Accurate characteristic of structural surfaces roughness at the relevant scale is very important to understand mechanical properties of rock mass discontinuities. So, a systematic investigation has been carried out to understand the effect of scale on the structural surface roughness by fractal dimension method. Firstly, considering the shortcoming of the projective covering method (PCM), we improved this method based on stochastic approach. Secondly, to investigate the size effect of the structural surface roughness, we selected six sampling windows, respectively, from the central and four corners part of structural planes (2 m × 2 m). The sampling windows range from 62.5 mm × 62.5 mm to 2000 mm × 2000 mm. And then, we calculated fractal parameters of the different size surfaces using improved projective covering method (IPCM) at the same resolution. Thirdly, we discussed a new method of determining reasonable size of structural surfaces by the parameter \(\Delta D_{\max }^{SD}\). This parameter is difference of the maximum fractal dimension of the same size structural surface in different regions. The results show that: (1) The size effect of structure surfaces is different with different morphological surface. Generally, as the size increases, the roughness of structure surfaces increases and then decreases. There is positive size effect in small scale and negative size effect in large scale. (2) For a given structural surface, when the same size surfaces are selected from different locations of the structural planes, and the size effect characteristics are also different. (3) As the size of structure surfaces increases, the parameter \(\Delta D_{\max }^{SD}\) gradually decreases and tends to almost constant. The result of this study is a useful supplement to the comprehensive understanding of the size effect of structural surfaces roughness.

在相关尺度上，结构表面粗糙度的准确特征对于理解岩层间断的力学特性非常重要。因此，已经进行了系统的研究，以通过分形维数方法了解结垢对结构表面粗糙度的影响。首先，考虑到射影覆盖法（PCM）的不足，基于随机方法对这种方法进行了改进。其次，为了研究结构表面粗糙度的尺寸影响，我们分别从结构平面的中心和四个角部分（2 m×2 m）中选择了六个采样窗口。采样窗口的范围从62.5 mm×62.5 mm到2000 mm×2000 mm。然后，我们使用改进的投射覆盖法（IPCM）以相同的分辨率计算了不同尺寸表面的分形参数。第三，我们讨论了一种通过参数确定结构表面合理尺寸的新方法\（\ Delta D _ {\ max} ^ {SD} \）。此参数是不同区域中相同大小的结构表面的最大分形维数之差。结果表明：（1）结构表面的尺寸效应随形态表面的不同而不同。通常，随着尺寸的增加，结构表面的粗糙度先增大然后减小。小规模有正规模效应，大规模有负规模效应。（2）对于给定的结构表面，当从结构平面的不同位置选择相同尺寸的表面时，尺寸效果特性也不同。（3）随着结构表面尺寸的增加，参数\（\ Delta D _ {\ max} ^ {SD} \）逐渐减少并趋于几乎恒定。这项研究的结果为全面了解结构表面粗糙度的尺寸效应提供了有用的补充。