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在三维网络模型和灰色理论的基础上建立了确定岩体表征单元体(Representative elementary volume)的新方法。该方法在全面考虑岩体基本特征的同时,用灰色理论中的灰关联分析方法确定REV的大小。在三维网络模型中将裂隙按照其走向和倾角投影到极点图上,并将极点图遵循等面积原则划分成24份,统计出每一区块上的极点数量和该区块含有裂隙的平均直径,作为灰关联分析的参考序列。再用边长为r的立方体来分割网络模型,统计出该立方体投影到24份极点图中每一区块的极点数量和含有裂隙的平均直径,这作为比较序列。通过改变立方体边长r的大小,得出对应的比较序列。对参考序列和比较序列进行灰关联分析,随着立方体边长的增加,关联度值趋于稳定,稳定时的立方体的边长即为岩体REV的尺寸大小。在实际工程应用中得出REV的尺寸是裂隙平均迹长3倍以上的结论。
Based on the three-dimensional network model and the gray theory, a new method to determine the representative elementary volume is established. This method not only considers the basic characteristics of rock mass but also determines the size of REV by the gray relational analysis method in gray theory. In the 3D network model, the fractures are projected onto the pole map according to their strike and dip angles. The pole map is divided into 24 parts according to the principle of equal area. The number of poles on each block and the average diameter of fractures in the block , As the gray relational analysis of the reference sequence. Then, the network model is divided by a cube with side length of r, and the number of poles and the average diameter of the fracture containing each cube of the cube projected onto each of the 24 pole figures are counted. This is used as a comparison series. By changing the size of cube side length r, the corresponding comparison sequence is obtained. Gray relational analysis of reference sequence and comparison sequence, as the cube side length increases, the correlation value tends to be stable, and the side length of the cube when stable is the size of the REV of the rock mass. It is concluded that the size of REV is more than 3 times the average trace length of fractures in actual engineering applications.