岩体裂缝面数量三维分形分布规律研究

STUDY ON 3D FRACTAL DISTRIBUTION LAW OF THE SURFACE NUMBER IN ROCK MASS

采用计算机仿真的数值试验方法,首先证明了岩体裂隙面数量服从三维分形分布规律这一自然现象。然后根据大量的计算以及理论推演,得到了裂隙面的2个重要的分形参数(分形维数和分形分布初值),以及分形维数DS和分形分布初值NS与二维剖面裂隙迹线分形参数DL,NL的相关关系。即二维分形维数与三维分形维数遵循:DL = DS-1,二维分形维数DL与裂隙面的其他参数无关;二维分形分布初值NL与三维裂隙面的倾角ST,方位角SP遵循投影关系;二维分形分布初值NL与三维分形分布初值NS遵循正比关系:NL = kNS,k值决定与岩体剖面和三维裂隙面的投影关系。实测结果证实了这些关系的正确性。这些结论为研究裂隙岩体的其他物理力学性质奠定了基础。

Based on numerical simulation experiment, the fractal distribution law of surface number in rock mass is proved. According to large amount of calculate and theoretical inducement, the two important fractal parameters for fractured face are achieved. Through a great deal of calculation, the relationship between Ds and 2D fractal dimension DL of trace is obtained, which is DL = DS-1, and DL is not related to the other parameters, including Ns, dip angle ST, azimuth SP of 3D surface. The relationship of Ns and the initial value of trace number NL is obtained. There are projection relation between NL and ST and SP, and proportional relation between NL and Ns which is NL = kNs, where k depends on surface projection. These relations provide the foundation for studying number and scale of surface in rock masses.