The scale dependence of rock joint surface roughness

Abstract

Abstract Accurate determination of surface roughness of rock joints at the large-scale is essential for proper rock mass characterization. Surface roughness of rock joints is commonly characterized using small samples. However, since roughness parameters of rock joints are scale-dependent and their descriptors change with scale, a systematic investigation has been carried out to understand the effect of scale on the surface roughness of rock joints. A silicon rubber replica, 1000 mm×1000 mm in size, was moulded in-situ from a natural rock joint surface and its surface was digitized in the laboratory using a 3-D laser scanner having high accuracy and resolution. The fractal parameters, i.e. the fractal dimension D and amplitude parameter A describing surface roughness of the replica, were calculated on the basis of the Roughness–Length Method. To investigate the scale-dependency of surface roughness of rock joints, ten sampling windows ranging in size from 100 mm×100 mm to 1000 mm×1000 mm were selected from the central part of the replica and their fractal parameters were calculated. The results show that both D and A are scale-dependent and their values decrease with increasing size of the sampling windows. This scale-dependency is limited to a certain size, defined as the stationarity threshold, and for sampling windows larger than the stationarity threshold, the estimated parameters remain almost constant. It is concluded that, for surface roughness to be accurately characterized on a laboratory scale or in the field, samples need to be equal to or larger than the stationarity limit. In this paper we have indicated the methodology for establishing the value for the stationarity limit for rock joints.