Analysis of the Fractal and Sample Size Effects of the Rock Joint Surface Roughness

The surface roughness of rock joints is a major factor that influences the rock mass deformation,displacement and strength.So its determination is very important for the evaluation of rock mechanical properties.The rock joint surface may be assumed to have fractal characteristics,and its fractal dimension can be used to describe the roughness of the surface joints,but the surface roughness of rock joints generally does not strictly have the nature of fractal self-similarity,so,the measurement results of surface fractal parameters(fractal dimension D and the intercept A)would be affected by the scale.In this study,the 3-D superficial laser topography instrument was used to scan samples of 10 different sizes(ranging from 100mm×100mm to 1000mm×1000mm).It is shown that both the fractal dimension D and the intercept A are indeed scale-dependent,but the scale effect and their values decrease with the increase of the size of the sampling windows,and a limit size exists.Considering the rock surface size,the sample length and the measurement scale on the rock joint surface roughness,an acceptable solution for fractal measurements is proposed to assess the properties of rocks.