies no more. This certain value is named the structural representative elementary volume (SREV). That's to say, once the size of the specimen reaches SREV, then it is representative of the structure of the homogeneity. According to the definition of REV, only when the size of the specimen reaches REV, is the mechanical behavior of the rock mass representative. Because the similarity of structure is the prerequisite of the similarity of mechanical behavior, this means the SREV must be the lower bound of REV.