Size effect characteristics of structural surfaces by improved projective covering method

Abstract

Abstract 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 $$\Delta D_{\max }^{SD}$$ Δ 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 $$\Delta D_{\max }^{SD}$$ Δ 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.

Keywords

• Structural surfaces
• Size effect; fractal dimensions
• Projective covering method
• Stochastic analysis